SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 1

Large Intelligent Surface-Based Index Modulation:A New Beyond MIMO Paradigm for 6G

Ertugrul Basar, Senior Member, IEEE

Abstract—Transmission through large intelligent surfaces(LIS), which modify the phases of incident waves in a deliberatemanner to enhance the signal quality at the receiver, has beenrecently put forward as a promising candidate for future wirelesscommunication systems and standards. In this paper, we bringthe concept of LIS-assisted communications to the realm ofindex modulation (IM) by proposing LIS-space shift keying (LIS-SSK) and LIS-spatial modulation (LIS-SM) schemes. These twoschemes are realized through not only intelligent reflection ofthe incoming electromagnetic waves to improve the signal qualityat the receiver but also utilization of the IM principle for theindices of multiple receive antennas in a clever way to improve thespectral efficiency. Maximum energy-based suboptimal (greedy)and exhaustive search-based optimal (maximum likelihood) de-tectors of the LIS-SSK/SM schemes are formulated and a unifiedframework is presented for the derivation of the theoreticalaverage bit error probability of the proposed schemes using bothdetectors. Extensive computer simulation results are provided toassess the potential of LIS-assisted IM schemes as well as to verifyour theoretical derivations and remarks. Our findings also revealthat LIS-based IM, which enables ultra-reliable transmissionwith high spectral efficiency, can become a potential candidate forfuture wireless communication systems in the context of beyondmassive multiple-input multiple-output (MIMO) solutions.

Index Terms—6G, beyond massive MIMO, index modulation(IM), large intelligent surface (LIS), smart reflect-array, software-defined surface, space shift keying (SSK), spatial modulation(SM).

I. INTRODUCTION

AS of the second quaterter of 2019, the first commer-cial fifth generation (5G) wireless networks have beenalready deployed, in part or as a whole, at certain coun-tries while the first 5G compatible mobile devices are beingintroduced to the market. Although the initial stand-alone5G standard, which was completed in 2018, has broughtmore flexibility to the physical layer by exploiting millimeter-waves and multiple orthogonal frequency division multiplex-ing (OFDM) numerologies, researchers have already startedto explore the potential of alternative technologies for laterreleases of 5G. These technologies include index modulation(IM), non-orthogonal multiple access, alternative/advancedwaveforms, low-cost massive multiple-input multiple-output(MIMO) systems, terahertz communications, and new antennatechnologies. At the first glance, the future 6G technologies

Manuscript received April, 2019.The author is with the Communications Research and Innovation Labora-

tory (CoreLab), Department of Electrical and Electronics Engineering, KoçUniversity, Sariyer 34450, Istanbul, Turkey. e-mail: ebasar@ku.edu.tr

This work was supported in part by the Scientific and TechnologicalResearch Council of Turkey (TUBITAK) under Grant 117E869, the TurkishAcademy of Sciences (TUBA) GEBIP Programme, and the Science AcademyBAGEP Programme.

Codes available at https://corelab.ku.edu.tr/tools

may seem as the extension of their 5G counterparts [1], how-ever, new user requirements, completely new applications/use-cases, and new networking trends of 2030 and beyond maybring more challenging communication engineering problems,which necessitate radically new communication paradigms inthe physical layer.

Within the context of unconventional wireless commu-nication paradigms, there has been a growing interest incontrolling the propagation environment in order to increasethe quality of service and/or spectrum efficiency. IM-basedemerging schemes such as media-based modulation [2]–[4],spatial scattering modulation [5], and beam index modulation(IM) [6], use the variations in the signatures of received signalsby exploiting reconfigurable antennas or scatterers to transmitadditional information bits in rich scattering environments[7]. On the other hand, large intelligent surfaces/walls/reflect-arrays/metasurfaces are smart devices that intentionally controlthe propagation environment to boost the signal quality at thereceiver [8], [9].

As a matter of fact, the large intelligent surface (LIS)-based transmission concept, in which the large number ofsmall, low-cost, and passive elements on a LIS only reflectthe incident signal with an adjustable phase shift withoutrequiring a dedicated energy source for RF processing, de-coding, encoding, or retransmission, is completely differentfrom existing MIMO, beamforming, amplify-and-forward re-laying, and backscatter communication paradigms. Inspired bythe definition of software-defined radio, which is given as“radio in which some or all of the physical layer functionsare software defined” and considering the interaction of theintelligent surface with incoming waves in a software-definedfashion, we may also use the term of software-defined surface(SDS) for these intelligent surfaces. In other words, dueto the fact that reflection characteristics of these intelligentsurfaces/walls/arrays in the physical layer can be controlledby a software, they can be termed as SDS.

