Review Article A Survey on Beamforming Techniques for ... · networks where MIMO nodes cooperate to...

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2013 Article ID 745018 21 pageshttpdxdoiorg1011552013745018

Review ArticleA Survey on Beamforming Techniques for WirelessMIMO Relay Networks

Demosthenes Vouyioukas

Department of Information and Communication Systems Engineering University of the Aegean Samos 83200 Karlovassi Greece

Correspondence should be addressed to Demosthenes Vouyioukas dvouyiouaegeangr

Received 24 July 2013 Accepted 3 October 2013

Academic Editor Laurent Clavier

Copyright copy 2013 Demosthenes Vouyioukas 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

One of the major challenges the mobile broadband community faces is the exponential increase in mobile data traffic even moreso for cell-edge users Thus in a multitier network the demand for high-speed and interference-free transmission and receptionis inevitable Beamforming (BF) is an advanced technology that offers a significantly improved solution to reduce the interferencelevels and improve the system capacity Accordingly the establishment of relays in mobile data networks has emerged spectralefficiency enhancements and cell capacity gains from an overall system perspective This paper provides a comprehensive surveyfocused on the performance of adopted beamforming technique on MIMO relay networks that is expected to overcome crucialobstacles in terms of capacity and interference The main objective is to point out the state-of-the-art research activity on BFtechniques in MIMO relay networks under various network performance challenges Thereby it focuses on recently developedprocedures for interference modeling and mitigation BF channel modeling channel estimation and feedback complexity andpower consumption adaptive BF for multiuser relaying degrees of freedom diversity issues and spectral efficiency in cooperativeand opportunistic systems Different network topologies have been considered and categorized pertaining the challenges of BFimplementation in MIMO relay networks

1 Introduction

Next-generation wireless networks are bound to offer adramatic increase in data rate compared to the currentlydeployed networks One major limiting factor towards thisgoal is the interference that arises due to the increased tem-poral and spectral reuse of resources As a result novel tech-niques that exploit the spatial domain will contribute signif-icantly in the efficient operation of future networks Amongthem multiple-input multiple-output (MIMO) antenna con-figurations cooperative relays and beamforming (BF) havebeen very active research fields in the recent years as theyallow increased flexibility in interference mitigation

Equipping transmitters and receivers with MIMO capa-bilities can achieve increased diversity and multiplexinggains It was the seminal work of [1] which presented capacityresults of MIMO systems in Gaussian channels that sparkedgreat interest by the academia and the industry The gains incapacity offered byMIMO topologies led to their inclusion in

current and future wireless standards namely IEEE 80211n80216e 3GPP LTE and LTE-advanced MIMO systems takeadvantage of the rich scattering observed in urban envi-ronments that offers independent propagation paths for theemitted signals So the designer of aMIMO system can targetloading each antenna with a different information carryingsignal thus increasing the multiplexing gain or loading thesame signal on all the antennas thus improving the diversitygain The capacity bounds of MIMO channels were thetopic of [2] where realistic assumptions about time-varyingchannels and channel correlationwere considered and resultswere given also for the multiple-access channel (MAC) andthe broadcast channel (BC) The authors in [3] presentedan overview of single-user (SU) MIMO and multiuser (MU)MIMO techniques and discussed the advantages offered bythe latter at the cost of channel state information (CSI) atthe transmitter in order to form accordingly the antennabeams More recently [4] provided an extension to multicell

2 International Journal of Antennas and Propagation

networks where MIMO nodes cooperate to exploit intercellinterference Cooperative techniques were introduced suchas base station (BS) cooperation and schemes that employedrelays

In general the literature on cooperative relaying hasseen a tremendous rise in contributions in recent yearsThrough cooperative relaying coverage extension increasedreliability and diversity can be harvested The first studyof the capacity of the relay channel was conducted in [5]In addition various relaying strategies such as amplify-and-forward (AF) decode-and-forward (DF) and compress-and-forward (CF) were investigated in the seminal work of[6] Optimization efforts for AF MIMO relay systems aredepicted in [7] providing an overview of the fundamentalresults and practical implementation issues in designing AFMIMO relay systems Relays are attractive as they improvethree critical parameters of wireless networks By allowingmultihop transmission transmitters are brought closer tothe receiver thus reducing the path loss attenuation of thesignal In addition shadowing can be overcome by installingrelay nodes in places where obstacles affect single-hopcommunications Furthermoremultipath fading ismitigatedthrough the provision of independent propagation pathsFor example even when one relay is employed the signalpropagates through a two-hop path and also through thedirect path between the source and the destination Alsocooperative relaying offers increased diversity [8] even whencooperative relays choose not to transmit but rather chooseto cooperatively listen [9] thus improving the performancein terms of outage and error probability Additionally whenmultiple relays are available selecting the best one accordingto instantaneous CSI was proven to be outage optimal in[10] compared to the case where multirelay transmissions areperformed More recently buffer-aided relays were examined[11] and relay selection schemes that aim at improved spectralefficiency were presented in [12 13]

The third technique that is examined in this surveyis beamforming This technique uses BF matrices at thetransmitters and the receivers which form the antennasrsquobeam patterns in such a way as to optimize a specific designcriterion such as mean square error (MSE) or signal-to-noise ratio (SNR) The implementation of BF requires theuse of digital signal processors (DSPs) to shape accordinglythe beam patterns that are emitted by the antennas In thecontext of single-hop mobile communications the articlein [14] presented space-time processing to combat cochan-nel interference (CCI) and intersymbol interference (ISI)Another early work was [15] which proposed joint BF andpower control in order to minimize the total transmittedpower in the network while satisfying a signal-to-noise-plus-interference ratio (SINR) threshold at the receivers Anoverview of smart antennas is given in [16] where switchedbeam adaptive beam and spatial division multiple-access(SDMA) are discussed Moreover digital signal processingalgorithms such as direction-of-arrival (DoA) and adaptiveBF were presented in [17]

This survey provides a detailed presentation of works thatstudy BF techniques in networks where relays with MIMOcapabilities are deployed More specifically the increased

degrees of freedom (DoF) in exploiting the spatial resourcesare the main topic of the presented works This area hasseen a significant increase in contributions recently but asurvey depicting its importance and categorizing these workshas not been published except from a few articles whichprovide quick overviews of some techniques In [18] theauthors present BF schemes for scenarios where MIMOAF relays assist the communication in single and multiusernetworks either through one-way or two-way relaying Inanother article [19] relay classification is performed andBF techniques are presented for various combinations ofregenerative versus nonregenerative full-duplex versus half-duplex and one-way versus two-way The author discussesthe formulation of transmit-receive BF matrices amplifica-tion matrices for nonregenerative relays self-interference forfull-duplex relays and successive interference cancellation forthe two-way case Here descriptions and categorizations forvarious network topologies and communication strategies aregiven More specifically articles that investigate BF schemesfor single and multiuser communications are presented andtheirmain contributions are highlighted Also a classificationbased on various relaying topologies such as single andmultiple relaying as well as opportunistic relay selection isprovided and the corresponding BF schemes are discussedAs the included works consider channel models and fadingdistributions that are examined in depth in the context ofMIMO relaying there is no channel modeling literaturereview in the context of this survey as emphasis is given onBF schemes and their various implementations

This survey is organized by taking into consideration thedifferent network topologies where BF techniques can beemployed and its structure is as follows In Section 2 thechallenges of BF implementation in MIMO relay networksare given More specifically the design parameters thatinclude MSE minimization and SNR maximization undervarious power constraints are presented Also overhead dueto channel estimation and feedback is discussed Anotherchallenge that is often observed in MIMO networks isantenna correlation thus its effect on the design of BF matri-ces is herein presented In Section 3 BF schemes for single-user communications are presented Various different casesare presented such as single and multiple relay topologieswith and without relay selection In Section 4 networkswhere multiuser communications take place are investigatedand scenarios where single or multiple relays assist thecommunication for one or two-way communications aredescribed Discussion and open issues are the subject ofSection 5 while conclusions are given in Section 6

Notation In this work (sdot)119879 (sdot)119867 (sdot)lowast | sdot | sdot 2 and sdot

119865

denote transpose Hermitian transpose complex conjuga-tion the determinant of a complex number the Euclideannorm and the Frobenius norm respectively Upper (lower)boldface letters will be used for matrices (vectors)

2 Challenges

To better illustrate the challenges that are presented in thissection the system model of [20] is adopted and extended

International Journal of Antennas and Propagation 3

Figure 1 Block diagram of the two-hop relay equalization

for two-hop topologies as shown in Figure 1 [21] where atwo-hop equalization process is depicted The majority ofworks consider single-carrier transmission and reception buta multicarrier technology such as OFDM provides a moregeneral systemmodel Furthermore by focusing on a specificsubcarrier denoted by 119896 present works that use single-carrierblock-fading channel models can be included A networkwhere a source communicates with a destination through anAFhalf-duplex relay is taken into considerationHowever thereader should note that adjustments should be made in thesystemmodel for the cases of DF and CF types of relaying asthere is no amplification in the analog domain by the relayFurthermore it is assumed that the source the relay and thedestination have119872

119878119872119877 and119872

119863antennas respectively and

for simplicity119872119878= 119872119877= 119872119863= 119872 The received signal at

the destination is

y119896= H119877119863119896

FH119878119877119896

s119896+H119877119863119896

Fn119877119896+ n119863119896

1 le 119896 le 119873(1)

where H119877119863119896

is the 119872 times 119872 channel matrix of the RD linkF is the 119872 times 119872 amplification matrix at the relay s

119896is the

119872times 1 transmitted signal vector from the sourceH119878119877119896

is the119872times119872 channel matrix of the SR link and n

119877119896 n119863119896

are119872times1additive white Gaussian noise (AWGN) vectors at the relayand the destination respectively

The transmitted signal vector from the source is definedas

s119896= B119896x119896=

119871119896

sum119894=1

b119896119894x119896119894 (2)

where x119896are the 119871

119896transmitted symbols as 119871

119896established

substreams are assumed andB119896is the119872times119871

119896BFmatrix at the

source which can be designed jointly with the relay-amplifymatrix F or separately and this holds also for the receiverrsquosprocessing matrix A

119896 The transmitted symbols are assumed

to satisfy the constraint119871119896le 119872 as each node has119872 antennas

At the destination the received signal vector assuming anequalizer is expressed as

y119896= A119867119896y119896 (3)

In [21] equalization is performed first by designing theamplification matrix F at the relay and then for the overallchannel through the MIMO equalizer A

119896 Another approach

would consider joint optimization of F and A119896 Various

criteria can be considered in the optimization process andthey are discussed as follows

21 Performance Criteria In the works that investigate theformulation of BF matrices various performance criteriahave been proposed More specifically transmit and receiveBF matrices are derived through optimization problems thatare subject to various performance criteria

(a) Minimization of the Mean Square Error (MMSE) Manyworks take into consideration this important metric whichaims at the minimization of the estimation errors at thedestination under a target SNR Articles presenting problemswith MMSE are included in [21ndash30] In [20] a multicarriersystem has been presented and the MSE for the 119896th carrieris defined as the trace of the covariance matrix of the errorvector e

119896≜ (x119896minus x119896) where x

119896is the estimation of x

119896

As a result the problem of MSE minimization requires BFmatrices to provide

minE119896(B119896 FA119896) ≜ minΕ [(x

119896minus x119896) (x119896minus x119896)119867] (4)

The MSE of the substreams are the diagonal elements of E119896

so for the (119896th 119894th) substream its MSE value will be locatedat the 119894th diagonal position As a result MSE values can bedenoted through the trace of E

119896

(b) Minimization of the Sum of MSE In [31 32] two endnodes communicate simultaneously through a MIMO AFrelay So the minimization of MSE at both directions isconsidered thus the optimization target is transformed intothe minimization of the sum of MSE as follows

minE1119896(B1119896B2119896 FA1119896A2119896)

+minE2119896(B1119896B2119896 FA1119896A2119896)

≜ minΕ [(x1119896minus x2119896) (x1119896minus x2119896)119867]

+minΕ [(x2119896minus x1119896) (x2119896minus x1119896)119867]

(5)

where indices 1 and 2 are used to denote matrices andsignals which correspond to the two end nodes which areconcurrently communicating through the relay

(c) Maximization of SINR Other works form optimizationproblems by considering the maximization of the SNRor SINR in the cases of multiuser and two-way relayingnetworks From [20] the SINR for the 119894th spatial substreamof the 119896th subcarrier (119896th 119894th) substream is given in relationto MSE as

SINR119896119894=

1

MSE119896119894

minus 1 (6)


where MSE119896119894

is the MSE of the (119896th 119894th) substream andcorresponds to the 119894th diagonal element of E

119896

It is obvious that the maximization of the SINR isequivalent to theminimization of theMSEThe articles whichoptimize the BFmatrices under the maximization of SNR are[21 33ndash39]

When interference arises SNR is replaced by SINR byconsidering streams that interfere in the reception of thedesired signal Many works consider zero-forcing (ZF) asin [28 40ndash43] The goal of ZF is to cancel the interferenceat the receiver and is based on the ZF filter which usesthe pseudoinverse matrix of the channel matrix between thecommunicating nodes as follows

Z = H+ = (H119867H)minus1

H119867 (7)

(d) Maximization of Capacity Various articles target capacitymaximization as is the case in [21 27 44ndash57]The relation ofthe maximization of mutual information to MSE is given as[20]

119868 = minus log |E| (8)

From this equation it is concluded that the maximization ofthe mutual information derives from the minimization of theMSE

