Resource Allocation and Interference Mitigation Techniques for Cooperative Multi-Antenna and Spread Spectrum Wireless Networks

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by  Patrick Clarke

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Resource Allocation and Interference Mitigation
Techniques for Cooperative Multi-Antenna and
Spread Spectrum Wireless Networks
Rodrigo C. de Lamare and Patrick J. Clarke
Communications Research Group
Department of Electronics, University of York, York Y010 5DD, United Kingdom
Emails: [e-mail]
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0 Abstract—Thischapterpresentsjointinterferencesuppression or users relay signals to each other in order to propagate
2 andpowerallocation algorithms forDS-CDMAand MIMOnet- redundantcopiesofthesamesignalstothedestinationuseror
works with multiplehopsand amplify-and-forward and decode-
n terminal.Tothisend,thedesignermustresorttoacooperation
and-forward (DF) protocols. A scheme for joint allocation of
a protocol such as amplify-and-forward (AF) [3], decode-and-
J powerlevelsacrosstherelaysandlinearinterferencesuppression
isproposed.Wealsoconsideranotherstrategyforjointinterfer- forward (DF) [3], [20] and compress-and-forward(CF) [21].
4 encesuppressionandrelayselectionthatmaximizesthediversity In order to obtain the benefits of cooperative techniques,
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availableinthesystem.Simulationsshowthattheproposedcross- designersmustaddressanumberofproblemsthatareencoun-
layeroptimizationalgorithmsobtainsignificantgainsincapacity teredincooperativewirelesssystems.Theseproblemsinclude
] and performance over existing schemes.
T physical-layerstrategies such as synchronization, interference
I mitigation,andparameterestimation.However,designers also
.
s I. INTRODUCTION have to consider a number of associated problems that be-
c
long to higher protocol layers and include the allocation of
[ Multiple-antenna wireless communication systems can ex-
resources such as power, relays and rate. These tasks present
ploit the spatial diversity in wireless channels, mitigating
1 anopportunitytoperformcross-layerdesignandtoobtainvery
v the effects of fading and enhancing their performance and significant gains in performance and capacity for cooperative
2 capacity. Due to the size and cost of mobile terminals, it is
wireless networks. This chapter is concerned with cross-
1 considered impractical to equip them with multiple antennas.
layerdesigntechniquesforcooperativewirelessnetworks and
9 However,spatial diversity gainscan be obtainedwhen single-
5 investigates the benefits of approaches that jointly mitigate
antenna terminals establish a distributed antenna array via
. interference and perform resource allocation.
1 cooperation [1]- [3]. The use of cooperative strategies can
In this chapter, we will consider two types of schemes,
0 lead to several types of gains [4], [13], namely, pathloss,
namely, direct-sequence code-division multiple access (DS-
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diversity and multiplexing gains. Pathloss gains allow a sig-
1 CDMA)[7],[8]andmulti-inputmulti-output(MIMO)[5],[6]
nificant reduction in the transmitted power for an equivalent
: systems. Theformeris offundamentalimportancein wireless
v performance, can increase the coverage [15] and enhance the
ad-hocandsensornetworks[4],whereasthelatterisoneofthe
i interference suppression capability [4], [13]. The diversity
X main ingredients of future wireless cellular networks. When
gains improve the performance of the wireless system with
r implementing cooperativetechniques in wireless systems, de-
a respect to the probability of error because the transmission
signers often consider the transmission technologies available
of multiple copies of the signals reduce the probability that
and their suitability to certain applications. Therefore, the
the message will not be received correctly. The multiplexing
concept of distributed antenna arrays can be easily extended
gains [14], which correspondto the additional numberof bits
to techniquessuch as MIMO [5], [6] and DS-CDMA systems
that the system can transmit as compared to a single-antenna
[7], [8].
link, can be obtained when a designer can use relays to form
InthecontextofMIMOsystems,onecanobtainsubstantial
independentchannelsandincreasetherateofcommunication.
multiplexing [5], [6], [11] and diversity gains [9], [10] with
Despite the many advantages in terms of gains as previ-
the deployment of multiple antennas at both ends of the
ously outlined, cooperative communications also entail some
wireless system. MIMO technology is poised to equip most
disadvantages such as signalling overheads [13], more com-
of the future wireless systems and can be incorporated in
putationally complex scheduling algorithms [4] and increased
conjunction with other transmission systems. There are two
latency [16]. Forthis reason,it is importantto weigh the pros
basic configurations which exploit the nature of the wireless
andconsofcooperativetechniquespriortotheiradoptionand
channel: spatial multiplexing [11] and diversity [10]. Spatial
consider the practical scenarios of interest [17]. Motivated by
multiplexing relies on the concept of forming individual data
their performance and diversity gains, cooperative techniques
stream between pais of transmit and receive antennas. The
are now being considered for the next generation of mobile
capacity gains of spatial multiplexing grow linearly with the
networks [12], [18], [19]. In cooperative systems, terminals
minimum number of transmit and receive antennas [5], [6]
and allow a MIMO system to obtain a considerable increase
The work of the authors was supported by the University of York, York
Y0105DD,UnitedKingdom. in data rates. Diversity configurationsadopt space-time codes
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[9], [10] to transmit data from the antennas at the transmitter themes in the MIMO relaying literature [31]–[33]. However,
and can obtain a lower probability of error. currentapproachesare often limitedto stationary,single relay
DS-CDMA systems are a key multiple access technology systems and channels which assume the direct path from the
for current and future wireless communication systems. Such source to the destination is negligible [32].
systems rely on the idea of transmitting data with the aid of Most of these resource allocation and interference miti-
unique signatures, which are also known as spreading codes. gation strategies require a higher computational cost to im-
These signatures are responsible for spreading the informa- plement the power allocation and a significant amount of
tion in frequency, and allow the system to have multiple signalling, decreasing the spectral efficiency of cooperative
users on the same channel. The advantages of DS-CDMA networks. This problem is central to ad-hoc and sensor net-
include good performance in multi-path channels, flexibility works [30] that employ spread spectrum systems and require
in the allocation of channels, increased capacity in bursty multiple hops to communicate with nodes that are far from
and fading environments and the ability to share bandwidth the source node. This is also of paramount importance in
with narrowband communication systems without deteriora- cooperative cellular networks.
tion of either’s systems performance [7], [8]. Demodulating
a desired user in a DS-CDMA network requires processing
B. Contributions
the received signal in order to mitigate different types of
interference, namely, narrowband interference (NBI), multi- In this chapter, we present joint interference suppression
accessinterference(MAI),inter-symbolinterference(ISI)and and power allocation algorithms for DS-CDMA and MIMO
the noise at the receiver. The major source of interference in networks with multiple hops and AF and DF protocols. A
most CDMA systems is MAI, which arises due to the fact scheme that jointly considers the power allocation across the
that users communicate through the same physical channel relayssubjecttogroup-basedpowerconstraintsandthedesign
with non-orthogonalsignals. of linear receivers for interference suppression is proposed.
