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Resource Allocation and Interference MitigationTechniques for Cooperative Multi-Antenna and

Spread Spectrum Wireless NetworksRodrigo C. de Lamare and Patrick J. Clarke

Communications Research GroupDepartment of Electronics, University of York, York Y010 5DD, United Kingdom

Emails: rcdl500@ohm.york.ac.uk

Abstract—This chapter presents joint interference suppressionand power allocation algorithms for DS-CDMA and MIMO net-works with multiple hops and amplify-and-forward and decode-and-forward (DF) protocols. A scheme for joint allocation ofpower levels across the relays and linear interference suppressionis proposed. We also consider another strategy for joint interfer-ence suppression and relay selection that maximizes the diversityavailable in the system. Simulations show that the proposedcross-layer optimization algorithms obtain significant gains in capacityand performance over existing schemes.

I. I NTRODUCTION

Multiple-antenna wireless communication systems can ex-ploit the spatial diversity in wireless channels, mitigatingthe effects of fading and enhancing their performance andcapacity. Due to the size and cost of mobile terminals, it isconsidered impractical to equip them with multiple antennas.However, spatial diversity gains can be obtained when single-antenna terminals establish a distributed antenna array viacooperation [1]- [3]. The use of cooperative strategies canlead to several types of gains [4], [13], namely, pathloss,diversity and multiplexing gains. Pathloss gains allow a sig-nificant reduction in the transmitted power for an equivalentperformance, can increase the coverage [15] and enhance theinterference suppression capability [4], [13]. The diversitygains improve the performance of the wireless system withrespect to the probability of error because the transmissionof multiple copies of the signals reduce the probability thatthe message will not be received correctly. The multiplexinggains [14], which correspond to the additional number of bitsthat the system can transmit as compared to a single-antennalink, can be obtained when a designer can use relays to formindependent channels and increase the rate of communication.

Despite the many advantages in terms of gains as previ-ously outlined, cooperative communications also entail somedisadvantages such as signalling overheads [13], more com-putationally complex scheduling algorithms [4] and increasedlatency [16]. For this reason, it is important to weigh the prosand cons of cooperative techniques prior to their adoption andconsider the practical scenarios of interest [17]. Motivated bytheir performance and diversity gains, cooperative techniquesare now being considered for the next generation of mobilenetworks [12], [18], [19]. In cooperative systems, terminals

The work of the authors was supported by the University of York, YorkY010 5DD, United Kingdom.

or users relay signals to each other in order to propagateredundant copies of the same signals to the destination userorterminal. To this end, the designer must resort to a cooperationprotocol such as amplify-and-forward (AF) [3], decode-and-forward (DF) [3], [20] and compress-and-forward (CF) [21].

In order to obtain the benefits of cooperative techniques,designers must address a number of problems that are encoun-tered in cooperative wireless systems. These problems includephysical-layer strategies such as synchronization, interferencemitigation, and parameter estimation. However, designersalsohave to consider a number of associated problems that be-long to higher protocol layers and include the allocation ofresources such as power, relays and rate. These tasks presentan opportunity to perform cross-layer design and to obtain verysignificant gains in performance and capacity for cooperativewireless networks. This chapter is concerned with cross-layer design techniques for cooperative wireless networksandinvestigates the benefits of approaches that jointly mitigateinterference and perform resource allocation.

In this chapter, we will consider two types of schemes,namely, direct-sequence code-division multiple access (DS-CDMA) [7], [8] and multi-input multi-output (MIMO) [5], [6]systems. The former is of fundamental importance in wirelessad-hoc and sensor networks [4], whereas the latter is one of themain ingredients of future wireless cellular networks. Whenimplementing cooperative techniques in wireless systems,de-signers often consider the transmission technologies availableand their suitability to certain applications. Therefore,theconcept of distributed antenna arrays can be easily extendedto techniques such as MIMO [5], [6] and DS-CDMA systems[7], [8].

In the context of MIMO systems, one can obtain substantialmultiplexing [5], [6], [11] and diversity gains [9], [10] withthe deployment of multiple antennas at both ends of thewireless system. MIMO technology is poised to equip mostof the future wireless systems and can be incorporated inconjunction with other transmission systems. There are twobasic configurations which exploit the nature of the wirelesschannel: spatial multiplexing [11] and diversity [10]. Spatialmultiplexing relies on the concept of forming individual datastream between pais of transmit and receive antennas. Thecapacity gains of spatial multiplexing grow linearly with theminimum number of transmit and receive antennas [5], [6]and allow a MIMO system to obtain a considerable increasein data rates. Diversity configurations adopt space-time codes

2

[9], [10] to transmit data from the antennas at the transmitterand can obtain a lower probability of error.

DS-CDMA systems are a key multiple access technologyfor current and future wireless communication systems. Suchsystems rely on the idea of transmitting data with the aid ofunique signatures, which are also known as spreading codes.These signatures are responsible for spreading the informa-tion in frequency, and allow the system to have multipleusers on the same channel. The advantages of DS-CDMAinclude good performance in multi-path channels, flexibilityin the allocation of channels, increased capacity in burstyand fading environments and the ability to share bandwidthwith narrowband communication systems without deteriora-tion of either’s systems performance [7], [8]. Demodulatinga desired user in a DS-CDMA network requires processingthe received signal in order to mitigate different types ofinterference, namely, narrowband interference (NBI), multi-access interference (MAI), inter-symbol interference (ISI) andthe noise at the receiver. The major source of interference inmost CDMA systems is MAI, which arises due to the factthat users communicate through the same physical channelwith non-orthogonal signals.

The similarities between MIMO and CDMA systems in-clude their mathematically similar descriptions and theirfun-damental need for interference mitigation. Indeed, the datastreams of MIMO systems operating in a spatial multiplexingconfiguration are equivalent to the users of a DS-CDMAsystem. In order to separate data streams or users, a designermust resort to detection techniques [22], which are very similarwhen applied to either MIMO or DS-CDMA. The optimalmaximum likelihood (ML) detector is often too complex to beimplemented for systems with a large number of antennas. Forthis reason, designers often resort to suboptimal solutions thatan attractive trade-off between performance and complexity.These include the sphere decoder (SD) algorithms [23], lineardetectors [22], the successive interference cancellation(SIC)approach [11], the parallel interference cancellation (PIC)[22] and the decision feedback (DF) detectors [39], [69]are techniques that can offer an attractive trade-off betweenperformance and complexity. These detection algorithms canbe combined with cross-layer design techniques for enhancedinterference mitigation and improved overall performance. Inthis chapter, we are specifically interested in exploring theadvantages of linear detection with power allocation, datastream and relay selection.

A. Prior and Related Work

Prior work on cross-layer design for cooperative and multi-hop communications has considered the problem of resourceallocation [24], [25] in generic networks. These include powerand rate allocation strategies. Related work on cooperativemultiuser DS-CDMA networks has focused on the assessmentof the impact of multiple access interference (MAI) andintersymbol interference (ISI), the problem of partner selection[20], [26], the bit error ratio (BER) and outage performanceanalysis [27], and training-based joint power allocation andinterference mitigation strategies [28], [29]. Previous workshave also considered the problem of antenna selection, relayselection (RS) and diversity maximization, which are central

themes in the MIMO relaying literature [31]–[33]. However,current approaches are often limited to stationary, singlerelaysystems and channels which assume the direct path from thesource to the destination is negligible [32].