Transmission through intelligent walls is proposed in oneof the early works by utilizing active frequency-selectivesurfaces to control the signal coverage [10]. The promisingconcept of communications over smart reflect-arrays withpassive reflector elements is proposed in [11] as an alter-native to beamforming techniques that require large numberof antennas to focus the transmitted or received signals. Ithas been also demonstrated that reflect-arrays can be usedin an effective way to change the phase of incoming signalsduring smart reflection without buffering or processing themand the received signal quality can be enhanced through theadjustment of the phase shift of each reflector element on thereflect-array. As a beyond massive MIMO solution, the LIS

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LIS

LIS

RF

LIS

D

...

D

...

D

...

S

...

(a)

(b)

(c)

RF

Fig. 1. Three conceptual LIS-based IM system realizations: a) IM for source(S) transmit antennas, b) IM for LIS reflector regions, c) IM for destination(D) receive antennas.

concept is proposed in [12] by exploiting the whole contiguoussurface for transmission and reception1. The authors of [13]–[15] considered a LIS-assisted downlink transmission scenarioto support multiple users and focused on the maximizationof sum-rate and energy efficiency. The selection of optimumLIS phases is also investigated and low complexity algorithmsare considered for the formulated non-convex optimizationproblems. Recently, the interesting problem of joint activeand passive beamforming is investigated in [16] and [17], andthe user’s average received power is investigated. Even morerecently, the researchers focused on outage probability [18]and asymptotic data rate [19] analyses for LIS-based systems.Finally, we provided a mathematical framework in [20] forthe calculation of average symbol error probability (SEP) ofLIS-assisted systems. Furthermore, we proposed the promisingconcept of using the LIS itself as an access point (AP) byutilizing an unmodulated carrier for intelligent reflection.

The emerging IM concept also falls to the category of poten-tial beyond 5G technologies and has been widely recognizedby both academia and industry during the past few years[7], [21]–[23]. Contrary to the traditional modulation formats,the indices of the available transmit entities, such as transmitantennas for space modulation techniques [23] and subcarriersfor OFDM with IM [24], are used to convey information

1It is important to note that the LIS structure considered in this paper isconceptually different than that of [12].

for an IM scheme. The undeniable potential of both IM-and LIS-based communication schemes has been the mainmotivation of this study. With this purpose, we investigatedthree conceptual LIS-based IM system realizations in Figs.1(a)-(c), in which we consider IM for source transmit antennas,LIS regions, and destination receive antennas, respectively.Since the first concept requires the knowledge of activatedsource transmit antenna indices at LIS for optimum reflectionand the second concept reduces the effective gain of the LISby activating a part of the available reflectors, we decided tofocus on the third approach in this preliminary work.

In this paper, we propose the visionary concept of LIS-basedIM as a potential beyond MIMO solution by amalgamatingthe techniques of transmission over LIS and IM for receiveantenna indices to achieve ultra-reliable transmission with highspectral efficiency. First, considering the LIS as an AP, wepropose LIS-space shift keying (LIS-SSK) and LIS-spatialmodulation (LIS-SM) schemes by exploiting the LIS not onlyto boost the signal quality in hostile fading channels but alsoto realize IM by the selection of a particular receive antennaindex according to the information bits. Second, we formulatethe greedy and maximum likelihood (ML) detectors of bothschemes and investigate their complexity. Third, we present aunified framework for the calculation of the theoretical errorperformance of the proposed schemes and provided usefulinsights. Finally, extensive computer simulations are given toassess the potential of the LIS-SSK and LIS-SM schemes.

The rest of the paper is organized as follows. In Section II,we introduce the system model of LIS-based SSK/SM schemesand formulate their detectors. Sections III and IV respectivelyfocuses on the error performance of greedy and ML detectors.Computer simulation results and comparisons are given inSection V. Finally, conclusions are given in Section VI2.

II. SYSTEM MODEL

In this section, we present the system models of the pro-posed LIS-based SSK and SM schemes and investigate theproblem of optimal phase selection. We build the proposedschemes on the concept of LIS-AP introduced in [20], wherethe LIS reflects the signals generated by a near RF sourcein a deliberate manner to convey information bits. We as-sume that the LIS is consisting of N passive and low-costreflector elements, while the destination (D) is equipped withnR receive antennas. The wireless fading channel betweenthe lth receive antenna of D and ith reflector element ischaracterized by gl,i = βl,ie−jψl,i for l = 1, 2, . . . , nR and

2Notation: Bold, lowercase and capital letters are used for column vectorsand matrices, respectively. (·)∗ (·)T, and (·)H denote complex conjugation,transposition, and Hermitian transposition, respectively. The real and imag-inary parts of a complex variable X are denoted by X< (or

SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 3

RF

LIS

D

...1 2 nR

1

N

log2nR bits

I/Q & RF

LIS

D

...1 2 nR

1

N

log2nR bits

Bit Splitter

log2M bits

log2nR + log2M bits

(a)

(b)

gl,i

gl,i

Fig. 2. LIS-based IM schemes: a) LIS-SSK, b) LIS-SM.

i = 1, 2, . . . , N , and follows CN (0, 1) distribution under theassumption of flat Rayleigh fading channels. We also assumethat all wireless channels are uncorrelated and perfect channelstate information (CSI) is available at D if it is required bythe utilized detector. The phase induced by the ith reflector isshown by φi for i = 1, 2, . . . , N . For intelligent reflection, theLIS has the knowledge of channel phases ψl,i for all l and i.