The similarities between MIMO and CDMA systems in- The idea of a group-based power allocation constraint is
clude their mathematically similar descriptions and their fun- shown to yield close to optimal performance, while keeping
damental need for interference mitigation. Indeed, the data thesignallingandcomplexityrequirementslow.Aconstrained
streams of MIMO systems operating in a spatial multiplexing minimum mean-squarederror (MMSE) design for the receive
configuration are equivalent to the users of a DS-CDMA filtersandthepowerallocationvectorsisdevelopedalongwith
system. In order to separate data streams or users, a designer anMMSE channelestimatorforthecooperativesystem under
mustresorttodetectiontechniques[22],whichareverysimilar consideration. The linear MMSE receiver design is adopted
when applied to either MIMO or DS-CDMA. The optimal due to its mathematical tractability and good performance.
maximumlikelihood(ML)detectorisoftentoocomplextobe However, the incorporation of more sophisticated detection
implementedforsystemswithalargenumberofantennas.For strategiesincludinginterferencecancellationwithiterativede-
thisreason,designersoftenresortto suboptimalsolutionsthat coding [39] and advanced parameter estimation methods [49]
an attractive trade-off between performance and complexity. is also possible. In order to solve the proposed optimization
These includethe spheredecoder(SD) algorithms[23], linear problem efficiently, a method to form an effective group of
detectors [22], the successive interference cancellation (SIC) users and an alternating optimization strategy are presented
approach [11], the parallel interference cancellation (PIC) withrecursivealternatingleastsquares(RALS)algorithmsfor
[22] and the decision feedback (DF) detectors [39], [69] estimatingtheparametersofthereceiver,thepowerallocation
are techniques that can offer an attractive trade-off between andthechannels.Ajointrelayselectionandtransmitdiversity
performance and complexity. These detection algorithms can selection strategy for MIMO networks with linear receivers
be combined with cross-layer design techniquesfor enhanced is also proposed which optimizes relay transmissions with
interference mitigation and improved overall performance. In minimal feedback requirements. Effectively a novel approach
this chapter, we are specifically interested in exploring the to 1-bit power allocation, two joint discrete optimization
advantages of linear detection with power allocation, data functionsareformedwhicharesolvedusingdiscretestochastic
stream and relay selection. algorithms.
A. Prior and Related Work C. Organisation of the Chapter
Priorworkon cross-layerdesignforcooperativeandmulti- The chapter is organized as follows. Section II describes
hop communications has considered the problem of resource cooperative DS-CDMA and MIMO system models with mul-
allocation[24],[25]ingenericnetworks.Theseincludepower tiple hops. Section III formulates the problem, details the
and rate allocation strategies. Related work on cooperative constrainedMMSEdesignofthe receivefiltersandthe power
multiuserDS-CDMAnetworkshasfocusedontheassessment allocation vectors subject to a group-based power allocation
of the impact of multiple access interference (MAI) and constraint, and describes an MMSE channel estimator. An
intersymbolinterference(ISI),theproblemofpartnerselection extensionto cooperativeMIMOsystemsis also presentedand
[20], [26], the bit error ratio (BER) and outage performance discreteoptimizationproblemsareformulatedtojointlyselect
analysis [27], and training-based joint power allocation and the optimal relays and their transmit antennas. Section IV
interference mitigation strategies [28], [29]. Previous works presents an algorithm to form the group and the alternating
have also considered the problem of antenna selection, relay optimization strategy along with RLS-type algorithms for
selection (RS) and diversity maximization, which are central estimatingtheparametersofthereceiver,thepowerallocation
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and the channels. For the solution of the combinatorial prob- respectively,
lems posed by the relay selection strategy, a pair of discrete
K
stochastic algorithms are introduced and their joint operation r = ak C h b +η
detailed. Section V presents and discusses the simulation sd sd k sd,k k sd
k=1
results and Section VI draws the conclusions of this work. X
+n ,
sd
K
r = ak C h b +η
srj srj k srj,k k srj
II. SYSTEM ANDDATAMODELSOFCOOPERATIVE kX=1 (1)
WIRELESSSYSTEMS +nsr1j,
K
r = ak C h ˜b +η
In this section, we consider system and data models of rjd rjd k rjd,k k rjd
cooperative wireless systems. The basic idea is to use a kX=1
+n ,
linear algebra approach to describe models of the cooperative rjd
systems of interest. In particular, we focus on DS-CDMA j =1,...,n , i=1,...,P
r
and MIMO systems and we present a unified approach to the
where M =N +L−1, P is the number of packet symbols,
description of these systems.
n =n +1isthenumberoftransmissionphasesorhops,and
p r
n is the number of relays. The vectors n , n and n
r sd srj rjd
are zero mean complex Gaussian vectors with variance σ2
generatedatthereceiversofthedestinationandtherelaysfrom
A. Cooperative DS-CDMA System and Data Model
differentlinks,andthevectorsη ,η andη representthe
sd srj rjd
intersymbolinterference(ISI).Theamplitudesofthesourceto
destination, source to relay and relay to destination links for
user k are denoted by ak , ak and ak , respectively. The
sd srj rjd
quantities b and ˜b represent the original and reconstructed
k k
symbols by the AF or DF protocol at the relays, respectively.
The M × L matrix C contains versions of the signature
k
sequences of each user shifted down by one position at each
column as described by
c (1) 0
k
 ... ... ck(1) 
Ck = .. , (2)
 ck(N) . 