Most of these resource allocation and interference miti-gation strategies require a higher computational cost to im-plement the power allocation and a significant amount ofsignalling, decreasing the spectral efficiency of cooperativenetworks. This problem is central to ad-hoc and sensor net-works [30] that employ spread spectrum systems and requiremultiple hops to communicate with nodes that are far fromthe source node. This is also of paramount importance incooperative cellular networks.

B. Contributions

In this chapter, we present joint interference suppressionand power allocation algorithms for DS-CDMA and MIMOnetworks with multiple hops and AF and DF protocols. Ascheme that jointly considers the power allocation across therelays subject to group-based power constraints and the designof linear receivers for interference suppression is proposed.The idea of a group-based power allocation constraint isshown to yield close to optimal performance, while keepingthe signalling and complexity requirements low. A constrainedminimum mean-squared error (MMSE) design for the receivefilters and the power allocation vectors is developed along withan MMSE channel estimator for the cooperative system underconsideration. The linear MMSE receiver design is adopteddue to its mathematical tractability and good performance.However, the incorporation of more sophisticated detectionstrategies including interference cancellation with iterative de-coding [39] and advanced parameter estimation methods [49]is also possible. In order to solve the proposed optimizationproblem efficiently, a method to form an effective group ofusers and an alternating optimization strategy are presentedwith recursive alternating least squares (RALS) algorithms forestimating the parameters of the receiver, the power allocationand the channels. A joint relay selection and transmit diversityselection strategy for MIMO networks with linear receiversis also proposed which optimizes relay transmissions withminimal feedback requirements. Effectively a novel approachto 1-bit power allocation, two joint discrete optimizationfunctions are formed which are solved using discrete stochasticalgorithms.

C. Organisation of the Chapter

The chapter is organized as follows. Section II describescooperative DS-CDMA and MIMO system models with mul-tiple hops. Section III formulates the problem, details theconstrained MMSE design of the receive filters and the powerallocation vectors subject to a group-based power allocationconstraint, and describes an MMSE channel estimator. Anextension to cooperative MIMO systems is also presented anddiscrete optimization problems are formulated to jointly selectthe optimal relays and their transmit antennas. Section IVpresents an algorithm to form the group and the alternatingoptimization strategy along with RLS-type algorithms forestimating the parameters of the receiver, the power allocation

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and the channels. For the solution of the combinatorial prob-lems posed by the relay selection strategy, a pair of discretestochastic algorithms are introduced and their joint operationdetailed. Section V presents and discusses the simulationresults and Section VI draws the conclusions of this work.

II. SYSTEM AND DATA MODELS OFCOOPERATIVE

WIRELESSSYSTEMS

In this section, we consider system and data models ofcooperative wireless systems. The basic idea is to use alinear algebra approach to describe models of the cooperativesystems of interest. In particular, we focus on DS-CDMAand MIMO systems and we present a unified approach to thedescription of these systems.

A. Cooperative DS-CDMA System and Data Model

Fig. 1. (a) Uplink and (b) downlink of the cooperative DS-CDMA system.

Let us first consider a synchronous DS-CDMA networkwith multipath channels. The DS-CDMA system operates withQPSK modulation,K users,N chips per symbol andL asthe maximum number of propagation paths for each link.An outline of the system is depicted in (1). The system isequipped with AF and DF protocols that allow communicationin multiple hops usingnr fixed relays in a repetitive fashion.We assume that the source node or terminal transmits dataorganized in packets withP symbols, there is enough controldata to coordinate transmissions and cooperation, and thelinear receivers at the relay and destination terminals aresynchronized with their desired signals. The received signalsare filtered by a matched filter, sampled at chip rate andorganized intoM × 1 vectors rsd, rsrj and rrjd, whichdescribe the signal received from the source to the destination,the source to the relays, and the relays to the destination,

respectively,

rsd =K∑

k=1

aksdCkhsd,kbk + ηsd

+ nsd,

rsrj =

K∑

k=1

aksrjCkhsrj ,kbk + ηsrj

+ nsr1j ,

rrjd =

K∑

k=1

akrjdCkhrjd,kbk + ηrjd

+ nrjd,

j = 1, . . . , nr, i = 1, . . . , P

(1)

whereM = N + L− 1, P is the number of packet symbols,np = nr+1 is the number of transmission phases or hops, andnr is the number of relays. The vectorsnsd, nsrj andnrjd

are zero mean complex Gaussian vectors with varianceσ2

generated at the receivers of the destination and the relaysfromdifferent links, and the vectorsηsd, ηsrj

andηrjdrepresent the

intersymbol interference (ISI). The amplitudes of the source todestination, source to relay and relay to destination linksforuserk are denoted byaksd, aksrj and akrjd, respectively. The

quantitiesbk and bk represent the original and reconstructedsymbols by the AF or DF protocol at the relays, respectively.The M × L matrix Ck contains versions of the signaturesequences of each user shifted down by one position at eachcolumn as described by

Ck =

ck(1) 0

.... . . ck(1)

ck(N)...

0. . . ck(N)

, (2)

where ck =[ck(1), ck(2), . . . , ck(N)

]stands for the

signature sequence of userk, theL× 1 channel vectors fromsource to destination, source to relay, and relay to destinationarehsd,k, hsrj ,k, hrjd,k, respectively. By collecting the datavectors in (5) (including the links from relays to the destina-tion) into a J × 1 received vector at the destination, whereJ = (nr + 1)M , we obtain

rsdrr1d

...rrnrd

=

∑Kk=1 a

ksdCkhsd,kbk∑K

k=1 akr1d

Ckhr1d,kbr1dk

...∑Kk=1 a

krnrd

Ckhrnrd,kbrnrd

k

+ η + n

(3)

4

Rewriting the above signals in a compact form yields

r[i] =K∑

k=1

Bk[i]Ak[i] Ckhk[i]︸ ︷︷ ︸pk[i]

+η[i] + n[i]

=

K∑

k=1

Bk[i]Ak[i]Ckhk[i] + η[i] + n[i]

=

K∑

k=1

P k[i]Bk[i]ak[i] + η[i] + n[i],

(4)

where theJ × (nr + 1)L matrix Ck = diagCk . . .Ckcontains copies ofCk shifted down byM positions for eachgroup ofL columns and zeros elsewhere. TheQ × 1 vectorhk[i], whereQ = (nr + 1)L contains the channel gains ofthe links between the source, the relays and the destination,andpk[i] is the effective signature for userk. The (nr +1)×(nr+1) diagonal matrixBk[i] = diag(bk[i] b

r1dk [i] . . . brndk [i])

contains the symbols transmitted from the source to thedestination (bk[i]) and the nr symbols transmitted fromthe relays to the destination (br1dk [i] . . . brndk [i]) on themain diagonal, and theJ × J diagonal matrix Bk[i] =diag(bk[i]

⊗IM br1dk [i]

⊗IM . . . brndk [i]

⊗IM ), where

⊗

denotes the Kronecker product andIM is an identity matrixwith dimensionM . The (nr + 1)× 1 power allocation vectorak[i] = [aksd akr1d . . . a

krnrd

]T has the amplitudes of the links,the (nr + 1) × (nr + 1) diagonal matrixAk[i] is given byAk[i] = diagak[i], and theJ × J diagonal matrixAk[i] =[aksd

⊗IM akr1d

⊗IM . . . akrnrd

⊗IM ]T . The J × (nr + 1)

matrix P k has copies of the effective signaturepk[i] shifteddown byM positions for each column and zeros elsewhere.The J × 1 vectorη[i] represents the ISI terms and theJ × 1vectorn[i] has the noise components.

