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IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION 1

Multiple-Symbol Joint Signal Processing forDifferentially Encoded Single- and Multi-Carrier

Communications: Principles, Designs andApplications

Li Wang, Member, IEEE, Li Li, Chao Xu, Dandan Liang, Soon Xin Ng, SM, IEEE, andLajos Hanzo, Fellow, IEEE

Abstract—Bypassing the potentially excessive-complexity andyet inaccurate channel estimation, differentially encoded modu-lation in conjunction with low-complexity non-coherent detectionconstitutes a viable candidate for future multiple-antenna aidedsystems, where estimating all the links may become unrealis-tic, especially in high-speed environments. Upon exploiting thecorrelation between the phase distortions experienced by theconsecutively transmitted symbols and/or based on mutuallyand iteratively utilizing the increasingly improved bit reliabil-ity information among the associated multiple symbols in thecontext of differentially modulated systems using channel codeaided iterative receivers, the joint processing on consecutivelyreceived multiple symbols improves the system’s performance.For example, an increased robustness against rapid channelfluctuation, improved flexibility in the system’s performance-complexity compromise as well as a reduced performance lossis achieved in comparison to its coherent detection aided coun-terpart. In order to stimulate further research on differentiallymodulated systems and on the associated multiple-symbol signalprocessing based advanced receiver design, a comprehensivereview on their related concepts and fundamental principles iscarried out in this treatise, followed by a number of potentialchallenges encountered in their practical implementations infuture high-spectral-efficiency wireless transmissions, such astheir applications in high-order differentially modulated systemsand in differential interference suppression of spatial-divisionmultiplexing/multiple access scenarios.

I. INTRODUCTION

THE MAIN driving force behind the advances in wirelesscommunications over hostile, band-limited radio chan-

nels is the promise of mobile multimedia communicationwith seamless global mobility and ubiquitous accessibility. Atypical system of this kind is the mobile Internet, where infor-mation exchanges are supported among people and/or devices,regardless of their geographic positions, using different mediawithin the same radio link, such as video, graphics, speech,text or other data. This implies that a mobile multimedia

Manuscript received October 8, 2012; revised April 20, 2013. The researchleading to these results has received funding from the European Union’sSeventh Framework Programme ([FP7/2007-2013]) under grant agreementno [214625]. The financial support of the RC UK under the auspices of theUK-India Advanced Technology Centre of Wireless Communications and ofthe China-UK Science Bridge in 4G wireless communications, as well as thatof the EU’s Concerto project is also gratefully acknowledged.

The authors are with the School of ECS, University of Southampton, SO171BJ, U.K. (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/SURV.2013.081313.00218

communication system has to adapt itself to the very differentrequirements of the individual services in terms of data rates,quality of service (QoS), maximum delay, etc. Therefore,against the backcloth of the explosive expansion of the Internetand the continued dramatic increase in demand for high-data-rate high-mobile-velocity multimedia services, it is increas-ingly important to find both energy- and bandwidth-efficientsolutions for next-generation wireless communication, whichis capable of coping with the associated severely frequency-and time-selective wireless channels.

In the context of traditional single-carrier wireless com-munication systems using coherent detection techniques, theabove-mentioned propagation conditions encountered by high-data-rate and high-velocity applications are directly translatedto significant increases in the equalization complexity as wellas in channel estimation overheads. Although technologicaladvances in integrated circuits and radio-frequency electronicsfacilitate the employment of ever more sophisticated signalprocessing and coding algorithms, a key consideration forthe development of next-generation wireless communicationsystems is the support of small, low-cost user equipment (UE)with long battery life, both in stand-by and during activity.Thanks to its low-complexity discrete Fourier transform(DFT) based implementation, the orthogonal frequency-division multiplexing (OFDM) technique [1] and its vari-ants1 have become the predominant wideband transmis-sion techniques. Their main benefit is that they facilitatelow-complexity single-tap multiplicative equalization at thereceiver.

As an important further invention, the innovative con-cept of Spatial Multiplexing (SM) invoked for increasingthe throughput of wireless systems using multiple transmitand receive antennas (MIMO) was patented in 1994 [2].This concept was inspired by carefully evaluating thesignal separation experiments carried out by Paulraj andKailath [2]. In the late 90s, as the integrated circuitsand radio-frequency electronics have advanced in parallelto the increasing tele-traffic demands, the research of

1For example, orthogonal frequency-division multiple access (OFDMA),wideband code-division multiple access (WCDMA) and single-carrierfrequency-division multiple access (SC-FDMA) are broadband transmissiontechniques developed based on the fundamental OFDM principle.

1553-877X/13/$31.00 c© 2013 IEEE

2 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION

MIMO systems was further fuelled by the pioneeringwork of Foschini [3, 4] and Telatar [5]. The fundamentalphilosophy was centered around efficient space-time signalprocessing [6–10]. As a substantial benefit, the family ofMIMO techniques exhibits a capacity, which is linearlydependent on the minimum of the number of transmitand receive antennas [3, 11, 12]. Hence their throughputincreases linearly with the number of MIMO elementsand the transmit power. On the other hand, the benefitsof MIMO systems may also be exploited for mitigatingthe detrimental effects of multipath propagation withthe aid of their transmit/recieve diversity gain, whichis an explicit benefit of receiving multiple independentlyfaded transmit signal replicas [6, 7, 10]. Following years ofintensive research, MIMO techniques have found their wayinto the wireless standards and hence they constitute one ofthe most significant technical inventions in contemporarywireless communications [13, 14]. More explicitly, theyhave reached commercial maturity and hence they areemployed in wireless products and networks, such asbroadband wireless access systems, wireless local networks(WLAN), third generation networks and in the most recent3GPP LTE/LTE-Advanced networks.

However, it is typically impractical for the pocket-sizedmobile device to employ multiple antennas due to its size andcost constraints as well as owing to the associated hardwareimpairments2. In addition, owing to the limited separation ofthe antenna elements, the transmitted signal rarely experiencesindependent fading, which in turn erodes the achievable diver-sity gain. The diversity gain may be further compromised bythe deleterious effects of the large-scale shadow fading [15],since all the MIMO channels tend to fade together rather thanindependently, imposing further signal correlation amongstthe antennas in each other’s vicinity. Apart from the aboveobstacles in the way of achieving multiple-antenna-aided di-versity gains, wireless cellular networks aim for improvingthe coverage, capacity or the quality of end-user experience(QoE) in inadequately covered areas, such as for exampleindoor environments and rural areas. The dense deploymentof fully-fledged base stations (BSs) constitutes a high-qualitysolution, albeit this may impose a high infrastructure cost andthus may become economically unavailable, especially in low-traffic-density sparsely populated rural areas.

Hence, to meet the above challenging requirements ofnext-generation wireless networks, the family of relay-aidedcooperative transmission technique [16–20] appears to be oneof the most promising solutions. In a nutshell, in multi-userwireless systems, single-antenna-assisted mobile stations (MS)may cooperatively share their antennas in order to achievethe so-called cooperative diversity as well as a path-loss-reduction based power gain by forming a virtual antennaarray (VAA) [21, 22] in both uplink (UL) and downlink (DL)transmissions. The concept of user cooperation has been firstproposed in [19, 20] for a two-user cooperative CDMA system,where orthogonal codes are employed by the active usersin order to avoid the multiple access interference. Naturally,

2For example, the associated mixed-signal coupling and cross-talk that maybecome critical in integrated high performance wireless systems, where thedigital circuitry is tightly co-located with the analog RF electronics.

the extra tele-traffic between a source MS and a cooperat-ing MS serving as a relay station (RS) requires additionalradio resources to be allocated - any of the well-establishedmultiple access schemes can be employed by the users toguarantee their orthogonal interference-free transmission, suchas time-division multiple access (TDMA), frequency-divisionmultiple access (FDMA) or code-division multiple access(CDMA) [17].

According to the operations carried out at the RS, therelaying protocols may be classified into three categories,namely amplify-and-forward (AF), decode-and-forward (DF)and compress-and-forward (CF) relaying. In the AF scheme,which is also referred to as the analog-repeater-based arrange-ment [18], the RS simply amplifies and forwards the sourcenode’s ‘overheard’ signal to the intended destination, thuspotentially increasing the system’s overall noise level, sincethe signal and noise are amplified together. As to the DFscheme, the RS fully decodes the signal received from thesource and provides the destination with a re-encoded signal.Hence, the problem of error propagation may arise, whenthe RS forwards the erroneously recovered signal, which maydeteriorate the detection at the destination and hence the over-all system performance. Recently, the CF-based cooperativescheme also received increasing research attention [23, 24],where the RS forwards a quantized or compressed version ofthe signal received from the source.

A. Notations Used in this Treatise

Before continuing our discourse, let us first detail thenotations that we will shortly encounter in later sections. Wegenerally use boldface variables to denote matrices as well asvectors. Furthermore, vm is the mth element of the vector v,while Mi,j denotes the element located in the ith row andjth column of the matrix M. Similarly, we use Mi:j,m:n torepresent a (j−i+1)×(n−m+1)-dimension submatrix of thematrix M spanning the region extended from the ith to the jthrow and from the mth to the nth column. A block matrix Mis defined by vertically concatenating a number of matrices.Moreover, Md = diag{m} represents that the diagonal matrixMd is constructed by aligning the elements of the vector malong its diagonal. Likewise, we can define the block-wisediagonalization operation as: Md = diag{M}, where thevertically concatenated element submatrices of block matrixM is aligned along the diagonal of the block diagonal Md.Conventially, det(S) and S−1 are the determinant and inverseof a square matrix S, respectively. For any general matrix M,MH represents the conjugate transpose. Finally, E{·} meansexpectation.

B. Motivation Behind Differentially Encoded Wireless Com-munications

It is noteworthy that the substantial benefits promised by theabove-mentioned multiple-antenna-based non-cooperative andcooperative MIMO systems may only be realized under theassumption of sufficiently accurate channel estimation, whichhowever is likely to become a significantly more challeng-ing issue than in the conventional single-input single-output(SISO) scenario. To be specific, the estimation of MIMO

WANG et al.: MULTIPLE-SYMBOL JOINT SIGNAL PROCESSING FOR DIFFERENTIALLY ENCODED SINGLE- AND MULTI-CARRIER COMMUNICATIONS: PRINCIPLES, DESIGNS AND

channels imposes an exponentially increased complexity withthe number of antennas. This will become more explicit, ifwe consider the simple example of an (8×8)-element MIMOsystem, where the estimation of a total of 64 propagationlinks between one pair of transceiver is required! Moreover, asmentioned previously, since future wireless communicationswill have to support a high grade of mobility3 [25, 26], the rel-ative frequency of estimating the channel has to be increasedproportionately to the channel’s fluctuation rate characterizedby the Doppler frequency. Since the knowledge of channelstate information (CSI) is typically obtained using a channelsounding sequence in practice4, a substantially increased pilot-overhead is also expected, leading to a potentially significantreduction in both bandwidth and power efficiency.

Furthermore, performance degradations may occur whenthe receiver has imperfect CSI, as illustrated by the BERcurve of a (2 × 1)-element G2-aided MIMO system [6] inFig. 1, where we assume that the channel estimation errorsobey the Gaussian distribution and the degree of the CSIestimation errors is governed by the ratio ω (dB) with respectto the received signal power. Hence, the perfect CSI scenariocorresponds to ω = −∞. To be specific, given a target BER of10−5, a performance loss of 5 dB may be encountered, evenwhen the channel estimation errors are as low as ω = −24 dB.Furthermore, when this second-order transmit diversityachieved by the G2 scheme is attained with the aid ofa VAA in the context of a single-relay-aided cooperativesystem, the achievable BER performance may becomeeven more sensitive to the imperfect channel knowledge,as also evidenced in Fig. 1. Observe in Fig. 1 that evenwhen the channel estimation errors are as low as −26 dB,the BER curve of the single-relay-aided AF system tendsto exhibit an error floor above 10−5. Thus the second-order transmit diversity originally achieved in the presenceof perfect channel knowledge vanishes. This is becausethe cooperative system requires the CSI knowledge ofboth the source-to-relay and relay-to-destination links incomparison to the classic single-phase direct transmissionregime of non-cooperative MIMO systems [28, 29]. Bycontrast, it is particularly challenging for the destinationto accurately estimate the source-relay channel using pilotsignal forwarding in the context of AF-based cooperativesystems, since the pilots may be further contaminatedby relay-induced noise amplification. Based on our abovediscussions, obtaining sufficiently accurate CSI for MIMOsystems, particularly for the family of cooperative systems,may potentially impose both an excessive complexity anda high pilot overhead, especially when the number of an-tennas/cooperating users is high and/or when the channelconditions fluctuate relatively rapidly in high-velocity mobileenvironments.

Therefore, differentially encoded signaling combined with

3The major candidates for the next generation of broadband wireless accesssystems, such as 3GPP-LTE and IEEE 802.16m, are expected to deliver a datarate of at least 100 Mbps for high-velocity mobile users (up to 350 km/h).

4Channel estimation can be realized by inserting so-called pilot symbolswith known modulation into the transmitted signal. Based on these pilotsymbols the receiver can measure the channel transfer factors (CTF) for eachsubcarrier in an OFDM system using interpolation techniques [27]. In thiscase, each subcarrier can be demodulated coherently.