 
 0 ... c (N) 
 k 
 
where c = c (1), c (2), ..., c (N) stands for the
k k k k
signature sequence of user k, the L×1 channel vectors from
(cid:2) (cid:3)
source to destination, source to relay, and relay to destination
are h , h , h , respectively. By collecting the data
sd,k srj,k rjd,k
vectors in (5) (including the links from relays to the destina-
Fig.1. (a)Uplinkand(b)downlinkofthecooperative DS-CDMAsystem.
tion) into a J ×1 received vector at the destination, where
J =(n +1)M, we obtain
r
Let us first consider a synchronous DS-CDMA network rsd Kk=1aksdCkhsd,kbk
withmultipathchannels.TheDS-CDMAsystemoperateswith r K ak C h ˜br1d
QPSK modulation, K users, N chips per symbol and L as  r.1d = Pk=1 r1d .k r1d,k k 
tAehqneuiopmupatelxdiinmweuitomhfAtnhFuemasnbydesrtDemoFfpirpsortodopecapogilcasttetihodantinaplal(ot1hw)s.cTfoohmremesauycnshitceamlitniokins. rrn..rd  +η+PKk=n1akrnrdC..khrnrd,k˜bkrnrd (3)
in multiple hops using n fixed relays in a repetitive fashion. P
r
We assume that the source node or terminal transmits data
organizedin packets with P symbols, there is enoughcontrol
data to coordinate transmissions and cooperation, and the
linear receivers at the relay and destination terminals are
synchronized with their desired signals. The received signals
are filtered by a matched filter, sampled at chip rate and
organized into M × 1 vectors r , r and r , which
sd srj rjd
describethesignalreceivedfromthesourcetothedestination,
the source to the relays, and the relays to the destination,
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Rewriting the above signals in a compact form yields destination, respectively,
K K
r[i]= B [i]A [i]C h [i]+η[i]+n[i] r = ak h b [i]+η
k k k k sd sd sd,k k sd
k=1 k=1
X p [i] X
e e e k +n ,
K sd
| {z }
= B [i]A [i]C h [i]+η[i]+n[i] (4) K
k k k k r = ak h b [i]+η
Xk=1 srj srj srj,k k srj
K e e e Xk=1 (5)
= Pk[i]Bk[i]ak[i]+η[i]+n[i], +nsrj,
k=1 K
X r = ak h ˜b [i]+η
where the J × (n + 1)L matrix C = diag{C ...C } rjd rjd rjd,k k rjd
r k k k
k=1
contains copies of C shifted down by M positions for each X
k +n ,
group of L columns and zeros elsewehere. The Q×1 vector rjd
hk[i], where Q = (nr +1)L contains the channel gains of j =1,...,nr, i=1,...,P, p=1,2
the links between the source, the relays and the destination, where P is the number of packet symbols, n = 2 is the
p
and pk[i] is the effectivesignature for user k. The (nr+1)× numberof transmission phasesor hops, and nr is the number
(nr+1)diagonalmatrixBk[i]=diag(bk[i]˜bkr1d[i]...˜brknd[i]) of relays. The vectors nsd, nsrj and nrjd are zero mean
contains the symbols transmitted from the source to the complex Gaussian vectors with variance σ2 generated at the
destination (bk[i]) and the nr symbols transmitted from receiversofthedestinationandtherelaysfromdifferentlinks,
the relays to the destination (˜br1d[i]...˜brnd[i]) on the and the vectors η , η and η represent the intersymbol
k k sd srj rjd
main diagonal, and the J × J diagonal matrix Bk[i] = interference (ISI).
diag(b [i] I ˜br1d[i] I ...˜brnd[i] I ), where
k M k M k M
denotes the Kronecker product and IM is an identitey matrix The amplitudesof the sourceto destination,source to relay
N N N N
with dimension M. The (nr+1)×1 power allocation vector and relay to destination links for user k are denoted by ak ,
tahke[i(]n=r +[aks1d)a×kr1d(n.r..+akr1n)rdd]TiaghoansatlhemaamtripxlitAudke[is]oifstghievelninkbsy, areksprjresaenndt tahkrejdo,rirgeisnpaelcatinvdelyre.cTonhsetruqcutaendtistiyemsbbokl[si]byantdhe˜bkAs[diF]
Ak[i]=diag{ak[i]}, and the J×J diagonalmatrix Ak[i]= or DF protocol at the relays, respectively. The M ×1 spatial
[aksd IM akr1d IM...akrnrd IM]T. The J ×(nr +1) channel vectors from source to destination, source to relay,
matrNix Pk has cNopies of the effeNctive signature pk[i]eshifted andrelaytodestinationare hsd,k,hsrj,k,hrjd,k, respectively.
down by M positions for each column and zeros elsewhere. By collecting the data vectorsin (5) (includingthe links from
The J ×1 vector η[i] represents the ISI terms and the J ×1 relays to the destination) into a J ×1 received vector at the
vector n[i] has the noise components. destination, where J =n M for MIMO systems, we obtain
p
K ak h b [i]
r[i]= k=1 sd sd,k k
B. Cooperative MIMO System and Data Model " njr PKk=1akrnrdhrnrd,k˜bkrnrd[i]# (6)
+nP[i] P
Let us now consider a synchronous MIMO system model,
which has similarities with the DS-CDMA system model of
the previous subsection. We consider a narrowband MIMO
system with flat fadingchannels,QPSK modulation,K trans-
mit antennas, and M receive antennas as illustrated in Fig.
2. The cooperative MIMO network is equipped with DF
protocol that allows communication in n = 2 hops using
p
n fixed relays in a repetitive fashion where a non-negligible,
r
direct source to destination link exists during the first phase.
We assume that the source node or terminal transmits data
organizedin packets with P symbols, there is enoughcontrol
data to coordinate transmissions and cooperation, and the
linear receivers at the relay and destination terminals are
synchronized with their desired signals. It should be noted
that the MIMO and CDMA system and data models are
mathematically equivalent and the main difference is that
we employ for the MIMO version a spreading code matrix
C =1.
k
Thereceivedsignalsarefilteredbyamatchedfilter,sampled
at chip rate and organized into M ×1 vectors r , r and
sd srj
r , which describe the signal received from the source to
rd Fig.2. Blockdiagram of2-phasecooperative MIMOsystem.
the destination, the source to the relays, and the relays to the
5
Rewriting the above signals in a compact form yields contains the symbols transmitted from the sources to
the destination and from the relays to the destination
Knr
of the G users in the group on the main diagonal,
r[i]= B [i]A [i]h [i]+n[i]
k k k
the G(n + 1) × 1 power allocation vector a [i] =
kX=1 (7) [aS1[i]aSr1 [i]...aS1 [i], ..., aSG[i]aSG[i]...aSGS,k[i]]T of
K e e sd r1d rnrd sd r1d rnrd
= P [i]B [i]a [i]+n[i], theamplitudesofthelinksusedbytheGusersordatastreams
k k k
in the group.
k=1
X
The J ×1 vector h [i] contains the spatial channel gains of
k A. Linear MMSE Receiver Design and Power Allocation
the links between the source, the relays and the destination.
