Research Article Spatial Modulation Concept for Massive...

10
Research Article Spatial Modulation Concept for Massive Multiuser MIMO Systems Khaled M. Humadi, Ahmed Iyanda Sulyman, and Abdulhameed Alsanie Department of Electrical Engineering, King Saud University, Riyadh 11421, Saudi Arabia Correspondence should be addressed to Ahmed Iyanda Sulyman; [email protected] Received 18 February 2014; Accepted 18 May 2014; Published 9 June 2014 Academic Editor: Shahram Yousefi Copyright © 2014 Khaled M. Humadi et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is paper presents the concept of spatial modulation (SM) scheme for massive multiuser MIMO (MU-MIMO) system. We consider a MU-MIMO system where users, each equipped with multiple antennas, are jointly serviced by a multiantenna base station transmitter (BSTx) using appropriate precoding scheme at the BSTx. e main idea introduced here is the utilization of the user’s subchannel index corresponding to the precoding matrix used at the BSTx, to convey extra useful information. is idea has not been explored, and it provides significant throughput enhancements in a multiuser system with large number of users. We examine the performance of the proposed scheme by numerical simulations. e results show that as the number of users and the receiving antennas for each user increase, the overall system throughput gets better, albeit at the cost of some degradation in the BER performance due to interantenna interference (IAI) experienced at the receiver. We then explore zero-padding approach that helps to remove these IAI, in order to alleviate the BER degradations. 1. Introduction Massive multiuser multiple input multiple output (MIMO) systems have gained significant research attentions lately because they provide significant boost in the capacity of MIMO systems [1–3]. Multiuser MIMO systems have been investigated for long time now. However, a recent new development in this research area is the aggressive use of very large number of antennas, known as massive multiuser MIMO systems. Currently in the fourth-generation (4G) long-term evolution (LTE) for cellular system, the use of up to 8 × 8 MIMO systems have been standardized, both for single-user and multiuser systems. It is hoped however that massive MIMO systems with hundreds of antennas at the base station (BS) will eventually be standardized in the fiſth-generation (5G) cellular system, as part of the major data rate enhancement techniques to be introduced in 5G [4]. To this end, several research efforts have been devoted to studying the benefits of massive MIMO systems under different considerations. Spatial modulation (SM) is another new promising trans- mission technique that uses antenna indexes in a multiple antenna system, as additional means of data transmissions. e main idea behind spatial modulation is to use the index of the active antennas at any time instant, transmitting or receiving antenna depending on whether the spatial modu- lation scheme is applied at the transmitter or at the receiver, to convey extra information. us, the information bits to be transmitted are divided into blocks of two parts [5]. e first part is mapped to a symbol chosen from the signaling constellation, where the number of bits per symbol depends on the type of modulation used. e second part determines the index of the antenna to be selected from a set of anten- nas available for data transmission or reception. erefore, unlike antenna selection in the conventional MIMO systems which depends on the channel states and the received signal strength, antenna selection in spatial modulation depends on the incoming user data stream [6, 7]. Spatial modulation schemes were first introduced in [8, 9], where the principle of wireless transmission in which the information is carried by both the index of the active antenna and the symbol transmitted through this active antenna was illustrated. In [10], then, the idea of space shiſt keying (SSK) modulation was introduced as a modulation Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2014, Article ID 563273, 9 pages http://dx.doi.org/10.1155/2014/563273

Transcript of Research Article Spatial Modulation Concept for Massive...

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Research ArticleSpatial Modulation Concept for Massive MultiuserMIMO Systems

Khaled M Humadi Ahmed Iyanda Sulyman and Abdulhameed Alsanie

Department of Electrical Engineering King Saud University Riyadh 11421 Saudi Arabia

Correspondence should be addressed to Ahmed Iyanda Sulyman asulymanksuedusa

Received 18 February 2014 Accepted 18 May 2014 Published 9 June 2014

Academic Editor Shahram Yousefi

Copyright copy 2014 Khaled M Humadi et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper presents the concept of spatialmodulation (SM) scheme formassivemultiuserMIMO(MU-MIMO) systemWe considera MU-MIMO system where 119870 users each equipped with multiple antennas are jointly serviced by a multiantenna base stationtransmitter (BSTx) using appropriate precoding scheme at the BSTx The main idea introduced here is the utilization of the userrsquossubchannel index corresponding to the precoding matrix used at the BSTx to convey extra useful information This idea hasnot been explored and it provides significant throughput enhancements in a multiuser system with large number of users Weexamine the performance of the proposed scheme by numerical simulations The results show that as the number of users and thereceiving antennas for each user increase the overall system throughput gets better albeit at the cost of some degradation in theBER performance due to interantenna interference (IAI) experienced at the receiver We then explore zero-padding approach thathelps to remove these IAI in order to alleviate the BER degradations

1 Introduction

Massive multiuser multiple input multiple output (MIMO)systems have gained significant research attentions latelybecause they provide significant boost in the capacity ofMIMO systems [1ndash3] Multiuser MIMO systems have beeninvestigated for long time now However a recent newdevelopment in this research area is the aggressive use ofvery large number of antennas known as massive multiuserMIMO systems Currently in the fourth-generation (4G)long-term evolution (LTE) for cellular system the use ofup to 8 times 8 MIMO systems have been standardized bothfor single-user and multiuser systems It is hoped howeverthat massive MIMO systems with hundreds of antennas atthe base station (BS) will eventually be standardized in thefifth-generation (5G) cellular system as part of the majordata rate enhancement techniques to be introduced in 5G[4] To this end several research efforts have been devotedto studying the benefits of massive MIMO systems underdifferent considerations

Spatial modulation (SM) is another new promising trans-mission technique that uses antenna indexes in a multiple

antenna system as additional means of data transmissionsThe main idea behind spatial modulation is to use the indexof the active antennas at any time instant transmitting orreceiving antenna depending on whether the spatial modu-lation scheme is applied at the transmitter or at the receiverto convey extra information Thus the information bits tobe transmitted are divided into blocks of two parts [5] Thefirst part is mapped to a symbol chosen from the signalingconstellation where the number of bits per symbol dependson the type of modulation used The second part determinesthe index of the antenna to be selected from a set of anten-nas available for data transmission or reception Thereforeunlike antenna selection in the conventional MIMO systemswhich depends on the channel states and the received signalstrength antenna selection in spatial modulation depends onthe incoming user data stream [6 7]

Spatial modulation schemes were first introduced in [89] where the principle of wireless transmission in whichthe information is carried by both the index of the activeantenna and the symbol transmitted through this activeantenna was illustrated In [10] then the idea of space shiftkeying (SSK) modulation was introduced as a modulation

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2014 Article ID 563273 9 pageshttpdxdoiorg1011552014563273

2 International Journal of Antennas and Propagation

scheme which uses only the spatial modulation concept Inthe SSK scheme there were no transmitted symbols Only theantennasrsquo indices were used to convey information Becauseno symbols were transmitted SSK reduces the system com-plexity by removing the amplitudephase modulation (APM)required in the transmission and detection components butat the expense of some degradation in the systemrsquos spectralefficiency Since only one antenna is active at a time in the SSKscheme the scheme exhibits no interantenna interference(IAI) just like a single antenna wireless system In [11]a combination of spatial modulation (SM) and space-timeblock coding (STBC) were considered in order to takeadvantage of the benefits of both schemes A generalizedversion of SM called generalized spatial modulation (GSM)system with multiple active transmitting antennas (MA-SM)and low complexity detection scheme was introduced in [12]In the GSM system more than one transmitting antennas areactive at the same time which increases the system spectralefficiency In [13] Rong Zhang proposed a spatial modulation(SM) scheme at the receiver side for single user MIMOsystem called generalised precoding aided spatialmodulation(GPASM)

In this paper we propose the concept of spatial modu-lation (SM) at the receiver side for multiuser MIMO (MU-MIMO) system Our work can be considered a generalizationof the work in [13] to the case of multiuser system We studythe performance of the proposed scheme by simulation andwedemonstrate that significant throughput enhancement canbe obtained using the proposed scheme

2 System Model and Analysis

Consider a downlink multiuser MIMO system shown inFigure 1 in which a base station transmitter (BSTx) with 119873

119905

transmitting antennas communicates simultaneously with 119870independent users on the same time-frequency resourcesEach user is equipped with 119873

119903receiving antennas and

assuming that 119873119905gt 119873119903 At any transmission time instance

the data for each user is divided into blocks of 119899 + 119901 bitswhere 119899 = log

2119872 (119872 is the symbol constellation size) and

119901 = log2119873119903 The first 119899 bits [119887

11198872sdot sdot sdot 119887119899] are mapped to

a corresponding symbol in the constellation while the next119901 bits [119887

119899+1119887119899+2

sdot sdot sdot 119887119899+119901] are used to activate a particular

receiving antennas For simplicity of representation we haveconsidered here only the case where one receiving antennais switched for each user However our works and resultsare easily extended to cases where two or more antennasare activated per user At the receiver side when the userreceives the correct symbol the first 119899 bits of the user datatransmitted by the BSTx over a particular receiving antennawill be decoded using maximum likelihood (ML) estimate ofthe received signal while the next 119901 bits are added based onthe index of the antenna from where the signal (or symbol)is received or detected Thus the index of this antenna alsoconveys useful information in addition to the transmittedsymbol

Let the vector x = [1199091

119898119895 1199092

119898119895 119909

119870

119898119895]119879 represent

the transmitted super symbols from the BSTx to all users

where the notation 119909119896119898119895

indicates that the BSTx transmits amodulated symbol 119904

119898isin 1199041 1199042 119904119872 to the 119896th user and

the symbol is to be received at the 119895th receiving antenna ofthe user 119895 = 1 2 119873

119903 We first assume that the channel is

totally uncorrelated and that the channel state information(CSI) is available at the transmitter side The MU-MIMOchannel matrixH for this system can be written as

H =[[[[

[

H1H2

H119870

]]]]

]

(1)

where H119896 119896 = 1 2 119870 is the 119873119903times 119873119905channel matrix

corresponding to the 119896th user and is given by

H119896 =[[[[[

[

ℎ119896

11ℎ119896

12 ℎ119896

1119873119905

ℎ119896

21ℎ119896

22 ℎ119896

2119873119905

ℎ119896

1198731199031ℎ119896

1198731199032 ℎ119896

119873119903119873119905

]]]]]

]

(2)

Now we will discuss two methods proposed here to activatethe receiving antenna for each user namedhere the ldquosubchan-nel selectionrdquo method and the ldquozero-paddingrdquo method

21 Subchannel Selection Method The main idea of thismethod is the utilization of usersrsquo subchannels as a meansof additional data transmission by collecting the rows ofuser channelmatrices into amultiuser precodingmatrix usedat the BSTx For the case when one antenna is switchedper user one row is taken from a user channel matrix at atime If more than one antenna are needed to be switchedthen the corresponding number of rows are taken After thetransmitter precoding operations the resulting transmittedvector x isin c119873119905times1 can be written as

x = Gx (3)

where G isin c119873119905times119870 is the multiuser precoding matrix for thecurrent transmitted symbols which is determined by the 119901bits subblocks for all users The received vector y isin c119873119903119870times1

may be written as

y = Hx + w (4)

where w isin c119873119903119870times1 is the Gaussian noise vector with allits elements having a zero mean and a variance of 1205902 =11987302 The precoding is applied in a way that it can eliminate

the effects of channel fading and multiuser interference atthe desired receiving antennas This can be achieved usingeither minimum mean square error (MMSE) precoding orzero forcing (ZF) precoding In this paper we choose ZFprecoding in which the precoding matrix is given by

G = 120573H119867119904(H119904H119867119904)minus1

(5)

where (sdot)119867 represents the conjugate transpose of a matrixand H

119904isin c119870times119873119905 is the subchannel selected from H as enu-

merated above (and also explained in detail later) and 120573 is

International Journal of Antennas and Propagation 3

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

User 1

User 2

User K

User 1

User 2

User K

Mapped toantenna index

Mapped tosymbols

Base stationtransmitter

(BSTx)

modulatorprecoder

etc

11

1

1

2

Nt Nr

Nr

Nr

Figure 1 SM for multiuser MIMO System

a normalization factor introduced in order to meet the totaltransmitted power constraint after precoding This factor isgiven by

120573 = radic

119873119905

tr [(H119904H119867119904)minus1

]

(6)

where tr[sdot] denotes the trace of a matrix If the transmittedsymbol of the 119896th user is precoded at the BSTx such that thefading-free data is received at the 119895th antenna of the userthen the vector y119896 isin c119873119903times1 received by the 119896th user can bedescribed as

119910119896= 120573119909119896

119898119895+ 119908119896

119895 119895 = 119895

119910119896= V119896119895+ 119908119896

119895 119895 = 119895

(7)

where V119896119895= sum119873119905

119894=1ℎ119896

119895119894119909119894 119895 = 119895 is the effect of channel fading

and multiuser interference while119908119896119895represents the Gaussian

noise for the 119896th user at the 119895th receiving antenna Foreach user the ML detector computes the Euclidean distancesbetween the received signal and the set of possible supersymbols x119896

119898119895isin 119909

119896

1198981 119909119896

1198982 119909

119896

119898119873119903

119898 = 1 2 119872

transmitted Then the ML detection operation at each userreceiving device can be expressed as

[119895 ] = arg min119898isin12119872

119895isin12119873119903

10038171003817100381710038171003817100381710038171003817

1

120573y119896 minus x119896

119898119895

10038171003817100381710038171003817100381710038171003817

2

(8)

where is the argument of the symbol 119904in the constellation

that gives theminimumdistance while 119895 is the antenna indexat which the ML detector gets the minimum distance Thecorrect decision is obtained when = 119898 and 119895 = 119895

Selecting the Subchannel Subchannel H119904is selected in a way

that the precoding operation at the BSTx can remove the

effect of channel fading and multiuser interference at thedesired receiving antennas of the users For simplicity ofillustration we considered the case where only one antennais switched per user here In this case we need to receive thecorrect data at only one receiving antenna per user This canbe obtained by choosing the elements of the subchannel H

119904

from the MU-MIMO channel H such that the 119896th row of H119904

is selected from the 119896th user channel H119896 according to the119901 subblock in the user data Therefore the total number ofavailable subchannels is 2119870119901 = (119873

119903)119870

Example 1 As an illustration of the subchannel selectionmethodconsider a system with two users (119870 = 2) fourtransmitting antennas (119873

119905= 4) and two receiving antennas

for each user (119873119903= 2) as shown in Figure 2 TheMU-MIMO

channel matrixH can be written as

H = [H1

H2] =[[[

[

ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]]]

]

(9)

whereH1 andH2 are the channel matrices for user 1 and user2 respectively If we assume that QPSK modulation formatis used at the transmitter the incoming data for each useris divided into blocks of 3 bits The first 2 bits are mappedonto the appropriate QPSK symbol while the third bit foreach user determineswhich row from the user channelmatrixH119896 is selected to constitute the subchannel H

119904to be used

as percoding matrix for the transmitted symbols Instead ofdetermining the subchannel matrix H

119904according to the 119901

subblock for each user separately we group the subblock119901 forall users into subchannel selection code 119862 isin 00 01 10 11and then selectH

119904according to the code119862 at any time instant

4 International Journal of Antennas and Propagation

middot middot middot b3b2b1

middot middot middot b3b2b1

User 1User 1

11

1

User 2 User 2

2

22

3

4

h111

h121

h112

h113

h114

h213

h214

h123

h124

h224

h223

h212

h211h

221

h222

h122

Base stationtransmitter

(BSTx)

modulatorprecoder

etc

Figure 2 Example of SM for MU-MIMO system with 119870 = 2119873119905= 4 and119873

119903= 2

The number of the available subchannels is given by (119873119903)119870equiv

4 for this example withH119904 119904 = 1 4 is given by

H1= [ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

] H2= [ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]

H3= [ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

] H4= [ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]

(10)

The code 119862 is mapped to the subchannel sets as follows

119862 = 00 997888rarr H1 119862 = 01 997888rarr H

2

119862 = 10 997888rarr H3 119862 = 11 997888rarr H

4

(11)

At the receiver side after theMLdetection for each user if thesymbol is detected at the first receiving antenna then 119887

3= 0

and if the symbol is detected at the second antenna 1198873= 1

22 Zero-Padding Method In the subchannel selectionmethod we activated the desired receiving antennas for allusers by choosing the appropriate elements of the subchannelmatrix H