A. LIS-Assisted Space Shift Keying

In this scenario, the unmodulated carrier signal generatedby the RF source, is reflected to D with the aim of maxi-mizing the instantaneous received SNR at a specific receiveantenna, which is selected according to the incoming log2 nRinformation bits, as shown in Fig. 2(a). In other words, theLIS phase terms are adjusted in such a way that the SNR atthe target receive antenna is maximized, while the task of D isto detect the index of its receive antenna with the maximizedinstantaneous received SNR.

For this system, the received baseband signal at the lthreceive antenna of D is expressed as

rl =√Es

[N∑i=1

gl,iejφi

]+ nl, l ∈ {1, . . . , nR} (1)

where Es is the transmitted signal energy of the unmodulatedcarrier and nl is the additive white Gaussian noise (AWGN)sample at the lth receiver, which follows CN (0, N0) distribu-tion. Here, the reflector phases {φi}Ni=1 are adjusted accordingto the information bits to maximize the received SNR ata specific receive antenna. For this purpose, the incominglog2 nR bits specify the index m of a receive antenna andthe LIS adjusts its phases according to this selected receiveantenna as φi = ψm,i for i = 1, 2, . . . , N . More specifically,

the received instantaneous SNR at the lth receive antenna isexpressed as

γl =

∣∣∣∑Ni=1 βl,iej(φi−ψl,i)∣∣∣2EsN0

. (2)

Considering∣∣∣∣∣N∑i=1

ziejξi

∣∣∣∣∣2

=

N∑i=1

z2i + 2

N∑i=1

N∑k=i+1

zizk cos(ξi − ξk) (3)

which can be maximized by ensuring ξi = ξ for all i, tomaximize the instantaneous SNR at the mth receive antenna,we select φi = ψm,i. This results in the following maximumSNR value at the selected receive antenna:

γm =

∣∣∣∑Ni=1 βm,i∣∣∣2EsN0

. (4)

Later, we will also show that this selection of LIS phasesis optimal in terms of error performance. We propose twodifferent detectors for the LIS-SSK scheme.

i) Greedy Detector: This simple yet effective detector elim-inates the need for channel estimation at D, that is, performsnon-coherent detection, and simply detects the selected receiveantenna as the one with the highest instantaneous energy:

m̂ = arg maxm|rm|2 . (5)

As seen from (5), this detector does not require CSI, whichcan be prohibitive at D for increasing N and nR.

In order to shed light on the derivation of the optimumLIS phases, let us consider the selection of the mth receiveantenna of D at the LIS and its erroneous detection as m̂. For

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this case, the corresponding pairwise error probability (PEP)can be easily expressed from (5) as

P (m→ m̂) = P (|rm|2 < |rm̂|2)

=P

∣∣∣∣∣√EsN∑i=1

gm,iejφi +nm

∣∣∣∣∣2

<

∣∣∣∣∣√EsN∑i=1

gm̂,iejφi +nm̂

∣∣∣∣∣2(6)

where {φi}Ni=1 is determined according to the mth receiveantenna (with a predefined method). As seen from (6), a logicalselection of φi’s should minimize this PEP for the selectedreceive antenna m. The above phase optimization problem canbe reformulated as follows by ignoring the noise terms:

min{φi}Ni=1

P

∣∣∣∣∣N∑i=1

βm,iej(φi−ψm,i)

∣∣∣∣∣2

<

∣∣∣∣∣N∑i=1

βm̂,iej(φi−ψm̂,i)

∣∣∣∣∣2 .(7)

As seen from (7), even for a specific pair of m and m̂, thisoptimization is not a straightforward task. Consequently, weaim to maximize the first term by letting φi = ψm,i for all ito minimize this probability. We will also show later that thisselection maximizes the mean of the first term in (7), whileproviding a zero-mean for the second one.

ii) ML Detector: The ML detector of the LIS-SSK schemeconsiders the received signals at all receive antennas of D andperforms the detection as follows:

m̂ = arg minm

nR∑l=1

∣∣∣∣∣rl −√Es[N∑i=1

gl,iejψm,i

]∣∣∣∣∣2

. (8)

Comparing (5) and (8), we observe that the ML detectorrequires not only CSI but also ∼Nn2R real multiplications(RMs), while the GD detector requires only nR squaredcomplex modulus operations (∼ nR RMs). As we will showin later sections, the price paid for this increased complexitycan be compensated with the improved error performance.