Scheme with Group-Based Constraints
The n × n diagonal matrix B [i] = diag(b [i] ˜brkd[i]),
for 1 p≤ kp ≤ K, and B [i]k = diag(0 k˜brkd[ik]), for The linear MMSE interference mitigation for user or
k k data stream k is performed by the receive filter w [i] =
K < k ≤ Kn , contains the symbols transmitted from k
r
[w [i], ..., w [i]]withJ coefficientsonthereceiveddata
the source to the destination (b [i]) and the n symbols k,1 k,J
k r
transmitted from the relays to the destination (˜brkd[i]) on vector r[i] and yields
k
the main diagonal, and the J ×J diagonal matrix Bk[i] = zk[i]=wHk [i]r[i], (9)
diag(b [i] I ˜brkd[i] I ), for 1 ≤ k ≤ K, and
k M k M wherez [i]isanestimateofthesymbols,whichareprocessed
B [i] = diag(0 I ˜brkd[i] I ), for K < k ≤e Kn ,. k
k N M kN M r byaslicerQ(·)thatperformsdetectionandobtainsthedesired
The n ×1 power allocation vector a [i] = [ak ... ak ]T
heas thep amplitudNes of the linksN, the npk×np disadgonal mraktdrix symLebtoluassnˆbokw[i]d=etaQil(ztkh[ei])li.near MMSE-based design of the
A [i]isgivenbyA [i]=diag{a [i]},andtheJ×J diagonal
k k k receiversforuserordatastreamkrepresentedbyw [i]andfor
matrix A [i] = [ak I ... ak I ]T. The J ×n k
k sd M rnkd M p the computationof the G(nr+1)×1 powerallocation vector
matrix P has copies of the spatial signatures h [i] shifted
k N N k aS,k[i].Thisproblemcanbecastasthefollowingconstrained
down byeM positions for each column and zeros elsewhere.
optimization
The J ×1 vector n[i] has the noise components.
[wopt, aopt]=arg min E[(|b [i]−wH[i]r[i]|2]
k S,k k k
III. JOINT MMSERECEIVER DESIGN, POWER wk[i],aS,k[i]
subject to aH [i]a [i]=P ,
ALLOCATION,RELAY SELECTIONANDCHANNEL S,k S,k G
(10)
ESTIMATION
Inthissection,ouraimistodescribetechniquestomitigate In orderto obtain expressionsfor the receivefilter wk[i] and
interference and allocate the power and select the best relays the powerallocation vector aS,k[i] subjectto the group-based
powerconstraints,weneedthehelpofthemethodofLagrange
according to the mean square error (MSE) criterion. We
multipliers(10)[51]thattransformsaconstrainedoptimization
present a joint receiver design and power allocation strat-
into an unconstrained one. The MMSE expressions for w [i]
k
egy using constrained linear MMSE estimation and group- and a [i] are given by
S,k
based power constraints along with a linear MMSE channel
estimator. The interesting aspect of the group-based power Lk =E(cid:2)|bk[i]−wHk [i](cid:0)PS[i]BS[i]aS,k[i]
constraints is that a designer can choose a subset of users +XPk[i]Bk[i]ak[i]+η[i]+n[i](cid:1)|2(cid:3) (11)
or data streams for power adjustment. Another technique that k6=S
is detailed here is a methodcalled transmitdiversity selection +λk(aS,k[i]−PG),
(TDS) which operates with the linear MMSE receivers. With
where λ is a Lagrange multiplier.
k
the TDS technique the relay selection is used to jointly
Since the Lagrangian in (11) is a function of both w [i]
k
optimize the selection of antennas in a strategy equivalent to
and a [i], we need to employ a strategy for optimization
S,k
a 1-bit transmit antenna power allocation.
the functionwith respectto bothparametervectors.The main
In order to describe the techniques necessary for inter-
idea is to fix one of the parameter vectors and compute the
ference mitigation and resource allocation, we introduce an
gradient terms with respect to the other parameter vector
alternativeway of expressingthe J×1 receivedvectorin (7).
that minimizes the Lagrangian and obtain the expression of
Our goal is to separate the subset of users or data streams
interest. In particular,an expressionfor a [i] is obtainedby
S,k
that will be used for resource allocation with the group-based
fixing w [i], taking the gradient terms of the Lagrangian and
k
powerconstraints. The modified J×1 received vectorcan be
equating them to zero, which yields
expressed as
a [i]=(R [i]+λ I)−1p [i] (12)
S,k S,k k S,k
r[i]=P [i]B [i]a [i]+ P [i]B [i]a [i]+η[i]+n[i],
S S S,k k k k
where the G(n + 1) × G(n + 1) covariance matrix
k6=S r r
X (8) R [i] = E[BH[i]PH[i]w [i]wH[i]P [i]B [i]] and the
S,k S S k k S S
where S = {S1,S2,...,SG} denotes the group of vectorpS,k[i]=E[bk[i]BHS[i]PHS[i]wk[i]] is a G(nr+1)×1
G users to consider in the design. The J × G(nr + cross-correlation vector. The Lagrange multiplier λk plays
1) matrix P = [P P ... P ] contains the role of a regularization term and has to be determined
S S1 S2 SG
the G effective signatures of the group of users. The numerically due to the difficulty of evaluating its expression.
G(n + 1) × G(n + 1) diagonal matrix B [i] = Inordertocomputetheexpressionforw [i],wefixa [i],
r r S k S,k
diag(b [i] ˜br1d[i]...˜brnd[i] ... b [i] ˜br1d[i]...˜brnd[i]) calculatethegradienttermsoftheLagrangianandequatethem
S1 S1 S1 SG SG SG
6
to zero which leads to and its cardinality improved without overly restricting the
second-phase channels available to the TDS process. The
w [i]=R−1[i]p [i], (13)
k k selection of the single highest MSE relay can be expressed
where the covariance matrix of the received vector is given as a discrete maximization problem given by
by R[i] = E[r[i]rH[i]] and p [i] = E[b∗[i]r[i]] is a J ×1
k k j =arg max F i,r ,
cornostsh-ecoprroewlaetrioanllvoeccattoior.nThveecqtouranatities[iR]. [Ti]haendexppkre[is]sidoenpsenind opt j∈ΩR srj
S,k (cid:2)K (cid:3)
(12) and (13) donothavea closed-formsolutionas theyhave 2
=arg max E b [i]−w [i]r [i] , (15)
a dependence on each other. Moreover, the expressions also k j,k srj
require the estimation of the channel vector hk[i]. Thus, it j∈ΩR Xk=1 h(cid:13) (cid:13) i
is necessary to iterate (12) and (13) with initial values to where ΩR is the set of can(cid:13)didate relays and wj,(cid:13)k[i] is the
obtain a solution and to estimate the channel. The network MMSE filter for the kth symbol at the jth relay. On the
has to convey the information from the group of users which solution of (15), a refined subset, Ω¯T ∈ ΩT, is generated by
is necessary to compute the group-based power allocation removing members of ΩT which involve transmission from
including the filter wk[i]. The expressions in (12) and (13) relay jopt, i.e. membersof ΩT where [a1rjoptd...aKrjoptd]6=0.