119904to precode the input data at the BSTx in order

to eliminate the effect of channel fading and multiuserinterference at the desired receiving antennas for the usersHowever the other antennas are affected by these channelimpairments Now we will activate the receiving antennasby zero-padding method such that all receiving antennas foreach user will receive zeros except for the activated antennaswhich will receive the transmitted symbols In this way wecan totally cancel the effect of channel fading and multiuserinterference on the received data by precoding the zero-padded input data using the MU-MIMO channel matrix H(assuming H is available at the transmitter side) Considerthe general system in Figure 1 after zero-padding the inputvector x we will get a vector xzp = [x1zp x

2

zp x119870

zp]119879 where

x119896zp isin c1times119873119903 denotes the zero-padded vector corresponding to

the 119896th user For the case where only one receiving antenna isactivated per user this can be written as

x119896zp = [0 0 0⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119895minus1

119909119896

119898119895 0 0 0⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119873119903minus119895

] (12)

After zero-forcing precoding the transmitted vector xzp isinc119873119905times1 can be written as

xzp = Gxzp (13)

where in this case G = 120573H119867(HH119867)minus1 and 120573 =

radic119873119905 tr[(HH119867)minus1] The received vector y isin c119873119903119870times1 may be

written as

y = Hxzp + w (14)

where w is defined in (4) The received vector y119896 isin c119873119903times1 forthe 119896th user can be described as

119910119896= 120573119909119896

119898119895+ 119908119896

119895 119895 = 119895

119910119896= 0 + 119908

119896

119895 119895 = 119895

(15)

where 119908119896119895is defined in (7) From (15) it is obvious that

for each user only one receiving antenna will receive thetransmitted symbol and the other antennas will receive zerosThe ML detector is then applied as in (8)

Example 2 As an illustration of the zero-padding methodconsider the system in Figure 2 with the same information

International Journal of Antennas and Propagation 5

as in Example 1 Here the code 119862 determines how the inputvector x is zero-padded to obtain xzp as

119862 = 00 997888rarr xzp = [1199091

1198981 0 1199092

1198981 0]

119862 = 01 997888rarr xzp = [1199091

1198981 0 0 119909

2

1198982]

119862 = 10 997888rarr xzp = [0 1199091

1198982 1199092

1198981 0]

119862 = 11 997888rarr xzp = [0 1199091

1198982 0 1199092

1198982]

(16)

The vector xzp is then precoded using the system matrix HFor a system with 119870 users and 119873

119903receive antennas for each

user there will be 2119870119901 = 119873119870119903available combinations of zero-

padded input vector xzp

3 Performance Analysis

Average Bit Error Probability Analysis When a symbol 119909119896119898119895

is transmitted there are three cases in which the error mayoccur These are the error in the modulated symbol 119904

119898only

the error in the spatial symbol 119895 only and the joint errorswhen both of themoccur simultaneouslyTherefore as shownin [14] the average bit error probability (ABEP) can be upper-bounded by the expression

ABEP le ABEPsymbol + ABEPspatial + ABEPjoint (17)

In [14] analytical formulas for the above three cases werepresented for the case where the spatial modulation scheme isapplied at the transmitter side Each expression for the ABERwas derived by summing the average pairwise error prob-abilities (APWEP) weighted by the corresponding averageHamming distances of the given bitmappingThe summationis taken over all the possible transmitted modulated andspatial symbols Applying this principle at the receiver sidefor our case here we get the following expressions

ABEPsymbol

=1

119872119873119903log2(119872119873119903)

times

119873119903

sum

119895=1

119872

sum

119898=1

119872

sum

=1

=119898

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPsymbol

ABEPspatial =1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)APWEPspatial

ABEPjoint

=1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119872

sum

=1

=119898

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPjoint

(18)

where 119889119867(119909119896

119898119895rarr 119909

119896

119895) is the Hamming distance be-

tween the transmitted and the received modulated symbol119889119867(119909119896

119898119895rarr 119909

119896

119898119895) is the Hamming distance between the

transmitted and the received spatial symbol and 119889119867(119909119896

119898119895rarr

119909119896

119895) is the Hamming distance between the transmitted and

received super symbol such that

119889119867(119909119896

119898119895997888rarr 119909119896

119895) = 119889

119867(119909119896

119898119895997888rarr 119909119896

119895)

+ 119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)

(19)

The APWEP can be defined for these three cases as

APWEPsymbol = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898

APWEPspatial = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119898119895)] 119895 = 119895

APWEPjoint = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898 119895 = 119895

(20)

where 119864[sdot] denotes the expectation operation Next wepresent formulas for analyzing theAPWEP for the three casesabove In this analysis we will follow the same procedure in[13] by introducing the effect of multiuser interference andchannel fading in the symbol spatial and joint cases

31 APWEP of Subchannel Selection Method APWEPsymbolmay occur when the symbol is received at the intended spatialantenna 119895 but theMLdetector (MLD) detects awrong symbol119904where =119898 Since APWEPsymbol is affected only by the

Euclidean distances of the points in the signal constellationdiagram then Pr(119909119896

119898119895rarr 119909119896

119895)may be written as [13]

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

minus 2Re (119904lowast119898119904)

1003816100381610038161003816119904 minus 1199041198981003816100381610038161003816 radic21198730

)

(21)

where Re(sdot) and (sdot)lowast denote the real part and the complexconjugate of a symbol respectively

6 International Journal of Antennas and Propagation

APWEPspatial can occur when the MLD detects thecorrect symbol 119904

119898at a wrong receiving antenna 119895 where 119895 = 119895

Then

Pr (119909119896119898119895997888rarr 119909119896

119898119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

119898) minus Re (119908119896

119895119904lowast

119898) gt

12057310038161003816100381610038161199041198981003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

119898)]

(22)

where119908119896119895and119908119896

119895are independent and identically distributed

(iid) random variables with zero mean and variance 1205902 =11987302 Thus Re(119908119896

119895119904lowast

119898) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random

variable with zero mean and variance 1205902 = |119904119898|21198730 Then

Pr(119909119896119898119895

rarr 119909119896

119898119895) can be written as

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(

12057310038161003816100381610038161199041198981003816100381610038161003816

2

minus 2Re (V119896119895119904lowast

119898)

210038161003816100381610038161199041198981003816100381610038161003816 radic1198730

) (23)

APWEPjoint may occur when the MLD detects a wrongsymbol 119904

at a wrong spatial antenna 119895 where =119898 and

119895 = 119895 Then

Pr (119909119896119898119895997888rarr 119909119896

119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt10038161003816100381610038161199041003816100381610038161003816

2

minus

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

) minus Re (119908119896

119895119904lowast

119898)

gt 120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

)]

(24)

where Re(119908119896119895119904lowast

) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random variable

with zero mean and variance 1205902 = (|119904119898|2+ |119904|2)11987302 The

final expression for this case is given by

Pr (119909119896119898119895997888rarr 119909119896

119895)

= 119876(

120573(10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

) minus 2Re (V119896119895119904lowast

)

radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

)

(25)

In (23) and (25) the terms which contain V119896119895are the contri-

butions of multiuser interference and channel fading as aresult of the new considerations in this paperThe subtractionof this term from the argument of the 119876-function impliesthat the overall APWEP will be higher or degraded (since119876(119909) gt 119876(119910) if 119909 lt 119910) compared to MU-MIMO withoutSM

32 APWEP of Zero-Padding Method In this method theeffect of multiuser interference and channel fading is totallycancelled Using similar steps above to obtain the APWEPformulas for the zero-padding method we found thatPr(119909119896119898119895

rarr 119909119896

119895) is exactly expressed as in (22) while

Pr(119909119896119898119895

rarr 119909119896

119898119895) and Pr(119909119896

119898119895rarr 119909119896

119895) may be respectively

expressed as in (24) and (26) by eliminating the contributionof themultiuser interference and channel fadingThuswe canwrite for this case that

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

radic1198730

) (26)

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(

120573radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

) (27)

Then the error probability given by (26) and (27) is lessthan that given by (23) and (25) which means that the zero-padding method can improve the total ABER performance

Throughput and Complexity Analysis We will quantify thesystem throughput in terms of the effective number of trans-mitted bits per channel use (bpcu) while the complexity ischaracterized by the total number of multiplications requiredat the MLD Because we considered here the case where onlyone antenna is activated per user we will compare theseparameters with that of the conventional multiuser MIMOsystem with one data stream per user (119873

119903= 1) The effective

number of bits per channel use for MU-SM is given by

119899MU-SM = 119870 [log2 (119872) + log2 (119873119903)] (28)

while the effective number of bits per channel use forconventional MU-MIMO is 119899MU-MIMO = 119870 log

2(119872) Then

International Journal of Antennas and Propagation 7

Table 1 The increase in throughput and complexity of MU-SM relative to those of conventional MU-MIMO

119872 119873119903

Relative increase in throughput((log2(119873119903)log2(119872)) times 100)

Relative increase in complexity((1198731199032119872) times 100)

2 2 100 502 4 200 1004 2 50 254 4 100 504 8 150 1008 2 3333 1258 4 6667 258 8 100 508 16 13333 10016 2 25 62516 4 50 12516 8 75 2516 16 100 5016 32 125 100

the throughput ofMU-SM relative to that of the conventionalMU-MIMO is given by

119877rel =119899MU-SM119899MU-MIMO

= 1 +log2(119873119903)

log2(119872)

(29)

where log2(119873119903)log2(119872) is the relative increase in the

throughput As shown in [13] separate detection can be usedin SMsystem inwhich the spatial symbol 119895 and themodulatedsymbol 119904

119898are detected separately such that

119895 = arg max119895isin12119873119903

10038161003816100381610038161003816119910119896

119895

10038161003816100381610038161003816

2

(30)

where 119910119896119895is the 119895th element of y119896

= arg min119898isin12119872

10038161003816100381610038161003816100381610038161003816

1

120573119910119896

119895minus 119904119898

10038161003816100381610038161003816100381610038161003816

2

= arg min119898isin12119872

2Re( 1120573119910119896

119895119904119898) minus

10038161003816100381610038161199041198981003816100381610038161003816

2

(31)

As explained above the correct decision is obtained when = 119898 and 119895 = 119895 The number of multiplications requiredin (30) to get 119895 is 119873

119903while the number of multiplications

required in (31) to get 119904is 2119872 The MLD computational

complexity for MU-SM which is defined here as the totalnumber of multiplications required for the detection processcan be expressed as

119862MU-SM = 119873119903 + 2119872 (32)

whereas the MLD computational complexity of the conven-tional MU-MIMO system with one receiving antenna foreach user is 119862MU-MIMO = 2119872 because there is no spatial

symbol to be detected in this case Thus the relative MLDcomplexity for the MU-SM versus the conventional MU-MIMO is

119862rel =119862MU-SM119862MU-MIMO

= 1 +119873119903

2119872

(33)

where 1198731199032119872 is the relative increase in complexity Table 1

presents a tabulation of the relative increase in throughputand complexity for MU-SM in comparison with the conven-tional MU-MIMO system From this table it is observed thatsignificant throughput enhancement can be achieved in theproposed scheme at moderate complexity Also noticeablefrom this table is the lack of dependence of the throughputand complexity increase on the BSTx antennas 119873

119905 This is

because we are comparing with another MU-MIMO systemthat has the same number of BSTx antennas

4 Simulation Results

In this section we present simulation results for the bit errorrate (BER) performance of the proposed SM for multiuserMIMO scheme The BER curves presented in all figures areaveraged over all users In the simulations we consideredQPSK and 16-QAM modulation formats Figure 3 comparesthe analytical results of (17)ndash(25) with simulation where itis easily observed that both analytical and simulation resultshave very closematching (especially in high SNR)This figurealso depicts the effect of increasing the number of receivingantennas for each user on the average (BER) performanceIn Figure 3 we considered transmitting antennas for cases of2 and 4 users with different number of receiving antennasfor each user As shown in the figure the BER performanceof the MU-SM system degrades as the number of receivingantennas119873

119903for each user increasesThis is due to the fact that

8 International Journal of Antennas and Propagation

100

10minus1

10minus2

10minus3

BER

Simulation (Nr = 2)

Simulation (Nr = 4)

Simulation (Nr = 8)

minus4 minus2 0 2 4 6 8 10 12 14 16

SNR (dB)

Analytical (K = 2)Analytical (K = 4)

Figure 3 BER performance of subchannel selection method withdifferent number of receiving antennas for 119873

119905= 10 119870 = 2 and

119870 = 4 for QPSK modulation

100

10minus1

10minus2

10minus3

BER

minus5 0 5 10 15

Nt = 10

Nt = 20

Nt = 30

Nt = 40

SNR (dB)

Figure 4 BER Performance of subchannel selection method withdifferent number of transmit antennas for 119870 = 5 and 119873

119903= 2 for

QPSK modulation

the multiple receiving antennas are not used for diversity butfor SM The receiver would not know ahead what antenna isintended to be switched by the BSTxThus the ML detectionis applied over all the receiving antennas which also increasethe probability of error in the received data with increasing119873119903for each userFigure 4 shows the BER performance of a multiuser

MIMO system with spatial modulation at the receiver sidefor different number of transmitting antennas In this figurewe considered 5 users with 119873

119903= 2 per user and 119873

119905=

100

10minus1

10minus2

10minus3

BER

minus5 0 5

SNR (dB)

Zero-paddingmethod

Subchannelselection method

Nr = 2

Nr = 2

Nr = 4

Nr = 4

and K = 4

and K = 2

and K = 4

and K = 2

Figure 5 BER of subchannel selection method and zero-paddingmethod with 119870 = 2 and 119870 = 4 and119873

119905= 16 for QPSK modulation

100

10minus1

10minus2

10minus3

10minus4

BER

Zero-paddingmethod

Subchannelselection method

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Nr = 2

Nr = 4

Nr = 8

SNR (dB)

Figure 6 BER of subchannel selection method and zero-paddingmethod with massive BSTx antennas (119873

119905= 50)119870 = 5 for 16-QAM

modulation

10 20 30 and 40 As shown in this figure the BER perfor-mance gets better when the number of transmitting antennasincreases due to the diversity gain achieved at the transmitterFigure 5 compares the BERperformance for the twoproposedmethods As shown in the figure zero-padding method givesa significant improvement in the BER performance oversubchannel selection method The figure also shows thatin the zero-padding method the BER performance is notaffected by the number of users because there is no multiuserinterference in this case Figure 6 shows the BERperformanceresults of the two proposedmethods for 16-QAMmodulation

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

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Page 2: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

2 International Journal of Antennas and Propagation

scheme which uses only the spatial modulation concept Inthe SSK scheme there were no transmitted symbols Only theantennasrsquo indices were used to convey information Becauseno symbols were transmitted SSK reduces the system com-plexity by removing the amplitudephase modulation (APM)required in the transmission and detection components butat the expense of some degradation in the systemrsquos spectralefficiency Since only one antenna is active at a time in the SSKscheme the scheme exhibits no interantenna interference(IAI) just like a single antenna wireless system In [11]a combination of spatial modulation (SM) and space-timeblock coding (STBC) were considered in order to takeadvantage of the benefits of both schemes A generalizedversion of SM called generalized spatial modulation (GSM)system with multiple active transmitting antennas (MA-SM)and low complexity detection scheme was introduced in [12]In the GSM system more than one transmitting antennas areactive at the same time which increases the system spectralefficiency In [13] Rong Zhang proposed a spatial modulation(SM) scheme at the receiver side for single user MIMOsystem called generalised precoding aided spatialmodulation(GPASM)

In this paper we propose the concept of spatial modu-lation (SM) at the receiver side for multiuser MIMO (MU-MIMO) system Our work can be considered a generalizationof the work in [13] to the case of multiuser system We studythe performance of the proposed scheme by simulation andwedemonstrate that significant throughput enhancement canbe obtained using the proposed scheme

2 System Model and Analysis

Consider a downlink multiuser MIMO system shown inFigure 1 in which a base station transmitter (BSTx) with 119873

119905

transmitting antennas communicates simultaneously with 119870independent users on the same time-frequency resourcesEach user is equipped with 119873

119903receiving antennas and

assuming that 119873119905gt 119873119903 At any transmission time instance

the data for each user is divided into blocks of 119899 + 119901 bitswhere 119899 = log