0 5 10 15 20 25 30 35 4010

−5

10−4

10−3

10−2

10−1

100

SNR (dB)

BE

R

Coherent Transmission (ω=−∞ dB)

Coherent Transmission (ω=−26 dB)

Coherent Transmission (ω=−24 dB)

STBC G2

AF CooperativeSystem

DAF CooperativeSystem

(D)QPSK

Single−InputSingle−Output (perfec CSI)

Figure 1. Performance sensitivity to imperfect channel knowledge of thesingle-relay amplify-and-forward TDMA cooperative system in conjunctionwith coherent detection.

low-complexity non-coherent detection [30] and thus bypass-ing the complex yet potentially inaccurate channel estimationprocess at the receiver becomes an attractive design alternative,whose applications in MIMO systems has attracted consid-erable attention in the last decade, especially in cooperativecommunications [31–39].

C. Focus and Outline of the Paper

In view of the benefits of by-passing the potentiallyexcessive-complexity and yet inaccurate channel estima-tion, the family of differential modulation schemes com-bined with non-coherent detection is advocated in thistreatise as a viable candidate to be employed in thecontext of multiple-antenna-assisted systems, particularlyfor VAA-based cooperative systems. Nonetheless, as we willreveal in our forthcoming introduction of the conventionaldifferential detection (CDD) scheme in Section II, CDDhas its own limitations. For example, it is sensitive torapid channel fluctuations owing to the radically fadedreference symbols, which leads to a potential error-floor.Furthermore, typically exhibits a 3-dB performance lossin comparison to its coherent detection aided counterpart,which is due to the fact that in the presence of any channel-induced errors the next symbol also becomes erroneousowing to using an erroneous reference symbol. Hencesubstantial further research is required for designingadvanced, improved-performance non-coherent receiversfor mitigating the above-mentioned limitations of differen-tially encoded systems. Thanks to the recursive differentialencoding procedure, joint processing of multiple successivelyreceived symbols constitutes a promising solution for signifi-cantly enhancing the performance of the conventional single-symbol signal processing based non-coherent receiver. Theunderlying philosophy behind the multiple-symbol joint signal


Dv[n]

s[n − 1]

s[n]2pPSK

2p-DPSK Modulator

bn1 , · · · , bn

p

Figure 2. The schematics of 2p-DPSK modulator.

processing is to exploit the correlation between the phasedistortions experienced by the consecutively transmitted sym-bols and/or to mutually and iteratively exploit the increasinglyimproved bit reliability information of the associated multiplesymbols in the context of a channel code aided iterativereceiver.

Against this backdrop, our goal is to stimulate furtherresearch on differentially encoded wireless systems. Hencewe identify and address a number of fundamental chal-lenges encountered in their maximum-a-posteriori (MAP)multiple-symbol joint signal processing based advancedreceiver design. We will consider a variety of applicationscenarios and further develop the sphere detection (SD)mechanism for the sake of achieving a substantial com-plexity reduction, as detailed below:

• Differential amplitude and phase shift keying (DAPSK)[40, 41] - also known as Star Quadrature AmplitudeModulation (Star-QAM) - constitutes an attractive designalternative for high-data-rate differentially encoded trans-missions. The decision-feedback differential detection(DF-DD) principle has been successfully applied toDAPSK systems in [42] as a low-complexity solution.This is complexity reduction is achieved at a modest,but non-negligible performance loss in comparisonto the optimum maximum-likelihood multiple-symboldifferential detection (ML-MSDD) owing to the po-tential feedback error propagation. Thus, designing alow-complexity near-optimum differential detector isbeneficial.

• An efficient implementation of the MSDD specificallydesigned for the high-data-rate differential unitary space-time modulation (DUSTM) using the non-constant-modulus QAM constellation - rather than the conven-tional constant-modulus PSK constellation - constitutesanother challenging problem to solve.

• For the sake of further improving the spectral effi-ciency, spatial-domain co-channel interference suppres-sion scheme has been proposed for multiple-antenna-assisted differentially encoded wireless systems by takingadvantage of the recursive nature of the differentialencoding mechanism. In order to enhance the system’srobustness against hostile wireless channels, the multiple-symbol joint processing regime may be further developedto amalgamate both interference filtering and signal de-tection, which is a challenging, but worthwhile issue totackle.

To this end, we commence by reviewing the fundamentalprinciple of the conventional differential encoding anddecoding process in Section II. Then, following the con-struction of the generalized multiple-symbol system modelsfor both co-located and distributed/cooperative MIMO

D

ConjDem.

2pPSK

2p-DPSK Demodulator

y[n]

y∗[n − 1]y[n − 1] v[n] bn1 , · · · , bn

p

Figure 3. The schematics of 2p-DPSK demodulator.

systems in Section III-A, the principle of the maximum-likelihood-based MSDD (ML-MSDD) and that of its SD-based version, namely the MSDSD, is reviewed in Sec-tion III-B. Subsequently, the challenging design of MSDSDfor non-constant-modulus modulation assisted bandwidth-efficient orthogonal SISO and MIMO systems is discussedin Sections IV-A and IV-B, respectively. Then, we move onto another promising mechanism capable of achieving ahigh bandwidth-efficiency for nonorthogonal transmissionrelying on spatial-domain interference mitigation and itsmultiple-symbol filtering as well as detector design inSection V. Finally, our concluding remarks are providedin Section VI.

II. DIFFERENTIAL ENCODING AND DECODING

A. Fundamental Principles

Let us now consider the classic differential phase shiftkeying (DPSK) scheme for the single-transmit-antenna sce-nario, as portrayed in Fig. 2. In order to avoid channelestimation at the receiver, the transmitter differentially encodesits PSK-modulated information symbols v[n] ∈ Mc ={ej2πm/2p ;m = 0, 1, · · · , 2p − 1} as s[n] = s[n − 1]v[n],where v[n] contains the p-bit information [bn1 , b

n2 , · · · , bnp ].

Essentially, the information is encoded as the phase differ-ence between consecutively transmitted symbols, as shown inFig. 2. At the receiver the corresponding conventional differ-ential detector (CDD) [30], as depicted in Fig 3, may extractthe data by simply calculating the phase difference betweensuccessive time samples without any CSI knowledge, underthe assumption of slow channel-fluctuation. When the extraspatial dimension becomes available, which is an explicitbenefit of having multiple antennas at both the transmitterand the receiver, the information can be differentiallyencoded using the previous symbols as reference in boththe spatial and temporal dimensions, instead of using onlythe classic differentially encoded time-domain modulationscheme of Fig. 2. This leads to the differential space-time modulation (DSTM) aided transmission philosophyof S[n] = S[n−1]V[n] [43, 44]. This philosophy is shown inFig. 4, where S[n] and V[n] are typically unitary matricesrepresenting the differentially encoded space-time signaland the space-time information signal, respectively. Readerswho are interested in more details on DSTM are referred to thecitations seen in Tables I and II, as well as to the referencestherein. Naturally, in the light of the distributed space-timecoding principles, the differential space-time coding regimecan also be implemented in a distributed manner for user-cooperation aided systems [45–48].


Space−TimeCoding

DSpace−Time

Mapper

DSTBC Encoder

2pPSKv1[n] · · · vQ[n]

Q Symbols

V[n] S[n]

S[n − 1]

Figure 4. Schematic of a co-located MIMO system equipped Nt transmit and Nr receive antennas employs DUSTM, while transmitting Q symbols over Ttime slots using a differentially encoded space-time matrix S[n].

Table IMAJOR CONTRIBUTIONS ADDRESSING THE DESIGN OF DUSTM FOR

NON-COOPERATIVE MIMO SYSTEMS.

Author(s) Contribution[49] Tarokh et. al. 2000 Proposed the differential version of Ala-

mouti’s scheme [6].[43] Hochwald et. al. 2000 Introduced the family of differential unitary[44] Hughes 2000 space-time modulation (DUSTM).

Proposed to design DUSTM using the[50] Shokrollahi et. al. 2001 theory of fixed-point free groups and

their representations.[51] Hassibi et. al. 2002 Designed DUSTM based on the Cayley

transform.[52] Zheng and Tse 2003 Derived the capacity of non-coherent

MIMO channels.[53] Nam et. al. 2004 Extended the work of [49] to four an-

tennas.[54] Zhu et. al. 2005 Designed DUSTM using the quasi-

orthogonal philosophy.[55] Oggier 2007 Proposed to design DUSTM based on

cyclic algebra [56].

Table IIMAJOR CONTRIBUTIONS ADDRESSING THE DESIGN OF DUSTM FOR

DISTRIBUTED MIMO SYSTEMS.

Author(s) Contribution[57] Wang et. al. 2006 Proposed DSTBC for AF relaying

and its power allocation scheme.[58] Yiu et. al. 2006 Proposed DSTBC using a unique node

signature vector for DF relaying.[59] Jing and Hamid 2008 Proposed distributed DSTBC for any

relay numbers via circulant matrices.[60] Rajan et. al. 2008 Designed distributed DSTBC using

the extended Clifford algebras.[61] Oggier et. al. 2009 Design distributed DSTM based on

Cayley codes for any relay numbers.[62] Gao et. al. 2011 Design DSTM for multi-source cooper-

ration based on network coding.[63] Huo et. al. 2012 Designed distributed DSTM for two-way

relay using analog network coding.

B. Inherent 3 dB Performance Loss

Since the CDD recovers the information by directly calcu-lating the phase difference of the two consecutively receivedsymbols, it is intuitive that in the CDD-aided system, anyreceived symbol that has been heavily noise-contaminated islikely to cause errors in recovering a pair of the consecutivelydifferentially encoded information symbols. In other words,the differentially modulated transmission detected by the CDDscheme circumvents the channel estimation at the expense ofdoubling the equivalent noise power, which in turn leads to a 3dB performance loss in comparison to its coherent-detection-aided counterpart assuming perfect CSI knowledge, as indi-cated by the gap between the BER curves associated with thesingle-relay AF and differential AF (DAF) TDMA cooperative

systems in Fig. 1. However, this coarse comparison betweenthe coherent and non-coherent detection based systems seemsto be unfair, since the perfect channel estimation is simplyassumed for the coherent detection assisted system withouttaking the indispensable pilot overhead into account. Forinstance, if the avoidance of periodic transmission of pilotsymbols can be exchanged for the adoption of a lower codingrate channel coding in the non-coherent system, the above-mentioned performance loss is in all fairness actually lowerthan what it seems to be, let alone the detrimental impactof an imperfect CSI knowledge on the coherent detectionbased system. Please refer to [64] for more comprehensivecomparative studies between the relevant non-coherentand pilot-based coherent schemes. In order to mitigatethe associated performance loss, the ML-MSDD schemeexploits the correlation between the phase distortionsexperienced by the consecutively transmitted symbols, asdetailed in the forthcoming Section III.

C. Effects of Channel Fluctuations on Differential Decoding

According to the differential encoding mechanism illus-trated in Fig. 2, the nth information symbol v[n], which isencoded as the phase difference between the correspondingconsecutively transmitted symbols s[n− 1] and s[n], may notbe recovered by the CDD process, if the two successivelytransmitted symbols experience quite different phase distor-tions caused by the rapid fluctuations of the fading coefficientin high-velocity mobile environments, even in the absenceof noise. Similar high-Doppler-induced impairments mayalso occur in pilot-assisted coherent detection based trans-missions. More explicitly, owing to the channel-inducednoise-contamination of pilots, it is insufficient to samplethe channel’s frequency-domain transfer function at itsNyquist-frequency. Hence typically an over-sampling isused, thus imposing an increased pilot overhead. As a sim-ple example, which quantitatively shows the detrimentaleffects of the channel’s fluctuation on the performanceof CDD, we consider here a DQPSK modulated uncodedOFDM system employing a sufficiently long cyclic prefixlength. Hence we assume that no inter-OFDM-symbolinterference is imposed. We assume furthermore that dif-ferential encoding is carried out along the time direction, i.e.between the same subcarriers of consecutive OFDM symbols5.Since a temporally Rayleigh-distributed fading is assumed

5Similar results may be obtained if the differential encoding is conductedalong the frequency direction, i.e. among adjacent subcarriers of a givenOFDM symbol. The channel fluctuation rate in the frequency direction isa function of the maximum delay spread.


for each subcarrier employed by the OFDM system,where the fading coefficients are correlated as a functionof the time, the temporal autocorrelation function of thefrequency domain channel transfer function (FD-CTF) h maybe expressed as:

ϕhh[κ] � E{h[n+ κ]h∗[n]} = J0(2πfdκ), (1)

where J0(·) denotes the zero-order Bessel function of the firstkind and fd is the normalized Doppler frequency. Figure 5(a)depicts the magnitude of temporal correlation function forvarious normalized Doppler frequencies fd, while Figure 5(b)plots the corresponding BER curves of the DQPSK modulatedCDD-aided OFDM system. It is observed that the BER curvetends to create an error floor, when fd becomes high, whichis caused by the high grade of relative mobility between thetransmitter and the receiver.