require matrix inversions with cubic complexity ( O((J)3) TDSthen operateswith thissubset, where |Ω¯ |= K(nr−1) .
and O((G(nr +1))3). ExtensiontotheselectionofmultiplerelaysinTvolvessuKmsumbing
(cid:0) (cid:1)
the MSE from candidate relays and populating Ω with sets
R
of these relays. However, the selection of the number of
B. Transmit Diversity Selection and Relay Selection
relays to remove is vital, as too high a value will result in
In this subsection,we explorethe idea of transmitdiversity a overlyrestrictingthe second phase channelsavailable to the
selection (TDS) and relay selection (RS) and how they can TDS processtherefore increasing the probabilityof a channel
be used to improve the performance of cooperative systems. mismatch.
In cooperative wireless systems with multiple relays, there
are links that have very poor propagation conditions that can
degradetheperformanceoftheoverallsystem.Theselinkscan
be identified and removed from the operation of the system
via TDS and RS. To this end, we formulate a TDS and RS
strategyfora2DFMIMOnetworkasadiscretecombinatorial C. Cooperative MMSE Channel Estimation
MSE problem which optimizes the use of the channels of
the second phase via 1-bit power allocation [55]. It turns out
The next task that is necessary for the interference mit-
that the problemsof TDS and RS are combinatorialproblems
igation and resource allocation is to compute the channel
which require either an exhaustive search or some relaxation
gains of the links of the cooperative system. In order to
approach. We specify that a subset of K antennas of the
sub estimate the channel in the cooperative system under study,
n K relay antennas are active at each time instant in order
r let us first consider the transmitted signal for user k, x [i]=
to reduce the optimization complexity but also to ensure a k
B [i]A [i]C h [i] = Q [i]h [i], and the covariance matrix
minimum available level of diversity. The destination node’s k k k k k k
given by
MSE TDS optimization function is given by
Topt =arg min C i,T ,r eR=e[r[i]erH[i]]
r r
Tr∈ΩT K
K(cid:2) (cid:3) (14) = Qk[i]E[hk[i]hHk [i]]QHk [i]+E[η[i]ηH[i]]+σ2I
2
=arg min E bk[i]−wk[i]r[i] , kX=1
where T =Tr∈dΩiaTg(akX1=1 ..h.(cid:13)(cid:13)aK ,...,a1 ..(cid:13)(cid:13).aiK ) and = K Qk[i]PhkQHk [i]+Pη+σ2I
r r1d r1d rnrd rnrd k=1
akrjd = {0,1}, and wk is the linear MMSE filter for the X (16)
kth symbol. Under the assumption of no inter-relay com-
A linear estimator of h [i] applied to r[i] can be represented
munication and that each data stream is allocated to its k
as hˆ [i] = FHr[i]. The linear MMSE channel estimation
correspondinglynumbered transmit antenna at each relay, the k k
set Ω has a cardinality of |Ω | = nrK and contains all problem for the cooperative system under consideration is
T T Ksub formulated as
possiblecombinationsofrelaytransmitantennaspatterns.The
performance and complexity of solut(cid:0)ions t(cid:1)o (14) depend on F =argminE ||h [i]−hˆ [i]||2
k,opt k k
|Ω | and its elements. However, |Ω | is significant even for Fk (17)
moTdest numbers of antennas and rTelays, e.g. nr ≥ 4 and =argmTiknE(cid:2)||hk[i]−THk r[i]|(cid:3)|2 .
K ≥2.Furtherimprovementscanbeachievedbyaprocesswe
Computing the gradient terms(cid:2)of the argument an(cid:3)d equating
term RS which addresses the possibility of mismatching poor
them to zero yields the MMSE solution
first phase channels with optimized second phase channels as
well as reducing the cardinality of ΩT. F =R−1P , (18)
k,opt k
By removing one or more relays based on their MSE
performancefromconsiderationby(14), Ω canbeoptimized where P = E[r[i]hH[i]] = Q [i]E[h [i]hH[i]] =
T k k k k k
7
Q [i]P . Using the relation hˆ [i]=FHr[i], we obtain where α is a forgetting factor that should be close to but less
k hk k k
than 1.
hˆ [i]=FH r[i]=PHR−1r[i]
k k,opt k
K
=PH QH[i] Q [i]P QH[i]+P +σ2I −1r[i], B. Joint Interference Suppression and Power Allocation
hk k k hk k η The approach for allocating the power within a group is
k=1
(cid:0)X (cid:1) (19) to drop the constraint, estimate the quantities of interest and
thenimposetheconstraintviaasubsequentnormalization.The
The expressions in (19) require matrix inversions with cu-
group-based power allocation algorithm is computed by
bic complexity ( O(J3)), however, this matrix inversion is
common to (13) and needs to be computed only once for aˆ [i]=Rˆ [i]pˆ [i]
S,k S,k S,k
both expressions. In what follows, computationally efficient
=Rˆ [i](αpˆ [i−1]+b [i]v [i]) (25)
algorithms with quadratic complexity (O(J2)) based on an S,k S,k k k
alternating optimization strategy will be detailed. =aˆS,k[i−1]+ξa[i]kS,k[i],
where ξ [i] = b [i]−aˆH [i−1]v [i] is the a priori error,
IV. ADAPTIVEALGORITHMS v [i]=aBH[i]PHk[i]w [iS],kis the inpkut signal to the recursion
k S S k
In this section, we present algorithms to compute the pa-
rametersofinterestandtheexpressionsderivedintheprevious k [i]= α−1RˆS,k[i−1]vk[i] , (26)
section with lowercomputationalcomplexity.Specifically,we S,k 1+α−1vH[i]Rˆ [i−1]v [i]
k S,k k
develop adaptive RALS algorithms using a method to build
the group of G users based on the power levels, and then RˆS,k[i]=α−1RˆS,k[i−1]−α−1kS,k[i]vHk [i]RˆS,k[i−1].