B. LIS-Assisted Spatial Modulation

For the LIS-SM scheme, ordinary M -ary modulation for-mats are also considered at the RF source to further improvethe spectral efficiency. As shown in Fig. 2(b), the incominglog2 nR + log2M information bits are partitioned into twogroups. While the first group of log2 nR bits adjusts the LISphases according to the selected receive antenna with indexm as done for the LIS-SSK scheme, i.e., φi = ψm,i fori = 1, 2, . . . , N , the second group of log2M bits is passedto the RF source for the generation of an amplitude/phasemodulated signal through an RF chain. Consequently, thereceived signal at the lth receive antenna of D is expressedas

rl =

[N∑i=1

gl,iejφi

]x+ nl, l ∈ {1, . . . , nR} (9)

where x is the data symbol selected from M -QAM/PSKconstellations, E[|x|2] = Es, and nl ∼ CN (0, N0) is thenoise term. In a similar way, we propose the greedy and MLdetectors of LIS-SM in the sequel.

i) Greedy Detector: This detector simplifies the receiverdesign by detecting the selected receive antenna index and thetransmitted symbol in a sequential fashion. For this purpose,the selected receive antenna is determined similar to the LIS-SSK scheme: m̂ = arg maxm |rm|2. After the detection of theselected receive antenna index as m̂, this detector demodulatesthe transmitted data symbol as

x̂ = arg minx

∣∣∣∣∣rm̂ −(

N∑i=1

βm̂,i

)x

∣∣∣∣∣2

. (10)

Here, compared to LIS-SSK, an additional (but minor) com-plexity comes during the search for the constellation point x,however, due to disjoint detection of m and x, the overall com-plexity still linearly increases with nR and M . Furthermore,this detector requires only channel amplitudes for detection.It is worth noting that for constant-envelope constellationssuch as M -PSK, the transmitted symbol can be detected evenwithout channel amplitudes since

∑Ni=1 βm̂,i is a real variable:

x̂ = arg minx|rm̂ − x|2 . (11)

ii) ML Detector: This detector performs a joint search forthe selected receive antenna index m and the transmitted datasymbol x by considering all received signals as

(m̂, x̂) = arg min(m,x)

nR∑l=1

∣∣∣∣∣rl −[N∑i=1

gl,iejψm,i

]x

∣∣∣∣∣2

. (12)

As seen from (12), the ML detector of the LIS-SM schemerequires the full CSI along with ∼ (N + M)n2R RMs whilemaking a joint decision on (m,x).

III. GREEDY DETECTION: PERFORMANCE ANALYSIS

In this section, we investigate the theoretical bit error prob-ability (BEP) of the proposed LIS-SSK and LIS-SM schemesin the presence of greedy detection. We also provide usefulinsights regarding the asymptotic behavior of the proposedschemes with this type of detection.

A. Performance of LIS-SSK

Based on the detection rule given in (5), the correspondingPEP is given in (6) for the erroneous detection of the selectedreceive antenna index m as m̂. Considering φi = ψm,i fori = 1, 2, . . . , N , (6) simplifies to

P (m→ m̂) = P(∣∣∣√EsB + nm∣∣∣2< ∣∣∣√EsB̂ + nm̂∣∣∣2) (13)

where B =∑Ni=1βm,i and B̂ =

∑Ni=1 βm̂,ie

j(ψm,i−ψm̂,i).Here, we resort to the central limit theorem (CLT) under theassumption of N � 1 for the calculation of this PEP. Underthe CLT, B and B̂ follow Gaussian distribution regardlessof the distributions of their components. Specifically, sinceβm,i is a Rayleigh distributed RV with E[βm,i] =

√π/2 and

Var[βm,i] = (4 − π)/4, we have B ∼ N (N√π/2, N(4 −

π)/4). Since ψm,i and ψm̂,i are independent and uniformly

SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 5

distributed in (0, 2π), the distribution of ψ̄i = ψm,i − ψm̂,i isobtained as

fψ̄i(x) =

{1

2π

(1 + x2π

), −2π < x < 0

12π

(1− x2π

), 0 < x < 2π.

(14)

Then defining B̂i = βm̂,iejψ̄i , we have E[B̂i] = 0 andVar[(B̂i) 2, we use the following union bound:

Pb ≤1

log2 nR

∑m̂

P (m→ m̂)e(m, m̂)

=nR2P (m→ m̂) (23)

where e(m, m̂) is the Hamming distance between the binaryrepresentations of m and m̂. Here, we considered the fact thatthe resulting PEP is independent of m and m̂, and identicalfor all pairs (uniform error probability) and

∑m̂ e(m, m̂) =

(nR/2) log2 nR for all m due to bit symmetry. For simplicity,we adopt natural mapping for receive antenna indices.