III. MULTIPLE-SYMBOL DIFFERENTIAL DETECTION FORGENERALIZED MIMO SYSTEMS

A. Generalized Multiple-Symbol Reception Models

1) Co-Located MIMO System: In the context of the MIMO-OFDM system, non-dispersive fading is encountered by eachsub-carrier, provided that the number of sub-carriers is suffi-ciently high. Since the differential encoding is assumed to beconducted along the time-domain for each frequency domain(FD) sub-carrier throughout this treatise unless otherwisestated, the multiple-symbol signal processing mechanismsdiscussed in the ensuing sections may be carried out on aper-sub-carrier basis at the receiver, which are thus equallyapplicable to the single-carrier narrowband modems. Hence,let us consider the following per-sub-carrier-based FD systemmodel constructed for multiuser OFDM systems supporting Udifferential-modulation-based Nt-antenna-aided uplink (UL)MSs with the aid of Nr receiver antennas at the BS [1]. Weassume that orthogonal interference-free transmission amongstthe U MSs is guaranteed by means of the conventionalmultiple access schemes, such as for example TDMA, thus thesingle-symbol transmission model constructed for the uth MSand corresponding to the nth space-time signal’s transmissioncan be formulated as6:

Y[n] = S[n]H[n] +W[n], (2)

where Y[n] ∈ CNt×Nr , S[n] ∈ CNt×Nt and W[n] ∈ CNt×Nr

denote the FD received and transmitted space-time signalmatrices as well as the AWGN matrix having a distributionof CN (0, 2σ2

wNrINt), respectively. Each Nt-antenna-aidedMS first generates the space-time information signal V[n],which is then differentially encoded as S[n] = V[n]S[n− 1],where the rows and columns of S[n] denote the time andspace dimensions, respectively. Furthermore, the FD-CTFmatrix H[n] is a (Nt × Nr)-dimensional i.i.d. zero-meanunit-variance complex Gaussian matrix, which is assumed toremain unchanged within the nth space-time signal duration,i.e. Nt time slots. Thanks to the differential encoding processat the MS, the knowledge of the FD-CTF matrix H[n] isnot required for recovering the transmitted information V[n]

6Both the user and sub-carrier indices are omitted here for notationalsimplicity.

0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

κ

|ψt [κ

]|

fd=0.001

fd=0.01

fd=0.03

(a) Magnitude of temporal correlation function of Rayleigh fading channels

0 5 10 15 20 25 30 35 40

10−4

10−3

10−2

10−1

100

SNR (dB)

BE

R

fd=0.03

fd=0.01

fd=0.001

DQPSK

(b) Effects of dopper frequency on performance of CDD

Figure 5. Impact of mobility on the performance of CDD.

at either the MS or the BS of the MIMO-OFDM systemconsidered. For instance, the CDD decision rule V[n] =argminV[n]{||Y[n]−V[n]Y[n−1]||2} may be invoked, whichis capable of achieving a reasonably good performance in aslow-fading channel where we have H[n− 1] ≈ H[n].

On the basis of the single-symbol system model of (2)we now construct the per-sub-carrier-based multiple-symbolMIMO-OFDM system model as:

Y[kN ] = Sd[kN ]H[kN ] +W[kN ], (3)

where the block matrix index kN denotes the kth blockmatrix constituted of Nwind component matrices. For ex-ample, the kth received space-time signal block matrix Y[kN ]


Frequency

Ch.U

Ch.1

Ch.2

Time

transmitsT1

transmitsT2

TU

... ...

T2 relays T1

T3 relays T2

T1 relays TU

T1 relays T2

TU relays T1

...

TU−1 relays TU

...

· · ·. . .

Phase I Phase II

· · ·

transmits · · ·

Figure 6. Channel allocation scheme for the cooperative cluster formed byU MSs in a celluar UL system.

of (3) contains Nwind consecutively received space-time signalmatrices. Hence we have Y[kN ] = [Y[(Nwind − 1)(k −1)]T · · · Y[(Nwind−1)k]T ]T . Similarly, both the kth FD-CTFblock matrix H[kN ] as well as the AWGN’s kth block matrixW[kN ] are defined by vertically stacking the Nwind matricesH[n] and W[n] (n = (Nwind − 1)(k− 1), · · · , (Nwind− 1)k)of (2), respectively. Moreover, the kth diagonal block matrixof the transmitted signal Sd[kN ] of each MS is constructedas Sd[kN ] = diag{S[kN ]} = diag{[S[(Nwind − 1)(k −1)]T · · · S[(Nwind − 1)k]T]T}, which corresponds to thelength-(Nwind−1) space-time information signal block matrixV[kN ] = [V[(Nwind − 1)(k − 1) + 1]T · · · V[(Nwind −1)k]T ]T .

It is worth emphasizing that both the single-symbol andmultiple-symbol MIMO-OFDM system models of (2) and (3)subsume the single-antenna-based SISO-OFDM system as aspecial case by setting Nt = Nr = 1.

2) Distributed MIMO System: Due to pratical cost and sizeconstraints, the employment of multiple transmit antennas byeach MS is typically infeasible. Fortunately, the cooperativesharing of antennas amongst MSs in multi-user scenariosconstitutes a promising solution in order to achieve bothcooperative diversity as well as a path-loss-reduction basedpower gain, as discussed in Section I. The often-used two-hoprelay-aided systems will be considered in this section, whichmay be readily extended to more sophisticated cooperativesystems. Moreover, only the AF and DF relaying stratageswill be considered in this treatise, since they have becomethe most popular ones, thanks to their simplicity and intuitivedesigns.

As an example of the channel allocation depicted in Fig. 6for the two-hop-relaying-based cooperative cluster formed byU MSs in a cellular UL system, the signal transmissioninvolves two transmission phases owing to the half-duplexcommunications of practical transceivers, namely the broad-cast phase and the relay phase. These are also often referredto as phase I and II. For the sake of simplicity, both TDMAas well as FDMA are considered, as illustrated in Fig. 6, inorder to guarantee orthogonal, i.e. non-interfering transmissionamongst cooperating MSs. Furthermore, since the channelallocation employed among cooperative users may be deemedto be symmetric, as indicated in Fig. 6, we now focus ourattention on the information transmission of a specific MS(e.g. T1) in the cellular UL scenario of Fig. 7. The MS T1

may be assisted by Mr = (U − 1) RSs activated from theset of available cooperating MS candidate pool. Consequently,upon using the TDMA scheme of Fig. 6, the Mr = (U − 1)

BS

source destination

relay

T3

T1

T2

hsrU−1

hr1d

hr2d

hrU−1d

hsd

hsr1

hsr2

TU

Figure 7. Schematic of a U -MS cooperative celluar UL system.

activated RSs of Fig. 7 successively process and forward thesignal broadcast from the source MS to the BS.

For the differential DF (DDF) system, under the assumptionof accurate signal recovery at each RS7, an entire single-symbol-based cooperative transmission cycle of a specificsource MS may be mathematically described in a formidentical to (2) in co-located MIMO transmissions, albeitwe have a different interpretation for each term therein. Tobe specific, when we employ (2) for describing the DDFsystem, we redefine Y[n] ∈ CUNt×Nr , S[n] ∈ CUNt×UNt

and W[n] ∈ CUNt×Nr as the U -user-cooperation-based FD

received and transmitted space-time signal matrices as well asthe AWGN matrix having a distribution of CN (0, 2σ2

wNrINt),respectively. More specifically, since the classic TDMA-basedmechanism is used during each cooperation cycle for aspecific MS, S[n] is a diagonal block matrix with its top-left submatrix S[n]1:Nt,1:Nt denoting the space-time signaltransmitted by the source MS and the diagonal submatrixS[n]mNt:(m+1)Nt,mNt:(m+1)Nt

(1 ≤ m ≤ U − 1) being thespace-time signal radiated by the mth RS. Accordingly, boththe user-cooperation-based channel matrix H[n] ∈ CUNt×Nr

and the AWGN matrix W[n] of (2) encapsulate the corre-sponding FD-CTF and additive noise between each cooperat-ing MS and the BS, respectively, as illustrated in the single-antenna-based example (i.e. Nt = Nr = 1 as depicted inFig. 7) of Table III. Note that a total power P is assumed tobe shared by the collaborating MSs for transmitting a symbol.Thus, by assuming that Mr cooperating MSs are activated,we can express the associated power contraint as: P =Ps +

∑Mr

m=1 Prm , where Ps and Prm (m = 1, 2, · · · , Mr)are the transmit power employed by the source MS and themth RS, respectively.

Similarly, in the context of the differential AF (DAF)cooperative system, the entire cooperative transmission cycleof a specific source MS may also be formulated in a formidentical to (2). However, in contrast to the case of the DDFcooperative system, where the broadcast phase is actually

7It was recently demonstrated in [21, 65] that the fixed DF system dispens-ing with any error-aware mechanisms at the RS, such as for example, thecyclic redundancy check [66], offers no diversity gain over its conventionaldirect-transmission-based counterpart. Hence, the selective DF scheme [21,65] is assumed here with the aid of error detection codes and/or intelligentRS selection schemes, where only the RSs that correctly recover the source’ssignal may be activated in the the relay phase.


Table IIISTRUCTURE OF H[n] AND W[n] OF (2) FOR BOTH THE DAF AND DDF SYSTEMS (Nt = Nr = 1 SEE FIG. 7)

H[n] = W[n] =

DDF System[√

Pshsd[n],√

Pr1hr1d[n], · · · ,√

PrU−1hrU−1d[n]

]T [wsd[n], wr1d[n], · · · , wrU−1d

]T

DAF System[√

Pshsd[n],√PsfAMr1

hsr1 [n]hr1d[n],

[wsd[n], fAMr1

wsr1 [n]hr1d[n] +wr1d[n], · · · ,

· · · ,√PsfAMrU−1

hsrU−1 [n]hrU−1d[n]

]TfAMrU−1

wsrU−1 [n]hrU−1d[n] + wrU−1d[n]

]T

excluded from (2) by invoking the perfect relaying assumption,the construction of (2) for the DAF cooperative system trulyencapsulates a complete cycle of the cooperative transmission,including both the broadcast phase and the relaying phase.Specifically, the broadcast space-time signal matrix S[n] is adiagonal block matrix with its top-left submatrix S[n]1:Nt,1:Nt

denoting the space-time signal transmitted from the sourceMS to the BS via the direct transmission path. The remain-ing diagonal sub-matrices S[n]mNt:(m+1)Nt,mNt:(m+1)Nt

=S[n]1:Nt,1:Nt (1 ≤ m ≤ U − 1) represent the space-timesignal transmitted from the source MS to the BS with the aidof the mth RS, which successively passes through the source-relay (SR) and relay-destination (RD) links. Again, for thesake of simplicity, in Table III we highlight the structure ofthe user-cooperation-based channel matrix H[n] and AWGNmatrix W[n] in the context of the single-antenna-based (i.e.Nt = Nr = 1 as depicted in Fig. 7) DAF system. Note thatfAMrm

is the power amplification factor employed by themth RS in order to ensure that the average transmit powerof the mth RS becomes Prm , which is given in [67] asfAMrm

=√

Prm

Psσ2srm

+N0, with σ2

srm and N0 = 2σ2w being

the variance of the channel’s envelope between the source aswell as the mth RS and the noise variance8, respectively.

Therefore, based on the above discourse, we know that boththe DAF and DDF cooperative systems may be mathemati-cally described using the single-symbol system model in theform of (2). Furthermore, by employing the same approachof constructing the multiple-symbol system model from itssingle-symbol counterpart, as used for the co-located MIMOsystem in Section III-A1, it is now plausible that the multiple-symbol system models constructed for both the DAF and DDFcooperative systems obey the form of (3). In a nutshell, boththe co-located and distributed MIMO systems considered maybe formulated by the same mathematical model, which isadvantageous for our non-coherent receiver design.

B. Multiple-Symbol Differential Detection

1) Principle of MSDD: It is worth emphasizing that allthe elements in H[n] and W[n] exhibit a standard Gaus-sian distribution for all the systems discussed above, exceptfor the DAF-based coopeartive system, where the relay-link-related components in H[n] and W[n] are products oftwo complex Gaussian variables, as we may observe fromTable III. However, the detailed simulation-based investi-gations of [68] suggest that the resultant noise processes

8The same noise variance is assumed at each receiver within the cooperativesystem throughout this treatise.

are near-Gaussian distributed. As a result, the PDF of thereceived signal vector Y[kN ] in (3) recorded for the DAFcooperative system is also near-Gaussian, especially for rel-atively low SNRs, where the effects of the AWGN becomemore dominant. Hence, under the simplifying assumptionthat the equivalent fading and noise are zero-mean com-plex Gaussian processes, the PDF of the non-coherent re-ceiver’s output Y[kN ] in (3) conditioned on the transmittedsignal Sd[kN ] may be approximately expressed as followsfor all the co-located and distributed MIMO scenarios con-sidered9: p(Y|Sd) ≈ exp(−Tr{YHΨ−1Y})/(det(πΨ))Nr ,where the conditional autocorrelation matrix is given by:Ψ = E{YYH|Sd} = SdE{HHH}SdH + E{WWH}.The decision metric of the maximum-likelihood multiple-symbol differential detector (ML-MSDD) designed forthe differentially encoded cooperative system may beexpressed with the aid of Bayes’ theorem as V

d

ML =argmin

Vd∈M(Nwind−1)

cTr{YH(Ψ)−1Y} [69], where Mc is

the set of legitimate constellation points for V[n]. Note thatthe choice of the first space-time signal of the current transmit-ted signal block contained in Sd serves as the reference signal,which does not affect the resultant ML solution. Therefore, theentire search space becomes M(Nwind−1)

c instead of MNwindc .