(e) Maximization of the Distance of Network-Coded SymbolsOther works employ network coding (NC) and consider themaximization of the minimum symbol distance as a designcriterion In two-way relay networks uncoded symbolsare transmitted simultaneously by the two end nodes andreceived by the relay Next the relay broadcasts anNCversionof the two symbols such as an XOR combination in orderfor the end nodes to decode their signal of interest Theminimum distance of the different network-coded symbolsis given as [58]

119889(NC)min = min (119886

1 1198862) sdot 119889min (9)

where 1198861 1198862are the BF gains of each end node chosen to align

the signal subspaces at the relay and 119889min is the minimumdistance of the transmit constellation 119878 which contains M-QAM symbols These works include [58 59]

22 Power Constraints A critical parameter in designing BFschemes is the power constraint imposed on different nodesin the system Power constraints are practical considerationsas network nodes may be battery-operated and regulatoryauthorities define maximum power levels for transmission inwireless systems The following focus on the 119896th subcarrieras most works consider single-carrier transmissions in theirsystem models

(a) Power Constraint at the Relay(s) Many works imposevarious types of power constraints at the relays dependingon their number and whether or not multi- or single-relaytransmissions take place For single-relay topologies [23 27

28 40 45 51 52] impose a power constraint at the single relayexpressed by

1003817100381710038171003817FH119878119877119896B11989610038171003817100381710038172

2+ 1205902

119877119896F2119865le 1198752119896 (10)

When multiple relays are used individual and sum-powerconstraints are imposed The algorithms in [33 42 60]impose an individual power constraint of the form

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 1198752119877119895119896

(11)

at each relay 119895 while [21 22 43 44 46 56 61] employ sum-power constraints of the form

119873119877

sum119895=1

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 1198752119896 (12)

Finally when one relay is selected from a set of availablerelays [62] sets a power constraint at the selected relay thatis similar to the constraint of the single relay topologies

(b) Power Constraint at the Source and the Relays Otherworks search for BFmatrices under power constraints at boththe source(s) and the relay(s) In networks where a singlerelay is available [24ndash26 34 48 49] have individual powerconstraints for the source and the relay and the sourcersquosconstraint is defined as B

1198962

2le 1198751 In a multiple-relay

scenario [61] considers individual constraints for the sourceand the relays that operate under a sum-power constraintAlso for similar use cases [33 38 39] impose joint powerconstraints at the source and the relays expressed by

1003817100381710038171003817B11989610038171003817100381710038172

2+

119873119877

sum119895=1

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 119875119896 (13)

In topologies where relay selection is performed [36]imposes a separate power constraint at the source and theselected relay while [47] has individual power constraintsat the source and the selected set of relays For multiple-source scenarios where a single relay is available the works in[29 31 53ndash55 58 59] consider individual and separate powerconstraints at the sources and the relay In networks wheremultiple relays are employed [41 63 64] have individualpower constraints at the sources and a sum power constraintat the relayswhile [50] imposes individual sum-power con-straints at the sources and the relays

(c) Power Constraint at the Receiver Side In this category formultiple source-destination pairs the target is the minimiza-tion of the interference which is received at each destinationas in [21 42] For a similar setup the maximization of thedesired signal power is the goal of [57]

23 Complexity Many works present optimal BF schemeshowever in practical setups these techniques are very dif-ficult to implement due to the induced computational com-plexity As a result there have been a number of suboptimalmethods that do not significantly degrade the networkrsquos


performance For the optimization of the BF vectors there areseveral published papers providing reduced complexity andthus enhancing some of the aforementioned performancecriteria

For single-user communications various works provideefficient algorithms for the calculation of the BF matrices In[33 61] the authors provide two suboptimal methods whichoptimize the source BF vectors and can be used in networkswith larger scale than the three-node networks under studyThe first suboptimal solution is based on the gradientmethodthat finds the local optimum and the second uses max-min optimization that leads to a semidefinite programmingproblem whose solution can be obtained Furthermore theauthors of [22] provide two suboptimal techniques whichoffer simpler solutions to the power allocation problem atthe relays In the first equal power allocation to all thefrequencies is employed while the second performs equalpower allocation to all the frequencies and the relays thussignificantly reducing the amount of channel estimationoverhead Also in [24] the optimization problem that isformed by the transceiver design is nonconvex and theauthors provide a decomposition method that transformsthe optimization problem into a master problem and asubproblem The master problem is formulated as a relay-precoder design problem whereas the subproblem is asource-precoder design problem By solving the subproblemthe source precoder is obtained and then the solution istransferred to the master problem for the derivation of therelay precoder

Other works provide reduced complexity BF algorithmsfor multiuser communication networks In [38 39] thesystem performance is improved through a low-complexityBF vector optimization technique that targets the maxi-mization of the effective channel gains By considering therelaying functionality of the two destinations as an auxiliarymechanism the low-complexity algorithm focuses on themaximization of the broadcast channel gainsThis is achievedby initializing the combining vectors according to a blindalgorithm and then by updating them as the eigenvectorscorresponding to the largest eigenvalue for the two SDchannelsMoreover in [48] aMIMObroadcast relay channelis studied targeting sum-rate maximization It is shown thatthe problem of finding the input covariance matrices and therelay BF matrix is nonconvex and in order to solve it theauthors propose to examine the dual multiple access relaychannel (MARC) By matching the relay BF matrix to theleft and right singular vectors of the first and second hopchannels the solution to this problem is tractable and sum-rate optimization is performed for this case The MIMObroadcast relay channel is also the topic of [49] and thegoal is to maximize the weighted sum rate However findingthe source precoding matrix B and the relay BF matrixF is a non-linear and nonconvex problem To achieve atractable solution the authors set an equivalent problemthat aims to minimize MSE This problem consists of fourvariables B F the receive matrix A

119896of user 119896 and the

weight matrix W119896of user 119896 By keeping three of the four

variables fixed the problem is convex with respect to theremaining variable and has a closed-form solution Another

work [50] examines the relay interference broadcast channeland targets the end-to-end rate maximization The proposedlow-complexity algorithm is performed through a three-stepprocedureDuring the first step the precoders at the relays aredesigned in order to maximize the second-hop sum rates Inthe second step using the knowledge of the second-hop ratesand the time-sharing value that is the fraction of time whereeach hop is performed the source precoders are designed andan approximation of the optimal end-to-end rate is achievedIn the last step power control is employed to balance any ratemismatch The uplink case of a cellular network is studied in[26] where multiple users communicate with one BS throughone RS This algorithm is proposed when the number of thetransmitted independent streams from the users is greaterthan or equal to their number of antennas that is for fullyloaded scenarios

For networks where multiple source-relay-destinationlinks are present various less complex algorithms have beenproposed In [56] the authors study a two-hop topology withmultiple MIMO relays As the optimal sum-rate maximiza-tion BF strategy introduces increased complexity a reducedcomplexity suboptimal scheme is presented This iterativealgorithm decouples the effective channels and aligns theirchannel gains at the same level thus offering a tractablesolution to the sum-rate maximization problem Moreoveranother scheme based on interference neutralization is givenwhich cancels the interference at the last hop Moreover in[57] the authors present an approximation in the computa-tion of the end-to-end rate in a multisource multidestina-tion network with relays Through this approximation therelationship between the two-hop channel gains are takeninto account and suboptimal solutions can be achieved whendesigning the relay BF matrix In this way rate mismatch isavoided as the dominance of a specific two-hop is consideredand the end-to-end sum rates are improved

When two or more end nodes communicate with eachother simultaneously two-way communication occurs andmany other works present suboptimal algorithms in suchcases In [58] the authors study a two-way MIMO relaynetwork that employs network codingMore specifically theyaim to improve the networkrsquos performance by maximizingthe minimum distance of the NC symbols As the derivationof the global optimum depends on the individual constel-lation and their mapping rule a closed-form solution forthe transmit precoders at the end nodes is not known Inorder to reduce the complexity of optimization a suboptimalprecoding strategy that consists of elements of three differentprecoders is proposed The resulting precoding strategyadapts between precoding with subspace alignment precod-ing with subspace separation and precoding with maximumratio transmission In addition [29] considers linear MMSEreceivers in a two-way MIMO relay network As the jointsource relay and receiver matrices optimization dependson multiple matrix variables a suboptimal relay precodingmatrix design is presented The suboptimal algorithm isproposed in cases where the relay has more or equal numberof antennas than both end nodes To reach to a tractablesolution themain problem is decomposed into subproblemswhich are solved using the projected gradient algorithm


Furthermore in [31] a simplified algorithm is proposedwhich computes transmit and receive BF matrices at the endnodes of a two-way network This is achieved by computingthe receive BF matrices given all other BF vectors and thencomputing the transmit BF matrices through one-step SVDdecomposition Finally the relay BF matrix is obtained Theauthors of [53] give a suboptimal solution to the sum-rateoptimization problem in a two-way MIMO relay networkAs the original problem is nononvex a decomposition intothree separate subproblems is proposed to find the transmitreceive and relay BFmatrices However the problem of find-ing the relay BF matrix is nonconvex and an approximationis given based on the power iteration technique Also [54]examines a two-way MIMO relay network where subopti-mal schemes to compute the relay BF matrix structure arepresented The first is based on the combination of maximalratio reception and maximal ratio transmission while thesecond on ZF reception and ZF transmission Finally in[27] a multiuser two-way relay network is examined whereprecoding design aims to suppress co-channel interferenceIn contrast to BS precoding design with a fixed RS precoderthe design of the RS precoder with a fixed BS precoderis nonconvex As a result the authors propose an iterativealgorithm that finds a local optimal solution either througheigenvalue decomposition or through randomization whichleads in a quasioptimal solution

All the aforementioned papers are categorized accord-ingly in Table 1 with respect to their network configurationdepicting the complexity in quantitative way (wheneverpossible) and elsewhere in qualitative way and the utilizedsuboptimal optimization method along with the detailedconfiguration and the relay strategy scheme that they adopt

24 Channel Estimation and Feedback The formulation oftransmit and receive BF matrices is based on successfulchannel estimation and the feedback of CSI to the nodesthat perform BF The works presented in this subsectionconsider cases where full CSI is not available and so efficientmethods that are based on partial CSI are devised to allow BFtechniques to take place Furthermore the operation of BFwith reduced CSI exchange minimizes additional overheadto the network and allows increased QoS

In scenarios where only a single destination is present thefollowing works aim to give BF algorithms with reduced CSIexchange in order to provide scalablemethods formore com-plex network topologies In [65] clusters of multiple-antennarelays assist the communication of a multiple-antenna sourceand a single-antenna destination In addition transmit max-imal ratio combining BF (TMRC-BF) is employed at therelays which double the duration of the effective channelthrough which the transmitted signal propagates As a resultadditional overhead is needed due to pilot signals that areused to estimate the channel By using the real value propertyof the equivalent channel the pairing of relay clusters isproposed in conjunction with corresponding pilot designsSimulations for MSE performance reveal that when the pilotSNR is not less than 5 dB below the pilot SNR during TMRC-BF optimal performance can be achieved In [34] a modified

quantization scheme at the destination is presented in orderto reduce the amount of CSI feedback This scheme is basedon the fact than in the extreme cases where the SD link orthe SRD link is weak no feedback or only the knowledge ofthe right singular vector of the direct link is required at therelay to determine the source BF vector The article in [66]proposes antenna selection in order to reduce the overhead offeedback compared to multiple-antenna BFThe authors mapthis scenario to a case where a dominant channel is present orwhen diversity is preferred compared to multiplexing gainThe antenna selection with limited feedback is describedwhere narrowband tones are transmitted from each sourceand relay antennas and at the end the destination is able toperformMMSEThis selection process requires log

2(119872119878119872119877)

bits of feedback where 119872119878and 119872

119877are the number of

antennas at the source and relay respectively and119872119877+ 2119872119878

are time slots for SNR estimation thus the minimization ofSNR estimation time is important in this scheme From theanalysis it is shown that full diversity order can be achieved

When relay selection takes place instantaneous channel-gain values are needed and CSI availability is critical for theperformance of the selection algorithm In [35] the authorsconsider the relay selection scheme as a special case of BFwhere limited feedback equal to log

2(119898) where 119898 is the

number of relays is needed The compared schemes includerelay selection and multiple-relay BF with various amountsof feedback ranging From the results it is concluded thatthe selection scheme achieves better performance than BF forlimited feedback cases in AF relay networks Also in [36]partial relay selection (PRS) is employed in order to reducethe CSI requirements of the optimal opportunistic relay (OR)selection More specifically the selection process is based onthe quality of the SR links In this way no additional CSIfeedback from the RD links is required Comparisons withORwith full CSI indicate that whenmin(119872

11990311198721198891198721199032119872119889) ge

1198721199041198721199031+ 1198721199041198721199032 where119872

119904119872119889and119872

119903119902are respectively

the numbers of antennas at the source destination and the119902th relay PRS and OR achieve the same diversity gain

For a network where one BS serves multiple users theauthors in [67] study user selection based only on partialCSI of transmit correlation As a result in each transmissionone user is served by the BS and one by the RS and theirselection is based on an orthogonal pair of userswhich has thelargest phase difference of the transmit correlation in order toreduce the interference received by each user and maximizethe achievable sum rate of multiuser dual-hop MISO relaychannels

25 Antenna Correlation Another challenge for MIMO BFis the correlation between the antennas at each node Suchscenarios are of great importance as colocated antennas insmall devices such as smartphones result in spatial correlationin transmission and reception

In [68] a network with a MIMO source a single-antennafixed gain relay and a MIMO destination is explored Theanalysis takes into account the correlation between the anten-nas at the source and at the destination using the Kroneckercorrelation model Closed-form expressions are derived for


Table 1 Classification of articles based on network topology with their corresponding complexity and suboptimal optimization methodused