2119872 (119872 is the symbol constellation size) and

119901 = log2119873119903 The first 119899 bits [119887

11198872sdot sdot sdot 119887119899] are mapped to

a corresponding symbol in the constellation while the next119901 bits [119887

119899+1119887119899+2

sdot sdot sdot 119887119899+119901] are used to activate a particular

receiving antennas For simplicity of representation we haveconsidered here only the case where one receiving antennais switched for each user However our works and resultsare easily extended to cases where two or more antennasare activated per user At the receiver side when the userreceives the correct symbol the first 119899 bits of the user datatransmitted by the BSTx over a particular receiving antennawill be decoded using maximum likelihood (ML) estimate ofthe received signal while the next 119901 bits are added based onthe index of the antenna from where the signal (or symbol)is received or detected Thus the index of this antenna alsoconveys useful information in addition to the transmittedsymbol

Let the vector x = [1199091

119898119895 1199092

119898119895 119909

119870

119898119895]119879 represent

the transmitted super symbols from the BSTx to all users

where the notation 119909119896119898119895

indicates that the BSTx transmits amodulated symbol 119904

119898isin 1199041 1199042 119904119872 to the 119896th user and

the symbol is to be received at the 119895th receiving antenna ofthe user 119895 = 1 2 119873

119903 We first assume that the channel is

totally uncorrelated and that the channel state information(CSI) is available at the transmitter side The MU-MIMOchannel matrixH for this system can be written as

H =[[[[

[

H1H2

H119870

]]]]

]

(1)

where H119896 119896 = 1 2 119870 is the 119873119903times 119873119905channel matrix

corresponding to the 119896th user and is given by

H119896 =[[[[[

[

ℎ119896

11ℎ119896

12 ℎ119896

1119873119905

ℎ119896

21ℎ119896

22 ℎ119896

2119873119905

ℎ119896

1198731199031ℎ119896

1198731199032 ℎ119896

119873119903119873119905

]]]]]

]

(2)

Now we will discuss two methods proposed here to activatethe receiving antenna for each user namedhere the ldquosubchan-nel selectionrdquo method and the ldquozero-paddingrdquo method

21 Subchannel Selection Method The main idea of thismethod is the utilization of usersrsquo subchannels as a meansof additional data transmission by collecting the rows ofuser channelmatrices into amultiuser precodingmatrix usedat the BSTx For the case when one antenna is switchedper user one row is taken from a user channel matrix at atime If more than one antenna are needed to be switchedthen the corresponding number of rows are taken After thetransmitter precoding operations the resulting transmittedvector x isin c119873119905times1 can be written as

x = Gx (3)

where G isin c119873119905times119870 is the multiuser precoding matrix for thecurrent transmitted symbols which is determined by the 119901bits subblocks for all users The received vector y isin c119873119903119870times1

may be written as

y = Hx + w (4)

where w isin c119873119903119870times1 is the Gaussian noise vector with allits elements having a zero mean and a variance of 1205902 =11987302 The precoding is applied in a way that it can eliminate

the effects of channel fading and multiuser interference atthe desired receiving antennas This can be achieved usingeither minimum mean square error (MMSE) precoding orzero forcing (ZF) precoding In this paper we choose ZFprecoding in which the precoding matrix is given by

G = 120573H119867119904(H119904H119867119904)minus1

(5)

where (sdot)119867 represents the conjugate transpose of a matrixand H

119904isin c119870times119873119905 is the subchannel selected from H as enu-

merated above (and also explained in detail later) and 120573 is

International Journal of Antennas and Propagation 3

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

User 1

User 2

User K

User 1

User 2

User K

Mapped toantenna index

Mapped tosymbols

Base stationtransmitter

(BSTx)

modulatorprecoder

etc

11

1

1

2

Nt Nr

Nr

Nr

Figure 1 SM for multiuser MIMO System

a normalization factor introduced in order to meet the totaltransmitted power constraint after precoding This factor isgiven by

120573 = radic

119873119905

tr [(H119904H119867119904)minus1

]

(6)

where tr[sdot] denotes the trace of a matrix If the transmittedsymbol of the 119896th user is precoded at the BSTx such that thefading-free data is received at the 119895th antenna of the userthen the vector y119896 isin c119873119903times1 received by the 119896th user can bedescribed as

119910119896= 120573119909119896

119898119895+ 119908119896

119895 119895 = 119895

119910119896= V119896119895+ 119908119896

119895 119895 = 119895

(7)

where V119896119895= sum119873119905

119894=1ℎ119896

119895119894119909119894 119895 = 119895 is the effect of channel fading

and multiuser interference while119908119896119895represents the Gaussian

noise for the 119896th user at the 119895th receiving antenna Foreach user the ML detector computes the Euclidean distancesbetween the received signal and the set of possible supersymbols x119896

119898119895isin 119909

119896

1198981 119909119896

1198982 119909

119896

119898119873119903

119898 = 1 2 119872

transmitted Then the ML detection operation at each userreceiving device can be expressed as

[119895 ] = arg min119898isin12119872

119895isin12119873119903

10038171003817100381710038171003817100381710038171003817

1

120573y119896 minus x119896

119898119895

10038171003817100381710038171003817100381710038171003817

2

(8)

where is the argument of the symbol 119904in the constellation

that gives theminimumdistance while 119895 is the antenna indexat which the ML detector gets the minimum distance Thecorrect decision is obtained when = 119898 and 119895 = 119895

Selecting the Subchannel Subchannel H119904is selected in a way

that the precoding operation at the BSTx can remove the

effect of channel fading and multiuser interference at thedesired receiving antennas of the users For simplicity ofillustration we considered the case where only one antennais switched per user here In this case we need to receive thecorrect data at only one receiving antenna per user This canbe obtained by choosing the elements of the subchannel H

119904

from the MU-MIMO channel H such that the 119896th row of H119904

is selected from the 119896th user channel H119896 according to the119901 subblock in the user data Therefore the total number ofavailable subchannels is 2119870119901 = (119873

119903)119870

Example 1 As an illustration of the subchannel selectionmethodconsider a system with two users (119870 = 2) fourtransmitting antennas (119873

119905= 4) and two receiving antennas

for each user (119873119903= 2) as shown in Figure 2 TheMU-MIMO

channel matrixH can be written as

H = [H1

H2] =[[[

[

ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]]]

]

(9)

whereH1 andH2 are the channel matrices for user 1 and user2 respectively If we assume that QPSK modulation formatis used at the transmitter the incoming data for each useris divided into blocks of 3 bits The first 2 bits are mappedonto the appropriate QPSK symbol while the third bit foreach user determineswhich row from the user channelmatrixH119896 is selected to constitute the subchannel H

119904to be used

as percoding matrix for the transmitted symbols Instead ofdetermining the subchannel matrix H

119904according to the 119901

subblock for each user separately we group the subblock119901 forall users into subchannel selection code 119862 isin 00 01 10 11and then selectH

119904according to the code119862 at any time instant

4 International Journal of Antennas and Propagation

middot middot middot b3b2b1

middot middot middot b3b2b1

User 1User 1

11

1

User 2 User 2

2

22

3

4

h111

h121

h112

h113

h114

h213

h214

h123

h124

h224

h223

h212

h211h

221

h222

h122

Base stationtransmitter

(BSTx)

modulatorprecoder

etc

Figure 2 Example of SM for MU-MIMO system with 119870 = 2119873119905= 4 and119873

119903= 2

The number of the available subchannels is given by (119873119903)119870equiv

4 for this example withH119904 119904 = 1 4 is given by

H1= [ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

] H2= [ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]

H3= [ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

] H4= [ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]

(10)

The code 119862 is mapped to the subchannel sets as follows

119862 = 00 997888rarr H1 119862 = 01 997888rarr H

2

119862 = 10 997888rarr H3 119862 = 11 997888rarr H

4

(11)

At the receiver side after theMLdetection for each user if thesymbol is detected at the first receiving antenna then 119887

3= 0

and if the symbol is detected at the second antenna 1198873= 1

22 Zero-Padding Method In the subchannel selectionmethod we activated the desired receiving antennas for allusers by choosing the appropriate elements of the subchannelmatrix H

119904to precode the input data at the BSTx in order

to eliminate the effect of channel fading and multiuserinterference at the desired receiving antennas for the usersHowever the other antennas are affected by these channelimpairments Now we will activate the receiving antennasby zero-padding method such that all receiving antennas foreach user will receive zeros except for the activated antennaswhich will receive the transmitted symbols In this way wecan totally cancel the effect of channel fading and multiuserinterference on the received data by precoding the zero-padded input data using the MU-MIMO channel matrix H(assuming H is available at the transmitter side) Considerthe general system in Figure 1 after zero-padding the inputvector x we will get a vector xzp = [x1zp x

2

zp x119870

zp]119879 where

x119896zp isin c1times119873119903 denotes the zero-padded vector corresponding to

the 119896th user For the case where only one receiving antenna isactivated per user this can be written as

x119896zp = [0 0 0⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119895minus1

119909119896

119898119895 0 0 0⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119873119903minus119895

] (12)

After zero-forcing precoding the transmitted vector xzp isinc119873119905times1 can be written as

xzp = Gxzp (13)

where in this case G = 120573H119867(HH119867)minus1 and 120573 =

radic119873119905 tr[(HH119867)minus1] The received vector y isin c119873119903119870times1 may be

written as

y = Hxzp + w (14)

where w is defined in (4) The received vector y119896 isin c119873119903times1 forthe 119896th user can be described as

119910119896= 120573119909119896

119898119895+ 119908119896

119895 119895 = 119895

119910119896= 0 + 119908

119896

119895 119895 = 119895

(15)

where 119908119896119895is defined in (7) From (15) it is obvious that

for each user only one receiving antenna will receive thetransmitted symbol and the other antennas will receive zerosThe ML detector is then applied as in (8)

Example 2 As an illustration of the zero-padding methodconsider the system in Figure 2 with the same information

International Journal of Antennas and Propagation 5

as in Example 1 Here the code 119862 determines how the inputvector x is zero-padded to obtain xzp as

119862 = 00 997888rarr xzp = [1199091

1198981 0 1199092

1198981 0]

119862 = 01 997888rarr xzp = [1199091

1198981 0 0 119909

2

1198982]

119862 = 10 997888rarr xzp = [0 1199091

1198982 1199092

1198981 0]

119862 = 11 997888rarr xzp = [0 1199091

1198982 0 1199092

1198982]

(16)

The vector xzp is then precoded using the system matrix HFor a system with 119870 users and 119873

119903receive antennas for each

user there will be 2119870119901 = 119873119870119903available combinations of zero-

padded input vector xzp

3 Performance Analysis

Average Bit Error Probability Analysis When a symbol 119909119896119898119895

is transmitted there are three cases in which the error mayoccur These are the error in the modulated symbol 119904

119898only

the error in the spatial symbol 119895 only and the joint errorswhen both of themoccur simultaneouslyTherefore as shownin [14] the average bit error probability (ABEP) can be upper-bounded by the expression

ABEP le ABEPsymbol + ABEPspatial + ABEPjoint (17)

In [14] analytical formulas for the above three cases werepresented for the case where the spatial modulation scheme isapplied at the transmitter side Each expression for the ABERwas derived by summing the average pairwise error prob-abilities (APWEP) weighted by the corresponding averageHamming distances of the given bitmappingThe summationis taken over all the possible transmitted modulated andspatial symbols Applying this principle at the receiver sidefor our case here we get the following expressions

ABEPsymbol

=1

119872119873119903log2(119872119873119903)

times

119873119903

sum

119895=1

119872

sum

119898=1

119872

sum

=1

=119898

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPsymbol

ABEPspatial =1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)APWEPspatial

ABEPjoint

=1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119872

sum

=1

=119898

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPjoint

(18)

where 119889119867(119909119896

119898119895rarr 119909

119896

119895) is the Hamming distance be-

tween the transmitted and the received modulated symbol119889119867(119909119896

119898119895rarr 119909

119896

119898119895) is the Hamming distance between the

transmitted and the received spatial symbol and 119889119867(119909119896

119898119895rarr

119909119896

119895) is the Hamming distance between the transmitted and

received super symbol such that

119889119867(119909119896

119898119895997888rarr 119909119896

119895) = 119889

119867(119909119896

119898119895997888rarr 119909119896

119895)

+ 119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)

(19)

The APWEP can be defined for these three cases as

APWEPsymbol = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898

APWEPspatial = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119898119895)] 119895 = 119895

APWEPjoint = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898 119895 = 119895

(20)

where 119864[sdot] denotes the expectation operation Next wepresent formulas for analyzing theAPWEP for the three casesabove In this analysis we will follow the same procedure in[13] by introducing the effect of multiuser interference andchannel fading in the symbol spatial and joint cases

31 APWEP of Subchannel Selection Method APWEPsymbolmay occur when the symbol is received at the intended spatialantenna 119895 but theMLdetector (MLD) detects awrong symbol119904where =119898 Since APWEPsymbol is affected only by the

Euclidean distances of the points in the signal constellationdiagram then Pr(119909119896

119898119895rarr 119909119896

119895)may be written as [13]

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

minus 2Re (119904lowast119898119904)

1003816100381610038161003816119904 minus 1199041198981003816100381610038161003816 radic21198730

)

(21)

where Re(sdot) and (sdot)lowast denote the real part and the complexconjugate of a symbol respectively

6 International Journal of Antennas and Propagation

APWEPspatial can occur when the MLD detects thecorrect symbol 119904

119898at a wrong receiving antenna 119895 where 119895 = 119895

Then

Pr (119909119896119898119895997888rarr 119909119896

119898119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

119898) minus Re (119908119896

119895119904lowast

119898) gt

12057310038161003816100381610038161199041198981003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

119898)]

(22)

where119908119896119895and119908119896

119895are independent and identically distributed

(iid) random variables with zero mean and variance 1205902 =11987302 Thus Re(119908119896

119895119904lowast

119898) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random

variable with zero mean and variance 1205902 = |119904119898|21198730 Then

Pr(119909119896119898119895

rarr 119909119896

119898119895) can be written as

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(

12057310038161003816100381610038161199041198981003816100381610038161003816

2

minus 2Re (V119896119895119904lowast

119898)

210038161003816100381610038161199041198981003816100381610038161003816 radic1198730

) (23)

APWEPjoint may occur when the MLD detects a wrongsymbol 119904

at a wrong spatial antenna 119895 where =119898 and

119895 = 119895 Then

Pr (119909119896119898119895997888rarr 119909119896

119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt10038161003816100381610038161199041003816100381610038161003816

2

minus

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

) minus Re (119908119896

119895119904lowast

119898)

gt 120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

)]

(24)

where Re(119908119896119895119904lowast

) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random variable

with zero mean and variance 1205902 = (|119904119898|2+ |119904|2)11987302 The

final expression for this case is given by

Pr (119909119896119898119895997888rarr 119909119896

119895)

= 119876(

120573(10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

) minus 2Re (V119896119895119904lowast

)

radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

)

(25)

In (23) and (25) the terms which contain V119896119895are the contri-

butions of multiuser interference and channel fading as aresult of the new considerations in this paperThe subtractionof this term from the argument of the 119876-function impliesthat the overall APWEP will be higher or degraded (since119876(119909) gt 119876(119910) if 119909 lt 119910) compared to MU-MIMO withoutSM

32 APWEP of Zero-Padding Method In this method theeffect of multiuser interference and channel fading is totallycancelled Using similar steps above to obtain the APWEPformulas for the zero-padding method we found thatPr(119909119896119898119895

rarr 119909119896

119895) is exactly expressed as in (22) while

Pr(119909119896119898119895

rarr 119909119896

119898119895) and Pr(119909119896

119898119895rarr 119909119896

119895) may be respectively

expressed as in (24) and (26) by eliminating the contributionof themultiuser interference and channel fadingThuswe canwrite for this case that

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

radic1198730

) (26)

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(

120573radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

) (27)

Then the error probability given by (26) and (27) is lessthan that given by (23) and (25) which means that the zero-padding method can improve the total ABER performance

Throughput and Complexity Analysis We will quantify thesystem throughput in terms of the effective number of trans-mitted bits per channel use (bpcu) while the complexity ischaracterized by the total number of multiplications requiredat the MLD Because we considered here the case where onlyone antenna is activated per user we will compare theseparameters with that of the conventional multiuser MIMOsystem with one data stream per user (119873

119903= 1) The effective

number of bits per channel use for MU-SM is given by

119899MU-SM = 119870 [log2 (119872) + log2 (119873119903)] (28)

while the effective number of bits per channel use forconventional MU-MIMO is 119899MU-MIMO = 119870 log