B. Cooperative MIMO System and Data Model

Let us now consider a synchronous MIMO system model,which has similarities with the DS-CDMA system model ofthe previous subsection. We consider a narrowband MIMOsystem with flat fading channels, QPSK modulation,K trans-mit antennas, andM receive antennas as illustrated in Fig.2. The cooperative MIMO network is equipped with DFprotocol that allows communication innp = 2 hops usingnr fixed relays in a repetitive fashion where a non-negligible,direct source to destination link exists during the first phase.We assume that the source node or terminal transmits dataorganized in packets withP symbols, there is enough controldata to coordinate transmissions and cooperation, and thelinear receivers at the relay and destination terminals aresynchronized with their desired signals. It should be notedthat the MIMO and CDMA system and data models aremathematically equivalent and the main difference is thatwe employ for the MIMO version a spreading code matrixCk = 1.

The received signals are filtered by a matched filter, sampledat chip rate and organized intoM × 1 vectorsrsd, rsrj andrrd, which describe the signal received from the source tothe destination, the source to the relays, and the relays to the

destination, respectively,

rsd =K∑

k=1

aksdhsd,kbk[i] + ηsd

+ nsd,

rsrj =

K∑

k=1

aksrjhsrj ,kbk[i] + ηsrj

+ nsrj ,

rrjd =

K∑

k=1

akrjdhrjd,kbk[i] + ηrjd

+ nrjd,

j = 1, . . . , nr, i = 1, . . . , P, p = 1, 2

(5)

whereP is the number of packet symbols,np = 2 is thenumber of transmission phases or hops, andnr is the numberof relays. The vectorsnsd, nsrj and nrjd are zero meancomplex Gaussian vectors with varianceσ2 generated at thereceivers of the destination and the relays from different links,and the vectorsηsd, ηsrj

andηrjdrepresent the intersymbol

interference (ISI).

The amplitudes of the source to destination, source to relayand relay to destination links for userk are denoted byaksd,aksrj and akrjd, respectively. The quantitiesbk[i] and bk[i]represent the original and reconstructed symbols by the AFor DF protocol at the relays, respectively. TheM × 1 spatialchannel vectors from source to destination, source to relay,and relay to destination arehsd,k, hsrj ,k, hrjd,k, respectively.By collecting the data vectors in (5) (including the links fromrelays to the destination) into aJ × 1 received vector at thedestination, whereJ = npM for MIMO systems, we obtain

r[i] =

[ ∑Kk=1 a

ksdhsd,kbk[i]∑nr

j

∑Kk=1 a

krnrd

hrnrd,kbrnrd

k [i]

]

+ n[i]

(6)

Fig. 2. Block diagram of2-phase cooperative MIMO system.

5

Rewriting the above signals in a compact form yields

r[i] =

Knr∑

k=1

Bk[i]Ak[i]hk[i] + n[i]

=

K∑

k=1

P k[i]Bk[i]ak[i] + n[i],

(7)

The J × 1 vectorhk[i] contains the spatial channel gains ofthe links between the source, the relays and the destination.The np × np diagonal matrixBk[i] = diag(bk[i] brkdk [i]),for 1 ≤ k ≤ K, and Bk[i] = diag(0 brkdk [i]), forK < k ≤ Knr, contains the symbols transmitted fromthe source to the destination (bk[i]) and the nr symbolstransmitted from the relays to the destination (brkdk [i]) onthe main diagonal, and theJ × J diagonal matrixBk[i] =diag(bk[i]

⊗IM brkdk [i]

⊗IM ), for 1 ≤ k ≤ K, and

Bk[i] = diag(0⊗

IM brkdk [i]⊗

IM ), for K < k ≤ Knr,.The np × 1 power allocation vectorak[i] = [aksd . . . akrkd]

T

has the amplitudes of the links, thenp × np diagonal matrixAk[i] is given byAk[i] = diagak[i], and theJ×J diagonalmatrix Ak[i] = [aksd

⊗IM . . . akrnk

d

⊗IM ]T . The J × np

matrix P k has copies of the spatial signatureshk[i] shifteddown byM positions for each column and zeros elsewhere.The J × 1 vectorn[i] has the noise components.

III. JOINT MMSE RECEIVER DESIGN, POWER

ALLOCATION , RELAY SELECTION AND CHANNEL

ESTIMATION

In this section, our aim is to describe techniques to mitigateinterference and allocate the power and select the best relaysaccording to the mean square error (MSE) criterion. Wepresent a joint receiver design and power allocation strat-egy using constrained linear MMSE estimation and group-based power constraints along with a linear MMSE channelestimator. The interesting aspect of the group-based powerconstraints is that a designer can choose a subset of usersor data streams for power adjustment. Another technique thatis detailed here is a method called transmit diversity selection(TDS) which operates with the linear MMSE receivers. Withthe TDS technique the relay selection is used to jointlyoptimize the selection of antennas in a strategy equivalenttoa 1-bit transmit antenna power allocation.

In order to describe the techniques necessary for inter-ference mitigation and resource allocation, we introduce analternative way of expressing theJ × 1 received vector in (7).Our goal is to separate the subset of users or data streamsthat will be used for resource allocation with the group-basedpower constraints. The modifiedJ × 1 received vector can beexpressed as

r[i] = P S [i]BS [i]aS,k[i]+∑

k 6=S

P k[i]Bk[i]ak[i]+η[i]+n[i],

(8)where S = S1,S2, . . . ,SG denotes the group ofG users to consider in the design. TheJ × G(nr +1) matrix P S = [P S1 P S2 . . . P SG

] containsthe G effective signatures of the group of users. TheG(nr + 1) × G(nr + 1) diagonal matrix BS [i] =diag(bS1 [i] br1dS1

[i] . . . brndS1[i] . . . bSG

[i] br1dSG[i] . . . brndSG

[i])

contains the symbols transmitted from the sources tothe destination and from the relays to the destinationof the G users in the group on the main diagonal,the G(nr + 1) × 1 power allocation vectoraS,k[i] =[aS1

sd [i] aS1

r1d[i] . . . aS1

rnrd[i], . . . , aSG

sd [i] aSG

r1d[i] . . . aSG

rnrd[i]]T of

the amplitudes of the links used by theG users or data streamsin the group.