Referencearticle Complexity Suboptimal optimization method Configurationrelay

strategySingle relaysingle user

[24]

The cost function that expresses theminimization of MSE is a nonlinearfunction of the two precoding matrices atthe source and the relay resulting in anonconvex optimization problem

Source-precoder subproblem is solved byapplying Karush-Kuhn-Tucker (KKT)conditions to single relay-precoderoptimization

S single MIMOR single AF MIMOD single MIMO

[54]

MRR-MRT proportional to MF-basedreceive and transmit beamforming tomaximize the total signal powerZFR-ZFT proportional to ZF-basedreceive and transmit beamforming toremove the interference

Relay BF matrix calculations based on(i) Maximal-Ratio Reception andMaximal-Ratio Transmission(MRR-MRT)(ii) Zero-Forcing Reception andZero-Forcing Transmission (ZFR-ZFT)

S single-antenna singlesourceR single AF two-waysingle-pair MIMOD single-antenna singleuser

[31] 119874(1198733) N number of antennas at the

source

Optimal beamforming at all nodes basedon the minimization of the sumMSEadopting KKT conditions

S single MIMOR single AF two-waysingle-pair MIMOD Single MIMO

[53]

The sum-rate maximization problem inthis two-way AF single-relay network isnot convex and an approximate solutioncan be derived through decomposition

Joint optimization of the transceivers atboth sources and relay in terms ofsum-rate maximization and based onKKT conditions

S single MIMOR single AF two-waysingle-pair MIMOD single MIMO

[58]

The global optimum regarding themaximization of the distance ofnetwork-coded symbols is complicated tobe found as it depends on the symbolconstellation and the correspondingmapping rule Moreover for generalMIMO channels between the two sourcesand the relay a closed-form solution hasnot been derived

Design of a hybrid precoder combiningthree different classes of suboptimalprecoders with additional constraints ofsubspace alignment subspace separationand the maximal ratio transmissionDefine the optimal precoding vectorswithin each class in terms of maximizingthe minimum distance between differentnetwork coding symbols


Multiple relayssingle user

[22]For each relay log

2(119873119888)1198731198731198882 + 1198732119873

119888

119873119888 iid symbols

N number of antennas at the relay

(i) frequency domain (FD) basedprocessing at the relays(ii) equal power allocation (EPA) acrossall frequencies(iii) equal power allocation (EPA) acrossall frequencies and relays

S single-antenna singlesourceR multiple AF MIMOD single-antenna singleuser

[33] The optimization of the source BF matrixis nonconvex

Gradient algorithm for finding localoptimum of the source BF vector

S single MIMOR Multiple AF MIMOD single-antenna singleuser

[29]

The joint source relay and receivematrices optimization problem that aimsat two-way MSE minimization isnon-convex The global optimum cannotbe achieved with reasonable complexity(nonexhaustive searching)

Iterative algorithm for joint source relayand receive matrices optimization fortwo-way sumMSE minimization

S single MIMOR multiple AF two-waysingle-pair MIMOD single MIMO

[61]

Depending on the imposed powerconstraints the optimization problemsfor each optimal case induce differentcomplexity When multiple relays areemployed the optimization is nonconvexfor the case of joint relay powerconstraints and joint source-relay powerconstraints

Max-min optimization of the source BFvector under joint relay and jointedsource-relay power constraints(i) transformation method(ii) gradient method(iii) relaxation method

S single MIMOR multiple AF MIMOD single-antenna singleuser


Table 1 Continued


strategySingle relaymultiple users

[26]Proportional to the beamformingalgorithm for the fully loaded oroverloaded uplink

Linear MMSE criterion for bothdownlinkuplink utilizing iterativebeamforming algorithm(i) equalizer design at the userBS(ii) forwarding matrix design at the relaystation(iii) precoder design at the BSuser

S single MIMOR single AF MIMOD multiple MIMO users

[38 39] 22119861 for each channel matrix (SR RD RR)B bits

(i) blind algorithm(ii) broadcast channel optimization


[48]The formulated sum-rate optimization isnon-convex and a global optimal solutioncannot be obtained

Optimization of the dual multiple accessrelay channel (MARC) applyingalternating minimization algorithm(AMA) that maximizes the network sumrate


[49] Proportional to two linear relaybeamforming schemes

Weighted MMSE method for MSEminimization

S single MIMOR single AF MIMOD single-antenna Multipleusers

[27]

119899BS = (119873119870 + 1)2(119870 + 2)

05(2119873119870 + 1198702 +

2119870 + 4) log(1120576)119899RS =

119897RS(max (1198722 119870 + 2)4119872 log(1120576) + 119899rd)N number of BS antennaM number of relay antennaK number of MS single antenna119897RS iteration number in Algorithms 1 and2119899rd the complexity of randomization

(i) Iterative algorithm for RS precodingdesign with the BS precoder fixed(ii) Design of joint BS-RS precoding bysolving the BS and RS precodingalternately

S single MIMOR single AF two-waymulti-pair MIMOD single-antenna multipleusers

Multiple relaysmultiple users

[42]

(i) The complexity of the centralizedadaptive BF is 119874(119869(sum

1198961198982119896)2

) periterationJ is the number of sources anddestination nodes119898119896 is the number of antennas at the kth

relay(ii) For the decentralized algorithm thecomplexity per iteration is equal to119874(1198691198984

119894) at the ith relay

(i) Centralized adaptive BF algorithmwith the existence of a local processingcenter connected to all the relays andminimizing a cost function usingstate-space modeling approach(ii) Decentralized adaptive BF algorithmallowing each relay terminal to computeits beamforming matrix locally withlimited amount of data exchange with theother relays employing Kalman filteringto estimate its beamforming coefficientsiteratively

S single-antenna MultiplesourcesR multiple AF MIMOD single-antenna Multipleusers

[43]The optimization problem of meeting theQoS constraint with minimal relay powerexpenditure is non-convex

ZF-BF is used in order to reducecomplexity by projecting the BF vector toa low dimensional space thus reducingthe number of variables that are used foroptimization

S single-antenna multiplesourcesR multiple AF MIMOD single-antenna multipleusers

[56]

As the problem of sum-ratemaximization is NP-hard the process ofchecking whether a set of SINR values areachievable in order to obtain the optimalsolution is highly complex

(i) Sum-rate maximization through aniterative algorithm subject to asum-power constraint of the relay BFmatrices(ii) Interference neutralizationbeamforming scheme subject to a linearconstraint on the desired signals

S single-antenna multiplesourcesR Multiple AF MIMOD single-antenna multipleusers


Table 1 Continued


strategy

[50]Proportional to three-phase cooperativealgorithms with distributedimplementation

Sum-utility maximization viamatrix-weighted sum-MSE Minimizationfor end-to-end sum-rate maximization

S multiple MIMOR multiple AF MIMOD multiple MIMO users

[57]

The sum-rate optimization problem isNP-hard and the global optimal solutioncannot be derived with realisticcomputation complexity

Distributed two-hop interference pricingalgorithm for relay beamforming designfor maximizing end-to-end sum rates


S source R relay D destination

the outage probability and BER performance Moreover thediversity order of the network is found to be dependent on thenumber of the sourcersquos antennas a result that is in contrastto CSI-assisted relaying where the diversity order is equalto the minimum number of antennas between the sourceand the destination Also the case where the second hopis stronger reveals that the systemrsquos performance dependsonly on the antenna configuration at the source The strongpoint of this work is that realistic assumptions are made andmapped to cases such as the uplink of a cellular networkwhere antenna spacing causes correlation at the terminalsor when two BSs communicate with the help of a single-antenna relay that is when these BSs have the same numberof antennas CSI-assisted relaying has a higher array gain andoffers superior performance In [37] the authors extend theirprevious published work [68] by examining the performanceof two different relay protocols The first is called channel-noise assisted (CNA) AF relaying that uses the statistics ofthe channel and the noise The second protocol is calledchannel-assisted AF relaying and uses the statistics of thechannels The two protocols exhibit similar performance athigh SNR From the analysis SER expressions are obtainedand the diversity order and array gain for both protocolsare extracted The results indicate that antenna correlation isbeneficial for cases where low SNR dominates the networkwhile in the high SNR regime it is detrimental for theoutage probability and SER Finally the achieved diversityorder is equal to the minimum number of antennas betweenthe source and the destination The article in [69] studiesa similar scenario with the above works where a MIMOsource communicates with a MIMO destination through asingle-antenna relay The analysis is given for two differentsystemsThefirst employsmaximal ratio transmission (MRT)at the source and maximal ratio combining (MRC) at thedestination and assumes general correlation structures Thesecond is based on transmit antenna selection (TAS) andassumes antenna correlation only at the destination Fromthe analysis closed-form expressions for outage probabil-ity average symbol-error-rate (SER) and generalized highermoments of SNR are obtained for CSI-assisted and fixed-gainrelaying Also a high SNR analysis is performed to gain aninsight on the diversity of the system It is concluded that CSI-assisted relaying outperforms the fixed-gain and this holds forthe MRTMRC system in comparison to the TAS system

In a different setup the authors in [63] study a multiple-access scenario where MIMO users want to communicatewith MIMO BSs through MIMO relays The antennas atall the nodes are considered correlated and modeled withKronecker correlation The challenge in this setup is that theBSs have perfect CSI while UEs and RTs have the channelcovariance information (CCI) As a result to maximize thesystem sum rate the authors perform a joint optimization ofthe UEs covariance matrices and relay precoding matricesFrom the analysis the asymptotic sum-rate expression isderived for the large-system scenario where the antennasare increased in every network node with constant ratiosMoreover results are obtained for various given signalinginputs and an iterative algorithm is given which obtains theasymptotically optimal users and RS precoding matrices

3 Beamforming forSingle-User Communications

In this section various works are presented that studyMIMOBF techniques in cases where a single user is present inthe network Following and for each scenario an analyticaldescription is performed evaluating the BF scheme

31 Beamforming with Single Relay In Figure 2 a networkwhere a single relay is used to establish communicationbetween a source and one user is depicted Under thesingle-relay consideration and when capacity and poweroptimization arises the authors in [45] provide the three basicmodes for the three-terminal MIMO relay network namelythe direct link (mode A) the relay without direct link (modeB) and the relay with direct link (mode C) A weightingmatrix at the relay is designed in such a way as to minimizecapacity loss This is achieved by transforming the MIMOrelay channel in parallel SISO relay subchannels and thenthrough waterfilling power allocation is performed

The Grassmannian codebooks are proved appropriatefor the design of the source and relay BF based on thedistributions of the optimal source and relay BF vectors[34] The authors aim at SNR maximization through BF atthe source and the relay The explored scenarios includean SRD topology with and without the presence of the SDlink Moreover when perfect CSI is available at the source


middot middot middot

Figure 2 Single-relay communication

and the relay a mapping of the source and relay signalsto the dominant right singular vectors of the SR and RDchannel should be performed On the other hand whenlimited feedback is available Grassmannian BF codebooks atthe source and the relay should be adopted which quantizethe optimal BF vectors In order to reduce the complexitya modified quantized scheme can be employed for the casewhere SD connectivity is feasible Through this schemeonly one singular vector needs to be quantized resulting insignificant reduction of feedback from the destination to therelay

The optimization (minimization) of the MSE in a single-user single-relay scenario is considered in [23] where theauthors consider the optimal BF in three stages First theMIMO relay performs receive BF by using the Hermitiantranspose of the left singular matrix of the SR channelThen linear precoding takes place at the relay and finallytransmit BF is performed through the use of the right singularmatrix of the RD channel The work in [25] extends theprevious one by performing joint source-relay precodingdesign As the derivation of the optimal relay amplification Fand source precodingBmatrices in closed form is intractablean iterative algorithm is provided The algorithm optimizesF for a given B under a relay power constraint Also Bis optimized for a fixed F under power constraints at thesource and the relay Following the precoding techniquethe authors in [24] propose a non-linear precoding schemewhich adopts a Tomlinson-Harashima precoder (THP) atthe source while the relay uses a linear precoder Moreovera direct SD link exists and the destination uses an MMSEreceiver The proposed scheme performs a joint source-relay precoder design and to make the solution tractable itdecomposes the problem into one subproblem and a masterproblem which provide the precoders of the source and therelay correspondingly Comparison with the schemes of [2124] shows improved MSE performance from the proposedprecoding method Finally the work in [70] studies thedegrading effect of self-interference and provides precodingdesigns to mitigate it More specifically transmit and receivebeams at the relay are formed in such a way to minimize theself-interference signal experienced at the receive antennas


Figure 3 Multiple-relay communication

of the relay This is achieved by pointing these beams tothe minimum eigenmodes of the channel between transmitand receive relay antennas Also the authors provide thecondition which corresponds to the null-space projectionscheme of the optimal eigen-BF thus providing orthogonalsubspaces to relay reception and transmission The maincontribution of this work is the formulation of precodingdesigns that allow the minimization of the degrading effectsof self-interference

32 Beamforming with Multiple Relays Figure 3 illustratesthe scenario where multiple relays are allocated for the com-munication between a source and one user Moving forwardand considering single-user BF for multiple-relay nodes in[44] the authors compare signaling and routing techniquesfor various relaying protocols namely amplify-and-forward(AF) decode-and-forward (DF) and hybrid relaying wherethe relay decodes only the necessary information to obtainCSI for the SR or RD channels Several MIMO spatial multi-plexing (SM) techniques are presented which take advantageof CSI knowledge at the relay by coordinating the SR andRD channels eigenmodes The authors compare SM to singlesignal BF (SSB) which exploits the spatial diversity of MIMOchannels If CSI is available at the transmitter then SSB canbe performed In continuity two cases of SSB are given forboth DF and hybrid relaying It is shown that in the low SNRregime SSB is preferable compared to spatial multiplexingdue to its increased diversity The main contribution of thisarticle is the consideration of three types of relaying and thecomparison of SM and SSB for various SNR regimes