(27)
we employ an alternating optimization strategy for efficiently
estimatingtheparametersofthereceivefilters,thepowerallo- The normalization aˆS,k[i] ← PG aˆS,k[i]/||aˆS,k[i]|| is then
performed to ensure the power constraint.
cationvectorsandthechannels.Despitethejointoptimization
The linear receive filter is computed by
that is associated with a non-convex problem, the proposed
RALS algorithms have been extensively tested and have not wˆ [i]=wˆ [i−1]+k[i]ξ∗[i], (28)
k k
presented problems with local minima.
where the a priori error is given by ξ[i] = b [i]−wˆH[i−
k k
1]r[i]andk[i]isgivenby(22).Theproposedschemeemploys
A. Group Allocation and Channel Estimation
the algorithm in (20) to allocate the users in the group and
Thefirststepintheproposedstrategyistobuildthegroupof the channel estimation approach of (21)-(24). The alternating
G users thatwill be used forthe powerallocationand receive optimization strategy uses the recursions (25) and (28) with
filter design. A RAKE receiver [7], which is equivalent to a 1 or 2 iterations per symbol i.
filter matchedto the signaturesequence of the desired useror
the spatial signature of the desired data stream will be used
C. TransmitDiversitySelectionandRelaySelectionBasedon
for the group allocation. The RAKE receiver is employed to
obtain zRAKE[i]=(C hˆ [i])Hr[i]=pˆH[i]r[i]. The group is Discrete Stochastic Gradient Algorithms
k k k k
then formed according to In this part, we describe a low-complexity solution to the
joint TDS and RS problem based on a discrete stochastic
e
compute the G largest |zkRAKE[i]|, k =1,2,...,K. gradient algorithm (DSA) that can compute the optimal com-
(20) binatorialsolutionoutlinein(14)and(15)withasubstantially
The design of the RAKE and the other tasks require channel reduced cost as compared with the exhaustive search. We
estimation. The power allocation, receive filter design and presentapairoflow-complexityDSAthatwasfirstreportedin
channel estimation expressions given in (12), (13) and (19), [33],[52],whichjointlyoptimizesRSandTDSinaccordance
respectively,are solved by replacing the expected values with with (14) and (15), and converges to the optimal exhaustive
time averages, and RLS-type algorithms with an alternating solution.
optimization strategy. In order to solve (19) efficiently, we The RS portion of the DSA is given by the algorithm of
develop a variant of the RLS algorithm that is described by Table I. At each iteration the MSE of a randomly chosen
hˆ [i]=PˆH [i]QH[i]Rˆ−1[i]r[i], (21) candidaterelay (jC) (step2) and thatofthe worstperforming
k hk k relay currently known (jW) are calculated (step 3). Via a
where Q [i] = B [i]A [i]C , the estimate of the inverse of comparison, the higher MSE relay is designated jW for the
k k k k
the covariance matrix Rˆ−1[i] is computed with the matrix next iteration (step 3). The current solution and the relay
chosenforremoval(j) is denotedas the currentoptimumand
inversion lemmae[51] e e
is the relay which has occupied jW most frequently over the
α−1Rˆ[i−1]r[i] course of the packet up to the ith time instant; effectively
k[i]= , (22)
1+α−1rH[i]Rˆ[i−1]r[i] an average of the occupiers of jW. This averaging/selection
process is performed by allocating each member of Ω a
R
Rˆ[i]=α−1Rˆ[i−1]−α−1k[i]rH[i]Rˆ[i−1], (23) |Ω |×1 unitvector, v , which has a one in its corresponding
R l
positioninΩ ,i.e.,v [i]isthelabeloftheworstperforming
and R jW
relay at the ith iteration. The current optimum is then chosen
Pˆ [i]=αPˆ [i−1]+hˆ [i−1]hˆH[i−1], (24) andtrackedbymeansofa|Ω |×1stateoccupationprobability
hk hk k k R
8
TABLEI
interferencesuppressionschemes withoutcooperation(NCIS)
PROPOSEDDISCRETESTOCHASTICJOINTTDSANDRSALGORITHM
and with cooperation (CIS) using an equal power allocation
Step across the relays. Both uplink and downlink scenarios are
1. Initialization considered in the analysis. In Table I we show the computa-
choosej[1]∈ΩR,jW[1]∈ΩR,πR(cid:2)1,j[1](cid:3)=1,πR[1,¯j]=0 tional complexity required by each recursion associated with
for¯j6=j[1]
a parameter vector/matrix for the JPAIS-GBC with G = K,
2. Forthetime indexi=1,2,...,N
choosejC[i]∈ΩR which is more suitable for the uplink.
3. Comparison and updateof theworst performing relay
oifthFer(cid:2)wi,isresrjjWC[[ii]+(cid:3)>1]F=(cid:2)ij,Wrs[rij]W[i](cid:3)thenjW[i+1]=jC[i] COMPUTATIONALCOMPLEXITTAYBOLFEAIILGORITHMSWITHAGLOBAL
4. Stateoccupation probability (SOP)vector update POWERCONSTRAINTG=K .
πR[i+1]=πR[i]+µ[i+1](vjW[i+1]−πR[i])whereµ[i]=1/i
5. Determine largest SOPvector element and select theoptimum relay Number of operations per symbol
ifπR(cid:2)i+1,jW[i+1](cid:3)>πR[i+1,j[i]]thenj[i+1]=jW[i+1] Parameter Additions Multiplications
otherwise j[i+1]=j[i]
6. TDS SetReduction 2(J)2 3(J)2
removemembersof ΩT whichutilize relay j[i+1](ΩT →Ω¯T) Wˆ [i] +2K(J) +2K(J)
−J+1 +3J+1
3K(K(nr+1)) K(K(nr+1))2
(SOP) vector, πR. This vector is updated at each iteration +K(nr+1)(L−1) +4(K(nr+1))2
by adding vjW[i+1] and subtracting the previous value of aˆT[i] +K(M(nr+1)) +(K+L)(K(nr+1))2
πR (step 4). The current optimum is then determined by +K(K(nr+1)) −(K(nr+1))2
selectingthelargestelementinπR anditscorrespondingentry +6(K(nr+1))2 +K(MQ)
in ΩR (step 5). Through this process, the current optimum +3K(nr+1)+nr+2 +nr
convergestowardsand tracksthe exhaustivesolution[52]. An 5(KQ)2 +5(K(nr+1)2
alternative interpretation of the proposed algorithm is to view hˆ [i] +5KQ +6KQ
k
thetransitions, jW[i]→jW[i+1],asa Markovchainandthe
+3 +1
members of Ω as the possible transition states. The current
R
optimum can then be defined as the most visited state.