A. Linear MMSE Receiver Design and Power AllocationScheme with Group-Based Constraints

The linear MMSE interference mitigation for user ordata streamk is performed by the receive filterwk[i] =[wk,1[i], . . . , wk,J [i]] with J coefficients on the received datavectorr[i] and yields

zk[i] = wHk [i]r[i], (9)

wherezk[i] is an estimate of the symbols, which are processedby a slicerQ(·) that performs detection and obtains the desiredsymbol asbk[i] = Q(zk[i]).

Let us now detail the linear MMSE-based design of thereceivers for user or data streamk represented bywk[i] and forthe computation of theG(nr +1)× 1 power allocation vectoraS,k[i]. This problem can be cast as the following constrainedoptimization

[woptk , a

optS,k] = arg min

wk[i],aS,k[i]E[(|bk[i]−wH

k [i]r[i]|2]

subject to aHS,k[i]aS,k[i] = PG,

(10)

In order to obtain expressions for the receive filterwk[i] andthe power allocation vectoraS,k[i] subject to the group-basedpower constraints, we need the help of the method of Lagrangemultipliers (10) [51] that transforms a constrained optimizationinto an unconstrained one. The MMSE expressions forwk[i]andaS,k[i] are given by

Lk = E[

|bk[i]−wHk [i]

(

P S [i]BS [i]aS,k[i]

+∑

k 6=S

P k[i]Bk[i]ak[i] + η[i] + n[i])

|2]

+ λk(aS,k[i]− PG),

(11)

whereλk is a Lagrange multiplier.Since the Lagrangian in (11) is a function of bothwk[i]

and aS,k[i], we need to employ a strategy for optimizationthe function with respect to both parameter vectors. The mainidea is to fix one of the parameter vectors and compute thegradient terms with respect to the other parameter vectorthat minimizes the Lagrangian and obtain the expression ofinterest. In particular, an expression foraS,k[i] is obtained byfixing wk[i], taking the gradient terms of the Lagrangian andequating them to zero, which yields

aS,k[i] = (RS,k[i] + λkI)−1pS,k[i] (12)

where the G(nr + 1) × G(nr + 1) covariance matrixRS,k[i] = E[BH

S [i]PHS [i]wk[i]w

Hk [i]P S [i]BS [i]] and the

vectorpS,k[i] = E[bk[i]BHS [i]PH

S [i]wk[i]] is aG(nr +1)× 1cross-correlation vector. The Lagrange multiplierλk playsthe role of a regularization term and has to be determinednumerically due to the difficulty of evaluating its expression.

In order to compute the expression forwk[i], we fixaS,k[i],calculate the gradient terms of the Lagrangian and equate them

6

to zero which leads to

wk[i] = R−1[i]pk[i], (13)

where the covariance matrix of the received vector is givenby R[i] = E[r[i]rH [i]] and pk[i] = E[b∗k[i]r[i]] is a J × 1cross-correlation vector. The quantitiesR[i] andpk[i] dependon the power allocation vectoraS,k[i]. The expressions in(12) and (13) do not have a closed-form solution as they havea dependence on each other. Moreover, the expressions alsorequire the estimation of the channel vectorhk[i]. Thus, itis necessary to iterate (12) and (13) with initial values toobtain a solution and to estimate the channel. The networkhas to convey the information from the group of users whichis necessary to compute the group-based power allocationincluding the filterwk[i]. The expressions in (12) and (13)require matrix inversions with cubic complexity (O((J)3)andO((G(nr + 1))3).

B. Transmit Diversity Selection and Relay Selection

In this subsection, we explore the idea of transmit diversityselection (TDS) and relay selection (RS) and how they canbe used to improve the performance of cooperative systems.In cooperative wireless systems with multiple relays, thereare links that have very poor propagation conditions that candegrade the performance of the overall system. These links canbe identified and removed from the operation of the systemvia TDS and RS. To this end, we formulate a TDS and RSstrategy for a2 DF MIMO network as a discrete combinatorialMSE problem which optimizes the use of the channels ofthe second phase via1-bit power allocation [55]. It turns outthat the problems of TDS and RS are combinatorial problemswhich require either an exhaustive search or some relaxationapproach. We specify that a subset ofKsub antennas of thenrK relay antennas are active at each time instant in orderto reduce the optimization complexity but also to ensure aminimum available level of diversity. The destination node’sMSE TDS optimization function is given by

Toptr = arg min

T r∈ΩT

C[i,T r, r

]

= arg minT r∈ΩT

K∑

k=1

E[∥∥bk[i]−wk[i]r[i]

∥∥2],

(14)

where T r = diag(a1r1d . . . aKr1d

, . . . , a1rnrd. . . aKrnrd

) andakrjd = 0, 1, and wk is the linear MMSE filter for thekth symbol. Under the assumption of no inter-relay com-munication and that each data stream is allocated to itscorrespondingly numbered transmit antenna at each relay, theset ΩT has a cardinality of|ΩT | =

(nrKKsub

)and contains all

possible combinations of relay transmit antennas patterns. Theperformance and complexity of solutions to (14) depend on|ΩT | and its elements. However,|ΩT | is significant even formodest numbers of antennas and relays, e.g.nr ≥ 4 andK ≥ 2. Further improvements can be achieved by a process weterm RS which addresses the possibility of mismatching poorfirst phase channels with optimized second phase channels aswell as reducing the cardinality ofΩT .

By removing one or more relays based on their MSEperformance from consideration by (14),ΩT can be optimized

and its cardinality improved without overly restricting thesecond-phase channels available to the TDS process. Theselection of the single highest MSE relay can be expressedas a discrete maximization problem given by

jopt = arg maxj∈ΩR

F[i, rsrj ,

]

= arg maxj∈ΩR

K∑

k=1

E[∥∥bk[i]−wj,k[i]rsrj [i]

∥∥2], (15)

whereΩR is the set of candidate relays andwj,k[i] is theMMSE filter for the kth symbol at thejth relay. On thesolution of (15), a refined subset,ΩT ∈ ΩT , is generated byremoving members ofΩT which involve transmission fromrelay jopt, i.e. members ofΩT where[a1rjoptd . . . a

Krjoptd

] 6= 0.

TDS then operates with this subset, where|ΩT | =(K(nr−1)

Ksub

).

Extension to the selection of multiple relays involves summingthe MSE from candidate relays and populatingΩR with setsof these relays. However, the selection of the number ofrelays to remove is vital, as too high a value will result ina overly restricting the second phase channels available totheTDS process therefore increasing the probability of a channelmismatch.

C. Cooperative MMSE Channel Estimation

The next task that is necessary for the interference mit-igation and resource allocation is to compute the channelgains of the links of the cooperative system. In order toestimate the channel in the cooperative system under study,let us first consider the transmitted signal for userk, xk[i] =Bk[i]Ak[i]Ckhk[i] = Qk[i]hk[i], and the covariance matrixgiven by

R = [r[i]rH [i]]

=

K∑

k=1

Qk[i]E[hk[i]hHk [i]]QH

k [i] + E[η[i]ηH [i]] + σ2I

=K∑

k=1

Qk[i]PhkQH

k [i] + P η + σ2I

(16)

A linear estimator ofhk[i] applied tor[i] can be representedas hk[i] = FH

k r[i]. The linear MMSE channel estimationproblem for the cooperative system under consideration isformulated as

F k,opt = argminF k

E[||hk[i]− hk[i]||

2]

= argminT k

E[||hk[i]− TH

k r[i]||2].