Remark 1: We observe from the exact and upper-boundedPEP expressions of (16) and (22) that the resulting PEP isindependent of nR for greedy detection of LIS-SSK. As seenfrom (23), doubling nR doubles Pb in high SNR.

B. Performance of LIS-SM

To derive the theoretical BEP of the LIS-SM scheme withgreedy detection, we consider the following approximation:

Pb ≈Pc(m)Ps

log2(MnR)+ 0.5Pe(m) (24)

where Pc(m) is the average correct detection probabilityof the selected receive antenna with index m for LIS-SM,which is the same for all m, Ps is the average symbol errorprobability (SEP) conditioned on correct index detection, andPe(m) = 1−Pc(m) is the erroneous index detection probabil-ity. Here, we followed a conservative approach by assumingthat approximately 50% of the transmitted bits are erroneouslydetected if the receive antenna index is erroneously estimated,which is a valid assumption for IM-based systems due to errorpropagation. Resorting to the union bound on error probabilitywith uniform PEP values, we obtain

Pe(m) ≤nR∑

m̂=1,m̂6=m

P̄ (m→ m̂) = (nR−1)P̄ (m→ m̂) (25)

where P̄ (m→ m̂) is the PEP associated with index detectionaveraged over all data symbols for LIS-SM. From (25), Pc(m)is obtained as Pc(m) ≥ 1− (nR − 1)P̄ (m→ m̂).

6 SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING

Assuming that x is transmitted, the PEP for erroneousdetection of the selected receive antenna index m as m̂ isgiven as follows considering (5), which is also valid for LIS-SM:

P (m→ m̂ |x) = P(∣∣Bx+ nm∣∣2 < ∣∣B̂x+ nm̂∣∣2) . (26)

Here, B and B̂ are as defined in (13). In what follows, wecalculate (26) for different constellations.

i) BPSK: For this case, we have x ∈{±√Es}

and weobtain the same PEP derived from (17) or (21) for LIS-SSK,which is independent of x.

ii) M -QAM: For this case, we have x = x< + jx= withE[|x|2] = Es, and we may express the corresponding PEP as

P (m→ m̂ |x) = P (B21 +B22 −B23 −B24 < 0) = P (D < 0)(27)

where B1 = (Bx+ nm) 0) (38)

where we considered the fact that rl = Glx + nl for all l.Here, G ∼ N (µG, σ2G) with µG = −

∑nRl=1

∣∣Glx− Ĝlx̂∣∣2 and

SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 7

σ2G =∑nRl=1 2N0

∣∣Glx − Ĝlx̂∣∣2. Consequently, from P (G >0) = Q(−µG/σG), we arrive at

P (m,x→ m̂, x̂) = Q

√∑nRl=1 ∣∣Glx− Ĝlx̂∣∣22N0

(39)which is analogous to classical SM-based systems [28]. Defin-ing Γ ,

∑nRl=1

∣∣Glx − Ĝlx̂∣∣2 and considering the alternativeform of the Q-function, the unconditional (averaged overchannel coefficients) PEP can be calculated as follows:

P̄ (m,x→ m̂, x̂) =∫ ∞

0

Q

(√Γ

2N0

)fΓ(Γ)dΓ

=

∫ ∞0

1

π

∫ π/20

exp

(−Γ

4 sin2 ηN0

)fΓ(Γ)dηdΓ

=1

π

∫ π/20

MΓ

(−1

4 sin2 ηN0

)dη. (40)

Here, we need the MGF of Γ (MΓ(s)) to perform this inte-gration. This MGF can be derived by considering the generalquadratic form of correlated Gaussian RVs and depends onerroneous or correct detection of the receive antenna index m.

i) First Case (m 6= m̂): Let us rewrite Γ as Γ = Γ1+Γ2+Γ3,where

Γ1 =

∣∣∣∣∣[N∑i=1

βm,i

]x−

[N∑i=1

gm,iejψm̂,i

]x̂

∣∣∣∣∣2

=∣∣Gmx− Ĝmx̂∣∣2

Γ2 =

∣∣∣∣∣[N∑i=1

gm̂,iejψm,i

]x−

[N∑i=1

βm̂,i

]x̂

∣∣∣∣∣2

=∣∣Gm̂x− Ĝm̂x̂∣∣2

Γ3 =

nR∑l=1(l 6=m,l 6=m̂)

∣∣Glx− Ĝlx̂∣∣2. (41)Here, Γ1, Γ2, and Γ3 respectively stand for l = m, l = m̂, andl 6= m, l 6= m̂ in Γ. Different distributions of Gl and Ĝl withrespect to l as well as the correlation among them necessitatethe quadratic form of Gaussian RVs to derive MΓ(s).