When aMIMO equalizer is introduced for implementingthe BFmatrix at the receiver the authors in [21] study the SNRand MMSE designs under a global power constraint at therelays and at the receiver in a network with MIMO sourcemultiple MIMO relays and MIMO destination For theMMSE approach they provide two alternatives to formulatethe relaymatrix F and theMIMO equalizerA

119896at the receiver

Firstly they perform a two-step design where F is priorlyformed and then A

119896is derived Secondly they proceed in a

joint formulation of F andA119896 On the other hand for the SNR


approach they include two optimization cases with a zero-forcing constraint and with the global power constraint Fur-thermore they form the BF matrices aiming to maximize thetransmission rateThe simulations show that both approachesachieve similar BER performance when there is no powerconstraint at the relays By targeting SNRmaximization at thedestination under different power constraints the authors in[33 61] study a networkwhere aMIMOsource communicateswith a single-antenna destination through multiple MIMOAF relays Three different power constraints are derived forthe optimal BF-AF weights and for a given BF vector atthe source Firstly for the individual and joint relay powerconstraints closed-form solutions are given Secondly forthe joint source-relay power constraint a numerical methodis presented which offers optimal power allocation for thesource and the relays In order to decrease implementationcomplexity suboptimal methods for the joint relay and jointsource-relay power constraints are presentedThese methodsare based on the transformation of the optimization prob-lem into a nonconvex polynomial programming problemNumerical results illustrate that the performance of thesuboptimal methods follows closely that of the optimal oneBy targeting minimization of the MSE or equivalently themaximization of the SINR under a sum power constraint thestudy in [22] considers BF that is coupled with single-carrierfrequency domain equalization in a three-node networkFrom the proposed algorithm the optimal frequency-domainlinear equalization (LE) and decision-feedback equalization(DFE) to the receivers is derivedThe optimal relay BFmatri-ces are formed under a sum power constraint Moreovercomplexity issues are considered by providing suboptimalpower allocation algorithms without significant performancedegradation

33 Relay Selection The case of relay selection is shown inFigure 4 In order to reduce synchronization requirementsamong the multiple transmitting relays relay selection hasbeen proposed in [10] In addition the selection of onerelay or a subset of the available relays improves the spectralefficiency of the transmission as the amount of orthogonalchannels is less than the number of the relays in the networkfor the same diversity gain In [35] the authors illustrate theefficiency of relay selection through comparisons with BFschemes based on limited and unlimited CSI They developthe outage probability of the optimal AF BF with unlimitedfeedback noting that due to its impractical assumptions itserves only as a performance bound to other more practicalschemes Moreover the selection scheme is proven to be theunique optimal for AF BF as itminimizes noise amplificationAlso numerical comparisons are given for the cases of opti-mal codebook design and random BF with limited feedbackThe compared schemes include relay selection optimal BFand BFwith various amounts of feedback It is concluded thatthe selection scheme outperforms the other BF schemes inlimited feedback scenarios while alleviating synchronizationconcerns

Partial relay selection (PRS) is employed in [36] wheresuboptimal relay selection is presented as the only CSI


Figure 4 Communication with relay selection

considered in the selection algorithm is the quality of the SRlinks Furthermore transmit and receive BF is implementedat the source and the destination while for the selected AFMIMO relay the linear precoder is optimized Additionallythe outage probability of the proposed scheme is given inclosed form and for the asymptotically high SNR the diversitygain is extracted As a result PRS and OR achieve the samediversity gain

Another technique is the opportunistic selection of asemiorthogonal subset of relays [47] The proposed schemetakes place in two steps First spatial eigen-mode combiningbetween the forward and backward channels is performedThen for the selected subset the algorithm proceeds inantenna pair selection for reception in the first hop andtransmission in the second hop

The best relay selection is studied in [62] where a single-user network is examined with the consideration of multipleMIMO relaysThe proposed scheme selects the best relay thatsuccessively combines maximal ratio receiver combining inthe first hop and BF in the second In order for this process totake place the authors consider that in two sequential timeslots the channel coefficients remain constant Simulationsinclude comparisonswith various relay numbers and antennanumbers on each relay illustrating the reduction of the outageprobability as these values increase Along with the best relayselection there are other selection techniques that incor-porate for example max-rate selection with interferencemitigation issues The work in [46] considers a multihopbackbone networkwhereMIMO relays are employed In eachphase a relay is selected based onmaximum rate path routingand performs transmit BF Additionally mitigation of themultiple access interference that degrades the performanceof the network is achieved through cancellation The effectsof interference mitigation transmit BF and spatial reuse onthe performance of the proposed scheme are studied in agame theoretic approach aiming at the optimal combinationof these techniques

Finally the multi-relay network of [71] selects in eachtime slot two relays in order to achieve full-duplex operationthrough successive relaying To this end buffer-aided relayselection is combined with beamforming and two schemes


are proposed The first scheme is inspired by the case of noIRI between the relays and adopts MRC at the receiving relayand MRT BF at the transmitting relay As IRI is consideredthis scheme utilizes an SINR criterion for the SR link and therelay-pair that maximizes the instantaneous end-to-end rateis chosen The second scheme is based on ZF-BF to cancelthe IRI at the receiving relay and to maximize the effectivechannel power gain of the RD link Results illustrate that theSINR-based approach improves the rate performance of thenetwork in the low SNR region while the ZF scheme has thebest performance and approaches the upper boundof the IRI-free case

4 Beamforming forMultiuser Communications

An alternative approach for transmitting the signal throughthe relays is to serve multiple users simultaneously A relaybroadcast channel (RBC) can be considered which is atypical case for the so-called nondedicated relay system Anondedicated relay system is when the mobile users canhelp each other by relaying information for their peersbesides receiving their own data An RBC is based on abroadcast channel (BC) where a BS transmits to multipleusers simultaneously Relay mechanism is presented into theBC in such away that the users can benefit from each other byperforming cooperative procedures In addition another caseconsidered is that of two-way relaying as amultiuser scenariowhere the two sources exchanging information could besingle or multiple pairs of users that communicate and notnecessarily a BS and a user

There are several ways of exploiting this operation byemploying MIMO techniques as depicted in Figures 5ndash7Several scenarios can exist such asmultiuser communicationthrough a single relay multiuser communication throughmultiple relays two-way single pair communication andtwo-way multi-pair communication

41 Beamforming with Single Relay When a single relayis concerned as is the case in Figure 5 there are manystudies that take into consideration some or all of theaforementioned challenges discussed in Section 2 Differentpower constraints precoding techniques and feedbacks areintroduced to minimize MSE maximize sum rate anddecrease complexity The classification of the examinedpapers depends on whether users are equipped with multipleantennas or not

On one hand when only a MIMO BS and a MIMORS are considered a solution for the optimization prob-lem is introduced in [49] which exploits the downlinkperformance incorporating relay BF with source precodermatrix It deals with a formation ofMIMO relaying broadcastchannel to multiple users at the downlink based on weightedsum-rate criterion Accordingly the design of the sourceand relay matrices is based on non-linear and nonconvexWeightedMMSE (WMMSE) criterionTheWMMSE schemecan better deal with the multiuser interferences and noiseand the relation between downlink gains and source-relay


Figure 5 Multiuser communication through a single relay

users channel gains Because of the difficulty in solving thenon-linear and nonconvex problem decoupling it into twotractable subproblems solves an equivalent problem and analternative optimization based on efficient linear iterativedesign algorithm is proposed which always converges toa stationary point Following the previous topology theauthors in [40] consider a MIMO relay-assisted multiuserdownlink transmission with limited feedback and suggesttwo precoding schemes at the RS based on the ZF criterionand theMMSE criterionThese robust linear BF schemes takeonly channel direction information (CDI) feedback using afinite number of feedback bits to the RS and the effect ofchannel quantization errors for determining the BF vectors

On the other hand when all nodes have multiple anten-nas the authors in [39] considerMIMO relay broadcast chan-nels For simplicity a two-user system is taken into consid-eration A precoding relaying and combining (cooperative)scheme is proposed under an overall power constraint andan optimal power allocation solution in a closed form isdeveloped Instead of considering time-division broadcastschemes it is assumed that the BS transmits simultaneouslyto both users in the same frequency band Precoding is usedto steer the signals for the two users in different subspacesto avoid interuser interference employing the zero-forcingcriterion The user with better conditions acts as an AFrelay to the other user besides receiving its own signalBased on the proposed scheme an optimal power allocationsolution is established so as to minimize the BER which isequivalent to maximize the SNRs Moreover an optimizationalgorithm for the BF vectors is proposed in order to achievethemaximum effective channel gains utilizing three differentschemes for optimization of combining vectors exhaustivesearch blind algorithm and broadcasting optimization Theproposed algorithm is shown to achieve a near optimal per-formance (compared with the exhaustive search algorithm)and maximum diversity gain Nevertheless there are severalweaknesses only a fixed relay direction has been consideredthe BF and combining vectors have been determined insequence which is not optimal and only one data streamfor each user and flat fading channels have been taken intoconsideration


Figure 6 Multiuser communication through multiple relays

Accordingly a fully MIMO single-relay scheme is pre-sented in [48] where the topology comprises a MIMO BSwhere a dirty paper coding is applied a fixed infrastructure-based half-duplex MIMO relay station (RS) with linear pro-cessing and multiple users equipped with multiple antennasA MIMO BRC and its dual multiple access relay channel(MARC) network (uplink-downlink duality) is used to trans-form the problem and solve a nonconvex problem whichfinds the input covariance matrices and the RS BF matrixthat maximize the system sum rate To make the problemtractable the relay BF to the left and right singular vectors ofthe forward (RS-to-users) and backward (BS-to-RS) channelswasmatchedWith this RSBF structure the authors proposedan iterative algorithm for the sum-rate maximization for thedualMIMOMARCwhere theMIMO-AFduality was provedfor multiple-antenna-user networks The proposed schemefollows an alternating-minimization convergent procedureover the input covariance matrices at the transmitter and theBF matrix at the relay Also the derivation of the mappingfrom the resulting covariance matrices for the MARC tothe desired covariance matrices for the BRC is proposed Avaluable observation for better system performance is to havemore antennas at the RS than at the BS

Following the consideration of a fully MIMO single-relay topology a linear BF design for amplify-and-forwardrelaying cellular networks is considered in [26] The designis based on optimizing (minimizing) the sum mean squareerrors of multiple data streams while joint design of theprecoders forwarding matrix and equalizers for both uplinkand downlink is considered and under individual powerconstraints An iterative algorithm is proposed for thedownlink so as to jointly design the precoder at BS whileforwarding matrix at RS and equalizers at mobile terminalFor the uplink the duality of the BF design is demonstratedand the same downlink iterative algorithm can be appliedAdditionally a low-complexity algorithmhas been developedfor the uplink under a special case when the number ofindependent data streams from different mobile terminalsis greater than or equal to their number of antennas (fullyloaded or overloaded uplink systems) It is found that theresultant solution includes several existing algorithms for

Figure 7 (Left) Two-way single pair communication (right) two-way multi-pair communication

multiuser MIMO or AF relay network with single antenna asspecial cases and outperforms the suboptimal schemes It isverified that for AFMIMO relaying systems source precoderdesign is of great importance and offers additional designfreedom for performance improvement

Finally when both single- and distributed-relayingschemes are considered and compared in [43] multiplesingle-antenna SD pairs communicate via one MIMO relayin a network where linear BF techniques are employed Thegoal of BF is the sum-power minimization aiming at a targetSINR at the destinations The BF technique is based on ZFin order to cancel the interference at the destinations and theformulation of the relay BF matrix result in a least-squaresproblem that can be solved with convex optimization toolsFrom the numerical results it is concluded that the MIMOrelay with ZF-BF achieves the best performance compared toother schemes employing distributed single-antenna relays

42 BeamformingwithMultiple Relays Interferencemanage-ment is maybe the most fundamental open problem in wire-less networks When multiple MIMO relays are concernedas shown in Figure 6 thus enhancing the SD pairs equippedwithmultiple or single antennas and incorporate beamform-ing techniques for throughput improving interference issuesappear The following studies are inspired by this problemand confront the arising interference issues by introducingbeamforming algorithms under different network topologies

In regard with the first topology where multiple SD pairscommunicate throughmultipleMIMOAF relays the authorsof [42] develop two adaptive relay BF algorithms employinglinearly constrained BF algorithms with minimum variancebased on Kalman filtering As a result the received powerat the destinations is minimized by considering the linearconstraints on the relay BF matrices thus avoiding severedegradation of the reception by noise and interference whilepreserving the desired signal at each destination The maindifferentiation of these algorithms is that the first operates ina centralized fashion while the second is distributed In thecentralized approach the relays have a common processing


center that receives all the CSI and computes the BF coef-ficients which are fed back to the relays In the distributedcase each relay computes its own BF coefficients throughlocal channel estimation Additionally extensions to thesealgorithms are discussed through power control and QoSmodificationNumerical results indicate similar performanceof the proposed methods to the noniterative centralizedsecond-order cone program (SOCP)-based algorithm at lowand medium SNR regimes and with reduced computationalcomplexityThemain contribution of this work is the reducedcomplexity of the two proposed algorithms compared tothe SOCP-based BF algorithm and the formulation of adistributed BF algorithm