Consequently, the correlation between the phase distortionsexperienced by the consecutively transmitted symbols can beexploited by invoking the ML-MSDD decision metric, whichis actually contained in the channel’s covariance matrix Σh =E{HHH}. In practice, the channel’s correlation matrixmay be modelled by the well-known Jakes-model with theaid of the estimated Doppler frequency, namely relyingon (1). According to [70], the predictability of the channel ischaracterized by the rank Q of the channel’s covariance matrixΣh. For example, the block-fading channel, where the fadingenvelope remains constant over the entire fading block (i.e.kN space-time signal durations), is associated with the mostpredictable fading envelope, when the channel’s covariancematrix has a rank of Q = 1. By contrast, the fading process hasa finite differential entropy and becomes less predictable, whenwe have Q = kN · rows(H[n]). Let us now consider the two-user-cooperation-based DAF UL system as a simple examplefor demonstrating the performance improvement achieved bythe MSDD in a high-speed mobility environment, where twosingle-antenna-aided MSs cooperatively share their antennasto form a VAA. As observed in Fig. 8, upon using theCDD of Fig. 3 at the BS, the performance gain achievedby the DAF system over the traditional point-to-point direct

9In the interest of ease of presentation, the block index kN is omitted herewithout loss of accuracy.


0 5 10 15 20 25 30 35 4010

−5

10−4

10−3

10−2

10−1

100

SNR (dB)

BE

R

MSDD−Aided DAF (f

d=0.03, N

wind=6)

CDD−Aided DAF (fd=0.03)

CDD−Aided P2P (fd=0.001)

DQPSK

Figure 8. BER performance gain achieved by the MSDD for the single-relay-aided DAF system (U = 2, Nt = Nr = 1).

transmission system erodes significantly, when the channel’sfluctuation rate is high (e.g. associated with fd = 0.03 inthis case). Remarkably, the curve of Fig. 8 marked by circlessuggests that the time-selective-fading-induced error floor maybe substantially mitigated for the DAF system with the aidof MSDD by setting a sufficiently high window-length ofNwind = 6. Naturally, when using the classic ML MSDD,the associated complexity becomes equivalent to 26 = 64objective function evaluations.

2) Complexity Reduction for MSDD: On the other hand,finding the ML-MSDD solution Sd

ML is known to be NP-hard.Hence, a pontentially excessive computational complexity maybe imposed, which is exponentially increased with both theconstellation size Mc as well as the observation windowsize Nwind employed by the MSDD. Considering again theabove DAF-based cooperative system for example, under theassumption of an observation window size of Nwind = 10 andthat of DQPSK (Mc = 4), 220 = 1.048576× 106 legitimateuser-cooperation based space-time constellation points haveto be evaluated, thus precluding the practical implementationof the ML-MSDD at the BS of our differentially encodednon-coherent cooperative system. As a remedy, the classicsphere decoding (SD) algorithm may be invoked, which wasoriginally derived by Pohst and Finke [71] for efficientlycalculating a vector of short length in a lattice. The SD wasthen further developed for coherent-detection-based commu-nication systems [72] by Viterbo and Boutros. As a result,the coherent ML performance is approached at a moderatecomplexity, which is polynomially, rather than exponentiallydependent on the number of unknowns. Inspired by abovecontributions, the SD algorithm was first introduced by Lampeet al. in [73] for mitigating the complexity of the ML-MSDD[74, 75] in the context of a differentially modulated SISOsystem, leading to the multiple-symbol differential spheredetection (MSDSD) concept. More recently, the employment

of MSDSD is further extended to the family of co-locatedand distributed MIMO systems by Pauli and Lampe in [69] aswell as by Wang and Hanzo in [68], respectively. Basically,the transplantation of the SD mechanism into the MSDD relieson the fact that Sd of (3) formed in the context of both the co-located and distributed MIMO systems considered is unitary,owing to the employment of conventional DPSK schemes orunitary space-time codes. After a few mathematical manipu-lations, which are omitted here in the interest of simplicity,the original ML-MSDD decision metric may be refor-mulated as V

d

ML = argminV

d∈M(Nwind−1)c

||US||2 < R,

where Vd= diag{V} and U is an upper-triangular block

matrix, which can be obtained as U � (F⊗INr)(diag{Y})H,with F also being an upper-triangular matrix generated usingthe well-known Cholesky factorization [76] of the matrix(Σh + 2σ2

wINwind)−1. Consequently, thanks to the upper-

triangular structure of the matrix U, a layered tree search maybe carried out within a hyper-spheric search space, which iscentered at the origin and confined by the SNR-dependentsearch radius R.

The MSDSD mechanism can be interpreted as a geometricproblem, which is illustrated in Fig. 9. For the sake of simplevisualization, we consider here a traditional point-to-pointtransmission system, which employs the DBPSK scheme at thetransmitter and jointly detects (Nwind − 1 = 3) consecutivelytransmitted information symbols with the aid of the MSDSDscheme at the receiver upon observing the (Nwind = 4) suc-cessively received symbols. Thus, the corresponding multiple-symbol-based transmit domain constellation and the pertain-ing 3D search space in the receive domain is depicted inFig. 9(a) and Fig. 9(b), respectively, in order to demonstratehow the SD mechanism works in the context of MSDD. Atthe receiver, the shape of the multiple-symbol-based cubicconstellation of Fig. 9(a) is assumed to be distorted, due tothe routinely encountered multipath induced phase rotationand magnitude attenuation. Instead of carrying out a fullsearch in the receive domain over the entire candidate setof (23 = 8) trial point, as the ML-MSDD would in orderto find the optimum ML solution, the MSDSD initializes thesearch radius depending on the estimated SNR, which confinesthe search area to the outer-most sphere centered at theorigin. As seen from Fig. 9(b), the search area is significantlyreduced in comparison to that of the ML-MSDD scheme. It isindeed intuitive that only the trial lattice points residing in theimmediate neighbourhood of the origin are worth examining.All the points in the search space confined by the radius aredeemed to be tentative candidates for the three consecutivelytransmitted information symbols. Now the core operation ofthe MSDSD algorithm is activated. Specifically, a new radiusis calculated by measuring the distance between a candidaterandomly chosen within the spheric search space and theorigin, which should be no higher than the original radius.Then another arbitrary multiple-symbol-based point is chosenfrom the newly obtained search space as the trial transmittedsymbol. Again, the search radius is updated with the value ofthe distance between the newly obtained trial point and theorigin. These operations are repeated, until the MSDSD findsthat specific legitimate constellation point, which is nearest


−3−2

−10

12

3

−3−2

−10

12

3−3

−2

−1

0

1

2

3

XY

Z

Transmit Signal Domain

(a) Multiple-symbol-transmission-based transmit domain constellation.

−5

0

5

−5

0

5

−5

−4

−3

−2

−1

0

1

2

3

4

5

XY

Z

Receive Signal Domain

1st Radiu UpdateBased on this Point

The Last Point Found Insideis the ML Solution (4th Radiu Update)

2nd Radius UpdateBased on this Point

(b) MSDSD processing in the receive domain.

Figure 9. Geometrical interpretation of SD mechanism.

to the origin. At the end of the search, we assume thatthe last trial point that was found corresponds to the MLsolution. In the example shown in Fig. 9(b), the MSDSDreaches the optimum ML solution after two radius updates.Hence, only three trial points are examined in terms of theirEuclidean distance with respect to the origin. Therefore, theexcessive-complexity full search carried out by the ML-MSDDis avoided by incorporating the SD mechanism into the MSDDscheme.

Another way of illustrating the SD algorithm’s philosophyis constituted by the search tree example provided for the

1 (0.17)

2 (6.45) 3 (0.20)

4 (3.4)

5 (4.2) 6 (4.8) 8 (1.8)

7 (1.2)

9 (3.3) 14 (0.23) 15 (1.0)

13 (0.22) 16 (1.9)

12 (0.21)11 (2.1)

10 (0.18)

0 (0) R = 5

n = 1

n = 4

n = 2

"1""0"

n = 3

Figure 10. Illustration of the depth-first SD algorithm with the aid of theclassic tree searching: The figure in ( ) indicates the partial Euclidean distanceof a specific node for the trial point in the modulated constellation; while thenumber outside represents the order in which the points are visited. Finally, theML solution of 1100 is found by choosing the tree leaf having the minimumEuclidean distance of 0.23 and backtracking to the level n = 4.

scenario of a DBPSK modulated system in conjunction withNwind = 5 characterized in Fig. 10. As shown in Fig. 10,the depth-first SD commences its search procedure using aninitial search radius of R = 5 from the top level (n = 4).For each tree node, the number within the bracket denotes thecorresponding accumulated partial Euclidean distance (PED)of that node from the origin, while the number outside thebracket indicates the order in which the node is visited. Thebroken line represents a binary zero, whereas the continuousline denotes a binary one. As we can see in Fig. 10, thesearch is carried out from the left to the right, but in bothdownward and upward directions along the tree. Specifically,there are two scenarios that may be encountered during thetree search portrayed in Fig. 10. Firstly, the search may reacha leaf node at the bottom, i.e. level (n = 1). The other possiblescenario is that the detector cannot find any point inside thehyperspherical space for the nth element V[n], or equivalently,the accumulated PEDs of all the candidates for V[n] are higherthan the current search radius R.

For example, in the first case, once the search reaches aleaf node, as seen at its fifth step, where the detector reachesa tree leaf having an Euclidean distance of 4.2 in Fig. 10,which is smaller than the current search radius of R = 5, thenthe detector starts the search process again with the reducedradius R = 4.2. In the second case, the detector must havemade at least one erroneous tentative point selection for theprevious (Nwind−n− 1) lattice coordinates. In this scenario,the detector returns to the (n+1)th search tree level and selectsanother tentative point for V[n+1] within the hypersphericalspace confined by the search radius. Following this, it proceedsdownwards along the tree again to try and find a legitimatedecision for V[n]. If all the available tentative points for V[n+1] fail to lead to a legitimate decison, the search back-tracksto V[n+2] with the same objective, and so on. For example,at the ninth step seen in Fig. 10, the detector is unable to finda legitimate point within the new smaller hyper-sphere havingthe radius of 1.8, which was obtained at the previous step,hence the search back-tracks to level n = 4, since no moreavailable candidates can be found within the correspondingsearch area for V[2], and V[3]. In the end, after visiting a


0 5 10 15 20 25 30 35 4010

2

103

104

105

SNR (dB)

# of

Can

dida

te P

oint

Vis

ited

per

Sym

bol B

lock

fd=0.03

fd=0.001

Nwind

=6

Nwind

=9

DQPSKDAF System

Figure 11. Complexity imposed by the MSDSD versus SNR in the single-relay-aided DAF system (U = 2, Nt = Nr = 1).

total of 15 tree nodes and leaves in Fig. 10, the SD choosesthe specific tree leaf having a minimum Euclidean distance of0.23 and back-tracks to the level n = 4 to generate the finalML solution of VML.

The interested reader is referred to [77–80] and the refer-ences therein for a more comprehensive treatment of the SDalgorithms. Although our attention is focused on the MSDSDin this treatise, it is worth noting that a range mechanismsother than that of the SD scheme can also be employed forachieving a beneficial complexity reduction for the MSDD,such as those discussed in [81, 82].

The complexity quantified by the number of candidateblock-symbol points S enumerated during the tree searchcarried out by the MSDSD versus the SNR is plotted inFig. 11 in the scenario of a DQPSK single-relay-aided DAFcooperative system. It is observed that the complexity imposedby the MSDSD is a function of the observation window sizeNwind, of the receive SNR as well as of the normalizedDoppler frequency fd. Specifically, as observed in Fig. 11,the complexity of MSDSD increases dramatically, once theoriginal observation window size of Nwind = 6 is set toNwind = 9. On the other hand, the complexity imposed bythe MSDSD decreases only moderately, as the SNR increasesand finally levels out in the high-SNR range. This is notunexpected, since under the assumption of having a reducednoise contamination, it is more likely that the ML solutionpoint S

d

ML is located near the search center of the SD used forfinding the ML-MSDD solution. As a result, the SD’s searchprocess may converge much more rapidly, imposing a reducedcomplexity. Furthermore, we can also observe from Fig. 11that the Doppler frequency has a non-negligible effect on thecomplexity imposed by the MSDSD. Basically, for a constantvalue of Nwind, a reduced grade of channel predictabilityassociated with an increased Doppler frequency may lead toan increased complexity imposed by the MSDSD scheme.

IV. DESIGN OF MSDSD FORHIGH-SPECTRUM-EFFICIENCY DIFFERENTIAL SIGNALING

USING NON-CONSTANT-MODULUS CONSTELLATIONS

Differential amplitude and phase shift keying (DAPSK)[40, 41, 83] using non-constant-modulus constellations wasfirst proposed for digital terrestrial video broadcasting(DTVB) in [84, 85] in the context of a single-tranmsit-antenna-assisted systems employed in SISO or SIMOscenarios. Since broadcast receivers can be switched onat any moment in an asyncrhoneous manner, a high pilot-overhead would be necessary for a coherently detectedsystem to facilitate near-isntantaneous reception. Further-more, the coherent receivers are also prone to the carrierrecovery system’s false locking onto the wrong quadrantof the modulated signal constellation, as detailed in [83].Again, the non-coherently detected DAPSK solutions dis-pensed with a high pilot-overhead and eliminated theabove-mentioned synchronization problems with the aid ofso-called rotationally invarian constellations, while trans-mitting an increased number of bits/symbol [40, 41, 83].These schemes, which have recently received an increasingattention from the communication community owing totheir low decoding complexity and low peak power, willbe discussed in Section IV-A, where we design a low-complexity near-optimum MSDD receiver for bandwidth-efficient single-transmit-antenna-assisted systems.