Considering gl,i = βl,ie−jψl,i , let us rewrite Γ1 and Γ2 as

Γ1 = |γ1|2 = (γ1)2< + (γ1)2= =

∣∣∣∣∣N∑i=1

βm,i

(x− e−jψ̄i x̂

)∣∣∣∣∣2

Γ2 = |γ2|2 = (γ2)2< + (γ2)2= =

∣∣∣∣∣N∑i=1

βm̂,i

(xejψ̄i − x̂

)∣∣∣∣∣2

(42)

where ψ̄i = ψm,i−ψm̂,i has a triangle-shaped PDF defined in(14). It is obvious from (42) and the CLT that γ1 and γ2 followcomplex Gaussian distribution for increasing N , however, weneed to consider the correlation among their components. Aftertedious but straightforward calculations, the mean vector andthe covariance matrix of g =

[(γ1)< (γ1)= (γ2)< (γ2)=

]Tare obtained respectively as follows:

m =[N√πx<2

N√πx=2 −

N√πx̂<2 −

N√πx̂=2

]T(43)

C =

σ21 σ1,2 σ1,3 σ1,4σ1,2 σ

22 σ2,3 σ2,4

σ1,3 σ2,3 σ23 σ3,4

σ1,4 σ2,4 σ3,4 σ24

(44)where

σ21 =N(4−π)x2<

4 +N |x̂|2

2 , σ22 =

N(4−π)x2=4 +

N |x̂|22

σ23 =N(4−π)x̂2<

4 +N |x|2

2 , σ24 =

N(4−π)x̂2=4 +

N |x|22

σ1,2 =N(4−π)x

8 SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING

-35 -30 -25

SNR(dB)

10-6

10-5

10-4

10-3

10-2

10-1

BEP

LIS-SSK,N=128,nR

=2

LIS-SSK,N=128,nR

=8

LIS-SSK,N=128,nR

=32

LIS-SSK,N=128,nR

=64

-35 -30 -25

SNR(dB)

10-6

10-5

10-4

10-3

10-2

10-1

BEP

LIS-SM,N=128,nR

=2,M=2

LIS-SM,N=128,nR

=8,M=2

LIS-SM,N=128,nR

=32,M=2

LIS-SM,N=128,nR

=64,M=2

Fig. 3. Theoretical BEP performance of LIS-SSK and LIS-SM systems withincreasing nR.

where e(m,x→ m̂, x̂) stands for the number of bits in errorfor the corresponding pairwise error event.

Remark 3: The above analysis is general and can be consid-ered for all constellations. Derivation of simplified expressionsfor BPSK and QPSK (or M -PSK in general) is left tointerested readers.

B. Performance of LIS-SSK

Considering x = x̂ =√Es (i.e., an unmodulated carrier in

the baseband) in (39), we obtain the conditional PEP of theLIS-SSK scheme as

P (m→ m̂) = Q

√∑nRl=1Es∣∣Gl − Ĝl∣∣22N0

. (50)In light of this information, the analyses in Section IV.A (forthe case of m 6= m̂) is also valid for ML detection of LIS-SSKand the unconditional PEP P̄ (m→ m̂) can be easily derivedfrom (40) with suitable modifications in MΓ(s). Then the BEPupper bound of LIS-SSK can be calculated similar to (23) as

Pb ≤nR2P̄ (m→ m̂). (51)

Remark 4: We observe that unlike the greedy detector,increasing nR for ML detection improves the PEP perfor-mance of LIS-SM and LIS-SSK schemes through the MGFterms of (46) and (48), which include nR in their exponents.Since increasing nR also improves the data rate along withincreasing number of bit errors in (49) and (51), we facean interesting trade-off among complexity, performance, anddata rate. In Fig. 3, we show the theoretical BEP performanceof LIS-SSK and LIS-SM schemes calculated from (49) and(51) for N = 128 reflectors and increasing nR, with respectto Es/N0. As seen from Fig. 3, increasing nR eventuallyimproves the BER performance while providing a higher datarate, which is quite unusual for legacy communication systems.In other words, increasing nR both improves the spectralefficiency and overall BER performance for LIS-SSK/SMsystems in the presence of ML detection.

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SNR(dB)

10-5

10-4

10-3

10-2

10-1

100

BE

R

LIS-SSK,GD,N=64,nR

=2

LIS-SSK,GD,N=64,nR

=4

LIS-SSK,GD,N=64,nR

=8

LIS-SSK,GD,N=64,nR

=16

LIS-SSK,GD,N=128,nR

=2

LIS-SSK,GD,N=128,nR

=4

LIS-SSK,GD,N=128,nR

=8

LIS-SSK,GD,N=128,nR

=16

Theoretical

Fig. 4. Theoretical and computer simulation results for LIS-SSK with greedydetection.