Following the first topology there are several papers deal-ing with a new cooperative interference management schemenamed interference neutralization Accordingly in [55] illus-trative examples are discussed in a network consisting ofmultiple sources relays and destinations This technique isbased on the concept of neutralizing the interference signal atthe destination provided that this interference is propagatedthrough various paths In practice these interfering signalsare processed so that they have the same power level andneutralize each other by adding them at the destinationThis processing can take place at the relay using a properpermutation In addition the use of lattice codes to achievethe neutralization effect is shown and the signal receivedafter the summation of the interfering signals is the desiredpoint on the scaled lattice The main contribution of thiswork is the detailed description of interference neutralizationIn [56] authors deal with the mitigation of the cochannelinterference issues that arise when relays are equipped withmultiple antennas operating in AF and half-duplex modesSelecting a pair of multiple sources andmultiple destinationsboth of which are equipped with single antenna enhancesthe network performance A coordinated relay beamformingis considered to suppress interference and improve the daterates of two-hop interference networks under the sum-ratemaximization criterion A suboptimal solution of interfer-ence neutralization beamforming is then introduced whichallows the interference to be canceled over the air at the lasthop where the relay beamformer is designed to neutralizeinterferences at each destination terminal

Concerning the second topology where a number ofMIMO half-duplex relays aid the data transmission froma number of transmitters MIMO BSs to their associatedMIMO users the study in [50] conceived an interferencemanagement approachThis approach considers interferencebroadcast channels at relays and end users where a number ofMIMOhalf-duplexDF relays aid the data transmission fromanumber of transmittersMIMOBSs to their associatedMIMOusers A typically linear precoding design at the transmitterand BFmatrix at the relay is accomplished so as to maximizethe end-to-end sum rates The proposed algorithm solves ina suboptimum way the transmit precoder design followingthree phases (1) second-hop transmit precoder design wherethe relays are designed to maximize the second-hop sumrates (2) first-hop transmit precoder design where approx-imate end-to-end rates that depend on the time-sharingfraction and the second-hop rates are used to formulate a

sum-utilitymaximization problem to design the transmittersthis problem is solved by iteratively minimizing the weightedsum of mean square errors (3) first-hop transmit powercontrol where the norms of the transmit precoders at thetransmitters are adjusted to eliminate ratemismatchThe sec-ond hop is treated as the conventional single-hop interferencebroadcast channel and existing single-hop algorithms canbe applied to find the stationary points of second-hop sum-rate maximization The design of the first-hop precoders isdevised by applying a naive approach ignoring the designedsecond-hop transmit precoders The overall performance issubjected to the assumptions of each transmitting node (relayand BS) and has instantaneous and perfect local channel stateinformation (CSI) and there is a feedback channel to sendinformation froma receiving node to its serving node Finallythe algorithm is implemented in a quite reverse mode therelays are optimized for second-hop sum-rate maximizationbefore the transmitters are designed for end-to-end sum-ratemaximization An interesting interference pricing scheme isemployed in [57] where the authors investigate the two-hop interference channel and map it to a cellular networkwith relays Interference pricing is employed to allow therelays to take into consideration the impact of interferenceon the end-to-end rate In order to avoid rate mismatch inthe two-hop transmission an approximation is proposed inthe computation of the end-to-end achievable rate whichincorporates the interaction of the two-hop channels that iswhich hop is dominant

43 Two-Way Communication In Figure 7 two-way relay-ing scenarios are shown for single and multiple pairsTwo-way communication considers two source nodes thatexchange their information through an assisting relay nodeWhen beamforming algorithms are engaged at the exchangescheme the delivery of information can be completed in twotime slots In the first time slot both source nodes simultane-ously transmit signals to the relay node In the second timeslot the relay node precodes the received signals along withvarious beamforming techniques and broadcasts the signalsto both source nodes Self-interference and cointerferenceissues arise and several multiple access and network codingtechniques have been proposed for optimization of a two-way relay channel (TWRC) communication system Whenone relay is dedicated to a single user then a single-pair SD isaccounted for whereas when multiple users utilize one relaya multiple-pair SD is taken into consideration

431 Single Pair The first set of papers deal with precodingat the relay node In [32] the authors focus on designingthe precoders and decoders based on the MSMSE crite-rion in a topology where multiple MIMO relays assist twoMIMO sources To simplify the optimization process thedecomposition of the primal problem into four subproblemsis performed These problems include the derivation ofthe optimal decoders at the sources and the optimal relayprecoding matrix the optimal precoding matrix for thefirst source and then for the second source It is notedthat the solution of the second subproblem is one of the


main contributions of this work as it is converted intoa convex problem that can be solved Also a simulationsetup of the proposed scheme is presented and comparisonswith suboptimal versions and a nonprecoded scheme areperformed In [29] the main task is the derivation of theoptimal structure of the precoding matrices at the sourcesand the MIMO relay when MMSE receivers are used as theyreduce the complexity in comparison to joint ML detectionSince the joint optimization problem is proven to be non-convex (Schur-concaveShur-convex) an iterative algorithmis developed to find the optimal precoding matrices Thealgorithm is initialized by finding a simplified relay precodingmatrix designed for the cases where relay antennas are twice(or greater) the number of the antennas of each sourceAfterwards for fixed precoding matrices at the relay and onesource the optimal matrix at the other source is designedFinally joint optimization can be performed by updatingthe relay precoding matrix with fixed matrices at the sourceand then update the sourcesrsquo precoding matrices with a fixedrelay matrix Numerical results show the efficiency of theproposed algorithm in terms of normalized MSE and BERand with significantly lower complexity when the suboptimalrelay matrix is selected

Along with the precoding strategy various network cod-ing schemes found prolific field for increasing the spectralefficiency of the network alleviating interference issues andthus optimizing the single-pair BF performance The workin [58] presents a three-node topology where the end nodescommunicate through a MIMO relay The relay follows anetwork coding strategy based on either digital networkcoding or physical network coding As a result the precodingstrategy in the broadcast phase takes into consideration themaximization of the minimum distance of the network-coded symbols For this reason a hybrid precoder is proposedwhich switches among three suboptimal precoders that iswith subspace alignment with subspace separation andwithmaximum ratio transmission Numerical results includecomparisons of the three suboptimal precoders with thehybrid precoder and a reference schemewhere each end nodedoes not cause interference to the reception of the othernodersquos signal at the relayThe result proves the efficiency of theproposed scheme as it achieves a near-optimal frame errorrate (FER) performance The work in [54] studies a three-node topology with single-antenna source and a MIMOAF relay To increase the spectral efficiency of the networkanalogue network coding is performed which results in thecancellation of the self-interference at the sources causedby the previously transmitted messages The authors derivethe optimal BF matrix at the relay through SVD as wellas its achievable capacity region The capacity limits areextracted through the use of rate profiles which regulate theratio of the rate of a user to their sum rate as a predefinedvalue In addition power minimization is performed at therelay given specific SNR at the receivers In order to offermore practical schemes for this topology two suboptimalapproaches based on matched filter and ZF are presentedThe results indicate that the matched filter approach is thescheme which can offer the best performance considering itslower complexity compared to the optimal BF technique In

[30] relay selection is combined with two-way transmissionsin a network consisting of two single-antenna sources thatare assisted by 119870 MIMO relays The optimal relay selectioncriterion is extracted by considering the minimum PLNCdecoding error probability To perform the selection eachrelay transformation matrix is decided according to [54] andthen the one that provides the minimum decoding errorprobability is selected Numerical results show the diversitygain achieved by relay selection through the proposed crite-rion

A sum-rate maximizing technique is proposed in [53]which performs joint optimization at the relay The authorsaim at the maximization of the sum rate in a two-way com-munication scenario with a MIMO relay To this end a sum-rate maximizing technique is proposed which performs jointoptimization at the relay As the derivation of the optimalprocessing matrix is nonconvex an approximate solution isproposedwhich consists of the iteration of three optimizationproblems for the transmit beamformer the receive combinerand the linear relaying matrix Simulations compare theproposed scheme with other single and multiple antennatechniques in terms of sum-rate performance It is concludedthat the upper bound is achieved by the proposed BF schemewhile it converges rapidly to the final solution Alternativelywhen theminimization of the summean square error (SMSE)is evolved the authors in [31] jointly optimize the ideal BFvectors for the two communicating sources and the MIMOrelay with the target of SMSEminimization under individualpower constraints at all the nodes A simplification analysis isthen conducted stating that the BF pairs whichminimize theSMSE alsomaximize the SNR at both communicating nodesIn addition a schemewhich optimizes the BF vectors in threeconsecutive steps is given and is compared to the optimal onein terms of the number of iteration and BER Results indicatethat when the number of antennas is greater than two thesimplified scheme experiences only a small performance lossand can substitute the optimal one

432 Multiple Pairs Considering the multiple-pair two-way communication scheme numerous works exist thathave tried to improve all the above-mentioned challenges inSection 2 Regarding the channel estimation challenge theauthors in [51] consider multiple SD pairs that communicatethrough MIMO AF relays and adopt the two-way strategyThe nodes are assumed to be full-duplex and perfect CSI isavailable to all of them In this context two different cases arepresented The first is termed 119884 relay channel and consistsof three users that want to unicast independent messagesfor different two users through the relay For this settingthe achievable degrees of freedom (DoF) are extracted whenthe relay performs either analog network coding (ANC) orphysical layer network coding (PLNC) and are proven to beequal to 2119872 if all the nodes have 119872 antennas The secondcase considers multiple two-way relay links that operateconcurrently thus naming this case as two-way relay 119883channels By equipping the users with119872 = 3 antennas andthe relay with119873 = 4 antennas the DoF is found to be equalto 8 The main contribution of this article is the investigation


of the DoF in two-way relay networks Correspondinglythe formulation of a general model for topologies where 119873single-antenna nodes communicate simultaneously (119873-way)through aMIMO relay is presented in [64] From the analysisit is extracted that for this general case there should be at least119873 minus 1 antennas at the relays while the transmission shouldoccupy 119873 time slot Moreover the general BF matrix at therelay is constructed for various objective functions

An interesting relaying scheme termed Quantify-and-Forward (QF) is considered in [41] where the authorsinvestigate a topology consisting of 119870 single-antenna pairsthat perform two-way communication with the help of aMIMO relay which is equipped with119872 ge 2119870 antennas Therelaying strategies include AF and QF and the correspondingBF techniques are derived For AF relaying two possibilitiesare considered the first is BF with ZF transmitter andreceiver and the second performs block diagonalizationwhich takes into consideration that intrapair interference canbe cancelled Also the QF strategy which can be seen asa case of analog network coding due to the signal separa-tion is performed at the relay Furthermore the receivedsignals at the relay are quantized to a scalar that is a linearcombination of the two-dimensional vectors transmitted byeach pair In the next phase multicast aware BF is employedaiming tominimize distortion Additionally comparisons areperformed between the proposed schemes andDF relaying interms of the average sum rate showing improvedperformancein awide range of SNRsThemain contribution of this work isthe consideration of AF and QF strategies that do not requirethe knowledge of the codebooks of the mobiles by the relayAlso through the QF scheme simpler signal representationis achieved through signal separation at the relay

The challenge of power minimization is the subjectof [28] The article studies a topology where 2119870 MIMOusers communicate in pairs through a MIMO AF relayThe optimization problem is formulated for both ZF andMMSE criteria taking into consideration a power constraintat the relay and predetermined transmit-receive BF vectorswhich can be obtained from CSI Also four BF methods arepresented which deal with different CSI conditions firstlyeigen-BF that requires perfect CSI knowledge at the usersin order to produce the eigen-BF vector secondly antennaselection that can be performed with partial CSI as only theCSI of the selected antenna is fed back to the relay thirdlyrandom BF which does not assume CSI knowledge but needssynchronization information among the users and the relayfinally equal gain BF that also does not need any CSI andno further information at the relay Another area that theauthors investigate is the power control for ZF systems Twodifferent cases are studied starting with local power controlthat distributes the multiuser power to the users according totheir channel conditions and then global power control thatfor the high SNR regime divides network power to the usersand the relay with the target of system SNRmaximization Allthe proposed BF methods are evaluated through simulationsillustrating the tradeoff between improved performance andCSI overhead The main contribution of this paper is theinvestigation of four different BFmethods that can be chosenaccording to the availability of CSI in the network

In [52] physical layer network coding is proposed in atopology where one MIMO BS with 119872 antennas commu-nicates with 119872 single-antenna mobile stations through aMIMO relay that also has119872 antennas The communicationprotocol is based on two-way relaying in order to enhancethe spectral efficiency of the network The BF method isbased on interference alignment that aims to put the twomessages which are transmitted and received by each user inthe same spatial direction at the relay In this way cochannelinterference that is the major degrading factor in thisnetwork is mitigated Moreover the precoding designs forthe matrices at the BS and the RS are given in detail underindividual power constraints and the minimization of CCIThrough analytic results it is proven that the multiplexinggain achieved is equal to the number of the mobile stationswhile the diversity gain can be increased by employing mul-tiple MIMO relays and by increasing the number of antennasat the BS and RS to be greater than 119872 Finally simulationsare performed to compare the proposed network codedscheme to time sharing network coding approaches thusillustrating the improved performance of this scheme Themain contribution of this work is the interference alignmentinspired network coding technique and the discussions ofmultirelay and increased antenna number cases