In Table II we show the computationalcomplexityrequired
Once RS is complete at each time instant, set reduction
by each recursion associated with a parameter vector for the
(Ω →Ω¯ ,step6)andTDScantakeplace.ToperformTDS,
T T JPAIS-GBC algorithm, which is suitable for both the uplink
modified versions of steps 1−5 are used. The considered set
andthedownlink.AnoticeabledifferencebetweentheJPAIS-
is replaced, Ω → Ω¯ ; the structure of interest is replaced,
R T GBC with G = K and G = 1 is that the latter is employed
j → T ; the best performing matrix is sought jW → TB;
r r for each user, whereas the former is used for all the K users
the SOP vector is replaced πR → πT and C → F from in the system. Since the computationof the inverse of Rˆ[i] is
(14). Finally, the inequality of step 3 is reversed to enable
common to all users for the uplink in our system, the JPAIS-
convergence to the lowest MSE TDS matrix which is then
GBC with G=K is more efficientthan the JPAIS-GBC with
feedback to the relays in the form of 1-bit per relay antenna.
G=1 computed for all the K users.
Significant complexity savings result from the proposed
algorithm;savingswhichincreasewith K,nr andthenumber TABLEIII
relaysremovedintheRSprocess.Forexample,whennr =10, COMPUTATIONALCOMPLEXITYOFALGORITHMSWITH
K = 2 and 4 relays are removed, the number of complex INDIVIDUALPOWERCONSTRAINTS(G=1).
multiplications for MMSE reception and exhaustive TDS,
Number of operations per symbol
exhaustive TDS with RS, iterative TDS and iterative TDS
with RS are 5.8×108, 1.7×108, 1.8×105 and 5.9×104, Parameter Additions Multiplications
respectively, for each time instant. 2(J)2 3(J)2
wˆ [i] +J +5J
k
+1 +1
V. ANALYSIS ANDREQUIREMENTS OF THEALGORITHMS
2(nr+1)2 3(nr+1)2
In this section, we assess the requirements of the proposed
+3(nr+1) +7(nr+1)
and existing algorithms for cross-layer design in terms of
aˆ [i] +JL +JL
k
computational complexity and number of feedback bits. The
+Q +Q
basic idea is to showthe computationalcost ofthe algorithms
−3 +3
presentedandcomparethemwiththoseofexistingtechniques
2(Q)2 6(Q)2
for interference mitigation and/or resource allocation.
hˆ [i] +5MQ +MQ
k
−5(nr+1)+3 +4(nr+1)+1
A. Computational Complexity Requirements
We discuss here the computational complexity of the pro- TherecursionsemployedfortheproposedJPAIS-GBCwith
posed and existing algorithms. Specifically, we will detail the G = K and the JPAIS-GBC with G = 1 are general and
required number of complex additions and multiplications of partsofthemareusedintheexistingCISandNISalgorithms.
the proposed JPAIS-GBC algorithms and compare them with Therefore, we can use them to describe the required compu-
9
tationalcomplexityof the existingalgorithms.In Table IIIwe G=1. A typical numberof bits n requiredto quantize each
b
show the required recursions for the proposed and existing coefficient of the vectors a and a via scalar quantization
T k
algorithms, whose complexity is detailed in Tables I and II. is n = 4 bits. More efficient schemes employing vector
b
quantization [53], [54] and that take into account correlations
TABLEIV between the coefficients are also possible.
COMPUTATIONALCOMPLEXITYOFTHEPROPOSEDJPAISAND
Fortheuplink(ormultiple-accesschannel),thebasestation
EXISTINGALGORITHMS.
(oraccesspoint)needstofeedbackthepowerlevelsacrossthe
linkstotheK destinationusersinthesystem.WiththeJPAIS-
Algorithm Recursions
JPAIS-GPC(G=K) (Uplink) Wˆ [i], aˆT[i],hˆk[i] GBC with G = K algorithm, the parameter vector aT with
(n +1)Kn bits/packet must be broadcasted to the K users.
JPAIS-GBC (G=1) (Downlink) wˆ [i], aˆ [i], hˆ [i] r b
k k k FortheJPAIS-GBCalgorithmwithG=1,aparametervector
CIS (Uplink) Wˆ [i], aˆT[i] is fixed a with (n +1)n bits/packet must be broadcasted to each
k r b
CIS (Downlink) wˆ [i], aˆ [i] is fixed
k k user in the systems. In terms of feedback, the JPAIS-GBC
NCIS (Uplink) Wˆ [i] with nr =0 algorithm with G = 1 is more flexible and may require less
NCIS (Downlink) wˆk[i] with nr =0 feedback bits if there is no need for a constant update of the
power levels for all K users.
Complexity of RLS Algorithms DataPacketStructure Ntr Nsync Ndata
106
Feedback Packet Structure aT
s 105 (JPAIS-GBCwtihG=K) (nr+1)Knbbits/feedbackpacket
n
o
ati Feedback Packet Structure ak
multiplic 104 nr=3 (JPAIS-GBCwithG=1) Ktimes(nr+1)Knbbits/feedbackpacket
of
er Fig.4. Proposedstructure ofthedataandfeedback packets.
b
m
Nu 103 n=1 JPAIS−GBC(G=K)
r JPAIS−GBC(G=1) For the downlink (or broadcast channel), the K users must
CIS feedbackthe powerlevels across the links to the base station.
NCIS With the JPAIS-GBC algorithm with G = K, the parameter
1025 10 15 20 25 30 35 40 vector aT with (nr +1)Knb bits/packet must be computed
M by each user and transmitted to the base station, which uses
the a vector coming from each user. An algorithm for data
T
Fig. 3. Computational complexity in terms of the number of complex fusion or a simple averaging procedure can be used. For the
multiplications oftheproposedandexistingschemes fortheuplink. JPAIS-GBC algorithm with G = 1, a parameter vector a
k
with (n + 1)n bits/packet must be transmitted from each
r b
InFig.3,weillustratetherequiredcomputationalcomplex- userto thebase station.Intermsoffeedback,theJPAIS-GBC
ityfortheproposedandexistingschemesfordifferentnumber algorithmwith G=1 requiressignificantly less feedbackbits
ofrelays(n ).ThecurvesshowthattheproposedJPAIS-GBC than the JPAIS-GBC with G=K in this scenario.
r
with G=K and JPAIS-GBC with G= 1 are more complex The MIMO TDS and RS scheme can be interpreted as a
than the CIS scheme and the NCIS. This is due to the fact 1-bit power allocation scheme and therefore achieves perfor-
that the power allocation and channel estimation recursions mance improvements whilst utilizing the minimum number
are employed. However, we will show in the next section of feedback bits per antenna. Consequently, the feedback
thatthisadditionalrequiredcomplexity(whichismodest) can requirementsperupdateofacooperativeMIMOsystemusing
significantly improve the performance of the system. TDS and RS is given by the total number of relay transmit
antennasn K. This minimal feedback allows optimization of
r
the system whilst maintainingthe capacityof the system with
B. Feedback Channel Requirements
regards to the transmission of useful data.