2(119872) Then

International Journal of Antennas and Propagation 7

Table 1 The increase in throughput and complexity of MU-SM relative to those of conventional MU-MIMO

119872 119873119903

Relative increase in throughput((log2(119873119903)log2(119872)) times 100)

Relative increase in complexity((1198731199032119872) times 100)

2 2 100 502 4 200 1004 2 50 254 4 100 504 8 150 1008 2 3333 1258 4 6667 258 8 100 508 16 13333 10016 2 25 62516 4 50 12516 8 75 2516 16 100 5016 32 125 100

the throughput ofMU-SM relative to that of the conventionalMU-MIMO is given by

119877rel =119899MU-SM119899MU-MIMO

= 1 +log2(119873119903)

log2(119872)

(29)

where log2(119873119903)log2(119872) is the relative increase in the

throughput As shown in [13] separate detection can be usedin SMsystem inwhich the spatial symbol 119895 and themodulatedsymbol 119904

119898are detected separately such that

119895 = arg max119895isin12119873119903

10038161003816100381610038161003816119910119896

119895

10038161003816100381610038161003816

2

(30)

where 119910119896119895is the 119895th element of y119896

= arg min119898isin12119872

10038161003816100381610038161003816100381610038161003816

1

120573119910119896

119895minus 119904119898

10038161003816100381610038161003816100381610038161003816

2

= arg min119898isin12119872

2Re( 1120573119910119896

119895119904119898) minus

10038161003816100381610038161199041198981003816100381610038161003816

2

(31)

As explained above the correct decision is obtained when = 119898 and 119895 = 119895 The number of multiplications requiredin (30) to get 119895 is 119873

119903while the number of multiplications

required in (31) to get 119904is 2119872 The MLD computational

complexity for MU-SM which is defined here as the totalnumber of multiplications required for the detection processcan be expressed as

119862MU-SM = 119873119903 + 2119872 (32)

whereas the MLD computational complexity of the conven-tional MU-MIMO system with one receiving antenna foreach user is 119862MU-MIMO = 2119872 because there is no spatial

symbol to be detected in this case Thus the relative MLDcomplexity for the MU-SM versus the conventional MU-MIMO is

119862rel =119862MU-SM119862MU-MIMO

= 1 +119873119903

2119872

(33)

where 1198731199032119872 is the relative increase in complexity Table 1

presents a tabulation of the relative increase in throughputand complexity for MU-SM in comparison with the conven-tional MU-MIMO system From this table it is observed thatsignificant throughput enhancement can be achieved in theproposed scheme at moderate complexity Also noticeablefrom this table is the lack of dependence of the throughputand complexity increase on the BSTx antennas 119873

119905 This is

because we are comparing with another MU-MIMO systemthat has the same number of BSTx antennas

4 Simulation Results

In this section we present simulation results for the bit errorrate (BER) performance of the proposed SM for multiuserMIMO scheme The BER curves presented in all figures areaveraged over all users In the simulations we consideredQPSK and 16-QAM modulation formats Figure 3 comparesthe analytical results of (17)ndash(25) with simulation where itis easily observed that both analytical and simulation resultshave very closematching (especially in high SNR)This figurealso depicts the effect of increasing the number of receivingantennas for each user on the average (BER) performanceIn Figure 3 we considered transmitting antennas for cases of2 and 4 users with different number of receiving antennasfor each user As shown in the figure the BER performanceof the MU-SM system degrades as the number of receivingantennas119873

119903for each user increasesThis is due to the fact that

8 International Journal of Antennas and Propagation

100

10minus1

10minus2

10minus3

BER

Simulation (Nr = 2)

Simulation (Nr = 4)

Simulation (Nr = 8)

minus4 minus2 0 2 4 6 8 10 12 14 16

SNR (dB)

Analytical (K = 2)Analytical (K = 4)

Figure 3 BER performance of subchannel selection method withdifferent number of receiving antennas for 119873

119905= 10 119870 = 2 and

119870 = 4 for QPSK modulation

100

10minus1

10minus2

10minus3

BER

minus5 0 5 10 15

Nt = 10

Nt = 20

Nt = 30

Nt = 40

SNR (dB)

Figure 4 BER Performance of subchannel selection method withdifferent number of transmit antennas for 119870 = 5 and 119873

119903= 2 for

QPSK modulation

the multiple receiving antennas are not used for diversity butfor SM The receiver would not know ahead what antenna isintended to be switched by the BSTxThus the ML detectionis applied over all the receiving antennas which also increasethe probability of error in the received data with increasing119873119903for each userFigure 4 shows the BER performance of a multiuser

MIMO system with spatial modulation at the receiver sidefor different number of transmitting antennas In this figurewe considered 5 users with 119873

119903= 2 per user and 119873

119905=

100

10minus1

10minus2

10minus3

BER

minus5 0 5

SNR (dB)

Zero-paddingmethod

Subchannelselection method

Nr = 2

Nr = 2

Nr = 4

Nr = 4

and K = 4

and K = 2

and K = 4

and K = 2

Figure 5 BER of subchannel selection method and zero-paddingmethod with 119870 = 2 and 119870 = 4 and119873

119905= 16 for QPSK modulation

100

10minus1

10minus2

10minus3

10minus4

BER

Zero-paddingmethod

Subchannelselection method

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Nr = 2

Nr = 4

Nr = 8

SNR (dB)

Figure 6 BER of subchannel selection method and zero-paddingmethod with massive BSTx antennas (119873

119905= 50)119870 = 5 for 16-QAM

modulation

10 20 30 and 40 As shown in this figure the BER perfor-mance gets better when the number of transmitting antennasincreases due to the diversity gain achieved at the transmitterFigure 5 compares the BERperformance for the twoproposedmethods As shown in the figure zero-padding method givesa significant improvement in the BER performance oversubchannel selection method The figure also shows thatin the zero-padding method the BER performance is notaffected by the number of users because there is no multiuserinterference in this case Figure 6 shows the BERperformanceresults of the two proposedmethods for 16-QAMmodulation

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

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Page 3: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

International Journal of Antennas and Propagation 3

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

middot middot middot bn+p middot middot middot bn+2bn+1 bn middot middot middot b2b1

User 1

User 2

User K

User 1

User 2

User K

Mapped toantenna index

Mapped tosymbols

Base stationtransmitter

(BSTx)

modulatorprecoder

etc

11

1

1

2

Nt Nr

Nr

Nr

Figure 1 SM for multiuser MIMO System

a normalization factor introduced in order to meet the totaltransmitted power constraint after precoding This factor isgiven by

120573 = radic

119873119905

tr [(H119904H119867119904)minus1

]

(6)

where tr[sdot] denotes the trace of a matrix If the transmittedsymbol of the 119896th user is precoded at the BSTx such that thefading-free data is received at the 119895th antenna of the userthen the vector y119896 isin c119873119903times1 received by the 119896th user can bedescribed as

119910119896= 120573119909119896

119898119895+ 119908119896

119895 119895 = 119895

119910119896= V119896119895+ 119908119896

119895 119895 = 119895

(7)

where V119896119895= sum119873119905

119894=1ℎ119896

119895119894119909119894 119895 = 119895 is the effect of channel fading

and multiuser interference while119908119896119895represents the Gaussian

noise for the 119896th user at the 119895th receiving antenna Foreach user the ML detector computes the Euclidean distancesbetween the received signal and the set of possible supersymbols x119896

119898119895isin 119909

119896

1198981 119909119896

1198982 119909

119896

119898119873119903

119898 = 1 2 119872

transmitted Then the ML detection operation at each userreceiving device can be expressed as

[119895 ] = arg min119898isin12119872

119895isin12119873119903

10038171003817100381710038171003817100381710038171003817

1

120573y119896 minus x119896

119898119895

10038171003817100381710038171003817100381710038171003817

2

(8)

where is the argument of the symbol 119904in the constellation

that gives theminimumdistance while 119895 is the antenna indexat which the ML detector gets the minimum distance Thecorrect decision is obtained when = 119898 and 119895 = 119895

Selecting the Subchannel Subchannel H119904is selected in a way

that the precoding operation at the BSTx can remove the

effect of channel fading and multiuser interference at thedesired receiving antennas of the users For simplicity ofillustration we considered the case where only one antennais switched per user here In this case we need to receive thecorrect data at only one receiving antenna per user This canbe obtained by choosing the elements of the subchannel H

119904

from the MU-MIMO channel H such that the 119896th row of H119904

is selected from the 119896th user channel H119896 according to the119901 subblock in the user data Therefore the total number ofavailable subchannels is 2119870119901 = (119873

119903)119870

Example 1 As an illustration of the subchannel selectionmethodconsider a system with two users (119870 = 2) fourtransmitting antennas (119873

119905= 4) and two receiving antennas

for each user (119873119903= 2) as shown in Figure 2 TheMU-MIMO

channel matrixH can be written as

H = [H1

H2] =[[[

[

ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]]]

]

(9)

whereH1 andH2 are the channel matrices for user 1 and user2 respectively If we assume that QPSK modulation formatis used at the transmitter the incoming data for each useris divided into blocks of 3 bits The first 2 bits are mappedonto the appropriate QPSK symbol while the third bit foreach user determineswhich row from the user channelmatrixH119896 is selected to constitute the subchannel H

119904to be used

as percoding matrix for the transmitted symbols Instead ofdetermining the subchannel matrix H

119904according to the 119901

subblock for each user separately we group the subblock119901 forall users into subchannel selection code 119862 isin 00 01 10 11and then selectH

119904according to the code119862 at any time instant

4 International Journal of Antennas and Propagation

middot middot middot b3b2b1

middot middot middot b3b2b1

User 1User 1

11

1

User 2 User 2

2

22

3

4

h111

h121

h112

h113

h114

h213

h214

h123

h124

h224

h223

h212

h211h

221

h222

h122

Base stationtransmitter

(BSTx)

modulatorprecoder

etc

Figure 2 Example of SM for MU-MIMO system with 119870 = 2119873119905= 4 and119873

119903= 2

The number of the available subchannels is given by (119873119903)119870equiv

4 for this example withH119904 119904 = 1 4 is given by

H1= [ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

] H2= [ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]

H3= [ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

] H4= [ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]

(10)

The code 119862 is mapped to the subchannel sets as follows

119862 = 00 997888rarr H1 119862 = 01 997888rarr H

2

119862 = 10 997888rarr H3 119862 = 11 997888rarr H

4

(11)

At the receiver side after theMLdetection for each user if thesymbol is detected at the first receiving antenna then 119887

3= 0

and if the symbol is detected at the second antenna 1198873= 1

22 Zero-Padding Method In the subchannel selectionmethod we activated the desired receiving antennas for allusers by choosing the appropriate elements of the subchannelmatrix H

119904to precode the input data at the BSTx in order

to eliminate the effect of channel fading and multiuserinterference at the desired receiving antennas for the usersHowever the other antennas are affected by these channelimpairments Now we will activate the receiving antennasby zero-padding method such that all receiving antennas foreach user will receive zeros except for the activated antennaswhich will receive the transmitted symbols In this way wecan totally cancel the effect of channel fading and multiuserinterference on the received data by precoding the zero-padded input data using the MU-MIMO channel matrix H(assuming H is available at the transmitter side) Considerthe general system in Figure 1 after zero-padding the inputvector x we will get a vector xzp = [x1zp x

2

zp x119870

zp]119879 where

x119896zp isin c1times119873119903 denotes the zero-padded vector corresponding to

the 119896th user For the case where only one receiving antenna isactivated per user this can be written as

x119896zp = [0 0 0⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119895minus1

119909119896

119898119895 0 0 0⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119873119903minus119895

] (12)

After zero-forcing precoding the transmitted vector xzp isinc119873119905times1 can be written as

xzp = Gxzp (13)

where in this case G = 120573H119867(HH119867)minus1 and 120573 =

radic119873119905 tr[(HH119867)minus1] The received vector y isin c119873119903119870times1 may be

written as

y = Hxzp + w (14)

where w is defined in (4) The received vector y119896 isin c119873119903times1 forthe 119896th user can be described as

119910119896= 120573119909119896

119898119895+ 119908119896

119895 119895 = 119895

119910119896= 0 + 119908

119896

119895 119895 = 119895

(15)

where 119908119896119895is defined in (7) From (15) it is obvious that

for each user only one receiving antenna will receive thetransmitted symbol and the other antennas will receive zerosThe ML detector is then applied as in (8)

Example 2 As an illustration of the zero-padding methodconsider the system in Figure 2 with the same information

International Journal of Antennas and Propagation 5

as in Example 1 Here the code 119862 determines how the inputvector x is zero-padded to obtain xzp as

119862 = 00 997888rarr xzp = [1199091

1198981 0 1199092

1198981 0]

119862 = 01 997888rarr xzp = [1199091

1198981 0 0 119909

2

1198982]

119862 = 10 997888rarr xzp = [0 1199091

1198982 1199092

1198981 0]

119862 = 11 997888rarr xzp = [0 1199091

1198982 0 1199092

1198982]

(16)

The vector xzp is then precoded using the system matrix HFor a system with 119870 users and 119873

119903receive antennas for each

user there will be 2119870119901 = 119873119870119903available combinations of zero-

padded input vector xzp

3 Performance Analysis

Average Bit Error Probability Analysis When a symbol 119909119896119898119895

is transmitted there are three cases in which the error mayoccur These are the error in the modulated symbol 119904

119898only

the error in the spatial symbol 119895 only and the joint errorswhen both of themoccur simultaneouslyTherefore as shownin [14] the average bit error probability (ABEP) can be upper-bounded by the expression

ABEP le ABEPsymbol + ABEPspatial + ABEPjoint (17)

In [14] analytical formulas for the above three cases werepresented for the case where the spatial modulation scheme isapplied at the transmitter side Each expression for the ABERwas derived by summing the average pairwise error prob-abilities (APWEP) weighted by the corresponding averageHamming distances of the given bitmappingThe summationis taken over all the possible transmitted modulated andspatial symbols Applying this principle at the receiver sidefor our case here we get the following expressions

ABEPsymbol

=1

119872119873119903log2(119872119873119903)

times

119873119903

sum

119895=1

119872

sum

119898=1

119872

sum

=1

=119898

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPsymbol

ABEPspatial =1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)APWEPspatial

ABEPjoint

=1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119872

sum

=1

=119898

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPjoint

(18)

where 119889119867(119909119896

119898119895rarr 119909

119896

119895) is the Hamming distance be-

tween the transmitted and the received modulated symbol119889119867(119909119896

119898119895rarr 119909

119896

119898119895) is the Hamming distance between the

transmitted and the received spatial symbol and 119889119867(119909119896

119898119895rarr

119909119896

119895) is the Hamming distance between the transmitted and

received super symbol such that

119889119867(119909119896

119898119895997888rarr 119909119896

119895) = 119889

119867(119909119896

119898119895997888rarr 119909119896

119895)

+ 119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)

(19)

The APWEP can be defined for these three cases as

APWEPsymbol = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898

APWEPspatial = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119898119895)] 119895 = 119895

APWEPjoint = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898 119895 = 119895

(20)

where 119864[sdot] denotes the expectation operation Next wepresent formulas for analyzing theAPWEP for the three casesabove In this analysis we will follow the same procedure in[13] by introducing the effect of multiuser interference andchannel fading in the symbol spatial and joint cases

31 APWEP of Subchannel Selection Method APWEPsymbolmay occur when the symbol is received at the intended spatialantenna 119895 but theMLdetector (MLD) detects awrong symbol119904where =119898 Since APWEPsymbol is affected only by the

Euclidean distances of the points in the signal constellationdiagram then Pr(119909119896

119898119895rarr 119909119896

119895)may be written as [13]

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

minus 2Re (119904lowast119898119904)

1003816100381610038161003816119904 minus 1199041198981003816100381610038161003816 radic21198730

)

(21)

where Re(sdot) and (sdot)lowast denote the real part and the complexconjugate of a symbol respectively

6 International Journal of Antennas and Propagation

APWEPspatial can occur when the MLD detects thecorrect symbol 119904

119898at a wrong receiving antenna 119895 where 119895 = 119895

Then

Pr (119909119896119898119895997888rarr 119909119896

119898119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

119898) minus Re (119908119896

119895119904lowast

119898) gt

12057310038161003816100381610038161199041198981003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

119898)]

(22)

where119908119896119895and119908119896

119895are independent and identically distributed

(iid) random variables with zero mean and variance 1205902 =11987302 Thus Re(119908119896