Finally while aiming to optimize the total MSE and sumrate and combat interference different precoding schemes areapplied for enhancing the uplink transmission performance[59] This work investigates two-way relaying for a topologywhere a MIMO BS with an ML decoder communicates with119870 single-antenna users through a common MIMO AF relayTheobjective is tomaximize theminimumsymbol distance atthe BS that is to improve the uplink performance Moreoverthree different precoding cases are presented which requirevarying complexity and a clean relay model that assumesnegligible noise at the relay is introduced as well Firstlyprecoding at the BS is considered while the relaying onlyamplified the received signal under the imposed powerconstraint Secondly precoding at the RS under the afore-mentioned optimization target is proven to be nonconvexand to obtain a solution the transformation into anotheroptimization problem is given which can be solved throughbisection search to acquire the quasioptimal solution Thethird precoding design considers joint precoding at the BSand the RS to further improve the systemrsquos performanceThese precoding methods are compared via simulation andthe joint scheme shows the best performance but at thecost of increased complexity in its practical implementa-tion Through the proposed methods self-interference andcochannel interference are efficiently mitigated The authorsin [27] extend the study in [59] by considering a similarcellular multiuser two-way relaying topology and aimingto optimize the total MSE and sum rate Linear precodingdesigns are given for BS precoding RS precoding and jointBS-RS precoding

5 Discussion and Open IssuesThis section provides a discussion based on the works thatwere presented throughout this survey and in addition some


Table 2 Classification of articles based on network topology the optimization target with the corresponding power constraint and therelaying topology

Referencearticle Network topology Optimization target Power constraint Relaying topology

[21] Single-user MSE SINR Capacity Relay (total) receiver (interference level) Multirelay[22] Single-user MSE Relay (sum-power) Multirelay[23] Single-user MSE Relay Single-relay[24] Single-user MSE Source-relay (separate) Single-relay[25] Single-user MSE Source-relay (separate) Single-relay[26] Multiuser MSE Source-relay (separate) Single-relay[27] Two-way multipair MSE Relay Single-relay[28] Two-way multipair MSE SINR Relay Single-relay[29] Two-way single-pair MSE Sources-relay (separate and individual) Single-relay[30] Two-way single-pair MSE Sources-relays (separate and individual) Relay selection[31] Two-way single-pair MSE Sources-relay (separate and individual) Single-relay[32] Two-way single-pair MSE Sources (individual)-relays (sum-power) Multirelay[33] Single-user SNR Source-relay (joint) Multirelay

[61] Single-user SNR Source (individual)-relay (total) relay(joint and individual) Multirelay

[34] Single-user SNR Source-relay (separate) Single-relay[35] Single-user SNR Source-relay individual Relay selection[36] Single-user SNR Source-(selected) relay (separate) Relay selection[37] Single-user SNR Relay Relay selection[38] Multiuser SNR Source-relay (joint) Single-relay[39] Multiuser SNR Source-relay (joint) Single-relay[40] Multiuser SINR Relay Single-relay[41] Two-way multipair SINR Sources-relay (separate and individual) Single-relay

[42] Multiuser SINR Relay (individual) receiver (interferencelevel) Multirelay

[43] Multiuser SINR Relay (sum-power) Multirelay[44] Single-user Capacity Relay (sum-power) Multirelay[45] Single-user Capacity Relay Single-relay[46] Single-user Capacity Relay Relay selection[47] Single-user Capacity Sources-relays (separate sum-power) Relay selection[48] Multiuser Capacity Source-relay (separate) Single-relay[49] Multiuser Capacity Source-relay (separate) Single-relay[50] Multiuser Capacity Sources-relays (separate sum-power) Multirelay[51] Two-way multipair Capacity Relay Multirelay[52] Two-way multipair Capacity Relay Single-relay[53] Two-way single-pair Capacity Sources-relay (separate and individual) Single-relay[54] Two-way single pair Capacity Sources-relay (separate and individual) Single-relay[55] Multiuser Capacity Sources (individual)-relays (individual) Multirelay[56] Multiuser Capacity Relays (sum-power) Multirelay[57] Multiuser Capacity Receiver (interference levels) Multirelay[58] Two-way single-pair Minimum symbol distance Sources-relay (separate and individual) Single-relay[59] Two-way multipair Minimum symbol distance Sources-relay (separate and individual) Single-relay


open research topics that are of great interest and have notyet been sufficiently examined by the community Table 2depicts the references that were presented in the contextof this survey More specifically each article is classifiedbased on network topology the optimization target with thecorresponding power constraint and the relaying topologythat was employed In general most works investigate beam-forming with half-duplex relays to avoid self-interferencebut the performance of the network is limited by the half-duplex constraint Single user network has been a very activeresearch field as it is a simple communication paradigmthat allows the proposed BF techniques to clearly exposetheir operation It is observed that a lot of contributionshave been made in the two-way communications as it isa strategy that improves the spectral efficiency and canprovide significant gains if the interference between thecommunicating end nodes is efficiently mitigated On theother hand as it is also the case with one-way multiusercommunications relay selection has not been considered asan alternative cooperation strategy and this offers a possibleresearch direction towards complexity reduction From theoptimization targetrsquos perspective there are numerous worksthat aim at MSE minimization SNR or SINR increaseand capacity improvement As network-coding algorithmscombined with beamforming have recently been developedthere are a few works which aim at the maximization of theminimum distance of network-coded symbols

Although the area of BF with MIMO relaying has seena significant number of contributions there are many openissues that need to be investigated in the future An importantparameter that has to be taken into consideration is thesynchronization among the various network nodes especiallyin topologies where multiple relays are employed Morespecifically synchronization based on consensus algorithms[72] and single-hop on-off keying orthogonal signaling tech-nique [73] inspired by sensor networks distributed solutionssuch as those proposed in the context of relay selection [1074] should be adjusted so as to satisfy the needs of networksthat implement BF

An overall requirement for the efficient implementationof BF techniques is CSI As the majority of studies in the fieldexamine schemes where perfect CSI is assumed there is a lotof research to be done for practical schemes thatwill be robustwhen CSI is partially available or impairments such as delayand channel estimation uncertainties affect its exploitationMoreover distributed solutions must be developed that willmake use of local CSI knowledge as is the case in [36]and formulate accordingly the BF matrices based on partialstate informationThese limited CSI cases could be extendedto other network topologies such as broadcast channelsand full-duplex relaying schemes which are discussed sub-sequently The exploitation of CSI is also studied in [75]which addresses the optimization problem for a three-hopwireless network where collaborative AF relaying terminalsappear at both the transmitter and receiver ends to form avirtual MIMO system This work is a step towards extendingprevious published results which considered collaborative-relay beamforming (CRBF) only on one side giving rise to adual-hop communications system

Moreover recently there has been an increased interestin full-duplex relaying Novel BF techniques should benefitfrom the increased spectral efficiency of this relaying schemeBF algorithms should consider the loop interference amongthe receive and transmit antennas of the relay and findways to mitigate it appropriately forming the precodingmatrix at the source and the BF matrix at the relay Furtherschemes based on half-duplex relays but aiming at recoveringthe half-duplex loss are two-way and successive relayingIn networks where two-way relaying is applied to improvespectral efficiency network coding approaches have startedto receive significant contributions [52 54 58] but there isenough space for additional work in this area For successiverelaying topologies only [71] has proposedBF techniques andthere is increased interest in this field for further researchas the half-duplex loss can be recovered Successive relayingnetworks perform concurrent transmissions by the sourceand one transmitting relay As a result interrelay interferencearises and the BF matrix at the relay could be structured insuch a way tominimize IRI while achieving the performancetarget at the RD link Likewise the source precoding matrixshould aim at increasing the SINR at the receiving relay thusoffering increased protection to the IRI from the transmittingrelay

Another field that has not been sufficiently researcheduntil now is the BF designs for cognitive relay networkswhere only few works have considered such topologies In[76] various relay BF algorithms are proposed in a networkwhere primary and secondary users coexist BF aims atinterference minimization to the primary users and ratemaximization for the secondary users through iterative algo-rithms Also in [77] the authors propose cognitive MIMOrelay selection to maximize the capacity of the secondaryuser and by employing BF the interference to the primaryuser is minimized As the exploitation of spatial resourcesis at the heart of BF an adaptation of such a technique fornetworks consisting of primary and secondary users wouldprovide additional gains in spectral efficiency Moreover acombination of game theory and BF matrix formulation inorder to achieve a target spectral efficiency while keeping theinterference of the secondary users towards the primary usersat low levels is an interesting research approach

Since BF aims at the minimization of undesired recep-tions in order to minimize interference it can offer improvedsecurity at the physical layer A limited number of works haveproposed algorithms in this field In [78] a topologywhere anuntrusted AFMIMO relay that may try to decode the sourcersquosmessages is studied Two alternative solutions are developedfirst the relay is treated as an eavesdropper and does not assistthe source-destination communication while in the secondBF matrices at the source and the relay are jointly designedin order to increase the secrecy rate Moreover in [79] atwo-way relay network in the presence of an eavesdropperis studied and through various BF schemes the leakagesare avoided and the secrecy sum rate of the two sources isincreased

Finally regarding the formulation of precoding andBF matrices other metrics such as power consumptionshould be considered This is especially important as relays


may be battery-operated and the BF matrices they willuse must achieve increased energy efficiency The articlein [80] presents a cluster of distributed relays which forma virtual multiple-input-single-output (MISO) system Theoptimal number of relays that should participate in thecommunication in order to satisfy an outage threshold interms of energy efficiency is investigated Results indicatethat cooperative BF outperforms direct communication inenergy and spectral efficiency

6 ConclusionsIn this paper various works in the field of beamforming withmultiple-input multiple-output relays have been elaboratedas they constitute an utmost promising technique for reduc-ing interference levels and enhancing system capacity of nextgeneration mobile broadband systems Moreover aiming tooutline the importance of BF forMIMO relay networks whileproviding an overall perspective on the area this surveyincludes papers that constitute the state of the art in thisfield In order to facilitate the design and optimization of BFalgorithms various challenges that should be explicitly con-sidered were presented More specifically important designparameters such as the performance criteria and the powerconstraints were presented and classified Also a literaturereview regarding issues such as computational complexityand channel state information acquisition and feedback aswell as antenna correlation was provided Furthermore thearticles included in the survey were categorized based ontheir network topology Firstly articles on single-user com-munications were discussed and were further categorizedfor cases of single and multiple relaying as well as relayselection In continuity multiuser topologies that studied therelay broadcast channel and two-way communications werepresented

Recent research on BFMIMO relays has made significantsteps but unfortunately more research and developmentwork is necessary towards channel impairments synchro-nization and cognitive aspects To this end this paperhighlighted significant benefits regarding the formulationof precoding and BF matrices interference mitigation tech-niques and relay selection methods Finally a discussion wasgiven on the paperrsquos findings and on the open issues whichconstitute interesting research directions in the field of BFwith MIMO relays

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[2] A Goldsmith S A Jafar N Jindal and S Vishwanath ldquoCapac-ity limits of MIMO channelsrdquo IEEE Journal on Selected Areas inCommunications vol 21 no 5 pp 684ndash702 2003

[3] D Gesbert M Kountouris R W Heath Jr C-B Chae and TSalzer ldquoShifting the MIMO paradigmrdquo IEEE Signal ProcessingMagazine vol 24 no 5 pp 36ndash46 2007

[4] D Gesbert S Hanly H Huang S Shamai Shitz O SimeoneandW Yu ldquoMulti-cellMIMO cooperative networks a new lookat interferencerdquo IEEE Journal on Selected Areas in Communica-tions vol 28 no 9 pp 1380ndash1408 2010

[5] T M Cover and A A E Gamal ldquoCapacity theorems for therelay channelrdquo IEEE Transactions on Information Theory vol25 no 5 pp 572ndash584 1979

[6] J N Laneman D N C Tse and G W Wornell ldquoCooperativediversity in wireless networks efficient protocols and outagebehaviorrdquo IEEE Transactions on InformationTheory vol 50 no12 pp 3062ndash3080 2004

[7] L Sanguinetti A A D rsquoAmico and R Yue ldquoA tutorial onthe optimization of amplify-and-forwardMIMO relay systemsrdquoIEEE Journal on Selected Areas in Communications vol 30 no8 pp 1331ndash1346 2012

[8] C La Palombara V Tralli B M Masini and A ContildquoRelay-assisted diversity communicationsrdquo IEEE Transactionson Vehicular Technology vol 62 no 1 pp 415ndash421 2013

[9] A Bletsas H Shin and M Z Win ldquoCooperative commu-nications with outage-optimal opportunistic relayingrdquo IEEETransactions on Wireless Communications vol 6 no 9 pp3450ndash3460 2007

[10] A Bletsas A Khisti D P Reed and A Lippman ldquoA simplecooperative diversity method based on network path selectionrdquoIEEE Journal on Selected Areas in Communications vol 24 no3 pp 659ndash672 2006

[11] A Ikhlef D S Michalopoulos and R Schober ldquoMax-max relayselection for relays with buffersrdquo IEEE Transactions on WirelessCommunications vol 11 no 3 pp 1124ndash1135 2012

[12] N Nomikos D Vouyioukas T Charalambous I Krikidis DN Skoutas andM Johansson ldquoCapacity improvement throughbuffer-aided successive opportunistic relayingrdquo in Proceedingsof the IEEE Wireless Vitae Conference June 2013

[13] N Nomikos T Charalambous I Krikidis D N Skoutas DVouyioukas andM Johansson ldquoBuffer-aided successive oppor-tunistic relaying with inter-relay interference cancellationrdquo inProceedings of the IEEE International Symposium on PersonalIndoor and Mobile Radio Communication September 2013

[14] P Balaban and J Salz ldquoDual diversity combining and equal-ization in digital cellular mobile radiordquo IEEE Transactions onVehicular Technology vol 40 no 2 pp 342ndash354 1991

[15] F Rashid-Farrokhi K J R Liu and L Tassiulas ldquoTransmitbeamforming and power control for cellular wireless systemsrdquoIEEE Journal on Selected Areas in Communications vol 16 no8 pp 1437ndash1450 1998