(17)

Computing the gradient terms of the argument and equatingthem to zero yields the MMSE solution

F k,opt = R−1P k, (18)

where P k = E[r[i]hHk [i]] = Qk[i]E[hk[i]h

Hk [i]] =

7

Qk[i]Phk. Using the relationhk[i] = FH

k r[i], we obtain

hk[i] = FHk,optr[i] = PH

k R−1r[i]

= PHhk

QHk [i]

( K∑

k=1

Qk[i]PhkQH

k [i] + P η + σ2I)−1

r[i],

(19)

The expressions in (19) require matrix inversions with cu-bic complexity ( O(J3)), however, this matrix inversion iscommon to (13) and needs to be computed only once forboth expressions. In what follows, computationally efficientalgorithms with quadratic complexity (O(J2)) based on analternating optimization strategy will be detailed.

IV. A DAPTIVE ALGORITHMS

In this section, we present algorithms to compute the pa-rameters of interest and the expressions derived in the previoussection with lower computational complexity. Specifically, wedevelop adaptive RALS algorithms using a method to buildthe group ofG users based on the power levels, and thenwe employ an alternating optimization strategy for efficientlyestimating the parameters of the receive filters, the power allo-cation vectors and the channels. Despite the joint optimizationthat is associated with a non-convex problem, the proposedRALS algorithms have been extensively tested and have notpresented problems with local minima.

A. Group Allocation and Channel Estimation

The first step in the proposed strategy is to build the group ofG users that will be used for the power allocation and receivefilter design. A RAKE receiver [7], which is equivalent to afilter matched to the signature sequence of the desired user orthe spatial signature of the desired data stream will be usedfor the group allocation. The RAKE receiver is employed toobtainzRAKE

k [i] = (Ckhk[i])Hr[i] = p

Hk [i]r[i]. The group is

then formed according to

compute the G largest |zRAKEk [i]|, k = 1, 2, . . . ,K.

(20)The design of the RAKE and the other tasks require channelestimation. The power allocation, receive filter design andchannel estimation expressions given in (12), (13) and (19),respectively, are solved by replacing the expected values withtime averages, and RLS-type algorithms with an alternatingoptimization strategy. In order to solve (19) efficiently, wedevelop a variant of the RLS algorithm that is described by

hk[i] = PH

hk[i]QH

k [i]R−1

[i]r[i], (21)

whereQk[i] = Bk[i]Ak[i]Ck, the estimate of the inverse of

the covariance matrixR−1

[i] is computed with the matrixinversion lemma [51]

k[i] =α−1R[i− 1]r[i]

1 + α−1rH [i]R[i− 1]r[i], (22)

R[i] = α−1R[i− 1]− α−1k[i]rH [i]R[i− 1], (23)

and

P hk[i] = αPhk

[i− 1] + hk[i − 1]hH

k [i− 1], (24)

whereα is a forgetting factor that should be close to but lessthan1.

B. Joint Interference Suppression and Power Allocation

The approach for allocating the power within a group isto drop the constraint, estimate the quantities of interestandthen impose the constraint via a subsequent normalization.Thegroup-based power allocation algorithm is computed by

aS,k[i] = RS,k[i]pS,k[i]

= RS,k[i](αpS,k[i− 1] + bk[i]vk[i])

= aS,k[i − 1] + ξa[i]kS,k[i],

(25)

where ξa[i] = bk[i] − aHS,k[i − 1]vk[i] is the a priori error,

vk[i] = BHS [i]PH

S [i]wk[i] is the input signal to the recursion

kS,k[i] =α−1RS,k[i− 1]vk[i]

1 + α−1vHk [i]RS,k[i− 1]vk[i]

, (26)

RS,k[i] = α−1RS,k[i− 1]− α−1kS,k[i]vHk [i]RS,k[i− 1].

(27)The normalizationaS,k[i] ← PG aS,k[i]/||aS,k[i]|| is thenperformed to ensure the power constraint.

The linear receive filter is computed by

wk[i] = wk[i− 1] + k[i]ξ∗[i], (28)

where the a priori error is given byξ[i] = bk[i] − wHk [i −

1]r[i] andk[i] is given by (22). The proposed scheme employsthe algorithm in (20) to allocate the users in the group andthe channel estimation approach of (21)-(24). The alternatingoptimization strategy uses the recursions (25) and (28) with1 or 2 iterations per symboli.

C. Transmit Diversity Selection and Relay Selection Based onDiscrete Stochastic Gradient Algorithms

In this part, we describe a low-complexity solution to thejoint TDS and RS problem based on a discrete stochasticgradient algorithm (DSA) that can compute the optimal com-binatorial solution outline in (14) and (15) with a substantiallyreduced cost as compared with the exhaustive search. Wepresent a pair of low-complexity DSA that was first reported in[33], [52], which jointly optimizes RS and TDS in accordancewith (14) and (15), and converges to the optimal exhaustivesolution.

The RS portion of the DSA is given by the algorithm ofTable I. At each iteration the MSE of a randomly chosencandidate relay (jC) (step 2) and that of the worst performingrelay currently known (jW ) are calculated (step 3). Via acomparison, the higher MSE relay is designatedjW for thenext iteration (step 3). The current solution and the relaychosen for removal (j) is denoted as the current optimum andis the relay which has occupiedjW most frequently over thecourse of the packet up to theith time instant; effectivelyan average of the occupiers ofjW . This averaging/selectionprocess is performed by allocating each member ofΩR a|ΩR|× 1 unit vector,vl, which has a one in its correspondingposition inΩR, i.e.,vjW [i] is the label of the worst performingrelay at theith iteration. The current optimum is then chosenand tracked by means of a|ΩR|×1 state occupation probability

8

TABLE IPROPOSED DISCRETE STOCHASTIC JOINTTDS AND RS ALGORITHM

Step1. Initialization

choosej[1] ∈ ΩR, jW [1] ∈ ΩR, πR

[

1, j[1]]

= 1, πR[1, j] = 0for j 6= j[1]

2. For the time index i = 1, 2, ..., NchoosejC [i] ∈ ΩR

3. Comparison and update of the worst performing relayif F

[

i, rsrjC [i]

]

> F[

i, rsrjW [i]

]

then jW [i+ 1] = jC [i]

otherwisejW [i+ 1] = jW [i]4. State occupation probability (SOP) vector update

πR[i+ 1] = πR[i] + µ[i+ 1](vjW [i+1] − πR[i]) whereµ[i] = 1/i

5. Determine largest SOP vector element and select the optimum relayif πR

[

i+ 1, jW [i+ 1]]

> πR[i+ 1, j[i]] then j[i+ 1] = jW [i+ 1]otherwisej[i+ 1] = j[i]

6. TDS Set Reductionremove members ofΩT which utilize relayj[i+ 1] (ΩT → ΩT )

(SOP) vector,πR. This vector is updated at each iterationby addingvjW [i + 1] and subtracting the previous value ofπR (step 4). The current optimum is then determined byselecting the largest element inπR and its corresponding entryin ΩR (step 5). Through this process, the current optimumconverges towards and tracks the exhaustive solution [52].Analternative interpretation of the proposed algorithm is toviewthe transitions,jW [i]→ jW [i+1], as a Markov chain and themembers ofΩR as the possible transition states. The currentoptimum can then be defined as the most visited state.