On the other hand, when considering the employmentof non-constant-modulus constellation for DUSTM-basedMIMO systems in pursuit of high spectrum efficiency,DUSTM using APSK and QAM constellations, which havean increased minimum Euclidean distance over the PSKconstellation, were proposed in [86] and [87], respectively.However, in constrast to the single-transmit-antenna dif-ferential system, the DUSTM mechanism allows an easyemployment of the sqaure QAM constellation, which willbe considered instead of APSK in Section IV-B2 regardingthe low-complexity near-optimum MSDD design for high-spectrum-efficiency MIMO systems. This is because thatsquare QAM has a larger Euclidean distance between theconstellation symbols than the APSK, thus implying asuperior noise performance [88].

A. Design of MSDSD for SISO Systems Using DAPSK

In order to eliminate the typical emergence of an error-floor at high Doppler-frequencies, the application of thefull-search-based ML-MSDD discussed in Section III-B1has been extended to uncoded DAPSK-modulated systemin [75] as well as to channel-coded DAPSK receptionbasded on the MAP criterion in [89]. However, since theconstellation size of DAPSK is typically no smaller than16 in bandwidth-efficient communications, the ML-MSDDemploying even a moderate observation window size ofNwind may exhibit an excessive complexity. In order toreduce the potentially excessive complexity, the DF-DDscheme of [42] has been developed for the DAPSK system,which, however, may suffer from a moderate but non-negligible performance loss owing to its inherent vulnera-bility to feedback error propagation. As another promising


D

D

Channel

DecoderDifferential

Detector

Soft−Decision

Encoder

Channel π−1

ππ

v[n] s[n]

x[n]

w[n]

y[n]

h[n]

s[n − 1]u

LA(c)

LA(b)LE(c)bnθ,p−q

2(p−q)PSK

bnθ,1

2qASK

bnγ,1

bnγ,q

a[n]

a[n − 1]

γ[n]

2p-DAPSK Modulator

u

LE(b)

c

Figure 12. Overall system model of bit-interleaved coded 16-DAPSK over Rayleigh-fading channel.

Table IVAMPLITUDE MAPPING FOR 16- AND 64-DAPSK

16-DAPSK (q = 1) 64-DAPSK (q = 2)bnγ,1 bnγ,1, b

nγ,2

0 1 00 01 11 10a[n] γ[n] a[n] γ[n]

1 α 1 α α2 α3

a[n− 1]1 1 α

a[n− 1]

1 1 α α2 α3

α α α2 α3 1

α α 1α2 α2 α3 1 αα3 α3 1 α α2

complexity reduction technique, the SD mechansim has alsobeen proposed for MSDD of conventional DPSK, as reviewedin Section III-B2, leading to the MSDSD scheme. Unfortu-nately, the non-constant-modulus constellation DAPSK pre-cludes the direct application of the MSDSD scheme of [90].Therefore, the conception of an efficient MSDD for DAPSKsystems invoking the SD mechanism has been a challengingopen problem. Hence the solution of this problem mayconstitute a promising candidate for low-complexity near-optimum MSDD implementations.

1) Differential Amplitude and Phase Shift Keying: Here weconsider a bit-interleaved coded differential modulation SISOdesign example of Fig. 12 employing the iterative detection(ID) mechanism. At the transmitter a block of L informationbits u is first encoded by the channel encoder in order togenerate the coded bits c, which are then interleaved bythe interleaver π. The resultant permuted bits b are thenfed through the DAPSK modulator. The 2p-DAPSK employsmultiple concentric rings by combining the 2q-DASK and2(p−q)-DPSK modulation schemes. As illustrated in Fig. 12,the first q bits, bn

γ = [bnγ,1, · · · , bnγ,q], of the nth p-bit encodedAPSK symbol d[n] = γ[n]v[n] are mapped to one of thelegitimate radii R = {αiA | iA = 0, · · · , 2q − 1} in orderto generate the component ASK symbol γ[n]. Meanwhile,the remaining (p − q) bits, bn

θ = [bnθ,1, · · · , bnθ,p−q], aremapped to the component PSK symbol v[n] = ejθ[n] ∈ V =

{ej2πiP/2(p−q) |iP = 0, · · · , 2(p−q) − 1}. Then, the differentialamplitude and phase modulation processes are carried out inparallel, as observed in Fig. 12. More particularly, duringthe amplitude differential modulation the current ampli-tude state a[n] is chosen from the constellation diagramdepending on the previous amplitude state a[n−1], takinginto account the ASK symbol γ[n] according to Table IV.Finally, the DAPSK symbol x[n] may be generated as theproduct of the DASK and DPSK symbols according tox[n] = a[n]s[n]. As an example, the signal constellation set

1 α

I

Q

Figure 13. Signal constellation of 16-DAPSK (α denotes the ring ratio).

Mc of 16-DAPSK (p = 1, q = 4) is depicted in Fig. 13.2) MAP-Based MSDD for DAPSK: In the light of the

generalized multiple-symbol system model of (3), we maystraightforwardly obtain the multiple-symbol system modelfor the DAPSK modulated system of Fig. 12 as Y[kN ] =Xd[kN ]H[kN ] +W[kN ] = Ad[kN ]Sd[kN ]H[kN ] +W[kN ],where Xd[kN ], Ad[kN ] and Sd[kN ] are all diagonal matricescontaining the kth block of Nwind consecutively transmittedDAPSK symbols, ASK symbols as well as PSK symbols alongtheir diagonal, respectively.

Based on the above multiple-symbol system model,the MSDD discussed in Sction III-B1 may be directlyapplied to the single-transmit-antenna-assisted DAPSKsystem. However, we have to bear in mind that sincethe conditional PDF p(Y[kN ]|Xd[kN ]) is dependent onthe amplitude of the non-constant-modulus referencesymbol xref (i.e. on the first upper-left element of thediagonal matrix Xd[kN ]), the metric employed in theMSDD, namely, the conditional PDF p(Y[kN ]|b[kN ]) =p(Y[kN ]|Γ[kN ],Θ[kN ]) should be caculated by averag-ing p(Y[kN ]|Xd[kN ]) over all possible values of xref asp(Y[kN ]|Γ[kN ],Θ[kN ]) = Exref

{p(Y[kN ]|Xd[kN ])}, whereΓ[kN ] = [γ[k(Nwind−1)], · · · , γ[(k+1)(Nwind−1)−1]]T andΘ[kN ] = [θ[k(Nwind − 1)], · · · , θ[(k + 1)(Nwind − 1)− 1]]T

correspond to the kN th block of consecutively transmitted(Nwind − 1) pieces of the amplitude-ratio and phase-rotation information, respectively. The soft bit informationexpressed in terms of a posteriori LLRs may then be cal-culated with the aid of Bayes’ theorem at the output of the


D

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yN−3yN−2

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Figure 14. Iterative multiple-symbol differential amplitude/phase detection(Illustration for the first multiple-symbol block, i.e., kN = 0).

MAP-MSDD as (again, the block index kN is omitted fornotation simplicity):

LD(bni |Y) = ln

∑b∈Bn,i,+1

p(Y|Γ,Θ)Pr(b)∑b∈Bn,i,−1

p(Y|Γ,Θ)Pr(b), (4)

where Bn,i,±1 represents the set of 2(pN−1) legitimate trans-mitted bit vectors b associated with the ith bit of the nthp-bit-coded symbol being bni = ±1 (i ∈ {0, · · · , p− 1}).

According to (4), the asymptotic complexity of the MAP-MSDD of a 2p-DAPSK scheme using 2q concentric rings isO(p · 2(pN)). Therefore, employing the ML - search carriedout by the MAP-MSDD might impose a potentially excessivecomputational complexity and hence may preclude its practicalimplementation, especially for high-order modulation schemesand/or for high observation window sizes.

3) The Design of Iterative Amplitude/Phase MSDSD: Sincethe transmitted signal matrix Xd is no longer unitary inthe DAPSK modulated system, we are unable to transformthe maximization problem of the ML-MSDD decisionmetric into an efficient SD-aided layered tree search, as itwas observed in Section III-B2 for the DPSK modulatedscenario. As another approach of reducing the complexity, theidea of decoupling the joint amplitude and phase detection wasconceived in [91] for MSDD invoked for DAPSK modulatedtransmission over Rayleigh channels. Regretfully, this sub-optimum scheme only achieved a complexity reduction at thecost of a significant performance loss.

In order to recover from this potentially substantialperformance degradation, below a novel IAP-MSDSDmechanism is proposed for channel coded DAPSK modu-lated systems. As illustrated in Fig. 14, Nwind consecutivelyreceived symbols are collected and fed through the de-coupled serially concatenated multiple-symbol differentialamplitude detector (MSDAD) and multiple-symbol differ-ential phase detector (MSDPD) of Fig. 14. We note thatthe soft-decision-based detection of the amplitude- andphase-modulation-related bits is conducted independentlyand their generated soft amplitude and phase informationmay be iteratively exchanged between each other. Thedecoupling of the amplitude and phase detection rendersthe SD mechanism applicable to the computationally de-

manding MSDPD process of acquiring the phase estimateSd, which uses the amplitude estimates of the consecutively

transmitted symbols provided by the MSDAD as a prioriinformation. The step-by-step operation of IAP-MSDSD isbriefly summarized as follows:

Step 1: The IAP-MSDD process commences by obtainingthe phase information Θ based on the output of the phasedetector as Θ = [φ0, · · · , φ(N−1)]

T by toggling the phaseinformation feedback switch to the ‘1’ location of Fig. 14,in order to provide the initial phase estimates Θ for the firstround of MSDAD detection.

Step 2: In the presence of the estimated transmit-domainphase information Θ, the a posteriori amplitude-modulation-related bit LLRs are computed by the MSDAD as:

LD(bnγ,i|Y, Θ) = ln

∑bγ∈B

γn,i,+1

p(Y|Γ, Θ)Pr(bγ)∑bγ∈B

γn,i,−1

p(Y|Γ, Θ)Pr(bγ), (5)

where Bγn,i,±1 represents the set of 2[q(N−1)−1] legitimate

amplitude-modulation-related bit vectors bγ associated withbnγ,i = ±1 (i ∈ {1, · · · , q}).

Step 3: Subsequently, the amplitudes Ad

of the consec-utively transmitted symbols may be estimated based onthe a posteriori amplitude-modulation-related bit LLRs,i.e. LD(bγ |y, Θ) of (5), which are then delivered to theserially concantenated MSDPD.

Step 4: Thanks to the amplitude estimate matrix Ad,

the a posteriori phase-modulation-related bit LLRs may becomputed by the MSDPD of Fig. 14, where the efficientSD mechanism can be incorporated in a similar manneras seen in Section III-B2.

Step 5: From the second iteration of the MSDADprocess onwards, the phase information feedback switch ofFigure 14 is toggled to the ‘2’ position in order to exploitthe phase-modulation-related bit LLRs delivered by theMSDPD. Then, go back to Step 2, if further iterative A/Pdetection is required.

Step 6: Output both the amplitude- and phase-modulation-related bit LLRs LD(bA) and LD(bP).

4) Application Example - 16DAPSK SISO System: Letus now invoke the semi-analytical EXtrinsic Informa-tion Transfer (EXIT) charts of [92] for investigatingthe performance versus complexity of the IAP-MSDSDscheme conceived for the single-antenna-aided 16-DAPSK-modulated SISO system of Fig. 12 experiencing a nor-malized Doppler frequency of fd = 0.01. According tothe area properties of the EXIT chart [92], the upwards-shifted EXIT curve of the IAP-MSDSD in Fig. 15 suggeststhat a significantly higher maximum transmission rate maybe achieved in comparison to the CDD assisted system usingNwind = 2. This throughput gain was achieved by jointlydetecting Nwind > 2 data symbols using the IAP-MSDSD, asalso visualized in the 3D plot of Fig. 16, where the maximumachievable throughput of the IAP-MSDSD-aided 16-DAPSKmodulated system is portrayed versus both the SNR andthe ring-ratio α. Additionally, a compromise between theachievable performance and the complexity imposed maybe struck by employing the low-complexity conventional


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SNR=14 dBN=3,4,6

SNR=10 dB

N=6

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# of A/P Iterations=1

Figure 15. EXIT chart of the IAP-MSDSD employed in the 16-DAPSKsystem.

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Figure 16. Maximum achievable throughput of the 16-DAPSK system.

differential amplitude detection (CDAD) or conventionaldifferential phase detection (CDPD) philosophy in thecorresponding amplitude or the phase detection process, asindicated by the associated downwards-shifted dotted anddot-dashed EXIT curves of Fig. 15. Moreover, as implied bythe almost invisible gap between the EXIT curve of the IAP-MSDSD and that of the traditional MSDD seen in Fig. 15, boththe MSDAD and MSDPD of the IAP-MSDSD of Fig. 14 hasto be activated only once, in order to approach the performanceof the traditional MSDD. Thus, remarkably, the complexityimposed by the IAP-MSDSD becomes about five orders ofmagnitude lower than that of the traditional MSDSD for the

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ymbo

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Iterative A/P MSDSD (N=6)

Iterative A/P MSDSD (N=2)

Traditional MSDD (N=6)

Figure 17. Complexity reduction achieved by the IAP-MSDSD in the 16-DAPSK system.