119895119904lowast

119898) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random

variable with zero mean and variance 1205902 = |119904119898|21198730 Then

Pr(119909119896119898119895

rarr 119909119896

119898119895) can be written as

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(

12057310038161003816100381610038161199041198981003816100381610038161003816

2

minus 2Re (V119896119895119904lowast

119898)

210038161003816100381610038161199041198981003816100381610038161003816 radic1198730

) (23)

APWEPjoint may occur when the MLD detects a wrongsymbol 119904

at a wrong spatial antenna 119895 where =119898 and

119895 = 119895 Then

Pr (119909119896119898119895997888rarr 119909119896

119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt10038161003816100381610038161199041003816100381610038161003816

2

minus

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

) minus Re (119908119896

119895119904lowast

119898)

gt 120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

)]

(24)

where Re(119908119896119895119904lowast

) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random variable

with zero mean and variance 1205902 = (|119904119898|2+ |119904|2)11987302 The

final expression for this case is given by

Pr (119909119896119898119895997888rarr 119909119896

119895)

= 119876(

120573(10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

) minus 2Re (V119896119895119904lowast

)

radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

)

(25)

In (23) and (25) the terms which contain V119896119895are the contri-

butions of multiuser interference and channel fading as aresult of the new considerations in this paperThe subtractionof this term from the argument of the 119876-function impliesthat the overall APWEP will be higher or degraded (since119876(119909) gt 119876(119910) if 119909 lt 119910) compared to MU-MIMO withoutSM

32 APWEP of Zero-Padding Method In this method theeffect of multiuser interference and channel fading is totallycancelled Using similar steps above to obtain the APWEPformulas for the zero-padding method we found thatPr(119909119896119898119895

rarr 119909119896

119895) is exactly expressed as in (22) while

Pr(119909119896119898119895

rarr 119909119896

119898119895) and Pr(119909119896

119898119895rarr 119909119896

119895) may be respectively

expressed as in (24) and (26) by eliminating the contributionof themultiuser interference and channel fadingThuswe canwrite for this case that

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

radic1198730

) (26)

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(

120573radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

) (27)

Then the error probability given by (26) and (27) is lessthan that given by (23) and (25) which means that the zero-padding method can improve the total ABER performance

Throughput and Complexity Analysis We will quantify thesystem throughput in terms of the effective number of trans-mitted bits per channel use (bpcu) while the complexity ischaracterized by the total number of multiplications requiredat the MLD Because we considered here the case where onlyone antenna is activated per user we will compare theseparameters with that of the conventional multiuser MIMOsystem with one data stream per user (119873

119903= 1) The effective

number of bits per channel use for MU-SM is given by

119899MU-SM = 119870 [log2 (119872) + log2 (119873119903)] (28)

while the effective number of bits per channel use forconventional MU-MIMO is 119899MU-MIMO = 119870 log

2(119872) Then

International Journal of Antennas and Propagation 7

Table 1 The increase in throughput and complexity of MU-SM relative to those of conventional MU-MIMO

119872 119873119903

Relative increase in throughput((log2(119873119903)log2(119872)) times 100)

Relative increase in complexity((1198731199032119872) times 100)

2 2 100 502 4 200 1004 2 50 254 4 100 504 8 150 1008 2 3333 1258 4 6667 258 8 100 508 16 13333 10016 2 25 62516 4 50 12516 8 75 2516 16 100 5016 32 125 100

the throughput ofMU-SM relative to that of the conventionalMU-MIMO is given by

119877rel =119899MU-SM119899MU-MIMO

= 1 +log2(119873119903)

log2(119872)

(29)

where log2(119873119903)log2(119872) is the relative increase in the

throughput As shown in [13] separate detection can be usedin SMsystem inwhich the spatial symbol 119895 and themodulatedsymbol 119904

119898are detected separately such that

119895 = arg max119895isin12119873119903

10038161003816100381610038161003816119910119896

119895

10038161003816100381610038161003816

2

(30)

where 119910119896119895is the 119895th element of y119896

= arg min119898isin12119872

10038161003816100381610038161003816100381610038161003816

1

120573119910119896

119895minus 119904119898

10038161003816100381610038161003816100381610038161003816

2

= arg min119898isin12119872

2Re( 1120573119910119896

119895119904119898) minus

10038161003816100381610038161199041198981003816100381610038161003816

2

(31)

As explained above the correct decision is obtained when = 119898 and 119895 = 119895 The number of multiplications requiredin (30) to get 119895 is 119873

119903while the number of multiplications

required in (31) to get 119904is 2119872 The MLD computational

complexity for MU-SM which is defined here as the totalnumber of multiplications required for the detection processcan be expressed as

119862MU-SM = 119873119903 + 2119872 (32)

whereas the MLD computational complexity of the conven-tional MU-MIMO system with one receiving antenna foreach user is 119862MU-MIMO = 2119872 because there is no spatial

symbol to be detected in this case Thus the relative MLDcomplexity for the MU-SM versus the conventional MU-MIMO is

119862rel =119862MU-SM119862MU-MIMO

= 1 +119873119903

2119872

(33)

where 1198731199032119872 is the relative increase in complexity Table 1

presents a tabulation of the relative increase in throughputand complexity for MU-SM in comparison with the conven-tional MU-MIMO system From this table it is observed thatsignificant throughput enhancement can be achieved in theproposed scheme at moderate complexity Also noticeablefrom this table is the lack of dependence of the throughputand complexity increase on the BSTx antennas 119873

119905 This is

because we are comparing with another MU-MIMO systemthat has the same number of BSTx antennas

4 Simulation Results

In this section we present simulation results for the bit errorrate (BER) performance of the proposed SM for multiuserMIMO scheme The BER curves presented in all figures areaveraged over all users In the simulations we consideredQPSK and 16-QAM modulation formats Figure 3 comparesthe analytical results of (17)ndash(25) with simulation where itis easily observed that both analytical and simulation resultshave very closematching (especially in high SNR)This figurealso depicts the effect of increasing the number of receivingantennas for each user on the average (BER) performanceIn Figure 3 we considered transmitting antennas for cases of2 and 4 users with different number of receiving antennasfor each user As shown in the figure the BER performanceof the MU-SM system degrades as the number of receivingantennas119873

119903for each user increasesThis is due to the fact that

8 International Journal of Antennas and Propagation

100

10minus1

10minus2

10minus3

BER

Simulation (Nr = 2)

Simulation (Nr = 4)

Simulation (Nr = 8)

minus4 minus2 0 2 4 6 8 10 12 14 16

SNR (dB)

Analytical (K = 2)Analytical (K = 4)

Figure 3 BER performance of subchannel selection method withdifferent number of receiving antennas for 119873

119905= 10 119870 = 2 and

119870 = 4 for QPSK modulation

100

10minus1

10minus2

10minus3

BER

minus5 0 5 10 15

Nt = 10

Nt = 20

Nt = 30

Nt = 40

SNR (dB)

Figure 4 BER Performance of subchannel selection method withdifferent number of transmit antennas for 119870 = 5 and 119873

119903= 2 for

QPSK modulation

the multiple receiving antennas are not used for diversity butfor SM The receiver would not know ahead what antenna isintended to be switched by the BSTxThus the ML detectionis applied over all the receiving antennas which also increasethe probability of error in the received data with increasing119873119903for each userFigure 4 shows the BER performance of a multiuser

MIMO system with spatial modulation at the receiver sidefor different number of transmitting antennas In this figurewe considered 5 users with 119873

119903= 2 per user and 119873

119905=

100

10minus1

10minus2

10minus3

BER

minus5 0 5

SNR (dB)

Zero-paddingmethod

Subchannelselection method

Nr = 2

Nr = 2

Nr = 4

Nr = 4

and K = 4

and K = 2

and K = 4

and K = 2

Figure 5 BER of subchannel selection method and zero-paddingmethod with 119870 = 2 and 119870 = 4 and119873

119905= 16 for QPSK modulation

100

10minus1

10minus2

10minus3

10minus4

BER

Zero-paddingmethod

Subchannelselection method

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Nr = 2

Nr = 4

Nr = 8

SNR (dB)

Figure 6 BER of subchannel selection method and zero-paddingmethod with massive BSTx antennas (119873

119905= 50)119870 = 5 for 16-QAM

modulation

10 20 30 and 40 As shown in this figure the BER perfor-mance gets better when the number of transmitting antennasincreases due to the diversity gain achieved at the transmitterFigure 5 compares the BERperformance for the twoproposedmethods As shown in the figure zero-padding method givesa significant improvement in the BER performance oversubchannel selection method The figure also shows thatin the zero-padding method the BER performance is notaffected by the number of users because there is no multiuserinterference in this case Figure 6 shows the BERperformanceresults of the two proposedmethods for 16-QAMmodulation

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

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Page 4: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

4 International Journal of Antennas and Propagation

middot middot middot b3b2b1

middot middot middot b3b2b1

User 1User 1

11

1

User 2 User 2

2

22

3

4

h111

h121

h112

h113

h114

h213

h214

h123

h124

h224

h223

h212

h211h

221

h222

h122

Base stationtransmitter

(BSTx)

modulatorprecoder

etc

Figure 2 Example of SM for MU-MIMO system with 119870 = 2119873119905= 4 and119873

119903= 2

The number of the available subchannels is given by (119873119903)119870equiv

4 for this example withH119904 119904 = 1 4 is given by

H1= [ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

] H2= [ℎ1

11ℎ1

12ℎ1

13ℎ1

14

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]

H3= [ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

11ℎ2

12ℎ2

13ℎ2

14

] H4= [ℎ1

21ℎ1

22ℎ1

23ℎ1

24

ℎ2

21ℎ2

22ℎ2

23ℎ2

24

]

(10)

The code 119862 is mapped to the subchannel sets as follows

119862 = 00 997888rarr H1 119862 = 01 997888rarr H

2

119862 = 10 997888rarr H3 119862 = 11 997888rarr H

4

(11)

At the receiver side after theMLdetection for each user if thesymbol is detected at the first receiving antenna then 119887

3= 0

and if the symbol is detected at the second antenna 1198873= 1

22 Zero-Padding Method In the subchannel selectionmethod we activated the desired receiving antennas for allusers by choosing the appropriate elements of the subchannelmatrix H

119904to precode the input data at the BSTx in order

to eliminate the effect of channel fading and multiuserinterference at the desired receiving antennas for the usersHowever the other antennas are affected by these channelimpairments Now we will activate the receiving antennasby zero-padding method such that all receiving antennas foreach user will receive zeros except for the activated antennaswhich will receive the transmitted symbols In this way wecan totally cancel the effect of channel fading and multiuserinterference on the received data by precoding the zero-padded input data using the MU-MIMO channel matrix H(assuming H is available at the transmitter side) Considerthe general system in Figure 1 after zero-padding the inputvector x we will get a vector xzp = [x1zp x

2

zp x119870

zp]119879 where

x119896zp isin c1times119873119903 denotes the zero-padded vector corresponding to

the 119896th user For the case where only one receiving antenna isactivated per user this can be written as

x119896zp = [0 0 0⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119895minus1

119909119896

119898119895 0 0 0⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

119873119903minus119895

] (12)

After zero-forcing precoding the transmitted vector xzp isinc119873119905times1 can be written as

xzp = Gxzp (13)

where in this case G = 120573H119867(HH119867)minus1 and 120573 =

radic119873119905 tr[(HH119867)minus1] The received vector y isin c119873119903119870times1 may be

written as

y = Hxzp + w (14)

where w is defined in (4) The received vector y119896 isin c119873119903times1 forthe 119896th user can be described as

119910119896= 120573119909119896

119898119895+ 119908119896

119895 119895 = 119895

119910119896= 0 + 119908

119896

119895 119895 = 119895

(15)

where 119908119896119895is defined in (7) From (15) it is obvious that

for each user only one receiving antenna will receive thetransmitted symbol and the other antennas will receive zerosThe ML detector is then applied as in (8)

Example 2 As an illustration of the zero-padding methodconsider the system in Figure 2 with the same information

International Journal of Antennas and Propagation 5

as in Example 1 Here the code 119862 determines how the inputvector x is zero-padded to obtain xzp as

119862 = 00 997888rarr xzp = [1199091

1198981 0 1199092

1198981 0]

119862 = 01 997888rarr xzp = [1199091

1198981 0 0 119909

2

1198982]

119862 = 10 997888rarr xzp = [0 1199091

1198982 1199092

1198981 0]

119862 = 11 997888rarr xzp = [0 1199091

1198982 0 1199092

1198982]

(16)

The vector xzp is then precoded using the system matrix HFor a system with 119870 users and 119873

119903receive antennas for each

user there will be 2119870119901 = 119873119870119903available combinations of zero-

padded input vector xzp

3 Performance Analysis

Average Bit Error Probability Analysis When a symbol 119909119896119898119895

is transmitted there are three cases in which the error mayoccur These are the error in the modulated symbol 119904

119898only

the error in the spatial symbol 119895 only and the joint errorswhen both of themoccur simultaneouslyTherefore as shownin [14] the average bit error probability (ABEP) can be upper-bounded by the expression

ABEP le ABEPsymbol + ABEPspatial + ABEPjoint (17)

In [14] analytical formulas for the above three cases werepresented for the case where the spatial modulation scheme isapplied at the transmitter side Each expression for the ABERwas derived by summing the average pairwise error prob-abilities (APWEP) weighted by the corresponding averageHamming distances of the given bitmappingThe summationis taken over all the possible transmitted modulated andspatial symbols Applying this principle at the receiver sidefor our case here we get the following expressions

ABEPsymbol

=1

119872119873119903log2(119872119873119903)

times

119873119903

sum

119895=1

119872

sum

119898=1

119872

sum

=1

=119898

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPsymbol

ABEPspatial =1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)APWEPspatial

ABEPjoint

=1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119872

sum

=1

=119898

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPjoint

(18)

where 119889119867(119909119896

119898119895rarr 119909

119896

119895) is the Hamming distance be-

tween the transmitted and the received modulated symbol119889119867(119909119896

119898119895rarr 119909

119896

119898119895) is the Hamming distance between the

transmitted and the received spatial symbol and 119889119867(119909119896

119898119895rarr

119909119896

119895) is the Hamming distance between the transmitted and

received super symbol such that

119889119867(119909119896

119898119895997888rarr 119909119896

119895) = 119889

119867(119909119896

119898119895997888rarr 119909119896

119895)

+ 119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)

(19)

The APWEP can be defined for these three cases as

APWEPsymbol = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898

APWEPspatial = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119898119895)] 119895 = 119895

APWEPjoint = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898 119895 = 119895

(20)

where 119864[sdot] denotes the expectation operation Next wepresent formulas for analyzing theAPWEP for the three casesabove In this analysis we will follow the same procedure in[13] by introducing the effect of multiuser interference andchannel fading in the symbol spatial and joint cases

31 APWEP of Subchannel Selection Method APWEPsymbolmay occur when the symbol is received at the intended spatialantenna 119895 but theMLdetector (MLD) detects awrong symbol119904where =119898 Since APWEPsymbol is affected only by the

Euclidean distances of the points in the signal constellationdiagram then Pr(119909119896

119898119895rarr 119909119896

119895)may be written as [13]

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

minus 2Re (119904lowast119898119904)

1003816100381610038161003816119904 minus 1199041198981003816100381610038161003816 radic21198730

)

(21)

where Re(sdot) and (sdot)lowast denote the real part and the complexconjugate of a symbol respectively

6 International Journal of Antennas and Propagation

APWEPspatial can occur when the MLD detects thecorrect symbol 119904

119898at a wrong receiving antenna 119895 where 119895 = 119895

Then

Pr (119909119896119898119895997888rarr 119909119896

119898119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

119898) minus Re (119908119896

119895119904lowast

119898) gt

12057310038161003816100381610038161199041198981003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

119898)]

(22)

where119908119896119895and119908119896

119895are independent and identically distributed

(iid) random variables with zero mean and variance 1205902 =11987302 Thus Re(119908119896

119895119904lowast

119898) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random

variable with zero mean and variance 1205902 = |119904119898|21198730 Then

Pr(119909119896119898119895

rarr 119909119896

119898119895) can be written as

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(

12057310038161003816100381610038161199041198981003816100381610038161003816

2

minus 2Re (V119896119895119904lowast

119898)

210038161003816100381610038161199041198981003816100381610038161003816 radic1198730

) (23)