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SNR(dB)

10-5

10-4

10-3

10-2

10-1

100

BE

R

LIS-SM,GD,N=64,nR

=4,M=4

LIS-SM,GD,N=64,nR

=4,M=16

LIS-SM,GD,N=64,nR

=8,M=4

LIS-SM,GD,N=64,nR

=8,M=16

LIS-SM,GD,N=128,nR

=4,M=4

LIS-SM,GD,N=128,nR

=4,M=16

Theoretical

Fig. 5. Theoretical and computer simulation results for LIS-SM with greedydetection.

V. SIMULATION RESULTS

In this section, we provide computer simulation results forthe proposed LIS-based SSK and SM schemes and make com-parisons with our theoretical results and reference schemes.We consider Es/N0 as the SNR, similar to the classicaldiversity combining and space modulation schemes.

In Figs. 4 and 5, we provide BER performance curves ofthe LIS-SSK and LIS-SM systems for greedy detection andmake comparisons with the theoretical results obtained from(23) and (24), respectively. As seen from the given results, ourtheoretical findings are quite accurate for both schemes andthe performance of LIS-SSK and LIS-SM schemes degradewith increasing bits per channel use (bpcu), or equivalentlynR, values (see Remarks 1 and 2). It is worth noting thatBER performance of both schemes significantly improves byincreasing the N value from 64 to 128, which is consistentwith (22).

In Fig. 6, we focus on the performance of LIS-SSK andLIS-SM schemes with ML detection and make comparisonswith the theoretical results obtained from (49) and (51). Asseen from Fig. 6, while increasing nR does not cause aremarkable BER degradation for the LIS-SSK scheme, theeffect of increasing M is more evident for the LIS-SM scheme.

SUBMITTED TO IEEE TRANSACTIONS ON SIGNAL PROCESSING 9

-35 -30 -25 -20 -15 -10

SNR(dB)

10-5

10-4

10-3

10-2

10-1

100

BE

RLIS-SSK,MLD,N=64,n

R=2

LIS-SSK,MLD,N=64,nR

=8

LIS-SSK,MLD,N=128,nR

=2

LIS-SSK,MLD,N=128,nR

=8

LIS-SM,MLD,N=64,nR

=8,M=4

LIS-SM,MLD,N=64,nR

=8,M=16

LIS-SM,MLD,N=128,nR

=4,M=4

LIS-SM,MLD,N=128,nR

=4,M=16

Theoretical

Fig. 6. Theoretical and computer simulation results for LIS-SSK and LIS-SMwith ML detection.

We compare the BER performances of greedy and MLdetectors for both LIS-SSK and LIS-SM systems at variousbpcu values in Fig. 7. We observe that the ML detector ofLIS-SSK provides approximately 2 dB improvement in therequired SNR for the considered two setups (N = 64, nR = 2and N = 128, nR = 8). Although we observe a similarimprovement for LIS-SM in case of N = 64, the difference inBER performances of greedy and ML detectors is relativelysmaller for the case of N = 128.

Finally, in Fig. 8, we present BER performance comparisonresults for LIS-SSK, LIS-SM, LIS-AP [20], and conven-tional fully-digital (zero-forcing) precoding-based receive SSK(RSSK) [29] at 3, 4, and 6 bpcu values with ML detection.We have several important observations from Fig. 8. First,an interesting trade-off exists between the receiver cost andthe BER performance for LIS-SSK and LIS-SM schemes:while the former provides a better BER performance, thelatter exhibits a slight degradation by using a less numberof receive antennas at the same bpcu. Second, the LIS-APscheme proposed in [20], which utilizes a single receiveantenna, cannot compete with LIS-SSK/SM schemes since itcreates a virtual M -PSK constellation by altering LIS phasesand suffers at high bpcu values. Third, compared to LIS-based new schemes, a more than 15 dB difference in requiredSNR is observed for the conventional RSSK-MIMO scheme.Although utilizing a massive MIMO system, RSSK forces theMIMO channels into zero to realize a pure SSK-like reception,while LIS-based SM/SSK schemes constructively exploit thewireless channels to boost the signal quality at the intendedreceive antenna.