16-DAPSK modulation-aided system across a wide range ofSNRs, as seen in Fig. 17, where the complexity quantified interms of the number of transmitted symbol vector candidateenumerations during the differential detection is portrayedversus both the SNR and the ring-ratio α. Furthermore, thesimulation results seen in Figs. 16 and 17 suggest that settingthe ring-ratio employed by the 16-DAPSK to α ≈ 2.0 con-stitutes an appropriate choice for maximizing the achievablethroughput [93], while minimizing the complexity imposed.

B. Design of MSDSD for MIMO Systems Using QAM-DUSTM

1) DUSTM Using QAM Constellations: In contrast to thetraditional space-time block coding (STBC) framework, theDUSTM structure portrayed in Fig. 4 introduces a differentialencoding unit, in order to forgo the burden of channel estima-tion. However, the differential encoding structure imposes aunitary constraint on the resultant space-time coded matrices,otherwise the matrix product S[n] = V[n]V[n − 1] · · ·V[1]may become zero, infinity or possibly both in different spa-tial and temporal directions, as the differential space-timeencoding proceeds. In other words, the challenge of designingDUSTM can be described as that of designing a family ofSTBCs, where all the space-time matrices are unitary. Astraighforward way of designing DUSTM is based onAlamouti codes [6], where the challenge of constructing aset of unitary space-time matrices V[n] for the schematicof Fig. 4 is tackled by simply employing, for example, thewell-known G2 matrices with their elements drawn froma 2p-PSK constant-modulus constellation.

Let us now briefly review how the PSK constellationcan be replaced by its non-constant-modulus square QAMcounterpart, while still preventing the peak power of thetransmitted signals generated by the DUSTM encodingprocess from becoming infinity or zero. The reader’s fa-


miliarity with the Alamouti STBC is assumed here. Thenwe consider a co-located MIMO system equipped with twotransmit antennas as our design example. Thus the G2-basedDUSTM encoding process may be formulated as S[n] =

1ηn−1

S[n − 1]V[n] = 1ηn−1

S[n − 1]G2(v1[n], v2[n]), wherethe function G2(·) takes two input symbols drawn from the2p-QAM constellation for generating the associated (2 × 2)-dimensional space-time matrix. The first transmitted space-time signal is also a G2 matrix, which serves as the referencesymbol. Furthermore, it is the power normalization factorηn−1 =

√||S[n− 1]||2/2 =

√|v1[n− 1]|2 + |v2[n− 1]|2

that is introduced for confining the peak power of thetransmitted signals after differential encoding within acertain limit.

In order to recover the QAM symbols (v1[n], x2[n]) us-ing the CDD, which performs ML detection based on low-complexity linear processing, both the transmit power normal-ization factor ηn and the fading channel’s power envelope hasto be known by the receiver. The factor ηn may be directlyobtained from the previous decisions, but the fading channel’spower envelope has to be estimated, for example, by evaluatingthe auto-correlation of the received signal. Naturally, the accu-racy of this estimation highly depends on both the estimationwindow duration as well as on the Doppler frequency. Sincethe implementation of the related ML detection is a well-known standard process, we refer the interested reader to [87]for more details and continue our discourse focusing on howto efficiently carried out multiple-symbol-based detection forthe DUSTM system using QAM constellations for the sake ofenhancing its robustness against rapid channel fluctuation.

2) The Design of MSDSD for QAM-Based DUSTM: Byconstructing the multiple-symbol system model of (3) detailedin Section III-A1 for the QAM-based-DUSTM system, theML-MSDD discussed in Section III-B1 can be directly ap-plied. However, a problem precludes the direct applicationof the SD regime for reducing the ML-MSDD’s excessivecomplexity experienced in the context of QAM-basedDSTUM MIMO systems, which was also encountered inthe DAPSK-aided SISO scenario. This specific problem isthat the matrix Sd of (3) encapsulating the consecutivelytransmitted space-time signals is no longer unitary. Further-more, another challenging problem faced by the SD algorithmwhen aiming for complexity reduction is the estimation of thepower normalization factor ηn. Therefore, we will highlightthree major actions enabling an efficient implementationof the ML-MSDD relying on the SD mechanism in ourfollowing discourse:

Action 1 - Generation of Equivalent Unitary Signal Matrixand Its Associated Channel Matrix: In the light of ourmultiple-symbol system model of (3) let us consider thefirst transmission block as an example, where we mayhave S

d= diag{ 1√

2η1S[1] · · · 1√

2ηNwind

S[Nwind]} and H =

[√2η1H[1]T · · ·

√2ηNwind

H[Nwind]T]T. The so-called equiv-

alent unitary signal matrix Sd

is specifically constructed inorder to satisfy the above-mentioned unitary-matrix basedprerequisite of incorporating the SD mechanism.

Action 2 - Estimation of the Power Normalization Fac-tor: Since the first transmitted symbol of each detection

block constitutes a priori knowledge, as we mentionedabove, we re-order the layered signal detection processby rearranging each matrix of (3) upside down. Then, wenow have H = [

√2ηNwind

H[Nwind]T · · ·

√2η1H[1]T]T for

example. In the sequel, thanks to the layered tree searchmechanism of the SD scheme, we can now embark ona joint detection of the transmitted symbol Sn and itsassociated normalization factor ηn =

√||Sn||2/2, since the

previous transmission matrix estimates {Sj}n−1j=1 as well

as their associated transmit power normalization factorestimates {ηj}n−1

j=1 have already been temporarily obtainedfrom the previous tree search phases.

Action 3: - Construction of Partial Upper-Triangular Ma-trix: Unfortuntely, the upper-triangular matrix U used inthe layered tree search of the SD scheme, which is obtainedbased on the channel’s covariance matrix Σh = E{HH

H}may not be acquired, until all the decisions concerning thepower normalization factors {ηj}Nwind

j=1 have been attained.However, we found that a so-called partial upper-triangularmatrix ˜U of (nNtNr) × (nNt) elements may be generatedbased on the (nNt) × (nNt)-element partial channel covari-ance matrix ˜Σh, which corresponds to the partial equivalentchannel matrix ˜H obtained by removing the first (Nwind−n)rows of the complete channel matrix H. Furthermore, weobserved that the partial upper-triangular matrix ˜U constitutesa matrix which is identical to the lower-right submatrix of thecomplete upper-triangular matrix U used by the conventionalSD algorithm, as illustrated in Fig. 18. This is equivalent tosaying that the candidate search for the (n + 1)st transmit-ted symbol may be carried out based on the partial upper-triangular matrix ˜U, which is associated with the estimatesof {ηj}nj=1 that become available after the layered tree searchfor the previous n consecutively transmitted symbols. Moreexplicitly, this is achieved without acquiring all the decisionsof the power normalization factors {ηj}Nwind

j=1 . Consequently,as the tree search of the SD continues, the dimension ofthe partial upper-triangular matrix ˜U increases, and finallybecomes the complete matrix U, when the layered tree searchis completed.

3) Application Example - G2-DUSTM-16QAM System: Inthis section, we examine the performance of the proposedMSDSD scheme in the context of the two-transmit-antenna-aided G2-DUSTM-16QAM system. Its BER performanceis portrayed in Fig. 19(a). It can be seen that the errorfloor of the CDD imposed by rapidly fading channels issuccessfully mitigated by the proposed MSDSD. We notethat the MSDSD associated with Nwind = 2 is equivalentto the CDD. Furthermore, as the MSDSD window durationNwind increases, the performance of the noncoherent receiverapproaches that of the idealized coherent scheme relying onperfect CSI estimation apart from the irreducible 3 dB gap, asevidenced by Fig. 19(a).

Fig. 19(b) presents our complexity comparison betweenthe MSDD and the MSDSD, which is simply quantified asthe number of 16-QAM constellation points visited by theMSDD/MSDSD per detected DUSTM information matrix.As seen in Fig. 19(b), the ML MSDD imposes a constantbut potentially excessive complexity, even if the observation


Covariance MatrixPartial Channel

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se tw

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)

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˜U =0

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0(nNtNr) × (nNt)

Un,n

0

Figure 18. Generation of the partial upper-triangular matrix ˜U and its properties.

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MSDSD, Nw=2MSDSD, Nw=3MSDSD, Nw=5MSDSD, Nw=11

Figure 19. BER performance and Complexity of MSDSD aided DUSTMemploying 16QAM, for fd = 0.03.

window size of Nwind = 3 is only slightly higher thanthe Nwind = 2 value employed by the CDD. On the otherhand, the complexity imposed by the proposed MSDSD isa function of both the observation window size Nwind andthe received SNR. As the SNR increases, the MSDSD’scomplexity decreases steadily and finally becomes comparableto that of the MSDSD in conjunction with Nwind = 2.

V. DIFFERENTIAL INTERFERENCE SUPPRESSION BASEDON JOINT MULTIPLE-SYMBOL FILTERING AND DETECTION

Apart from the high-order modulation schemes dis-cussed in the previous sections, a more promising solutionto achieve a significantly improved bandwidth-efficiency isthe non-orthogonal transmission based on the exploitationof the spatial dimension. Explicitly, we may employ spatialdivision multiple access (SDMA) [1], where the user-specific CIRs are estimated and invoked for differentiatingthe parallel UL streams transmitted by the different users.Regretfully, it was revealed in [94] that the SDMA system’sperformance is highly sensitive to the channel estimationerrors, which may only be mitigated at the cost of an excessivecomputational complexity and/or high pilot overheads in many

practical time-varying fading scenarios. Fortunately, however,it is possible to circumvent the channel estimation. This maybe achieved by estimating and cancelling the multiple-accessinterference with the aid of an appropriately designed adaptivereceiver. For example, the adaptive minimum mean squareerror (MMSE) scheme [95] using the least mean square (LMS)or the recusive least squares (RLS) algorithm and the morerecently proposed maximum signal-to-interference-plus-noiseratio (MSINR) based differential interference suppression(DIS) scheme [96] may be invoked. For the LMS scheme theinterference suppression filter has to be adapted in an agilemanner, in order to minimize the MSE between the transmittedsignal and the filter’s output signal, while for the MSINRsolution the filter coefficients are adjusted to maximize theSINR at its output. It has been demonstrated in [96] theMSINR solution is also capable of mitigating the effects ofcarrier phase variations.

A. Multiple-Symbol SDMA-OFDM System Model

In the context of nonorthogonal transmissions, the signalstransmitted from multiple MSs are superimposed on eachother at the receive antennas, thus the per-sub-carrier-basedmultiple-symbol SDMA-OFDM system is formulated on thebasis of its orthogonal-transmission counterpart of (3) as:

Y[kN ] =

U∑u=1

Sdu[kN ]Hu[kN ]︸︷︷︸

Yu[kN ]

+W[kN ], (6)

where the subscript u is introduced here to differentiate theterms associated with each MS while the sub-carrier index isagain omitted here for notational simplicity. The dimensionof each term in (6) is in line with that of the correspondingterm of (3). Due to pratical cost- and sizeconstraints, theemployment of a single transmit antenna is assumed for eachMS without loss of generality, i.e. we have Nt = 1. Inorder to circumvent the channel estimation, the uth single-antenna-aided MS differentially encodes its information sym-bols Vu[n] ∈ Mc = {ej2πm/M ;m = 0, 1, · · · ,M − 1},


each of which contains (log2 M )-bit information, as Su[n] =Vu[n]Su[n− 1], resulting in the so-called differential SDMA(DSDMA) system.

B. Adaptive Multiple-Symbol Differential Interference Sup-pression

It is observed from (6) that non-coherent differential de-tection techniques cannot be directly applied at the BS torecover the information pertaining to a specific MS withoutsuppressing the interference imposed by all the other MSs.Therefore, we will use the MSINR approach of [96] for inter-ference suppression in the DSDMA-OFDM system. However,rather than computing the uth MS’s linear vector filter fu[n]of a specific sub-carrier for each OFDM symbol durationn, we propose updating fu[kN ] only once for Nwind OFDMsymbol durations based on the most recently received Nwind

signal matrices hosted by Y[kN ] of (6). The resultant newmultiple-symbol MSINR (MS-MSINR) criterion reduces thefilter-update overhead and additionally facilitates the imple-mentation of the powerful MSDSD in the ensuing stage, henceachieving significant performance improvements.

1) Multiple-Symbol MSINR Criterion: Our goal is to findthe specific filter fv[kN ] capable of maximizing the filter’soutput SINR, which may be mathematically expressed as:

fv[kN ] = maxfv [kN ]

fHv [kN ]R[kN ]fv[kN ]

fHv [kN ]Riv[kN ]fv[kN ]

, (7)

where R[kN ] � E{YH[kN ]Y[kN ]} is the correlation matrixof the multiple-symbol-based received signal Y[kN ] of (6)and Ri

v[kN ] � E{(Y[kN ] − Yv[kN ])H(Y[kN ] − Yv[kN ])}is the multiple-symbol-based interference-plus-noise corre-lation matrix. Using the method of Lagrange multipliers,we may solve (7) by maximizing fHv [kN ]R[kN ]fv[kN ] un-der the constraint that the interference-plus-noise componentfHv [kN ]Ri

v[kN ]fv[kN ] is fixed, leading to a so-called general-ized eigenvalue problem [97]:

R[kN ]fv[kN ] = λRiv[kN ]fv[kN ], (8)

where λ represents the real-valued Lagrange multiplier.2) MS-MSINR-Based Differential Interference Suppression:

Thanks to the differential encoding mechanism, despitedispensing with channel estimation in the DSDMA-OFDM system, the interference-plus-noise correlation ma-trix Ri

v[kN ] may be calculated by exploiting the dif-ferentially encoded transmission principles. To be spe-cific, under the assumption of a relatively slow fading chan-nel, the multiple-symbol-based interference-plus-noise corre-lation matrix Ri

v[kN ] may be approximately evaluated asRi

v[kN ] ≈ E{EHv [kN ]Ev[kN ]}, where the multiple-symbol-

based interference-plus-noise signal matrix Ev[kN ] is definedas Ev[kN ] �

√12 (Y[kN ] − V

d

v [kN ]Y[k−1N ]) with the block

index k−nN representing the kth block shifted backwards by

n OFDM symbol durations and the (NtNwind × NtNwind)-element diagonal block matrix V

d

v [kN ] = diag{Vv[kN ]} =diag{[Vv[(Nwind−1)(k−1)]T , Vv[kN ]T ]T } is the multiple-symbol-based transmitted information symbol matrix of thevth MS. The diagonal block matrix V

d

v [kN ] is known to the

receiver during the training session or may be estimated byusing the previous decisions [98].