APWEPjoint may occur when the MLD detects a wrongsymbol 119904

at a wrong spatial antenna 119895 where =119898 and

119895 = 119895 Then

Pr (119909119896119898119895997888rarr 119909119896

119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt10038161003816100381610038161199041003816100381610038161003816

2

minus

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

) minus Re (119908119896

119895119904lowast

119898)

gt 120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

)]

(24)

where Re(119908119896119895119904lowast

) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random variable

with zero mean and variance 1205902 = (|119904119898|2+ |119904|2)11987302 The

final expression for this case is given by

Pr (119909119896119898119895997888rarr 119909119896

119895)

= 119876(

120573(10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

) minus 2Re (V119896119895119904lowast

)

radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

)

(25)

In (23) and (25) the terms which contain V119896119895are the contri-

butions of multiuser interference and channel fading as aresult of the new considerations in this paperThe subtractionof this term from the argument of the 119876-function impliesthat the overall APWEP will be higher or degraded (since119876(119909) gt 119876(119910) if 119909 lt 119910) compared to MU-MIMO withoutSM

32 APWEP of Zero-Padding Method In this method theeffect of multiuser interference and channel fading is totallycancelled Using similar steps above to obtain the APWEPformulas for the zero-padding method we found thatPr(119909119896119898119895

rarr 119909119896

119895) is exactly expressed as in (22) while

Pr(119909119896119898119895

rarr 119909119896

119898119895) and Pr(119909119896

119898119895rarr 119909119896

119895) may be respectively

expressed as in (24) and (26) by eliminating the contributionof themultiuser interference and channel fadingThuswe canwrite for this case that

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

radic1198730

) (26)

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(

120573radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

) (27)

Then the error probability given by (26) and (27) is lessthan that given by (23) and (25) which means that the zero-padding method can improve the total ABER performance

Throughput and Complexity Analysis We will quantify thesystem throughput in terms of the effective number of trans-mitted bits per channel use (bpcu) while the complexity ischaracterized by the total number of multiplications requiredat the MLD Because we considered here the case where onlyone antenna is activated per user we will compare theseparameters with that of the conventional multiuser MIMOsystem with one data stream per user (119873

119903= 1) The effective

number of bits per channel use for MU-SM is given by

119899MU-SM = 119870 [log2 (119872) + log2 (119873119903)] (28)

while the effective number of bits per channel use forconventional MU-MIMO is 119899MU-MIMO = 119870 log

2(119872) Then

International Journal of Antennas and Propagation 7

Table 1 The increase in throughput and complexity of MU-SM relative to those of conventional MU-MIMO

119872 119873119903

Relative increase in throughput((log2(119873119903)log2(119872)) times 100)

Relative increase in complexity((1198731199032119872) times 100)

2 2 100 502 4 200 1004 2 50 254 4 100 504 8 150 1008 2 3333 1258 4 6667 258 8 100 508 16 13333 10016 2 25 62516 4 50 12516 8 75 2516 16 100 5016 32 125 100

the throughput ofMU-SM relative to that of the conventionalMU-MIMO is given by

119877rel =119899MU-SM119899MU-MIMO

= 1 +log2(119873119903)

log2(119872)

(29)

where log2(119873119903)log2(119872) is the relative increase in the

throughput As shown in [13] separate detection can be usedin SMsystem inwhich the spatial symbol 119895 and themodulatedsymbol 119904

119898are detected separately such that

119895 = arg max119895isin12119873119903

10038161003816100381610038161003816119910119896

119895

10038161003816100381610038161003816

2

(30)

where 119910119896119895is the 119895th element of y119896

= arg min119898isin12119872

10038161003816100381610038161003816100381610038161003816

1

120573119910119896

119895minus 119904119898

10038161003816100381610038161003816100381610038161003816

2

= arg min119898isin12119872

2Re( 1120573119910119896

119895119904119898) minus

10038161003816100381610038161199041198981003816100381610038161003816

2

(31)

As explained above the correct decision is obtained when = 119898 and 119895 = 119895 The number of multiplications requiredin (30) to get 119895 is 119873

119903while the number of multiplications

required in (31) to get 119904is 2119872 The MLD computational

complexity for MU-SM which is defined here as the totalnumber of multiplications required for the detection processcan be expressed as

119862MU-SM = 119873119903 + 2119872 (32)

whereas the MLD computational complexity of the conven-tional MU-MIMO system with one receiving antenna foreach user is 119862MU-MIMO = 2119872 because there is no spatial

symbol to be detected in this case Thus the relative MLDcomplexity for the MU-SM versus the conventional MU-MIMO is

119862rel =119862MU-SM119862MU-MIMO

= 1 +119873119903

2119872

(33)

where 1198731199032119872 is the relative increase in complexity Table 1

presents a tabulation of the relative increase in throughputand complexity for MU-SM in comparison with the conven-tional MU-MIMO system From this table it is observed thatsignificant throughput enhancement can be achieved in theproposed scheme at moderate complexity Also noticeablefrom this table is the lack of dependence of the throughputand complexity increase on the BSTx antennas 119873

119905 This is

because we are comparing with another MU-MIMO systemthat has the same number of BSTx antennas

4 Simulation Results

In this section we present simulation results for the bit errorrate (BER) performance of the proposed SM for multiuserMIMO scheme The BER curves presented in all figures areaveraged over all users In the simulations we consideredQPSK and 16-QAM modulation formats Figure 3 comparesthe analytical results of (17)ndash(25) with simulation where itis easily observed that both analytical and simulation resultshave very closematching (especially in high SNR)This figurealso depicts the effect of increasing the number of receivingantennas for each user on the average (BER) performanceIn Figure 3 we considered transmitting antennas for cases of2 and 4 users with different number of receiving antennasfor each user As shown in the figure the BER performanceof the MU-SM system degrades as the number of receivingantennas119873

119903for each user increasesThis is due to the fact that

8 International Journal of Antennas and Propagation

100

10minus1

10minus2

10minus3

BER

Simulation (Nr = 2)

Simulation (Nr = 4)

Simulation (Nr = 8)

minus4 minus2 0 2 4 6 8 10 12 14 16

SNR (dB)

Analytical (K = 2)Analytical (K = 4)

Figure 3 BER performance of subchannel selection method withdifferent number of receiving antennas for 119873

119905= 10 119870 = 2 and

119870 = 4 for QPSK modulation

100

10minus1

10minus2

10minus3

BER

minus5 0 5 10 15

Nt = 10

Nt = 20

Nt = 30

Nt = 40

SNR (dB)

Figure 4 BER Performance of subchannel selection method withdifferent number of transmit antennas for 119870 = 5 and 119873

119903= 2 for

QPSK modulation

the multiple receiving antennas are not used for diversity butfor SM The receiver would not know ahead what antenna isintended to be switched by the BSTxThus the ML detectionis applied over all the receiving antennas which also increasethe probability of error in the received data with increasing119873119903for each userFigure 4 shows the BER performance of a multiuser

MIMO system with spatial modulation at the receiver sidefor different number of transmitting antennas In this figurewe considered 5 users with 119873

119903= 2 per user and 119873

119905=

100

10minus1

10minus2

10minus3

BER

minus5 0 5

SNR (dB)

Zero-paddingmethod

Subchannelselection method

Nr = 2

Nr = 2

Nr = 4

Nr = 4

and K = 4

and K = 2

and K = 4

and K = 2

Figure 5 BER of subchannel selection method and zero-paddingmethod with 119870 = 2 and 119870 = 4 and119873

119905= 16 for QPSK modulation

100

10minus1

10minus2

10minus3

10minus4

BER

Zero-paddingmethod

Subchannelselection method

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Nr = 2

Nr = 4

Nr = 8

SNR (dB)

Figure 6 BER of subchannel selection method and zero-paddingmethod with massive BSTx antennas (119873

119905= 50)119870 = 5 for 16-QAM

modulation

10 20 30 and 40 As shown in this figure the BER perfor-mance gets better when the number of transmitting antennasincreases due to the diversity gain achieved at the transmitterFigure 5 compares the BERperformance for the twoproposedmethods As shown in the figure zero-padding method givesa significant improvement in the BER performance oversubchannel selection method The figure also shows thatin the zero-padding method the BER performance is notaffected by the number of users because there is no multiuserinterference in this case Figure 6 shows the BERperformanceresults of the two proposedmethods for 16-QAMmodulation

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

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Page 5: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

International Journal of Antennas and Propagation 5

as in Example 1 Here the code 119862 determines how the inputvector x is zero-padded to obtain xzp as

119862 = 00 997888rarr xzp = [1199091

1198981 0 1199092

1198981 0]

119862 = 01 997888rarr xzp = [1199091

1198981 0 0 119909

2

1198982]

119862 = 10 997888rarr xzp = [0 1199091

1198982 1199092

1198981 0]

119862 = 11 997888rarr xzp = [0 1199091

1198982 0 1199092

1198982]

(16)

The vector xzp is then precoded using the system matrix HFor a system with 119870 users and 119873

119903receive antennas for each

user there will be 2119870119901 = 119873119870119903available combinations of zero-

padded input vector xzp

3 Performance Analysis

Average Bit Error Probability Analysis When a symbol 119909119896119898119895

is transmitted there are three cases in which the error mayoccur These are the error in the modulated symbol 119904

119898only

the error in the spatial symbol 119895 only and the joint errorswhen both of themoccur simultaneouslyTherefore as shownin [14] the average bit error probability (ABEP) can be upper-bounded by the expression

ABEP le ABEPsymbol + ABEPspatial + ABEPjoint (17)

In [14] analytical formulas for the above three cases werepresented for the case where the spatial modulation scheme isapplied at the transmitter side Each expression for the ABERwas derived by summing the average pairwise error prob-abilities (APWEP) weighted by the corresponding averageHamming distances of the given bitmappingThe summationis taken over all the possible transmitted modulated andspatial symbols Applying this principle at the receiver sidefor our case here we get the following expressions

ABEPsymbol

=1

119872119873119903log2(119872119873119903)

times

119873119903

sum

119895=1

119872

sum

119898=1

119872

sum

=1

=119898

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPsymbol

ABEPspatial =1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)APWEPspatial

ABEPjoint

=1

119872119873119903log2(119872119873119903)

times

119872

sum

119898=1

119873119903

sum

119895=1

119872

sum

=1

=119898

119873119903

sum

119895=1

119895 = 119895

119889119867(119909119896

119898119895997888rarr 119909119896

119895)APWEPjoint

(18)

where 119889119867(119909119896

119898119895rarr 119909

119896

119895) is the Hamming distance be-

tween the transmitted and the received modulated symbol119889119867(119909119896

119898119895rarr 119909

119896

119898119895) is the Hamming distance between the

transmitted and the received spatial symbol and 119889119867(119909119896

119898119895rarr

119909119896

119895) is the Hamming distance between the transmitted and

received super symbol such that

119889119867(119909119896

119898119895997888rarr 119909119896

119895) = 119889

119867(119909119896

119898119895997888rarr 119909119896

119895)

+ 119889119867(119909119896

119898119895997888rarr 119909119896

119898119895)

(19)

The APWEP can be defined for these three cases as

APWEPsymbol = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898

APWEPspatial = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119898119895)] 119895 = 119895

APWEPjoint = 119864 [Pr (119909119896

119898119895997888rarr 119909119896

119895)] =119898 119895 = 119895

(20)

where 119864[sdot] denotes the expectation operation Next wepresent formulas for analyzing theAPWEP for the three casesabove In this analysis we will follow the same procedure in[13] by introducing the effect of multiuser interference andchannel fading in the symbol spatial and joint cases

31 APWEP of Subchannel Selection Method APWEPsymbolmay occur when the symbol is received at the intended spatialantenna 119895 but theMLdetector (MLD) detects awrong symbol119904where =119898 Since APWEPsymbol is affected only by the

Euclidean distances of the points in the signal constellationdiagram then Pr(119909119896

119898119895rarr 119909119896

119895)may be written as [13]

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

minus 2Re (119904lowast119898119904)

1003816100381610038161003816119904 minus 1199041198981003816100381610038161003816 radic21198730

)

(21)

where Re(sdot) and (sdot)lowast denote the real part and the complexconjugate of a symbol respectively

6 International Journal of Antennas and Propagation

APWEPspatial can occur when the MLD detects thecorrect symbol 119904

119898at a wrong receiving antenna 119895 where 119895 = 119895

Then

Pr (119909119896119898119895997888rarr 119909119896

119898119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

119898) minus Re (119908119896

119895119904lowast

119898) gt

12057310038161003816100381610038161199041198981003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

119898)]

(22)

where119908119896119895and119908119896

119895are independent and identically distributed

(iid) random variables with zero mean and variance 1205902 =11987302 Thus Re(119908119896

119895119904lowast

119898) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random

variable with zero mean and variance 1205902 = |119904119898|21198730 Then

Pr(119909119896119898119895

rarr 119909119896

119898119895) can be written as

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(

12057310038161003816100381610038161199041198981003816100381610038161003816

2

minus 2Re (V119896119895119904lowast

119898)

210038161003816100381610038161199041198981003816100381610038161003816 radic1198730

) (23)

APWEPjoint may occur when the MLD detects a wrongsymbol 119904

at a wrong spatial antenna 119895 where =119898 and

119895 = 119895 Then

Pr (119909119896119898119895997888rarr 119909119896

119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt10038161003816100381610038161199041003816100381610038161003816

2

minus

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

) minus Re (119908119896

119895119904lowast

119898)

gt 120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

)]

(24)

where Re(119908119896119895119904lowast

) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random variable

with zero mean and variance 1205902 = (|119904119898|2+ |119904|2)11987302 The

final expression for this case is given by

Pr (119909119896119898119895997888rarr 119909119896

119895)

= 119876(

120573(10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

) minus 2Re (V119896119895119904lowast

)

radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

)

(25)

In (23) and (25) the terms which contain V119896119895are the contri-

butions of multiuser interference and channel fading as aresult of the new considerations in this paperThe subtractionof this term from the argument of the 119876-function impliesthat the overall APWEP will be higher or degraded (since119876(119909) gt 119876(119910) if 119909 lt 119910) compared to MU-MIMO withoutSM

32 APWEP of Zero-Padding Method In this method theeffect of multiuser interference and channel fading is totallycancelled Using similar steps above to obtain the APWEPformulas for the zero-padding method we found thatPr(119909119896119898119895

rarr 119909119896

119895) is exactly expressed as in (22) while

Pr(119909119896119898119895

rarr 119909119896

119898119895) and Pr(119909119896

119898119895rarr 119909119896

119895) may be respectively

expressed as in (24) and (26) by eliminating the contributionof themultiuser interference and channel fadingThuswe canwrite for this case that

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

radic1198730

) (26)

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(

120573radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

) (27)

Then the error probability given by (26) and (27) is lessthan that given by (23) and (25) which means that the zero-padding method can improve the total ABER performance

Throughput and Complexity Analysis We will quantify thesystem throughput in terms of the effective number of trans-mitted bits per channel use (bpcu) while the complexity ischaracterized by the total number of multiplications requiredat the MLD Because we considered here the case where onlyone antenna is activated per user we will compare theseparameters with that of the conventional multiuser MIMOsystem with one data stream per user (119873

119903= 1) The effective

number of bits per channel use for MU-SM is given by

119899MU-SM = 119870 [log2 (119872) + log2 (119873119903)] (28)

while the effective number of bits per channel use forconventional MU-MIMO is 119899MU-MIMO = 119870 log

2(119872) Then

International Journal of Antennas and Propagation 7

Table 1 The increase in throughput and complexity of MU-SM relative to those of conventional MU-MIMO

119872 119873119903

Relative increase in throughput((log2(119873119903)log2(119872)) times 100)

Relative increase in complexity((1198731199032119872) times 100)

2 2 100 502 4 200 1004 2 50 254 4 100 504 8 150 1008 2 3333 1258 4 6667 258 8 100 508 16 13333 10016 2 25 62516 4 50 12516 8 75 2516 16 100 5016 32 125 100

the throughput ofMU-SM relative to that of the conventionalMU-MIMO is given by

119877rel =119899MU-SM119899MU-MIMO

= 1 +log2(119873119903)

log2(119872)

(29)

where log2(119873119903)log2(119872) is the relative increase in the

throughput As shown in [13] separate detection can be usedin SMsystem inwhich the spatial symbol 119895 and themodulatedsymbol 119904