[16] S Bellofiore C A Balanis J Foutz and A S Spanias ldquoSmart-antenna systems for mobile communication networks Part 1overview and antenna designrdquo IEEE Antennas and PropagationMagazine vol 44 no 3 pp 145ndash154 2002

[17] S Bellofiore J Foutz C A Balanis and A S Spanias ldquoSmart-antenna system for mobile communication networks Part 2beamforming and network throughputrdquo IEEE Antennas andPropagation Magazine vol 44 no 4 pp 106ndash114 2002

[18] S Berger M Kuhn A Wittneben T Unger and A KleinldquoRecent advances in amplify-and-forward two-hop relayingrdquoIEEE Communications Magazine vol 47 no 7 pp 50ndash56 2009

[19] Y Hua ldquoAn overview of beamforming and power allocation forMIMO relaysrdquo in Proceedings of the IEEE Military Communica-tions Conference pp 375ndash380 October 2010


[20] D P Palomar J M Cioffi and M A Lagunas ldquoJoint Tx-Rx beamforming design for multicarrier MIMO channels aunified framework for convex optimizationrdquo IEEE Transactionson Signal Processing vol 51 no 9 pp 2381ndash2401 2003

[21] A S Behbahani RMerched andAM Eltawil ldquoOptimizationsof aMIMO relay networkrdquo IEEE Transactions on Signal Process-ing vol 56 no 10 pp 5062ndash5073 2008

[22] P Wu and R Schober ldquoCooperative beamforming for single-carrier frequency-domain equalization systems with multiplerelaysrdquo IEEE Transactions on Wireless Communications vol 11no 6 pp 2276ndash2286 2012

[23] Y Rong and F Gao ldquoOptimal beamforming for non-regen-erative MIMO relays with direct linkrdquo IEEE CommunicationsLetters vol 13 no 12 pp 926ndash928 2009

[24] F-S Tseng M-Y Chang and W-R Wu ldquoJoint MMSEtransceiver design in amplify-and-forward mimo relay systemswith tomlinson-harashima source precodingrdquo in Proceedings ofthe IEEE 21st International Symposium on Personal Indoor andMobile Radio Communications pp 443ndash448 September 2010

[25] Y Rong ldquoOptimal joint source and relay beamforming forMIMO relays with direct linkrdquo IEEE Communications Lettersvol 14 no 5 pp 390ndash392 2010

[26] C Xing S Ma M Xia and Y C Wu ldquoCooperative beamform-ing for dual-hop amplify-and-forward multi-antenna relayingcellular networksrdquo Elsevier Signal Processing vol 92 no 11 pp2689ndash2699 2012

[27] R Wang M Tao and Y Huang ldquoLinear precoding designs foramplify-and-forward multiuser two-way relay systemsrdquo IEEETransactions on Wireless Communications vol 11 no 12 pp4457ndash4469 2012

[28] J Joung and A H Sayed ldquoMultiuser two-way amplify-and-forward relay processing and power control methods for beam-forming systemsrdquo IEEE Transactions on Signal Processing vol58 no 3 pp 1833ndash1846 2010

[29] Y Rong ldquoJoint source and relay optimization for two-wayMIMO multi-relay networksrdquo IEEE Communications Lettersvol 15 no 12 pp 1329ndash1331 2011

[30] C Chen L Bai B Wu and J Choi ldquoRelay selection andbeamforming for cooperative bi-directional transmissions withphysical layer network codingrdquo IET Communications vol 5 no14 pp 2059ndash2067 2011

[31] Z B Wang L J Xiang L H Zheng and H Ding ldquoMSMSE-based optimal beamforming design and simplification on AFMIMO two-way relay channelsrdquo Springer Journal of CentralSouthern University vol 19 pp 465ndash470 2012

[32] Z Hui Y Longxiang and Z Hongbo ldquoPrecoding and decodingdesign for two-way MIMO AF multiple-relay systemrdquo Journalof Electronics vol 29 no 3 pp 177ndash189 2012

[33] Y-W Liang and R Schober ldquoCooperative amplify-and-forwardbeamforming with multi-antenna source and relaysrdquo in Pro-ceedings of the 3rd IEEE International Workshop on Computa-tional Advances in Multi-Sensor Adaptive Processing pp 277ndash280 December 2009

[34] B Khoshnevis W Yu and R Adve ldquoGrassmannian beamform-ing for MIMO amplify-and-forward relayingrdquo IEEE Journal onSelected Areas in Communications vol 26 no 8 pp 1397ndash14072008

[35] Y Zhao R Adve and T J Lim ldquoBeamforming with lim-ited feedback in amplify-and-forward cooperative networksmdash[transactions letters]rdquo IEEE Transactions on Wireless Commu-nications vol 7 no 12 pp 5145ndash5149 2008

[36] B K Chalise L Vandendorpe Y D Zhang and M G AminldquoLocal CSI based selection beamforming for amplify-and-forward MIMO relay networksrdquo IEEE Transactions on SignalProcessing vol 60 no 5 pp 2433ndash2446 2012

[37] R H Y Louie Y Li H A Suraweera and B Vucetic ldquoPerfor-mance analysis of beamforming in twohop amplify and forwardrelay networks with antenna correlationrdquo IEEE Transactions onWireless Communications vol 8 no 6 pp 3132ndash3141 2009

[38] Z Zhou and B Vucetic ldquoAn optimized cooperative beamform-ing scheme in MIMO relay broadcast channelsrdquo in Proceedingsof the IEEE Global Telecommunications Conference pp 1ndash6December 2009

[39] Z Zhou and B Vucetic ldquoA cooperative beamforming scheme inmimo relay broadcast channelsrdquo IEEE Transactions on WirelessCommunications vol 10 no 3 pp 940ndash947 2011

[40] B Zhang Z He K Niu and L Zhang ldquoRobust linearbeamforming for MIMO relay broadcast channel with limitedfeedbackrdquo IEEE Signal Processing Letters vol 17 no 2 pp 209ndash212 2010

[41] E Yilmaz R Zakhour D Gesbert and R Knopp ldquoMulti-pairtwo-way relay channel with multiple antenna relay stationrdquo inProceedings of the IEEE International Conference on Communi-cations pp 1ndash5 May 2010

[42] A El-Keyi and B Champagne ldquoAdaptive linearly constrainedminimum variance beamforming for multiuser cooperativerelaying using the kalman filterrdquo IEEE Transactions on WirelessCommunications vol 9 no 2 pp 641ndash651 2010

[43] Y Liu and A P Petropulu ldquoCooperative beamforming inmulti-source multi-destination relay systems with SINR constraintsrdquoin Proceedings of the IEEE International Conference onAcousticsSpeech and Signal Processing pp 2870ndash2873 March 2010

[44] Y Fan and J Thompson ldquoMIMO configurations for relaychannels theory and practicerdquo IEEE Transactions on WirelessCommunications vol 6 no 5 pp 1774ndash1786 2007

[45] X Tang and Y Hua ldquoOptimal design of non-regenerativeMIMO wireless relaysrdquo IEEE Transactions on Wireless Commu-nications vol 6 no 4 pp 1398ndash1407 2007

[46] E Baccarelli M Biagi C Pelizzoni and N CordeschildquoMaximum-rate node selection for power-limitedmultiantennarelay backbonesrdquo IEEE Transactions on Mobile Computing vol8 no 6 pp 807ndash820 2009

[47] M A Torabi and J-F Frigon ldquoSemi-orthogonal relay selectionand beamforming for amplify-and-forward MIMO relay chan-nelsrdquo in Proceedings of the IEEE Wireless Communications andNetworking Conference pp 48ndash53 April 2008

[48] G Okeke W A Krzymien and Y Jing ldquoBeamforming in non-regenerative MIMO broadcast relay networksrdquo IEEE Transac-tions on Signal Processing vol 60 no 12 pp 6641ndash6654 2012

[49] H Wan W Chen and X Wang ldquoJoint source and relay designfor MIMO relaying broadcast channelsrdquo IEEE CommunicationsLetters vol 17 no 2 pp 345ndash348 2013

[50] K T Truong and R W Heath ldquoJoint transmit precoding forthe relay interference broadcast channelrdquo IEEE Transactions onVehicular Technology vol 62 no 3 pp 1201ndash1215 2013

[51] K Lee S-H Park J-S Kim and I Lee ldquoDegrees of freedomon mimo multi-link two-way relay channelsrdquo in Proceedingsof the 53rd IEEE Global Communications Conference pp 1ndash5December 2010

[52] Z Ding I Krikidis J Thompson and K K Leung ldquoPhysicallayer network coding and precoding for the two-way relay chan-nel in cellular systemsrdquo IEEE Transactions on Signal Processingvol 59 no 2 pp 696ndash712 2011


[53] N Lee C-B Chae O Simeone and J Kang ldquoOn the optimiza-tion of two-wayAFMIMOrelay channel with beamformingrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers pp 918ndash922 November 2010

[54] R Zhang Y-C Liang C C Chai and S Cui ldquoOptimalbeamforming for two-way multi-antenna relay channel withanalogue network codingrdquo IEEE Journal on Selected Areas inCommunications vol 27 no 5 pp 699ndash712 2009

[55] S Mohajer S N Diggavi and D N C Tse ldquoApproximatecapacity of a class of gaussian relay-interference networksrdquo inProceedings of the IEEE International Symposiumon InformationTheory pp 31ndash35 July 2009

[56] Y Shi J Zhang and K B Letaief ldquoCoordinated relay beam-forming for amplify-and-forward two-hop interference net-worksrdquo in Proceedings of the IEEE Global CommunicationsConference pp 2408ndash2413 December 2012

[57] K T Truong and R W Heath Jr ldquoRelay beamforming usinginterference pricing for the two-hop interference channelrdquo inProceedings of the 54th Annual IEEE Global TelecommunicationsConference pp 1ndash5 December 2011

[58] T M Kim B Bandemer and A Paulraj ldquoBeamforming fornetwork-coded MIMO two-way relayingrdquo in Proceedings of the44th Asilomar Conference on Signals Systems and Computerspp 647ndash652 November 2010

[59] G Ye and RWang ldquoTransceiver designs for multiuser two-wayrelay systemrdquo in Proceedings of the International Workshop onInformation and Electronics Engineering pp 4186ndash4191 March2012

[60] S Borade L Zheng and R Gallager ldquoAmplify-and-forward inwireless relay networks rate diversity and network sizerdquo IEEETransactions on Information Theory vol 53 no 10 pp 3302ndash3318 2007

[61] Y-W Liang and R Schober ldquoCooperative amplify-and-forwardbeamforming with multiple multi-antenna relaysrdquo IEEE Trans-actions on Communications vol 59 no 9 pp 2605ndash2615 2011

[62] Z Bai Y Xu D Yuan and K Kwak ldquoPerformance analysisof cooperative MIMO system with relay selection and powerallocationrdquo in Proceedings of the IEEE International Conferenceon Communications pp 1ndash5 May 2010

[63] C-K Wen K-K Wong and J-C Chen ldquoPrecoding designin MIMO multiple-access cellular relay systems with partialCSIrdquo in Proceedings of the IEEE Wireless Communications andNetworking Conference pp 1ndash6 April 2010

[64] F Gao T Cuiy B Jiangz and X Gaoz ldquoOn communicationprotocol and beamforming design for amplify-and-forward N-Way relay networksrdquo inProceedings of the 3rd IEEE InternationalWorkshop on Computational Advances inMulti-Sensor AdaptiveProcessing pp 109ndash112 December 2009

[65] B Xie D Munoz and H Minn ldquoA reduced overhead OFDMrelay system with clusterwise TMRC beamformingrdquo IEEECommunications Letters vol 16 no 12 pp 1913ndash1916 2012

[66] SW Peters and RW Heath ldquoNonregenerativeMIMO relayingwith optimal transmit antenna selectionrdquo IEEE Signal ProcessingLetters vol 15 pp 421ndash424 2008

[67] H-N Cho J-W Lee A-Y Kim and Y-H Lee ldquoCooperativeinterference mitigation with partial CSI in multi-user dual-hopMISO relay channelsrdquo in Proceedings of the 20th IEEE PersonalIndoor andMobile Radio Communications Symposium pp 1211ndash1215 September 2009

[68] H A Suraweera H K Garg and A Nallanathan ldquoBeam-forming in dual-hop fixed gain relay systems with antenna

correlationrdquo in Proceedings of the IEEE International Conferenceon Communications pp 1ndash5 May 2010

[69] N S Ferdinand and N Rajatheva ldquoUnified performance analy-sis of two-hop amplify-and-forward relay systems with antennacorrelationrdquo IEEE Transactions on Wireless Communicationsvol 10 no 9 pp 3002ndash3011 2011

[70] T Riihonen A Balakrishnan K Haneda S Wyne S Wernerand R Wichman ldquoOptimal eigenbeamforming for suppressingself-interference in full-duplex MIMO relaysrdquo in Proceedingsof the 45th Annual Conference on Information Sciences andSystems pp 1ndash6 March 2011

[71] S M Kim and M Bengtsson ldquoVirtual full-duplex buffer-aidedrelayingmdashrelay selection and beamformingrdquo in Proceedingsof the IEEE International Symposium on Personal Indoor andMobile Radio Communication September 2013

[72] M K Maggs S G OrsquoKeefe and D V Thiel ldquoConsensus clocksynchronization for wireless sensor networksrdquo IEEE SensorsJournal vol 12 no 6 pp 2269ndash2277 2012

[73] A G Kanatas A Kalis and G P Efthymoglou ldquoA single hoparchitecture exploiting cooperative beamforming for wirelesssensor networksrdquo Physical Communication vol 4 no 3 pp237ndash243 2011