Once RS is complete at each time instant, set reduction(ΩT → ΩT , step 6) and TDS can take place. To perform TDS,modified versions of steps1− 5 are used. The considered setis replaced,ΩR → ΩT ; the structure of interest is replaced,j → T r; the best performing matrix is soughtjW → T

Br ;

the SOP vector is replacedπR → πT and C → F from(14). Finally, the inequality of step 3 is reversed to enableconvergence to the lowest MSE TDS matrix which is thenfeedback to the relays in the form of 1-bit per relay antenna.

Significant complexity savings result from the proposedalgorithm; savings which increase withK, nr and the numberrelays removed in the RS process. For example, whennr = 10,K = 2 and 4 relays are removed, the number of complexmultiplications for MMSE reception and exhaustive TDS,exhaustive TDS with RS, iterative TDS and iterative TDSwith RS are5.8 × 108, 1.7 × 108, 1.8 × 105 and 5.9 × 104,respectively, for each time instant.

V. A NALYSIS AND REQUIREMENTS OF THEALGORITHMS

In this section, we assess the requirements of the proposedand existing algorithms for cross-layer design in terms ofcomputational complexity and number of feedback bits. Thebasic idea is to show the computational cost of the algorithmspresented and compare them with those of existing techniquesfor interference mitigation and/or resource allocation.

A. Computational Complexity Requirements

We discuss here the computational complexity of the pro-posed and existing algorithms. Specifically, we will detailtherequired number of complex additions and multiplications ofthe proposed JPAIS-GBC algorithms and compare them with

interference suppression schemes without cooperation (NCIS)and with cooperation (CIS) using an equal power allocationacross the relays. Both uplink and downlink scenarios areconsidered in the analysis. In Table I we show the computa-tional complexity required by each recursion associated witha parameter vector/matrix for the JPAIS-GBC withG = K,which is more suitable for the uplink.

TABLE IICOMPUTATIONAL COMPLEXITY OF ALGORITHMS WITH A GLOBAL

POWER CONSTRAINTG = K .

Number of operations per symbolParameter Additions Multiplications

2(J)2 3(J)2

W [i] +2K(J) +2K(J)

−J + 1 +3J + 1

3K(K(nr + 1)) K(K(nr + 1))2

+K(nr + 1)(L− 1) +4(K(nr + 1))2

aT [i] +K(M(nr + 1)) +(K + L)(K(nr + 1))2

+K(K(nr + 1)) −(K(nr + 1))2

+6(K(nr + 1))2 +K(MQ)

+3K(nr + 1) + nr + 2 +nr

5(KQ)2 +5(K(nr + 1)2

hk[i] +5KQ +6KQ

+3 +1

In Table II we show the computational complexity requiredby each recursion associated with a parameter vector for theJPAIS-GBC algorithm, which is suitable for both the uplinkand the downlink. A noticeable difference between the JPAIS-GBC with G = K andG = 1 is that the latter is employedfor each user, whereas the former is used for all theK usersin the system. Since the computation of the inverse ofR[i] iscommon to all users for the uplink in our system, the JPAIS-GBC with G = K is more efficient than the JPAIS-GBC withG = 1 computed for all theK users.

TABLE IIICOMPUTATIONAL COMPLEXITY OF ALGORITHMS WITH

INDIVIDUAL POWER CONSTRAINTS(G = 1).

Number of operations per symbolParameter Additions Multiplications

2(J)2 3(J)2

wk[i] +J +5J

+1 +1

2(nr + 1)2 3(nr + 1)2

+3(nr + 1) +7(nr + 1)

ak[i] +JL +JL

+Q +Q

−3 +3

2(Q)2 6(Q)2

hk[i] +5MQ +MQ

−5(nr + 1) + 3 +4(nr + 1) + 1

The recursions employed for the proposed JPAIS-GBC withG = K and the JPAIS-GBC withG = 1 are general andparts of them are used in the existing CIS and NIS algorithms.Therefore, we can use them to describe the required compu-

9

tational complexity of the existing algorithms. In Table III weshow the required recursions for the proposed and existingalgorithms, whose complexity is detailed in Tables I and II.

TABLE IVCOMPUTATIONAL COMPLEXITY OF THE PROPOSEDJPAISAND

EXISTING ALGORITHMS.

Algorithm Recursions

JPAIS-GPC(G = K) (Uplink) W [i], aT [i],hk[i]

JPAIS-GBC (G = 1) (Downlink) wk[i], ak[i], hk[i]

CIS (Uplink) W [i], aT [i] is fixedCIS (Downlink) wk[i], ak[i] is fixedNCIS (Uplink) W [i] with nr = 0

NCIS (Downlink) wk[i] with nr = 0

5 10 15 20 25 30 35 4010

2

103

104

105

106

Num

ber

of m

ultip

licat

ions

M

Complexity of RLS Algorithms

JPAIS−GBC(G=K)JPAIS−GBC(G=1)CISNCIS

nr=3

nr=1

Fig. 3. Computational complexity in terms of the number of complexmultiplications of the proposed and existing schemes for the uplink.

In Fig. 3, we illustrate the required computational complex-ity for the proposed and existing schemes for different numberof relays (nr). The curves show that the proposed JPAIS-GBCwith G = K and JPAIS-GBC withG = 1 are more complexthan the CIS scheme and the NCIS. This is due to the factthat the power allocation and channel estimation recursionsare employed. However, we will show in the next sectionthat this additional required complexity (which is modest)cansignificantly improve the performance of the system.

B. Feedback Channel Requirements

The JPAIS algorithms presented so far for cross-layer designrequire feedback signalling in order to allocate the powerlevels across the relays. In order to illustrate how theserequirements are addressed, we can refer to Fig. 4 whichdepicts the structure for both the data and feedback packets.The data packet comprises a number of allocated bits fortraining (Ntr), for synchronization and control (Nsync) andthe transmitted data (Ndata). The feedback packet requires thetransmission of the power allocation vectoraT for the case ofthe JPAIS-GBC algorithm withG = K, whereas it requiresthe transmission ofak for each user for JPAIS-GBC with

G = 1. A typical number of bitsnb required to quantize eachcoefficient of the vectorsaT andak via scalar quantizationis nb = 4 bits. More efficient schemes employing vectorquantization [53], [54] and that take into account correlationsbetween the coefficients are also possible.

For the uplink (or multiple-access channel), the base station(or access point) needs to feedback the power levels across thelinks to theK destination users in the system. With the JPAIS-GBC with G = K algorithm, the parameter vectoraT with(nr +1)Knb bits/packet must be broadcasted to theK users.For the JPAIS-GBC algorithm withG = 1, a parameter vectorak with (nr + 1)nb bits/packet must be broadcasted to eachuser in the systems. In terms of feedback, the JPAIS-GBCalgorithm withG = 1 is more flexible and may require lessfeedback bits if there is no need for a constant update of thepower levels for allK users.