119898are detected separately such that

119895 = arg max119895isin12119873119903

10038161003816100381610038161003816119910119896

119895

10038161003816100381610038161003816

2

(30)

where 119910119896119895is the 119895th element of y119896

= arg min119898isin12119872

10038161003816100381610038161003816100381610038161003816

1

120573119910119896

119895minus 119904119898

10038161003816100381610038161003816100381610038161003816

2

= arg min119898isin12119872

2Re( 1120573119910119896

119895119904119898) minus

10038161003816100381610038161199041198981003816100381610038161003816

2

(31)

As explained above the correct decision is obtained when = 119898 and 119895 = 119895 The number of multiplications requiredin (30) to get 119895 is 119873

119903while the number of multiplications

required in (31) to get 119904is 2119872 The MLD computational

complexity for MU-SM which is defined here as the totalnumber of multiplications required for the detection processcan be expressed as

119862MU-SM = 119873119903 + 2119872 (32)

whereas the MLD computational complexity of the conven-tional MU-MIMO system with one receiving antenna foreach user is 119862MU-MIMO = 2119872 because there is no spatial

symbol to be detected in this case Thus the relative MLDcomplexity for the MU-SM versus the conventional MU-MIMO is

119862rel =119862MU-SM119862MU-MIMO

= 1 +119873119903

2119872

(33)

where 1198731199032119872 is the relative increase in complexity Table 1

presents a tabulation of the relative increase in throughputand complexity for MU-SM in comparison with the conven-tional MU-MIMO system From this table it is observed thatsignificant throughput enhancement can be achieved in theproposed scheme at moderate complexity Also noticeablefrom this table is the lack of dependence of the throughputand complexity increase on the BSTx antennas 119873

119905 This is

because we are comparing with another MU-MIMO systemthat has the same number of BSTx antennas

4 Simulation Results

In this section we present simulation results for the bit errorrate (BER) performance of the proposed SM for multiuserMIMO scheme The BER curves presented in all figures areaveraged over all users In the simulations we consideredQPSK and 16-QAM modulation formats Figure 3 comparesthe analytical results of (17)ndash(25) with simulation where itis easily observed that both analytical and simulation resultshave very closematching (especially in high SNR)This figurealso depicts the effect of increasing the number of receivingantennas for each user on the average (BER) performanceIn Figure 3 we considered transmitting antennas for cases of2 and 4 users with different number of receiving antennasfor each user As shown in the figure the BER performanceof the MU-SM system degrades as the number of receivingantennas119873

119903for each user increasesThis is due to the fact that

8 International Journal of Antennas and Propagation

100

10minus1

10minus2

10minus3

BER

Simulation (Nr = 2)

Simulation (Nr = 4)

Simulation (Nr = 8)

minus4 minus2 0 2 4 6 8 10 12 14 16

SNR (dB)

Analytical (K = 2)Analytical (K = 4)

Figure 3 BER performance of subchannel selection method withdifferent number of receiving antennas for 119873

119905= 10 119870 = 2 and

119870 = 4 for QPSK modulation

100

10minus1

10minus2

10minus3

BER

minus5 0 5 10 15

Nt = 10

Nt = 20

Nt = 30

Nt = 40

SNR (dB)

Figure 4 BER Performance of subchannel selection method withdifferent number of transmit antennas for 119870 = 5 and 119873

119903= 2 for

QPSK modulation

the multiple receiving antennas are not used for diversity butfor SM The receiver would not know ahead what antenna isintended to be switched by the BSTxThus the ML detectionis applied over all the receiving antennas which also increasethe probability of error in the received data with increasing119873119903for each userFigure 4 shows the BER performance of a multiuser

MIMO system with spatial modulation at the receiver sidefor different number of transmitting antennas In this figurewe considered 5 users with 119873

119903= 2 per user and 119873

119905=

100

10minus1

10minus2

10minus3

BER

minus5 0 5

SNR (dB)

Zero-paddingmethod

Subchannelselection method

Nr = 2

Nr = 2

Nr = 4

Nr = 4

and K = 4

and K = 2

and K = 4

and K = 2

Figure 5 BER of subchannel selection method and zero-paddingmethod with 119870 = 2 and 119870 = 4 and119873

119905= 16 for QPSK modulation

100

10minus1

10minus2

10minus3

10minus4

BER

Zero-paddingmethod

Subchannelselection method

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Nr = 2

Nr = 4

Nr = 8

SNR (dB)

Figure 6 BER of subchannel selection method and zero-paddingmethod with massive BSTx antennas (119873

119905= 50)119870 = 5 for 16-QAM

modulation

10 20 30 and 40 As shown in this figure the BER perfor-mance gets better when the number of transmitting antennasincreases due to the diversity gain achieved at the transmitterFigure 5 compares the BERperformance for the twoproposedmethods As shown in the figure zero-padding method givesa significant improvement in the BER performance oversubchannel selection method The figure also shows thatin the zero-padding method the BER performance is notaffected by the number of users because there is no multiuserinterference in this case Figure 6 shows the BERperformanceresults of the two proposedmethods for 16-QAMmodulation

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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DistributedSensor Networks

International Journal of

Page 6: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

6 International Journal of Antennas and Propagation

APWEPspatial can occur when the MLD detects thecorrect symbol 119904

119898at a wrong receiving antenna 119895 where 119895 = 119895

Then

Pr (119909119896119898119895997888rarr 119909119896

119898119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

119898) minus Re (119908119896

119895119904lowast

119898) gt

12057310038161003816100381610038161199041198981003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

119898)]

(22)

where119908119896119895and119908119896

119895are independent and identically distributed

(iid) random variables with zero mean and variance 1205902 =11987302 Thus Re(119908119896

119895119904lowast

119898) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random

variable with zero mean and variance 1205902 = |119904119898|21198730 Then

Pr(119909119896119898119895

rarr 119909119896

119898119895) can be written as

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(

12057310038161003816100381610038161199041198981003816100381610038161003816

2

minus 2Re (V119896119895119904lowast

119898)

210038161003816100381610038161199041198981003816100381610038161003816 radic1198730

) (23)

APWEPjoint may occur when the MLD detects a wrongsymbol 119904

at a wrong spatial antenna 119895 where =119898 and

119895 = 119895 Then

Pr (119909119896119898119895997888rarr 119909119896

119895)

= Pr[100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119898119895

100381710038171003817100381710038171003817100381710038171003817

2

gt

100381710038171003817100381710038171003817100381710038171003817

y119896

120573minus x119896119895

100381710038171003817100381710038171003817100381710038171003817

2

]

= Pr[

[

minus10038161003816100381610038161199041198981003816100381610038161003816

2

minus

2Re (119908119896119895119904lowast

119898)

120573

gt10038161003816100381610038161199041003816100381610038161003816

2

minus

2Re (V119896119895119904lowast

119898)

120573minus

2Re (119908119896119895119904lowast

119898)

120573

]

]

= Pr[Re (119908119896119895119904lowast

) minus Re (119908119896

119895119904lowast

119898)

gt 120573

10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

2minus Re (V119896

119895119904lowast

)]

(24)

where Re(119908119896119895119904lowast

) minus Re(119908119896

119895119904lowast

119898) is a Gaussian random variable

with zero mean and variance 1205902 = (|119904119898|2+ |119904|2)11987302 The

final expression for this case is given by

Pr (119909119896119898119895997888rarr 119909119896

119895)

= 119876(

120573(10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

) minus 2Re (V119896119895119904lowast

)

radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

)

(25)

In (23) and (25) the terms which contain V119896119895are the contri-

butions of multiuser interference and channel fading as aresult of the new considerations in this paperThe subtractionof this term from the argument of the 119876-function impliesthat the overall APWEP will be higher or degraded (since119876(119909) gt 119876(119910) if 119909 lt 119910) compared to MU-MIMO withoutSM

32 APWEP of Zero-Padding Method In this method theeffect of multiuser interference and channel fading is totallycancelled Using similar steps above to obtain the APWEPformulas for the zero-padding method we found thatPr(119909119896119898119895

rarr 119909119896

119895) is exactly expressed as in (22) while

Pr(119909119896119898119895

rarr 119909119896

119898119895) and Pr(119909119896

119898119895rarr 119909119896

119895) may be respectively

expressed as in (24) and (26) by eliminating the contributionof themultiuser interference and channel fadingThuswe canwrite for this case that

Pr (119909119896119898119895997888rarr 119909119896

119898119895) = 119876(120573

10038161003816100381610038161199041198981003816100381610038161003816

radic1198730

) (26)

Pr (119909119896119898119895997888rarr 119909119896

119895) = 119876(

120573radic10038161003816100381610038161199041198981003816100381610038161003816

2

+10038161003816100381610038161199041003816100381610038161003816

2

radic21198730

) (27)

Then the error probability given by (26) and (27) is lessthan that given by (23) and (25) which means that the zero-padding method can improve the total ABER performance

Throughput and Complexity Analysis We will quantify thesystem throughput in terms of the effective number of trans-mitted bits per channel use (bpcu) while the complexity ischaracterized by the total number of multiplications requiredat the MLD Because we considered here the case where onlyone antenna is activated per user we will compare theseparameters with that of the conventional multiuser MIMOsystem with one data stream per user (119873

119903= 1) The effective

number of bits per channel use for MU-SM is given by

119899MU-SM = 119870 [log2 (119872) + log2 (119873119903)] (28)

while the effective number of bits per channel use forconventional MU-MIMO is 119899MU-MIMO = 119870 log

2(119872) Then

International Journal of Antennas and Propagation 7

Table 1 The increase in throughput and complexity of MU-SM relative to those of conventional MU-MIMO

119872 119873119903

Relative increase in throughput((log2(119873119903)log2(119872)) times 100)

Relative increase in complexity((1198731199032119872) times 100)

2 2 100 502 4 200 1004 2 50 254 4 100 504 8 150 1008 2 3333 1258 4 6667 258 8 100 508 16 13333 10016 2 25 62516 4 50 12516 8 75 2516 16 100 5016 32 125 100

the throughput ofMU-SM relative to that of the conventionalMU-MIMO is given by

119877rel =119899MU-SM119899MU-MIMO

= 1 +log2(119873119903)

log2(119872)

(29)

where log2(119873119903)log2(119872) is the relative increase in the

throughput As shown in [13] separate detection can be usedin SMsystem inwhich the spatial symbol 119895 and themodulatedsymbol 119904

119898are detected separately such that

119895 = arg max119895isin12119873119903

10038161003816100381610038161003816119910119896

119895

10038161003816100381610038161003816

2

(30)

where 119910119896119895is the 119895th element of y119896

= arg min119898isin12119872

10038161003816100381610038161003816100381610038161003816

1

120573119910119896

119895minus 119904119898

10038161003816100381610038161003816100381610038161003816

2

= arg min119898isin12119872

2Re( 1120573119910119896

119895119904119898) minus

10038161003816100381610038161199041198981003816100381610038161003816

2

(31)

As explained above the correct decision is obtained when = 119898 and 119895 = 119895 The number of multiplications requiredin (30) to get 119895 is 119873

119903while the number of multiplications

required in (31) to get 119904is 2119872 The MLD computational

complexity for MU-SM which is defined here as the totalnumber of multiplications required for the detection processcan be expressed as

119862MU-SM = 119873119903 + 2119872 (32)

whereas the MLD computational complexity of the conven-tional MU-MIMO system with one receiving antenna foreach user is 119862MU-MIMO = 2119872 because there is no spatial

symbol to be detected in this case Thus the relative MLDcomplexity for the MU-SM versus the conventional MU-MIMO is

119862rel =119862MU-SM119862MU-MIMO

= 1 +119873119903

2119872

(33)

where 1198731199032119872 is the relative increase in complexity Table 1

presents a tabulation of the relative increase in throughputand complexity for MU-SM in comparison with the conven-tional MU-MIMO system From this table it is observed thatsignificant throughput enhancement can be achieved in theproposed scheme at moderate complexity Also noticeablefrom this table is the lack of dependence of the throughputand complexity increase on the BSTx antennas 119873

119905 This is

because we are comparing with another MU-MIMO systemthat has the same number of BSTx antennas

4 Simulation Results

In this section we present simulation results for the bit errorrate (BER) performance of the proposed SM for multiuserMIMO scheme The BER curves presented in all figures areaveraged over all users In the simulations we consideredQPSK and 16-QAM modulation formats Figure 3 comparesthe analytical results of (17)ndash(25) with simulation where itis easily observed that both analytical and simulation resultshave very closematching (especially in high SNR)This figurealso depicts the effect of increasing the number of receivingantennas for each user on the average (BER) performanceIn Figure 3 we considered transmitting antennas for cases of2 and 4 users with different number of receiving antennasfor each user As shown in the figure the BER performanceof the MU-SM system degrades as the number of receivingantennas119873

119903for each user increasesThis is due to the fact that

8 International Journal of Antennas and Propagation

100

10minus1

10minus2

10minus3

BER

Simulation (Nr = 2)

Simulation (Nr = 4)

Simulation (Nr = 8)

minus4 minus2 0 2 4 6 8 10 12 14 16

SNR (dB)

Analytical (K = 2)Analytical (K = 4)

Figure 3 BER performance of subchannel selection method withdifferent number of receiving antennas for 119873

119905= 10 119870 = 2 and

119870 = 4 for QPSK modulation

100

10minus1

10minus2

10minus3

BER

minus5 0 5 10 15

Nt = 10

Nt = 20

Nt = 30

Nt = 40

SNR (dB)

Figure 4 BER Performance of subchannel selection method withdifferent number of transmit antennas for 119870 = 5 and 119873

119903= 2 for

QPSK modulation

the multiple receiving antennas are not used for diversity butfor SM The receiver would not know ahead what antenna isintended to be switched by the BSTxThus the ML detectionis applied over all the receiving antennas which also increasethe probability of error in the received data with increasing119873119903for each userFigure 4 shows the BER performance of a multiuser

MIMO system with spatial modulation at the receiver sidefor different number of transmitting antennas In this figurewe considered 5 users with 119873

119903= 2 per user and 119873

119905=

100

10minus1

10minus2

10minus3

BER

minus5 0 5

SNR (dB)

Zero-paddingmethod

Subchannelselection method

Nr = 2

Nr = 2

Nr = 4

Nr = 4

and K = 4

and K = 2

and K = 4

and K = 2

Figure 5 BER of subchannel selection method and zero-paddingmethod with 119870 = 2 and 119870 = 4 and119873

119905= 16 for QPSK modulation

100

10minus1

10minus2

10minus3

10minus4

BER

Zero-paddingmethod

Subchannelselection method

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Nr = 2

Nr = 4

Nr = 8

SNR (dB)

Figure 6 BER of subchannel selection method and zero-paddingmethod with massive BSTx antennas (119873

119905= 50)119870 = 5 for 16-QAM

modulation

10 20 30 and 40 As shown in this figure the BER perfor-mance gets better when the number of transmitting antennasincreases due to the diversity gain achieved at the transmitterFigure 5 compares the BERperformance for the twoproposedmethods As shown in the figure zero-padding method givesa significant improvement in the BER performance oversubchannel selection method The figure also shows thatin the zero-padding method the BER performance is notaffected by the number of users because there is no multiuserinterference in this case Figure 6 shows the BERperformanceresults of the two proposedmethods for 16-QAMmodulation

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 7: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

International Journal of Antennas and Propagation 7

Table 1 The increase in throughput and complexity of MU-SM relative to those of conventional MU-MIMO

119872 119873119903

Relative increase in throughput((log2(119873119903)log2(119872)) times 100)

Relative increase in complexity((1198731199032119872) times 100)

2 2 100 502 4 200 1004 2 50 254 4 100 504 8 150 1008 2 3333 1258 4 6667 258 8 100 508 16 13333 10016 2 25 62516 4 50 12516 8 75 2516 16 100 5016 32 125 100

the throughput ofMU-SM relative to that of the conventionalMU-MIMO is given by

119877rel =119899MU-SM119899MU-MIMO

= 1 +log2(119873119903)

log2(119872)

(29)

where log2(119873119903)log2(119872) is the relative increase in the

throughput As shown in [13] separate detection can be usedin SMsystem inwhich the spatial symbol 119895 and themodulatedsymbol 119904

119898are detected separately such that

119895 = arg max119895isin12119873119903

10038161003816100381610038161003816119910119896

119895

10038161003816100381610038161003816

2

(30)

where 119910119896119895is the 119895th element of y119896

= arg min119898isin12119872

10038161003816100381610038161003816100381610038161003816

1

120573119910119896

119895minus 119904119898

10038161003816100381610038161003816100381610038161003816

2

= arg min119898isin12119872

2Re( 1120573119910119896

119895119904119898) minus

10038161003816100381610038161199041198981003816100381610038161003816

2

(31)