VI. CONCLUSIONS

The general concept of LIS-assisted IM has been proposedin this paper as a new beyond massive MIMO paradigm fornext-generation (potentially 6G or beyond) wireless networks.It has been shown by comprehensive theoretical derivations aswell as computer simulations that the proposed LIS-SSK andLIS-SM schemes have the potential to provide considerablyhigh spectral efficiency at extremely low SNR values througha smart and LIS-assisted indexing mechanism for available

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SNR(dB)

10-5

10-4

10-3

10-2

10-1

100

BE

R

LIS-SSK,GD,N=64,nR

=2

LIS-SSK,MLD,N=64,nR

=2

LIS-SSK,GD,N=128,nR

=8

LIS-SSK,MLD,N=128,nR

=8

LIS-SM,GD,N=64,nR

=8,M=4

LIS-SM,MLD,N=64,nR

=8,M=4

LIS-SM,GD,N=128,nR

=4,M=4

LIS-SM,MLD,N=128,nR

=4,M=4

LIS-SM,GD,N=128,nR

=4,M=16

LIS-SM,MLD,N=128,nR

=4,M=16

Fig. 7. BER performance comparisons for greedy and ML detectors of LIS-SSK and LIS-SM schemes.

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SNR(dB)

10-5

10-4

10-3

10-2

10-1

100

BE

R

LIS-SSK,N=64,nR

=8

LIS-SM,N=64,nR

=4,M=2

LIS-AP,N=64,M=8

Conv.RSSK 64x8 MIMO

LIS-SSK,N=64,nR

=16

LIS-SM,N=64,nR

=4,M=4

LIS-AP,N=64,M=16

Conv.RSSK 64x16 MIMO

LIS-SSK,N=64,nR

=64

LIS-SM,N=64,nR

=16,M=4

LIS-AP,N=64,M=64

Conv.RSSK 128x64 MIMO

Fig. 8. BER performance comparison of LIS-SSK, LIS-SM, LIS-AP [20], andconventional RSSK [29] schemes for 3, 4, and 6 bpcu.

receive antennas. We conclude that the effective use of LIS-assisted IM schemes may be a game-changing paradigm fornext-generation (6G) communication networks by eliminatingthe need for sophisticated massive MIMO schemes that requireexpensive and power-hungry components. The extremely lowSNR regions of operation may also be a remedy to theincreasing need for advanced channel coding schemes toachieve ultra-reliable communications. As also discussed inIntroduction, potential application of IM for transmit antennasand/or LIS regions along with other advanced/generalizedschemes, the design of low-complexity receiver architectures,and analyses in the presence of potential system imperfections,remain as interesting and open research problems.

REFERENCES

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[4] E. Basar, “Media-based modulation for future wireless systems: Atutorial,” IEEE Wireless Commun. (to appear), Mar. 2019. [Online].Available: https://arxiv.org/abs/1811.08730

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[5] Y. Ding, K. J. Kim, T. Koike-Akino, M. Pajovic, P. Wang, and P. Orlik,“Spatial scattering modulation for uplink millimeter-wave systems,”IEEE Commun. Lett., vol. 21, no. 7, pp. 1493–1496, July 2017.

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Ertugrul Basar (S’09-M’13-SM’16) received theB.S. degree (Hons.) from Istanbul University,Turkey, in 2007, and the M.S. and Ph.D. degreesfrom Istanbul Technical University, Turkey, in 2009and 2013, respectively. He is currently an AssociateProfessor with the Department of Electrical andElectronics Engineering, Koç University, Istanbul,Turkey and the director of Communications Re-search and Innovation Laboratory (CoreLab). Hisprimary research interests include MIMO systems,index modulation, waveform design, visible light

communications, and signal processing for communications.Recent recognition of his research includes the Science Academy (Turkey)

Young Scientists (BAGEP) Award in 2018, Mustafa Parlar FoundationResearch Encouragement Award in 2018, Turkish Academy of SciencesOutstanding Young Scientist (TUBA-GEBIP) Award in 2017, and the first-ever IEEE Turkey Research Encouragement Award in 2017.

Dr. Basar currently serves as an Editor of the IEEE TRANSACTIONSON COMMUNICATIONS and Physical Communication (Elsevier), and as anAssociate Editor of the IEEE COMMUNICATIONS LETTERS. He served as anAssociate Editor for the IEEE ACCESS from 2016 to 2018.

https://arxiv.org/abs/1903.08925https://arxiv.org/abs/1903.08925https://arxiv.org/abs/1810.06934https://arxiv.org/abs/1810.10718https://arxiv.org/abs/1903.11456v1https://arxiv.org/abs/1810.05667v2https://arxiv.org/abs/1902.08463

I IntroductionII System ModelII-A LIS-Assisted Space Shift KeyingII-B LIS-Assisted Spatial Modulation

III Greedy Detection: Performance AnalysisIII-A Performance of LIS-SSKIII-B Performance of LIS-SM

IV Maximum Likelihood Detection: Performance AnalysisIV-A Performance of LIS-SMIV-B Performance of LIS-SSK

V Simulation ResultsVI ConclusionsReferencesBiographiesErtugrul Basar