Data Packet Structure

Feedback Packet Structure(JPAIS-GBC wtih G=K)

Feedback Packet Structure(JPAIS-GBC with G=1)

aT

ak

(nr + 1)Knb bits/feedback packet

K times (nr + 1)Knb bits/feedback packet

Ntr Nsync Ndata

Fig. 4. Proposed structure of the data and feedback packets.

For the downlink (or broadcast channel), theK users mustfeedback the power levels across the links to the base station.With the JPAIS-GBC algorithm withG = K, the parametervectoraT with (nr + 1)Knb bits/packet must be computedby each user and transmitted to the base station, which usesthe aT vector coming from each user. An algorithm for datafusion or a simple averaging procedure can be used. For theJPAIS-GBC algorithm withG = 1, a parameter vectorak

with (nr + 1)nb bits/packet must be transmitted from eachuser to the base station. In terms of feedback, the JPAIS-GBCalgorithm withG = 1 requires significantly less feedback bitsthan the JPAIS-GBC withG = K in this scenario.

The MIMO TDS and RS scheme can be interpreted as a1-bit power allocation scheme and therefore achieves perfor-mance improvements whilst utilizing the minimum numberof feedback bits per antenna. Consequently, the feedbackrequirements per update of a cooperative MIMO system usingTDS and RS is given by the total number of relay transmitantennasnrK. This minimal feedback allows optimization ofthe system whilst maintaining the capacity of the system withregards to the transmission of useful data.

VI. SIMULATIONS

In this section, we illustrate with Monte-Carlo simulationsthe performance of the cross-layer algorithms described inthischapter. Specifically, we assess the performance in terms ofthe bit error ratio (BER) of the JPAIS scheme and adaptivealgorithms with group-based power constraints (GBC). TheJPAIS scheme and algorithms are compared with schemeswithout cooperation (NCIS) and with cooperation (CIS) [26]using an equal power allocation across the relays (the power

10

allocation in the JPAIS scheme is disabled). We also assessthe proposed algorithms for transmit diversity selection andrelay selection (Iterative TDS with RS) are presented andcomparisons drawn against the optimal exhaustive solutions(Exhaustive TDS with RS), the unmodified system (No TDS),and the direct transmission (Non-Cooperative).

A. DS-CDMA System

A DS-CDMA network with randomly generated spreadingcodes and a processing gainN = 16 is considered. Thefading channels are generated considering a random powerdelay profile with gains taken from a complex Gaussianvariable with unit variance and mean zero,L = 5 pathsspaced by one chip, and are normalized for unit power. Thepower constraint parameterPA,k is set for each user so thatthe designer can control the SNR (SNR = PA,k/σ

2) andPT = PG + (K − G)PA,k, whereas it follows a log-normaldistribution for the users with associated standard deviationequal to3 dB. The DF cooperative protocol is adopted andall the relays and the destination terminal use either linearMMSE, which have full channel and noise variance knowl-edge, or adaptive receivers. The receivers are adjusted withthe proposed RALS with2 iterations for the JPAIS scheme,and with RLS algorithms for the NCIS and CIS schemes.We employ packets with1500 QPSK symbols and averagethe curves over1000 runs. For the adaptive receivers, weprovide training sequences withNtr = 200 symbols placedat the preamble of the packets. After the training sequence,the adaptive receivers are switched to decision-directed mode.

The first experiment depicted in Fig. 5 shows the BERperformance of the proposed JPAIS scheme and algorithmsagainst the NCIS and CIS schemes withnr = 2 relays. TheJPAIS scheme is considered with the group-based power con-straints (JPAIS-GBC). All techniques employ MMSE or RLS-type algorithms for estimation of the channels, the receivefilters and the power allocation for each user. The results showthat as the group sizeG is increased the proposed JPAISscheme and algorithms converge to approximately the samelevel of the cooperative JPAIS-MMSE scheme reported in [28],which employsG = K for power allocation, and has fullknowledge of the channel and the noise variance.

The proposed JPAIS-GBC scheme is then compared with anon-cooperative approach (NCIS) and a cooperative schemewith equal power allocation (CIS) across the relays fornr = 1, 2 relays. The results shown in Fig. 6 illustrate theperformance improvement achieved by the JPAIS scheme andalgorithms, which significantly outperform the CIS and theNCIS techniques. As the number of relays is increased sois the performance, reflecting the exploitation of the spatialdiversity. In the scenario studied, the proposed JPAIS-GBCwith G = 3 can accommodate up to3 more users as comparedto the CIS scheme and double the capacity as compared withthe NCIS for the same BER performance. The curves indicatethat the GBC for power allocation with only a few users isable to attain a performance close to the JPAIS-GBC withG = K users, while requiring a lower complexity and lessnetwork signalling. A comprehensive study of the signallingrequirements will be considered in a future work.

The next experiment considers the average BER perfor-mance against the normalized fading ratefdT (cycles/symbol),

0 500 1000 1500

10−3

10−2

10−1

N=16, SNR = 15 dB, K=6 users, P=1500

Number of received symbols

BE

R

NCIS−RLS(n

r=0)

CIS−RLS(nr=2)

JPAIS−GBC−RALS(nr=2,G=1)

JPAIS−GBC−RALS(nr=2,G=3)

JPAIS−GBC−RALS(nr=2,G=K)

JPAIS−GPC−MMSE [11]

Fig. 5. BER performance versus number of symbols. Parameters: AF proto-col, λT = λk = 0.025 (for MMSE schemes),α = 0.998, R

−1S,k[i] = 0.01I

andR−1

[i] = 0.01I .

5 10 15 2010

−5

10−4

10−3

10−2

10−1

N=16, K=6 users, P=1500

SNR (dB)

BE

R

2 4 6 8 10 1210

−4

10−3

10−2

10−1

N=16, SNR = 12 dB, P=1500

Number of users

BE

R

NCIS(nr=0)

RLSCIS−RLSJPAIS−GBC(G=1)−RALS

JPAIS−GBC(G=3)−RALS

JPAIS−GBC(G=K)−RALS

nr=1

nr=2

nr=2

nr=1

Fig. 6. BER performance versus SNR and number of users for theoptimallinear MMSE detectors. Parameters: AF protocol,α = 0.998, R

−1S,k[i] =

0.01I andR−1

[i] = 0.01I .

as depicted in Fig. 7. The idea is to illustrate a situation wherethe channel changes within a packet and the system transmitsthe power allocation vectors computed by the proposed JPAISalgorithms via a feedback channel. In this scenario, the JPAISalgorithms compute the parameters of the receiver and thepower allocation vector, which is transmitted only once to themobile users. This leads to a situation in which the powerallocation becomes outdated. The results show that the gains ofthe proposed JPAIS algorithms decrease gradually as thefdTis increased to the BER level of the existing CIS algorithms forbothnr = 2 andnr = 4 relays, indicating that the power al-location is no longer able to provide performance advantages.This problem requires the deployment of a frequent update ofthe power allocation via feedback channels.