TheJPAISalgorithmspresentedsofarforcross-layerdesign
require feedback signalling in order to allocate the power
levels across the relays. In order to illustrate how these VI. SIMULATIONS
requirements are addressed, we can refer to Fig. 4 which In this section, we illustrate with Monte-Carlo simulations
depicts the structure for both the data and feedback packets. theperformanceofthecross-layeralgorithmsdescribedin this
The data packet comprises a number of allocated bits for chapter. Specifically, we assess the performance in terms of
training (N ), for synchronization and control (N ) and the bit error ratio (BER) of the JPAIS scheme and adaptive
tr sync
thetransmitteddata(N ).Thefeedbackpacketrequiresthe algorithms with group-based power constraints (GBC). The
data
transmissionofthe powerallocationvector a forthecase of JPAIS scheme and algorithms are compared with schemes
T
the JPAIS-GBC algorithm with G = K, whereas it requires without cooperation (NCIS) and with cooperation (CIS) [26]
the transmission of a for each user for JPAIS-GBC with using an equal power allocation across the relays (the power
k
10
allocation in the JPAIS scheme is disabled). We also assess N=16, SNR = 15 dB, K=6 users, P=1500

the proposed algorithms for transmit diversity selection and NCIS−RLS(n=0)
r
relay selection (Iterative TDS with RS) are presented and CIS−RLS(n=2)
r
comparisons drawn against the optimal exhaustive solutions 10−1 JPAIS−GBC−RALS(nr=2,G=1)
(ExhaustiveTDSwith RS), theunmodifiedsystem (NoTDS), JPAIS−GBC−RALS(n=2,G=3)
r
and the direct transmission (Non-Cooperative). JPAIS−GBC−RALS(n=2,G=K)
r
JPAIS−GPC−MMSE [11]
A. DS-CDMA System R
BE10−2
A DS-CDMA network with randomly generated spreading
codes and a processing gain N = 16 is considered. The
fading channels are generated considering a random power
delay profile with gains taken from a complex Gaussian 10−3
variable with unit variance and mean zero, L = 5 paths
spaced by one chip, and are normalized for unit power. The
power constraint parameter PA,k is set for each user so that 0 500 1000 1500
the designer can control the SNR (SNR = P /σ2) and Number of received symbols
A,k
P = P +(K −G)P , whereas it follows a log-normal
T G A,k
Fig.5. BERperformanceversusnumberofsymbols.Parameters:AFproto-
deqisutrailbutotio3ndfBor. TthheeuDseFrscowoiptheraatsisvoecipartoetdocsotalnidsaarddodpetvediatainodn caonld,λRˆT−=1[iλ]k==0.00.10I2.5(forMMSEschemes),α=0.998,Rˆ−S,1k[i]=0.01I
all the relays and the destination terminal use either linear
MMSE, which have full channel and noise variance knowl-
edge, or adaptive receivers. The receivers are adjusted with
N=16, K=6 users, P=1500 N=16, SNR = 12 dB, P=1500
the proposed RALS with 2 iterations for the JPAIS scheme, 10−1 10−1
and with RLS algorithms for the NCIS and CIS schemes.
We employ packets with 1500 QPSK symbols and average
the curves over 1000 runs. For the adaptive receivers, we 10−2
provide training sequences with Ntr = 200 symbols placed 10−2 nr=1
at the preamble of the packets. After the training sequence,
n=1
the adaptivereceiversare switched to decision-directedmode. r
The first experiment depicted in Fig. 5 shows the BER BER10−3 NCnISr=(n2=0) BER
r
performance of the proposed JPAIS scheme and algorithms RLS
against the NCIS and CIS schemes with n = 2 relays. The CIS−RLS 10−3
r
JPAIS−GBC
JPAIS scheme is consideredwith the group-basedpowercon- 10−4 (G=1)−RALS
straints(JPAIS-GBC).AlltechniquesemployMMSEorRLS- JPAIS−GBC
type algorithms for estimation of the channels, the receive (JGP=A3IS)−−RGABLCS nr=2
filtersandthepowerallocationforeachuser.Theresultsshow (G=K)−RALS
10−5 10−4
that as the group size G is increased the proposed JPAIS 5 10 15 20 2 4 6 8 10 12
SNR (dB) Number of users
scheme and algorithms converge to approximately the same
levelofthecooperativeJPAIS-MMSEschemereportedin[28],
Fig.6. BERperformance versusSNRandnumberofusersforthe optimal
which employs G = K for power allocation, and has full linear MMSE detectors. Parameters: AF protocol, α = 0.998, Rˆ−1[i] =
S,k
knowledge of the channel and the noise variance. 0.01I andRˆ−1[i]=0.01I.
The proposedJPAIS-GBC scheme is then comparedwith a
non-cooperative approach (NCIS) and a cooperative scheme
with equal power allocation (CIS) across the relays for
n = 1,2 relays. The results shown in Fig. 6 illustrate the asdepictedinFig.7.Theideaistoillustrateasituationwhere
r
performanceimprovementachievedby the JPAIS scheme and the channel changeswithin a packet and the system transmits
algorithms, which significantly outperform the CIS and the thepowerallocationvectorscomputedbytheproposedJPAIS
NCIS techniques. As the number of relays is increased so algorithmsvia a feedbackchannel.In thisscenario,theJPAIS
is the performance, reflecting the exploitation of the spatial algorithms compute the parameters of the receiver and the
diversity. In the scenario studied, the proposed JPAIS-GBC powerallocationvector,which is transmitted onlyonce to the
withG=3canaccommodateupto3moreusersascompared mobile users. This leads to a situation in which the power
to the CIS scheme and double the capacity as compared with allocationbecomesoutdated.Theresultsshowthatthegainsof
theNCISforthesame BER performance.Thecurvesindicate the proposed JPAIS algorithmsdecrease gradually as the fdT
that the GBC for power allocation with only a few users is isincreasedtotheBERleveloftheexistingCISalgorithmsfor
able to attain a performance close to the JPAIS-GBC with both nr =2 and nr =4 relays, indicating that the power al-
G = K users, while requiring a lower complexity and less location is no longerable to provideperformanceadvantages.
network signalling. A comprehensive study of the signalling Thisproblemrequiresthe deploymentof a frequentupdate of
requirements will be considered in a future work. the power allocation via feedback channels.
The next experiment considers the average BER perfor- Thelastexperiment,showninFig.8,illustratestheaveraged
manceagainstthenormalizedfadingratef T (cycles/symbol), BER performance versus the percentage of errors in the
d