[74] N Nomikos P Makris D Vouyioukas D N Skoutas and CSkianis ldquoDistributed joint relay-pair selection for buffer-aidedsuccessive opportunistic relayingrdquo in Proceedings of the IEEEInternational Workshop on Computer- Aided Modeling Analysisof Design of Communication Links and Networks September2013

[75] L Chen K-K Wong H Chen J Liu and G Zheng ldquoOptimiz-ing transmitter-receiver collaborative-relay beamforming withperfect CSIrdquo IEEE Communications Letters vol 15 no 3 pp314ndash316 2011

[76] T Luan F Gao X D Zhang J C F Li and M LeildquoRate maximization and beamforming design for relay-aidedmultiuser cognitive networksrdquo IEEE Transactions on VehicularTechnology vol 61 no 4 pp 1940ndash1945 2012

[77] Q Li Q Zhang R Feng L Luo and J Qin ldquoOptimal relayselection and beamforming in MIMO cognitive multi-relaynetworksrdquo IEEE Communications Letters vol 17 no 6 pp 1188ndash1191 2013

[78] C Jeong I-M Kim and D I Kim ldquoJoint secure beamformingdesign at the source and the relay for an amplify-and-forwardMIMO untrusted relay systemrdquo IEEE Transactions on SignalProcessing vol 60 no 1 pp 310ndash325 2012

[79] HMWang YQinye andXG Xia ldquoDistributed beamformingfor physical-layer security of two-way relay networksrdquo IEEETransactions on Signal Processing vol 60 no 7 pp 3532ndash35452012

[80] G Lim and L J Cimini ldquoEnergy-efficient cooperative beam-forming in clustered wireless networksrdquo IEEE Transactions onWireless Communications vol 12 no 3 pp 1376ndash1385 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



networks where MIMO nodes cooperate to exploit intercellinterference Cooperative techniques were introduced suchas base station (BS) cooperation and schemes that employedrelays

In general the literature on cooperative relaying hasseen a tremendous rise in contributions in recent yearsThrough cooperative relaying coverage extension increasedreliability and diversity can be harvested The first studyof the capacity of the relay channel was conducted in [5]In addition various relaying strategies such as amplify-and-forward (AF) decode-and-forward (DF) and compress-and-forward (CF) were investigated in the seminal work of[6] Optimization efforts for AF MIMO relay systems aredepicted in [7] providing an overview of the fundamentalresults and practical implementation issues in designing AFMIMO relay systems Relays are attractive as they improvethree critical parameters of wireless networks By allowingmultihop transmission transmitters are brought closer tothe receiver thus reducing the path loss attenuation of thesignal In addition shadowing can be overcome by installingrelay nodes in places where obstacles affect single-hopcommunications Furthermoremultipath fading ismitigatedthrough the provision of independent propagation pathsFor example even when one relay is employed the signalpropagates through a two-hop path and also through thedirect path between the source and the destination Alsocooperative relaying offers increased diversity [8] even whencooperative relays choose not to transmit but rather chooseto cooperatively listen [9] thus improving the performancein terms of outage and error probability Additionally whenmultiple relays are available selecting the best one accordingto instantaneous CSI was proven to be outage optimal in[10] compared to the case where multirelay transmissions areperformed More recently buffer-aided relays were examined[11] and relay selection schemes that aim at improved spectralefficiency were presented in [12 13]

The third technique that is examined in this surveyis beamforming This technique uses BF matrices at thetransmitters and the receivers which form the antennasrsquobeam patterns in such a way as to optimize a specific designcriterion such as mean square error (MSE) or signal-to-noise ratio (SNR) The implementation of BF requires theuse of digital signal processors (DSPs) to shape accordinglythe beam patterns that are emitted by the antennas In thecontext of single-hop mobile communications the articlein [14] presented space-time processing to combat cochan-nel interference (CCI) and intersymbol interference (ISI)Another early work was [15] which proposed joint BF andpower control in order to minimize the total transmittedpower in the network while satisfying a signal-to-noise-plus-interference ratio (SINR) threshold at the receivers Anoverview of smart antennas is given in [16] where switchedbeam adaptive beam and spatial division multiple-access(SDMA) are discussed Moreover digital signal processingalgorithms such as direction-of-arrival (DoA) and adaptiveBF were presented in [17]

This survey provides a detailed presentation of works thatstudy BF techniques in networks where relays with MIMOcapabilities are deployed More specifically the increased

degrees of freedom (DoF) in exploiting the spatial resourcesare the main topic of the presented works This area hasseen a significant increase in contributions recently but asurvey depicting its importance and categorizing these workshas not been published except from a few articles whichprovide quick overviews of some techniques In [18] theauthors present BF schemes for scenarios where MIMOAF relays assist the communication in single and multiusernetworks either through one-way or two-way relaying Inanother article [19] relay classification is performed andBF techniques are presented for various combinations ofregenerative versus nonregenerative full-duplex versus half-duplex and one-way versus two-way The author discussesthe formulation of transmit-receive BF matrices amplifica-tion matrices for nonregenerative relays self-interference forfull-duplex relays and successive interference cancellation forthe two-way case Here descriptions and categorizations forvarious network topologies and communication strategies aregiven More specifically articles that investigate BF schemesfor single and multiuser communications are presented andtheirmain contributions are highlighted Also a classificationbased on various relaying topologies such as single andmultiple relaying as well as opportunistic relay selection isprovided and the corresponding BF schemes are discussedAs the included works consider channel models and fadingdistributions that are examined in depth in the context ofMIMO relaying there is no channel modeling literaturereview in the context of this survey as emphasis is given onBF schemes and their various implementations

This survey is organized by taking into consideration thedifferent network topologies where BF techniques can beemployed and its structure is as follows In Section 2 thechallenges of BF implementation in MIMO relay networksare given More specifically the design parameters thatinclude MSE minimization and SNR maximization undervarious power constraints are presented Also overhead dueto channel estimation and feedback is discussed Anotherchallenge that is often observed in MIMO networks isantenna correlation thus its effect on the design of BF matri-ces is herein presented In Section 3 BF schemes for single-user communications are presented Various different casesare presented such as single and multiple relay topologieswith and without relay selection In Section 4 networkswhere multiuser communications take place are investigatedand scenarios where single or multiple relays assist thecommunication for one or two-way communications aredescribed Discussion and open issues are the subject ofSection 5 while conclusions are given in Section 6

Notation In this work (sdot)119879 (sdot)119867 (sdot)lowast | sdot | sdot 2 and sdot

119865

denote transpose Hermitian transpose complex conjuga-tion the determinant of a complex number the Euclideannorm and the Frobenius norm respectively Upper (lower)boldface letters will be used for matrices (vectors)

2 Challenges

To better illustrate the challenges that are presented in thissection the system model of [20] is adopted and extended




119878119872119877 and119872



the destination is

y119896= H119877119863119896

FH119878119877119896

s119896+H119877119863119896

Fn119877119896+ n119863119896

1 le 119896 le 119873(1)

where H119877119863119896


119896is the



119877119896 n119863119896



s119896= B119896x119896=

119871119896

sum119894=1

b119896119894x119896119894 (2)



119896established







y119896= A119867119896y119896 (3)







119896≜ (x119896minus x119896) where x


119896


minE119896(B119896 FA119896) ≜ minΕ [(x

119896minus x119896) (x119896minus x119896)119867] (4)



119896


minE1119896(B1119896B2119896 FA1119896A2119896)

+minE2119896(B1119896B2119896 FA1119896A2119896)



(5)



SINR119896119894=

1

MSE119896119894

minus 1 (6)


where MSE119896119894


119896



Z = H+ = (H119867H)minus1

H119867 (7)


119868 = minus log |E| (8)



119889(NC)min = min (119886

1 1198862) sdot 119889min (9)






1003817100381710038171003817FH119878119877119896B11989610038171003817100381710038172

2+ 1205902

119877119896F2119865le 1198752119896 (10)


100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 1198752119877119895119896

(11)


119873119877

sum119895=1

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 1198752119896 (12)



1198962



1003817100381710038171003817B11989610038171003817100381710038172

2+

119873119877

sum119895=1

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 119875119896 (13)




















2(119872119878119872119877)






2(119898) where 119898 is the


11990311198721198891198721199032119872119889) ge

1198721199041198721199031+ 1198721199041198721199032 where119872

119904119872119889and119872










[24]




[54]





source



[53]




[58]






2(119873119888)1198731198731198882 + 1198732119873

119888








[29]




[61]





Table 1 Continued















[27]

119899BS = (119873119870 + 1)2(119870 + 2)

05(2119873119870 + 1198702 +

2119870 + 4) log(1120576)119899RS =





[42]


1198961198982119896)2









[56]





Table 1 Continued


strategy




[57]

































































































References






















































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119878119872119877 and119872



the destination is

y119896= H119877119863119896

FH119878119877119896

s119896+H119877119863119896

Fn119877119896+ n119863119896

1 le 119896 le 119873(1)

where H119877119863119896


119896is the



119877119896 n119863119896



s119896= B119896x119896=

119871119896

sum119894=1

b119896119894x119896119894 (2)



119896established







y119896= A119867119896y119896 (3)







119896≜ (x119896minus x119896) where x


119896


minE119896(B119896 FA119896) ≜ minΕ [(x

119896minus x119896) (x119896minus x119896)119867] (4)



119896


minE1119896(B1119896B2119896 FA1119896A2119896)

+minE2119896(B1119896B2119896 FA1119896A2119896)



(5)



SINR119896119894=

1

MSE119896119894

minus 1 (6)


where MSE119896119894


119896



Z = H+ = (H119867H)minus1

H119867 (7)


119868 = minus log |E| (8)



119889(NC)min = min (119886

1 1198862) sdot 119889min (9)






1003817100381710038171003817FH119878119877119896B11989610038171003817100381710038172

2+ 1205902

119877119896F2119865le 1198752119896 (10)


100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 1198752119877119895119896

(11)


119873119877

sum119895=1

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 1198752119896 (12)



1198962



1003817100381710038171003817B11989610038171003817100381710038172

2+

119873119877

sum119895=1

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 119875119896 (13)




















2(119872119878119872119877)






2(119898) where 119898 is the


11990311198721198891198721199032119872119889) ge

1198721199041198721199031+ 1198721199041198721199032 where119872

119904119872119889and119872










[24]




[54]





source



[53]




[58]






2(119873119888)1198731198731198882 + 1198732119873

119888








[29]




[61]





Table 1 Continued















[27]

119899BS = (119873119870 + 1)2(119870 + 2)

05(2119873119870 + 1198702 +

2119870 + 4) log(1120576)119899RS =





[42]


1198961198982119896)2









[56]





Table 1 Continued


strategy




[57]

































































































References






















































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










where MSE119896119894


119896



Z = H+ = (H119867H)minus1

H119867 (7)


119868 = minus log |E| (8)



119889(NC)min = min (119886

1 1198862) sdot 119889min (9)






1003817100381710038171003817FH119878119877119896B11989610038171003817100381710038172

2+ 1205902

119877119896F2119865le 1198752119896 (10)


100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 1198752119877119895119896

(11)


119873119877

sum119895=1

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 1198752119896 (12)



1198962



1003817100381710038171003817B11989610038171003817100381710038172

2+

119873119877

sum119895=1

100381710038171003817100381710038171003817FH119878119877119895 119896

B119896

100381710038171003817100381710038171003817

2

2

+ 1205902

119877119895 119896F2119865le 119875119896 (13)




















2(119872119878119872119877)






2(119898) where 119898 is the


11990311198721198891198721199032119872119889) ge

1198721199041198721199031+ 1198721199041198721199032 where119872

119904119872119889and119872










[24]




[54]





source



[53]




[58]






2(119873119888)1198731198731198882 + 1198732119873

119888








[29]




[61]





Table 1 Continued















[27]

119899BS = (119873119870 + 1)2(119870 + 2)

05(2119873119870 + 1198702 +

2119870 + 4) log(1120576)119899RS =





[42]


1198961198982119896)2









[56]





Table 1 Continued


strategy




[57]

































































































References






















































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























2(119872119878119872119877)






2(119898) where 119898 is the


11990311198721198891198721199032119872119889) ge

1198721199041198721199031+ 1198721199041198721199032 where119872

119904119872119889and119872










[24]




[54]





source



[53]




[58]






2(119873119888)1198731198731198882 + 1198732119873

119888








[29]




[61]





Table 1 Continued















[27]

119899BS = (119873119870 + 1)2(119870 + 2)

05(2119873119870 + 1198702 +

2119870 + 4) log(1120576)119899RS =





[42]


1198961198982119896)2









[56]





Table 1 Continued


strategy




[57]

































































































References






















































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













[24]




[54]





source



[53]




[58]






2(119873119888)1198731198731198882 + 1198732119873

119888








[29]




[61]





Table 1 Continued















[27]

119899BS = (119873119870 + 1)2(119870 + 2)

05(2119873119870 + 1198702 +

2119870 + 4) log(1120576)119899RS =





[42]


1198961198982119896)2









[56]





Table 1 Continued


strategy




[57]

































































































References






















































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 1 Continued















[27]

119899BS = (119873119870 + 1)2(119870 + 2)

05(2119873119870 + 1198702 +

2119870 + 4) log(1120576)119899RS =





[42]


1198961198982119896)2









[56]





Table 1 Continued


strategy




[57]

































































































References






















































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 1 Continued


strategy




[57]

































































































References






















































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































































































References






















































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Review Article A Survey on Beamforming Techniques for ... · networks where MIMO nodes cooperate to...

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