The last experiment, shown in Fig. 8, illustrates the averagedBER performance versus the percentage of errors in the

11

10−5

10−4

10−3

10−5

10−4

10−3

10−2

10−1

N=16, SNR = 12 dB, K=6 users, P=1500

fdT (cycles/symbol)

BE

R

NCISCISJPAIS−GBC(G=1)JPAIS−GBC(G=K)

nr =2 relays

nr = 4 relays

Fig. 7. BER performance versusfdT for the AF protocol. The parametersof the adaptive algorithms are optimized for eachfdT .

10−4

10−3

10−2

10−1

100

10−5

10−4

10−3

10−2

10−1

N=16, SNR = 12 dB, K=6 users, P=1500, fdT=10−5

Rate of feedback channel errors (%)

BE

R

NCISCISJPAIS−GBC(G=1)JPAIS−GBC(G=K)

nr = 2 relays

nr = 4 relays

Fig. 8. BER performance versus percentage of feedback errors.

feedback channel for an uplink scenario. Specifically, thefeedback packet structure is employed and each coefficientis quantized with4 bits. Each feedback packet is constructedwith a sequence of binary data (0s and1s) and is transmittedover a binary symmetric channel (BSC) with an associatedprobability of errorPe. We then evaluate the BER of theproposed JPAIS and the existing algorithms against severalvalues of thePe. The results show that the proposed JPAISalgorithms obtain significant gains over the existing CISalgorithm for values ofPe < 0.1%. As we increase the rateof feedback errors, the performance of the proposed JPAISbecomes worse than the CIS algorithms. This suggests the useof error-control coding techniques to keep the level of errorsin the feedback channel below a certain value.

B. MIMO System

In this part, simulations of the proposed algorithms (IterativeTDS with RS) are presented and comparisons drawn againstthe optimal exhaustive solutions (Exhaustive TDS with RS),

the unmodified system where all antennas are active (No TDS),and the direct transmission (Non-Cooperative). Plots of theschemes with TDS only (Exhaustive TDS, Iterative TDS)are also included to illustrate the performance improvementobtained by RS. Equal power allocation is maintained in eachphase so that the total transmit bit power of the relays isunity. RLS channel estimation (CE) is used where all auxiliarymatrices are initialized as identity matrices and estimationmatrices are zero matrices, and the exponential forgettingfactor is 0.9. Each simulation is averaged over 1000 packets(Np), each with training sequences of200 symbols.

0 500 1000 1500 200010

−3

10−2

10−1

100

Number of Received Symbols

BE

R

nr = 4, K = 2, M = 2, K

sub = 4, P = 1000, SNR = 15dB

Non − CoopeartiveNo TDSExhaustive TDSExhaustive TDS with RSIterative TDSIterative TDS with RSIterative TDS and CEIterative TDS with RS and CE

Fig. 9. Cooperative DF MIMO BER performance versus the number ofreceived symbols.

Fig. 9 gives the BER convergence performance of theproposed algorithms. The iterative TDS with RS algorithmconverges to the optimal BER as does TDS with RS and CE,albeit in a delayed fashion due to the CE. The TDS with RSscheme exhibits quicker convergence and lower steady stateBER. These results and the interdependence between elementsof the algorithm confirm that both the RS and TDS portionsof the algorithm converge to their exhaustive solutions.

Fig. 10 shows the BER versus SNR performance of theproposed and conventional algorithms. Increased diversityhas been achieved without sacrificing multiplexing gain andillustrates that although the maximum available diversityad-vantage decreases fromM(nr + 1) to M(Ksub/K + 1) withRS with TDS because fewer antennas are active, the actualdiversity achieved has increased. These diversity effectscanbe attributed to the removal of poor paths and therefore alower probability of first phase and second phase channelmismatch but also the increase in transmit power over theremaining paths. The largest gains in diversity are presentin the 15 − 25dB region and begin to diminish above thisregion because relay decoding becomes increasingly reliableand lower power paths become more viable for transmission.

VII. E XTENSIONS AND SUGGESTIONS FORFUTURE WORK

The algorithms for joint resource allocation and interferencemitigation described in this chapter are quite general andcan be employed in a variety of wireless communication

12

0 5 10 15 20 25 3010

−5

10−4

10−3

10−2

10−1

100

SNR(dB)

BE

Rn

r = 4, K = 2, M= 2, K

sub = 4, P = 1000

Non − CooperativeNo TDSExhaustive TDSExhaustive TDS with RSIterative TDSIterative TDS with RS

Fig. 10. Cooperative FD MIMO BER performance versus SNR.

systems that are equipped with cooperative techniques. Theseinclude orthogonal-frequency-division-multiplexing (OFDM)[57], single-carrier systems with frequency-domain equalisa-tion (SC-FDE) [58] and ultra-wide band (UWB) systems [59].

Possible extensions include the incorporation of more ad-vanced interference mitigation strategies than linear schemes.These include nonlinear detection techniques such as succes-sive interference cancellation [11], [38], decision feedbackstrategies [37], [39] and sphere decoders [23]. The detectionalgorithms could also be considered with space-time codingschemes [9], [10], channel coding and iterative processingapproaches [39], [62].

Another complementary set of techniques comprises algo-rithms for adaptive parameter estimation. These methods arefundamental to estimate key parameters such as channel gains,amplitudes and receive filters, whilst keeping the complexitylow and being able to track variations of the environment.Amongst the adaptive parameter estimation techniques, adesigner can choose between supervised and blind approaches[51]. Blind techniques [63]- [68] are appealing as they canincrease the spectral efficiency of wireless systems. This isespecially relevant for cooperative systems as they requireextra signalling for cross-layer design. Supervised adaptivealgorithms usually rely on training sequences that are sentatthe beginning of each data packet [69], [70]. One fundamentalissue in the choice of the adaptive parameter estimationalgorithm is the speed of convergence and the tracking perfor-mance. The literature suggests that reduced-rank algorithms[43]- [49], [72]–[74] are very attractive choices when fasttraining and accurate tracking are important issues.

VIII. C ONCLUDING REMARKS

We have presented in this work joint iterative power allo-cation and interference mitigation techniques for DS-CDMAand MIMO networks which employ multiple hops and the AFand DF cooperation protocols. A joint constrained optimiza-tion framework and algorithms that consider the allocationof power levels across the relays subject to group power

constraints and the design of linear receivers for interfer-ence suppression were proposed. A scheme for joint transmitdiversity optimisation and relay selection along with linearinterference suppression has also been detailed and applied toMIMO systems. A study of the requirements of the proposedand existing algorithms in terms of computational complexityand feedback channels has also been conducted. The results ofsimulations have shown that the proposed algorithms obtainsignificant gains in performance and capacity over existingnon-cooperative and cooperative schemes.

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[3] J. N. Laneman and G. W. Wornell, ”Cooperative diversity in wirelessnetworks: Efficient protocols and outage behaviour,”IEEE Trans. Inf.Theory, vol. 50, no. 12, pp. 3062-3080, Dec. 2004.

[4] M. Dohler and Y. Li, “Cooperative Communications: Hardware, Chan-nel and PHY”,Wiley, February 2010.

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