3) Adaptive Implementation of MS-DIS: In practice, ratherthan carrying out the high-complexity singular-value decom-position to solve the generalized eigenvalue problem of (8),we apply a multiple-symbol-version of the adaptive Newtonalgorithm of [99] for recursively updating the differentialinterference suppression (DIS) filter fv[kN ]. This modifiedadaptive Newton algorithm, which was shown in [99] to havea fast convergence and an excellent tracking capability10 isomitted here owing to the lack of space - the interested readeris referred to [98, 99]. It is worth noting that in constrast tothe conventional single-symbol based adaptive algorithm,the filter fv[kN ] is updated at the beginning of each Nwind-OFDM-symbol block and it is used unaltered throughoutthe Nwind-OFDM-symbol block to suppress the multiple-access interference imposed by the other MSs. This block-based filtering regime facilitates the implementation of theMSDSD scheme as a benefit of imposing no further dis-tortion on the phase difference between the consecutivelytransmitted symbols in addition to that caused by the time-varying fading channel.

C. MS-DSDMA Transceiver Design

We now consider a channel-code aided turbo DIS receiverfor the DSDMA-OFDM system supporting U MSs, which isdepicted in Fig. 20. Specifically, the BS receiver of Fig. 20 isconstituted by three modules, namely the DIS filter bank, theMSDSD and the channel decoder, where the extrinsic infor-mation may be exchanged amongst the three concantenatedcomponents in a number of consecutive iterations. As shownin Fig. 20, A(·) represents the a priori information expressedin terms of the LLRs, while E(·) denotes the correspondingextrinsic information, whereas the labels u and c representthe uncoded and coded bits, respectively, corresponding to thespecific module indicated by the subscript. Bearing in mindthe goal of striking an attractive compromise between theattainable system performance and the complexity, ourdesign guidelines may be summarized as follows:

a) Channel-Code-Aided Turbo DIS: At the early stageof the iterative detection process, Vv[kN ] which is usedfor evaluating Ri

v[kN ] should be obtained based on theoutput of the MSDSD by toggling the decision-directedmode switch to the ‘a’ location of Fig. 20, in orderto ensure that the system is operating in its decision-directed mode. However, as soon as the a priori informationdelivered by the channel decoder becomes more reliableduring the iterative detection process, namely when wehave IE(c1) > IE(u2), it is preferred to switch to the“channel-code-aided” decision-directed mode by togglingthe switch to the ‘b’ location in Fig. 20, so that Vv[kN ] iscalculated from the a priori information provided by thechannel decoder.

10Our investigations, which are omitted here owing to the lack of space,indicate that the MSINR-based DIS scheme exhibits a lower sensitivity to thequality of the feedback decision than that of its conventional RLS-LMMSE-based counterpart, resulting in a superior tracking capability.


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A(u2)

E(u2)

E(c1)A(u2)

A(c1)

A(c1)

E(c1)Channel

π−1

π

π

π−1

Channel

y1

yU

Figure 20. Multiple-symbol DSDMA-OFDM transceiver architecture.

Table VSUMMARY OF SYSTEM PARAMETERS

Modulation DQPSK in Time DomainUsers Supported 2Normalized Doppler Freq. 0.001System DSDMA-OFDM UplinkSub-Carriers 1024Rx at BS 2Channel Code Half-Rate RSC(2,1,3) (5/7)TDL Channel Model Typical Urban 6-Tap Channel ModelChannel Delay Profile [0 2 6 16 24 50]

b) Soft-Symbol-Decision-Direct DIS: Based on the ideaof retaining the valuable soft-information contained inthe a posteriori LLRs, which would be simply discardedby the action of subjecting the LLRs to hard decisions,soft-symbol-decision-directed (SSDD) DIS is advocated. Inthis context the soft- rather than hard-decision symbol iscalculated based on the a priori LLRs delivered either bythe MSDSD or by the channel decoder for Vv[kN ].

c) Adaptive-Window-Duration Based MSDSD: Insteadof using a fixed observation window size of Nwind duringthe entire iterative detection process, the observationwindow size employed by the MSDSD was initially setto Nwind = 2 for the sake of a low complexity. However,this window-size will be slightly increased, as soon as theiterative decoding process exchanging extrinsic informa-tion between the combined “DIS-MSDSD” decoder andthe channel decoder converges. The proposed AWD-aidedMSDSD scheme is characterized with the aid of the EXITchart seen in Fig. 21(a) in the context of a (2 × 2)-elementDQPSK modulated DSDMA-OFDM system, where we mayalso observe the transition of the decision-directed mode fromthe MSDSD-based mode to the channel-code-based modeat the second iteration, as we discussed above. Indeed, thecomplexity imposed by the MSDSD is significantly reducedby the AWD scheme, as observed in Fig. 21(b), where thecomplexity imposed by the MSDSD in terms of the numberof the PED evaluations per bit is plotted versus the SNR forthe systems operating both with and without the AWD scheme.

d) Apriori-LLR-Threshold Aided MSDSD: Bearing inmind that the sign of the resultant LLRs indicates whetherthe current bit is more likely to be +1 or −1, whereas themagnitude reflects how reliable the decision concerningthe current bit is, the search space of the MSDSD maybe significantly reduced by invoking an ALT controlledtechnique. To be specific, when calculating the a posteriori

LLR LD(bi) for the ith bit component bi of the bit vectorb, the vector candidates b associated with bj (j �= i, j ∈ J )having values opposite to those indicated by the sign oftheir a priori LLRs may be excluded from the search space,as long as their a priori LLRs exhibit magnitudes higherthan the preset threshold TALT. As seen in Fig. 21(b),the integration of ALT schemes (TALT = 10) furtherreduce the complexity of the MSDSD significantly withoutsacrificing the performance.

D. Simulation Results and Discussions

In Fig. 22 the BER performance of the proposed turboMS-DIS-aided DSDMA system of Fig. 20 is plotted incomparison to those of its LMMSE-based and MSINR-basedsingle-symbol-DIS-aided counterparts, in the specific contextwhere two single-antenna-aided users are assumed to transmitsimutaneously to the two-antenna-aided BS. The simulationparameters are summarized in Table V. It is observed inFig. 22 that for Nwind = 1 the coded RLS-based-LMMSEDSDMA-OFDM system is slightly inferior to its MSINR-based counterpart in terms of its BER performance withinthe SNR range of interest. Furthermore, when the MS-DISscheme operates in conjunction with Nwind = 7, the MSINR-based system using the ALT- and AWD-aided MSDSD iscapable of achieving an SNR gain of 5 dB over its LMMSE-based counterpart at the BER target of 10−4 in the channel-coded scenario associated with fd = 0.001. Finally, observein Fig. 22 that the error-floor induced by a more severelytime-selective channel may be significantly mitigated by theproposed MSINR-based MS-DIS scheme in conjunction withthe ALT- and AWD-aided MSDSD. More specifically, an SNRgain of about 7 dB can be achieved by the proposed turboMS-DIS-aided three-stage receiver employing Nwind = 7 incomparison to the conventional MSINR-based DIS-assistedsystem using Nwind = 1 in the time-varying fading channelassociated with fd = 0.005.

VI. CONCLUSIONS AND FUTURE RESEARCH

A. Summary and Conclusions

Multiple-symbol joint signal processing techniques, whichare capable of exploiting the fading channel’s memory, wereadvocated in this treatise as an appealing, practically im-plementable candidate for differentially modulated systemsdispensing with the potentially excessive-complexity and yet


0 0.2 0.4 0.6 0.8 10

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=2)


=4)


=7)

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Trajectory

MSDSD−BasedSSDD−DIS

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SNR=6 dB2x2 DQPSK DSDMAfd=0.001

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(a) EXIT trajectory.

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2x2 DQPSK DSDMAfd=0.001

Nwind

=7

(b) Complexity reduction achieved.

Figure 21. Characterization of the adaptive-window aided scheme for theMSDSD.

inaccurate channel estimation. The benefits of the multiple-symbol joint signal processing include the enhancement ofthe system’s robustness against rapid channel fluctuation,striking a flexible performance-complexity compromise byappropriately adapting the observation window size Nwind aswell as the provision of enhanced iterative gains achievedfor channel-code-aided iterative receivers. As a prominentscheme in the family of multiple-symbol signal processingtechniques conceived for differential signalling systems, theML MSDD and its SD-based reduced-complexity counterpart,namely MSDSD, were briefly reviewed based on our gener-alized MIMO-OFDM multiple-symbol transmission model ofSection III, which subsumes the SISO system as a special case.However, our discussions of multiple-symbol signal process-ing was not restricted to the family of differentially modulated

0 5 10 15 20 25 30 35 4010

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LMMSE

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ALT=10

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=1

CDD

Uncoded SystemN

wind=1

Figure 22. BER performance of the MS-DSMA OFDM system using theALT- and AWD-aided MSDSD.

systems relying on conventional constant-modulus constel-lations. Instead, communication systems using nonconstant-modulus constellation based signaling mechanisms, such asthe DAPSK and the DUSTM-QAM schemes were consid-ered, in the interest of more efficiently exploiting the scarcespectral resources for accommodating the ever-increasing traf-fic demands. Although the exhaustive-search-based MSDDmechanism is directly applicable to the above high-orderdifferential modulation schemes, they exhibit a potentiallyexcessive complexity, which is increased exponentially bothwith the modulation constellation size and with the multiple-symbol processing block size. The bottleneck of efficientlyimplementing the MSDD for the DAPSK and DUSTM-QAM schemes lies in the fact that the employment of thenonconstant-modulus constellation destroys the unitary natureof the transmitted multiple-symbol signal matrix. Thereforewe transplanted the SD regime into the MSDD. Hence, aniterative A/P detection framework for MSDD-aided DAPSKsystem was proposed in Section IV-A, which was shown to becapable of achieving a low-complexity near-ML performance.On the other hand, upon the construction of an equivalentmultiple-symbol transmission model for the DUSTM-QAMsystem, we proposed in Section IV-B2 to incorporate thejoint detection of the power normalization factor and of thetransmitted space-time information symbol into the layeredtree search conducted by our newly devised partial SD process,which exploits the properties of the corresponding partialchannel matrix, hence resulting in a low-complexity MSDDimplementation. In the final part of our treatise, namely inSection V, an in-depth discussion was dedicated to the so-called differential SDMA system, where the multiple accessinterference was removed by our adaptive differential interfer-ence suppression scheme.


B. Design Guideline

• MIMOs circumvent the capacity/power limitation of clas-sic single-antenna-aided systems, since they may be ableto increase the achievable throughpot linearly, rather thanlogarithmically with the transmit power.

• However, the MIMO-capacity degrades in the presenceof correlated shadow-fading. Hence the single-antenna-based mobiles, which are sufficiently far apart may forma VAA to circumvent this limitation with the aid ofcooperation.

• Another challenge in the design of MIMOs is their chan-nel camplex estimation, since they require the estimationof (NTx × NRx) links, which is extremely demandingboth in terms of its computational requirements as well asin terms of its potentially excessive pilot overhead. Thisis particularly so for high Doppler frequencies. Thesetwo factors may lead to a performance erosion, whichmay be mitigated with the aid of low-complexity non-coherent detection aided MIMOs dispensing with channelestimation.

• Indeed, coherent-detection aided VAAs would be evenmore challanging to design than their classic MIMOcounterparts relying on co-located elements, since itis somewhat unrealistic to expect the low-complexity,light-weight MSs to estimate each other’s channels, letalone the associated data-security aspects of potentialeavesdropping...

• However, the widely recognized impediment of low-complexity non-coherent detection is its typical 3dB per-formance loss and the potential BER-floor experiencedin case of high Doppler frequencies.

• Meanwhile, the need for more flexible compromise be-tween performance and complexity as well as enhancediteration gain in the context of channel-code-aided iter-ative receiver has become increasingly urgent for futurewireless communications dispensing with channel esti-mation.

• The joint multiple-symbol based signal processing, suchas the MSDD detection technique features prominentlyon the list of the recent technical advances with a chanceof resolving above-mentioned problems at a reasonablylow complexity with the aid of sphere decoding mecha-nism.

• Unfortunately, the direct application of MSDSD forfuture high-spectrum-efficiency transmissions employingthe DAPSK or DUSTM-QAM schemes is prevented bythe nonconstant-modulus modulation constellation struc-ture, since it undermines the unitarity of the multiple-symbol transmitted signal matrix.

• Hence, the multiple-symbol based detection may be de-coupled for the amplitude and phase of the transmittedDAPSK symbols and an iterative information exchangemechanism may be devised between them for retrievingthe performance loss potentially caused by the decoiu-pling of the A/P detection process.