As explained above the correct decision is obtained when = 119898 and 119895 = 119895 The number of multiplications requiredin (30) to get 119895 is 119873

119903while the number of multiplications

required in (31) to get 119904is 2119872 The MLD computational

complexity for MU-SM which is defined here as the totalnumber of multiplications required for the detection processcan be expressed as

119862MU-SM = 119873119903 + 2119872 (32)

whereas the MLD computational complexity of the conven-tional MU-MIMO system with one receiving antenna foreach user is 119862MU-MIMO = 2119872 because there is no spatial

symbol to be detected in this case Thus the relative MLDcomplexity for the MU-SM versus the conventional MU-MIMO is

119862rel =119862MU-SM119862MU-MIMO

= 1 +119873119903

2119872

(33)

where 1198731199032119872 is the relative increase in complexity Table 1

presents a tabulation of the relative increase in throughputand complexity for MU-SM in comparison with the conven-tional MU-MIMO system From this table it is observed thatsignificant throughput enhancement can be achieved in theproposed scheme at moderate complexity Also noticeablefrom this table is the lack of dependence of the throughputand complexity increase on the BSTx antennas 119873

119905 This is

because we are comparing with another MU-MIMO systemthat has the same number of BSTx antennas

4 Simulation Results

In this section we present simulation results for the bit errorrate (BER) performance of the proposed SM for multiuserMIMO scheme The BER curves presented in all figures areaveraged over all users In the simulations we consideredQPSK and 16-QAM modulation formats Figure 3 comparesthe analytical results of (17)ndash(25) with simulation where itis easily observed that both analytical and simulation resultshave very closematching (especially in high SNR)This figurealso depicts the effect of increasing the number of receivingantennas for each user on the average (BER) performanceIn Figure 3 we considered transmitting antennas for cases of2 and 4 users with different number of receiving antennasfor each user As shown in the figure the BER performanceof the MU-SM system degrades as the number of receivingantennas119873

119903for each user increasesThis is due to the fact that

8 International Journal of Antennas and Propagation

100

10minus1

10minus2

10minus3

BER

Simulation (Nr = 2)

Simulation (Nr = 4)

Simulation (Nr = 8)

minus4 minus2 0 2 4 6 8 10 12 14 16

SNR (dB)

Analytical (K = 2)Analytical (K = 4)

Figure 3 BER performance of subchannel selection method withdifferent number of receiving antennas for 119873

119905= 10 119870 = 2 and

119870 = 4 for QPSK modulation

100

10minus1

10minus2

10minus3

BER

minus5 0 5 10 15

Nt = 10

Nt = 20

Nt = 30

Nt = 40

SNR (dB)

Figure 4 BER Performance of subchannel selection method withdifferent number of transmit antennas for 119870 = 5 and 119873

119903= 2 for

QPSK modulation

the multiple receiving antennas are not used for diversity butfor SM The receiver would not know ahead what antenna isintended to be switched by the BSTxThus the ML detectionis applied over all the receiving antennas which also increasethe probability of error in the received data with increasing119873119903for each userFigure 4 shows the BER performance of a multiuser

MIMO system with spatial modulation at the receiver sidefor different number of transmitting antennas In this figurewe considered 5 users with 119873

119903= 2 per user and 119873

119905=

100

10minus1

10minus2

10minus3

BER

minus5 0 5

SNR (dB)

Zero-paddingmethod

Subchannelselection method

Nr = 2

Nr = 2

Nr = 4

Nr = 4

and K = 4

and K = 2

and K = 4

and K = 2

Figure 5 BER of subchannel selection method and zero-paddingmethod with 119870 = 2 and 119870 = 4 and119873

119905= 16 for QPSK modulation

100

10minus1

10minus2

10minus3

10minus4

BER

Zero-paddingmethod

Subchannelselection method

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Nr = 2

Nr = 4

Nr = 8

SNR (dB)

Figure 6 BER of subchannel selection method and zero-paddingmethod with massive BSTx antennas (119873

119905= 50)119870 = 5 for 16-QAM

modulation

10 20 30 and 40 As shown in this figure the BER perfor-mance gets better when the number of transmitting antennasincreases due to the diversity gain achieved at the transmitterFigure 5 compares the BERperformance for the twoproposedmethods As shown in the figure zero-padding method givesa significant improvement in the BER performance oversubchannel selection method The figure also shows thatin the zero-padding method the BER performance is notaffected by the number of users because there is no multiuserinterference in this case Figure 6 shows the BERperformanceresults of the two proposedmethods for 16-QAMmodulation

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 8: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

8 International Journal of Antennas and Propagation

100

10minus1

10minus2

10minus3

BER

Simulation (Nr = 2)

Simulation (Nr = 4)

Simulation (Nr = 8)

minus4 minus2 0 2 4 6 8 10 12 14 16

SNR (dB)

Analytical (K = 2)Analytical (K = 4)

Figure 3 BER performance of subchannel selection method withdifferent number of receiving antennas for 119873

119905= 10 119870 = 2 and

119870 = 4 for QPSK modulation

100

10minus1

10minus2

10minus3

BER

minus5 0 5 10 15

Nt = 10

Nt = 20

Nt = 30

Nt = 40

SNR (dB)

Figure 4 BER Performance of subchannel selection method withdifferent number of transmit antennas for 119870 = 5 and 119873

119903= 2 for

QPSK modulation

the multiple receiving antennas are not used for diversity butfor SM The receiver would not know ahead what antenna isintended to be switched by the BSTxThus the ML detectionis applied over all the receiving antennas which also increasethe probability of error in the received data with increasing119873119903for each userFigure 4 shows the BER performance of a multiuser

MIMO system with spatial modulation at the receiver sidefor different number of transmitting antennas In this figurewe considered 5 users with 119873

119903= 2 per user and 119873

119905=

100

10minus1

10minus2

10minus3

BER

minus5 0 5

SNR (dB)

Zero-paddingmethod

Subchannelselection method

Nr = 2

Nr = 2

Nr = 4

Nr = 4

and K = 4

and K = 2

and K = 4

and K = 2

Figure 5 BER of subchannel selection method and zero-paddingmethod with 119870 = 2 and 119870 = 4 and119873

119905= 16 for QPSK modulation

100

10minus1

10minus2

10minus3

10minus4

BER

Zero-paddingmethod

Subchannelselection method

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

Nr = 2

Nr = 4

Nr = 8

SNR (dB)

Figure 6 BER of subchannel selection method and zero-paddingmethod with massive BSTx antennas (119873

119905= 50)119870 = 5 for 16-QAM

modulation

10 20 30 and 40 As shown in this figure the BER perfor-mance gets better when the number of transmitting antennasincreases due to the diversity gain achieved at the transmitterFigure 5 compares the BERperformance for the twoproposedmethods As shown in the figure zero-padding method givesa significant improvement in the BER performance oversubchannel selection method The figure also shows thatin the zero-padding method the BER performance is notaffected by the number of users because there is no multiuserinterference in this case Figure 6 shows the BERperformanceresults of the two proposedmethods for 16-QAMmodulation

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 9: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

International Journal of Antennas and Propagation 9

with a large number of transmitting antennas at the BSTxIt is observed from this figure that despite using higherconstellation (16-QAM) and higher number of users (119870 = 5)compared to the results in Figure 5 the BER performanceis not too much degraded due to the extra diversity effectsprovided by the massive number of BSTx antennas used inFigure 6

5 Conclusion

In this paper we present the concept of spatial modulation(SM) scheme for massive multiuser MIMO (MU-MIMO)system In this scheme the index of the active receivingantenna of each user in a MU-MIMO system is used toconvey extra information in addition to the transmittedsymbols Simulation results show that significant increasein the system throughput is achieved as the number ofavailable receiving antennas per user is increased Twomethods are proposed for implementing the SM scheme formassive MU-MIMO system subchannel selection methodand zero-paddingmethod BER performance of the proposedmethods are also studied Our results show that for thesubchannel selectionmethod the BERperformance degradeswith increasing the number of users serviced by the BSTxor the number of receiving antennas per user For the zero-padding method increasing the number of users does notaffect the BER performance since the multiuser interferenceis totally removed by the combination of zero-padding andprecoding operations applied at the BSTx

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by NSTIP strategic technologiesprograms (number 11-ELE1854-02) in the Kingdom of SaudiArabia

References

[1] J Mietzner R Schober L LampeW Gerstacker and P HoeherldquoMultiple-antenna techniques for wireless communicationsmdasha comprehensive literature surveyrdquo IEEE Communications Sur-veys and Tutorials vol 11 no 2 pp 87ndash105 2009

[2] F Rusek D Persson B Lau and E Larsson ldquoScaling UpMIMO opportunities and challenges with very large arraysrdquoIEEE Signal Processing Magazine vol 30 no 1 pp 40ndash60 2013

[3] A Akhlaq A I Sulyman H Hassanein A Alsanie and SAlshebeili ldquoPerformance analysis of relay multiplexing schemein cellular systems employing massive MIMOantennasrdquo IETCommunications In press

[4] J Hoydis S Ten Brink andM Debbah ldquoMassive MIMO in theULDL of cellular networks how many antennas do we needrdquoIEEE Journal on Selected Areas in Communications vol 31 no2 pp 160ndash171 2013

[5] M Di Renzo H Haas and P M Grant ldquoSpatial modulation formultiple-antenna wireless systems a surveyrdquo IEEE Communi-cations Magazine vol 49 no 12 pp 182ndash191 2011

[6] Y Zhang C Ji W Q Malik D C OrsquoBrien and D J EdwardsldquoReceive antenna selection for MIMO systems over correlatedfading channelsrdquo IEEE Transactions on Wireless Communica-tions vol 8 no 9 2009

[7] R Rajashekar K V S Hari and L Hanzo ldquoAntenna selection inspatial modulation systemsrdquo IEEE Communications Letters vol17 no 3 pp 521ndash524 2013

[8] Y Yang and B Jiao ldquoInformation-guided channel-hopping forhigh data rate wireless communicationrdquo IEEE CommunicationsLetters vol 12 no 4 pp 225ndash227 2008

[9] R Y Mesleh H Haas S Sinanovic C W Ahn and S YunldquoSpatial modulationrdquo IEEE Transactions on Vehicular Technol-ogy vol 57 no 4 pp 2228ndash2241 2008

[10] J Jeganathan A Ghrayeb L Szczecinski and A Ceron ldquoSpaceshift keying modulation for MIMO channelsrdquo IEEE Transac-tions on Wireless Communications vol 8 no 7 pp 3692ndash37032009

[11] E Basar U Aygolu E Panayici and H V Poor ldquoSpace-time block coded spatial modulationrdquo IEEE Transactions onCommunications vol 59 pp 823ndash832 2010

[12] J Wang S Jia and J Song ldquoGeneralised spatial modula-tion system with multiple active transmit antennas and lowcomplexity detection schemerdquo IEEE Transactions on WirelessCommunications vol 11 no 4 pp 1605ndash1615 2012

[13] R Zhang L Yang and LHanzo ldquoGeneralised pre-coding aidedspatial modulationrdquo IEEE Transactions on Wireless Communi-cations vol 12 no 11 pp 5434ndash5443 2013

[14] M Di Renzo and H Haas ldquoBit error probability of SM-MIMO over generalized fading channelsrdquo IEEE Transactions onVehicular Technology vol 61 no 3 pp 1124ndash1144 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 10: Research Article Spatial Modulation Concept for Massive ...downloads.hindawi.com/journals/ijap/2014/563273.pdf · Research Article Spatial Modulation Concept for Massive Multiuser

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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DIFFERENTIAL SPATIAL MODULATION: LOW COMPLEXITY …

DIFFERENTIAL SPATIAL MODULATION: LOW COMPLEXITY …

Distributed Spatial Modulation in Cognitive Relay Networkweb2py.iiit.ac.in/research_centres/publications/download/masters... · Distributed Spatial Modulation in Cognitive Relay Network

Distributed Spatial Modulation in Cognitive Relay Networkweb2py.iiit.ac.in/research_centres/publications/download/masters... · Distributed Spatial Modulation in Cognitive Relay Network

Selective modulation of cortical state during spatial ...

Selective modulation of cortical state during spatial ...

Fast photothermal spatial light modulation for ...

Fast photothermal spatial light modulation for ...

Improved Super-Orthogonal Trellis-Coded Spatial Modulation ...

Improved Super-Orthogonal Trellis-Coded Spatial Modulation ...

Spatial Signature Modulation: A Novel Secure Modulation ...ejmtc.journals.ekb.eg/article_4155_4d9389ef2c19d375a08ca31a93ea4e... · spatial signature modulation. Corresponding Author:

Spatial Signature Modulation: A Novel Secure Modulation ...ejmtc.journals.ekb.eg/article_4155_4d9389ef2c19d375a08ca31a93ea4e... · spatial signature modulation. Corresponding Author:

Index Spatial Modulation with QAM/PSK and Pulse Amplitude ... fileIndex Spatial Modulation with QAM/PSK and Pulse Amplitude Modulation Fuchun Huanga), Xie Lib), Jiabing Luoc), Xuehua

Index Spatial Modulation with QAM/PSK and Pulse Amplitude ... fileIndex Spatial Modulation with QAM/PSK and Pulse Amplitude Modulation Fuchun Huanga), Xie Lib), Jiabing Luoc), Xuehua

Design and Implementation of Spatial Modulation Technique ...

Design and Implementation of Spatial Modulation Technique ...

Spatial Lattice Modulation for MIMO SystemsSpatial Lattice Modulation for MIMO Systems Jiwook Choi, Yunseo Nam, and Namyoon Lee Abstract This paper proposes spatial lattice modulation

Spatial Lattice Modulation for MIMO SystemsSpatial Lattice Modulation for MIMO Systems Jiwook Choi, Yunseo Nam, and Namyoon Lee Abstract This paper proposes spatial lattice modulation

Signed Quadrature Spatial Modulation for MIMO Systems

Signed Quadrature Spatial Modulation for MIMO Systems

Double Quadrature Spatial Intensity Modulation for Visible ...

Double Quadrature Spatial Intensity Modulation for Visible ...

Spatial Modulation for Joint Radar-Communications Systems ...

Spatial Modulation for Joint Radar-Communications Systems ...

Quadrature Spatial Modulation Performance Analysis over ... · PDF fileQuadrature Spatial Modulation Performance Analysis over Rician Fading Channels . Mohammed M. Alwakeel . University

Quadrature Spatial Modulation Performance Analysis over ... · PDF fileQuadrature Spatial Modulation Performance Analysis over Rician Fading Channels . Mohammed M. Alwakeel . University

Temporal and Spatial Modulation SOLIS VSM …home.strw.leidenuniv.nl/~keller/Teaching/AstroInstr_2010/... · Comparison of Temporal and Spatial Modulation Schemes Modulation Advantages

Temporal and Spatial Modulation SOLIS VSM …home.strw.leidenuniv.nl/~keller/Teaching/AstroInstr_2010/... · Comparison of Temporal and Spatial Modulation Schemes Modulation Advantages

Iaetsd vlsi implementation of spatial modulation receiver

Iaetsd vlsi implementation of spatial modulation receiver

Spatial and Intensity Modulation of Nanowire Emission ...

Spatial and Intensity Modulation of Nanowire Emission ...

Phase Modulation Characteristics of Spatial Light ...

Phase Modulation Characteristics of Spatial Light ...

Performance of Optical Spatial Modulation and Spatial ...hulk.bu.edu/pubs/papers/2014/TR-2014-01-03.pdf · Performance of Optical Spatial Modulation and Spatial Multiplexing with

Performance of Optical Spatial Modulation and Spatial ...hulk.bu.edu/pubs/papers/2014/TR-2014-01-03.pdf · Performance of Optical Spatial Modulation and Spatial Multiplexing with

Optical Spatial Modulation OFDM using Micro LEDs

Optical Spatial Modulation OFDM using Micro LEDs

Advanced Spatial Modulation Techniques for MIMO Systemsweb.itu.edu.tr/~basarer/index_dosyalar/advancedSM.pdf · Introduction Spatial Modulation Space-Time Block Coded Spatial Modulation

Advanced Spatial Modulation Techniques for MIMO Systemsweb.itu.edu.tr/~basarer/index_dosyalar/advancedSM.pdf · Introduction Spatial Modulation Space-Time Block Coded Spatial Modulation