• As for DUSTM-QAM systems, incorporating a jointdetection of the power normalization factor and of thetransmitted space-time information symbol into the lay-

ered tree search process may be invoked for the sakeof a low-complexity implementation, which exploits theproperties of the corresponding partial channel matrix.

• On the other hand, the signal separation capability atthe receiver of differentially modulated SDMA systemsdispensing with channel estimation requires further en-hancements in high-Doppler scenarios.

• To this end, inspired by the block-based least-squares al-gorithm of [95] designed for standard MMSE adaptation,the so-called multiple-symbol DIS scheme based on theMSINR criterion is devised, which is also capable ofreducing the filter adaptation overheads and - even moreimportantly - for facilitating the implementation of thepowerful MSDSD.

• In order to further exploit the differential coding gainsin the context of our adaptive MS-DIS scheme, a newchannel-code-aided three-stage turbo DIS receiver wasthen proposed, which allowed a beneficial informationexchange amongst the concatenated adaptive MS-DISfilter bank, the MSDSD and the channel decoder.

• Finally, a new adaptive-window-duration based MSDSDscheme was conceived, which was further aided by theproposed ALT technique for the sake of achieving sig-nificant complexity reductions in the turbo DIS receiver.

C. Future Research

Nonetheless, there are numerous interesting problemsassociated with the design of differentially modulatedwireless communication systems as well as with theirmultiple-symbol signal processing mechanism, which needfurther investigation in the future:

1) Achieving further complexity reductions for theMSDSD os conventional differentially detected systemsmay be a challenging but worthwhile issue to tackle.Amongst a range of interesting ideas proposed recently, theso-called forward/backward-MSDSD (FB-MSDSD) [100]has the potential of reducing the complexity by dividingthe original detection interval into forward and backwardoriented processes.

2) Recently, the MSDD has been proposed for thedouble-differential modulation aided system of [101] inorder to achieve an enhanced robustness against thefrequency variation which distorts the transmitted signalthrough attenuating its amplitude and introducing a time-varying phase shift to the information symbols. However,a more efficient implementation of the MSDD takingthe characteristic of double differential modulation intoaccount may require a further specialized design.

3) The multiuser/multistream interference managementis one of the most critical and challenging problemsthat requires further enhancements in order to designhigher-efficiency non-orthogonal differentially modulatedcooperative systems, since the channel estimation forall cooperating links beomes significantly more difficultthan in their point-to-point direct transmission basedcounterparts. A possible way forward is to design ajoint receiver and cooperative protocol, for example, asproposed in [102].


Table VIACRONYMS

QoS Quality of Service SD Sphere DetectionUE User Equipment DFT Discrete Fourier TransformOFDM Orthogonal Frequency-Division Multiplexing OFDMA Orthogonal Frequency-Division Multiple AccessWCDMA Wideband Code-Division Multiple Access SC-FDMA Single-Carrier Frequency-Division Multiple AccessFDM Frequency Divison Multiplexing MIMO Multiple-Input Multiple-OutputCIR channel impulse response QoE Quality of End-User ExperienceBS Base Station MS Mobile StationVAA Virtual Antenna Array UL UplinkDL Downlink RS Relay StationTDMA Time-Division Multiple Access CDMA Code-Division Multiple-AccessAF Amplify-and-Forward DF Decode-and-ForwardCF Compress-and-Forward SISO Single-Input Single-OutputCSI Channel State Information CTF Channel Transfer FactorDPSK Differential Phase Shift Keying CDD Conventional Differential DetectionDAF Differential Amplify-and-Forward FD-CTF Frequency Domain Channel Transfer FactorDAPSK Differential Amplitude and Phase Shift Keying Star-QAM Star Quadrature Amplitude ModulationMSDD Multiple-Symbol Differential DetectionMSDSD Multiple-Symbol Differential Sphere DetectionIAP-MSDD Iterative Amplitude/Phase Multiple-Symbol Differential DetectorIAP-MSDSD Iterative Amplitude/Phase Multiple-Symbol Differential Sphere DetectorMSDAD Multiple-Symbol Differential Amplitude DetectorMSDPD Multiple-Symbol Differential Phase DetectorDUSTM Differential Unitary Space-Time Modulation DIS Differential Interference SuppressionSDMA Spatial-Dvision Multiple Access MS-DSDMA Multiple-Symbol Differential SDMATD Time Domain DDF Differential Decode-and-ForwardCDAD Conventional Differential Amplitude Detection ML Maximum LikelihoodMSDSD Multiple-Symbol Differential Sphere Detection MAP Maximum-a-PosterioriID Iterative Detection MSDAD Multiple-Symbol Differential Amplitude DetectorMSDPD Multiple-Symbol Differential Phase Detector EXIT EXtrinsic Information TransferMI Mutual Information CDPD Conventional Differential Phase DetectionDOSTBC Differential Orthogonal STBC SSDD Soft-Symbol Decision DirectMMSE Minimum Mean Square Error LMS Least Mean SquareRLS Recursive Least Squares MSINR Maximum Signal-to-Interference-plus-Noise RatioAWD Adaptive Window Duration ALT Apriori-LLR Threshold

Labeling

optimization of differential unitary space-time modulation

4) Additionally, scheduling and adaptive rate control isanother issue associated with the family of differentiallymodulated systems based on multiple-symbol signal pro-cessing that has to be studied for the sake of achievinga high throughput, while maintaining a reasonably lowcomplexity. To this end, we may seek further solutionsdispensing with CSI, while using EXIT-chart-based designtechniques [103]. The adaptive window duration basedscheme discussed in this treatise may also be taken intoaccount in the design of link adaptation.

5) Finally, The synchronization issues of cooperativesystems require substantial further attention.

APPENDIX

Acronyms See Table VI.)

REFERENCES

[1] L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM andMC-CDMA for Broadband Multi-User Communications, WLANs andBroadcasting. John Wiley and IEEE Press, 2003.

[2] A. J. Paulraj and T. Kailath, “Increasing capacity in wireless broad-cast systems using distributed transmission/directional reception,” USPatent 5 345 599, 1994.

[3] G. J. Foschini, “Layered space-time architecture for wireless commu-nication in fading environments when using multiple antennas,” BellLabs Technical Journal, vol. 2, pp. 41–59, 1996.

[4] G. J. Foschini and M. J. Gans, “On limits of wireless communicationsin a fading environment when using multiple antennas,” WirelessPersonal Communications, vol. 6, pp. 311–335, Mar. 1998.

[5] N. Chiurtu, B. Rimoldi, and E. Telatar, “On the capacity of multi-antenna Gaussian channels,” in Proc. IEEE International Symposiumon Information Theory, (Washington, DC), p. 53, June 2001.

[6] S. M. Alamouti, “A simple transmit diversity technique for wirelesscommunications,” IEEE J. Sel. Areas Commun., vol. 16, pp. 1451–1458, Oct. 1998.

[7] B. Hochwald, T. L. Marzetta, and C. B. Papadias, “A transmitterdiversity scheme for wideband CDMA systems based on space-timespreading,” IEEE J. Sel. Areas Commun., vol. 19, pp. 48–60, Jan. 2001.

[8] W. F. Su, Z. Safar, and K. J. R. Liu, “Space-time signal design for time-correlated Rayleigh fading channels,” IEEE International Conferenceon Communications 2003., vol. 5, pp. 3175–3179, May 2003.

[9] W. Su and X. G. Xia, “On space-time block codes from complex or-thogonal designs,” Wireless Personal Communications, vol. 25, pp. 1–26, April 2003.

[10] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time blockcodes from orthogonal designs,” IEEE Trans. Inf. Theory, vol. 45,pp. 1456–1467, July 1999.

[11] G. D. Golden, C. J. Foschini, R. A. Valenzuela, and P. W. Wolniansky,“Detection algorithm and initial laboratory results using V-BLASTspace-time communication architecture,” Electronics Letters, vol. 35,pp. 14–16, Jan. 1999.

[12] H. Lee, B. Lee, and I. Lee, “Iterative detection and decoding with animproved v-BLAST for MIMO-OFDM systems,” IEEE J. Sel. AreasCommun., vol. 24, pp. 504–513, Mar. 2006.

[13] D. Gesbert, M. Shafi, D. shan Shiu, P. J. Smith, and A. Naguib, “Fromtheory to practice: an overview of MIMO space-time coded wirelesssystems,” IEEE J. Sel. Areas Commun., vol. 21, pp. 281–302, Apr.2003.

[14] J. Mietzner, R. Schober, L. Lampe, W. H. Gerstacker, and P. A.Hoeher, “Multiple-antenna techniques for wireless communications - acomprehensive literature survey,” IEEE Commun. Surveys & Tutorials,vol. 11, pp. 87–105, second quater 2009.

[15] T. S. Rappaport, Wireless Communications Principles and Practise.Pearson Education Asia Limited and Publishing House of ElectronicsIndustry, second ed., 2002.

[16] T. Cover and A. E. Gamal, “Capacity theorems for the relay channel,”IEEE Trans. Inf. Theory, vol. 25, pp. 572–584, Sept. 1979.

[17] R. Pabst, “Relay-based deployment concepts for wireless and mobilebroadband radio,” IEEE Commun. Mag., vol. 42, pp. 80–89, Sept. 2004.

[18] D. Soldani and S. Dixit, “Wireless relays for broadband access,” IEEECommun. Mag., vol. 46, pp. 58–66, Mar. 2008.


[19] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity.part I: System description,” IEEE Trans. Commun., vol. 51, pp. 1927–1938, Nov. 2003.

[20] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity.part II: Implementation aspects and performance analysis,” IEEE Trans.Commun., vol. 51, pp. 1939–1948, Nov. 2003.

[21] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversityin wireless networks: Efficient protocols and outage behavior,” IEEETrans. Inf. Theory, vol. 50, pp. 3062–3080, Dec. 2004.

[22] K. G. Seddik, A. K. Sadek, W. Su, and K. J. R. Liu, “Outage analysisand optimal power allocation for multinode relay networks,” IEEESignal Process. Lett., vol. 14, pp. 377–380, June 2007.

[23] G. Kramer, M. Gastpar, and P. Gupta, “Cooperative strategies andcapacity theorems for relay networks,” IEEE Trans. Wireless Commun.,vol. 51, pp. 3037–3063, Sept. 2005.

[24] S. Simoens, O. Muoz-Medina, J. Vidal, and A. D. Coso, “Compress-and-forward cooperative mimo relaying with full channel state infor-mation,” IEEE Trans. Wireless Commun., vol. 58, pp. 781–791, Feb.2010.

[25] K. Etemad, “Overview of mobile WiMAX technology and evolution,”IEEE Commun. Mag., vol. 46, pp. 31–40, Oct. 2008.

[26] K. Etemad, “Multisite filed trial for LTE and advanced concepts,” IEEECommun. Mag., vol. 47, no. 2, pp. 92–98, 2009.

[27] P. Hoher, “TCM on frequency-selective land-mobile fading channels,”5th International Workshop Digital Communications, B. V. M. Luiseand E. Biglieri, Eds. Pisa, Italy: Elsevier, pp. 8–12, 1991.

[28] Y. Wu and M. Patzold, “Performance analysis of cooperative communi-cation systems with imperfect channel estimation,” IEEE InternationalConference on Communications (ICC’09), June 2009.

[29] S. Han, S. Ahn, E. Oh, and D. Hong, “Effect of channel-estimationerror on ber performance in cooperative transmission,” IEEE Trans.Veh. Technol., vol. 58, pp. 2083–2088, May 2009.

[30] J. G. Proakis, Digital Communications. 4th edition, New York, NY:Mc-Graw-Hill, 2000.

[31] T. Himsoon, W. P. Siriwongpairat, W. Su, and K. J. R. Liu, “Differentialmodulations for multinode cooperative communications,” IEEE Trans.Signal Process., vol. 56, pp. 2941–2956, July 2008.

[32] T. Himsoon, W. P. Siriwongpairat, W. Su, and K. J. R. Liu, “Differentialmodulation with threshold-based decision combining for cooperativecommunications,” IEEE Trans. Signal Process., vol. 55, pp. 3905–3923, July 2007.

[33] W. Su, F. Chen, D. A. Pados, and J. D. Matyjas, “The outage probabilityand optimum power assignment for differential amplify-and-forwardrelaying,” IEEE International Conference on Communications, pp. 1–5, May 2010.

[34] Q. Zhao and H. Li, “Performance of differential modulation withwireless relays in Rayleigh fading channels,” IEEE Commun. Lett.,vol. 9, pp. 343–345, Apr. 2005.

[35] Q. Zhao and H. Li, “Differential modulation for cooperative wirelesssystems,” IEEE Trans. Signal Process., vol. 55, pp. 2273–2283, May2007.

[36] T. Cui, F. Gao, and C. Tellambura, “Differential modulation for two-way wireless communications: a perspective of differential networkcoding at the physical layer,” IEEE Trans. Commun., vol. 57, pp. 2977–2987, Oct. 2009.

[37] L. Hanzo, Y. Akhtman, L. Wang, and M. Jiang, MIMO-OFDM for LTE,WIFI and WIMAX: Coherent versus Non-Coherent and CooperativeTurbo-Transceivers. John Wiley and IEEE Press, 2010.

[38] L. Wang and L. Hanzo, “Dispensing with channel estimation: Dif-ferentially modulated cooperative wireless communications,” in IEEECommun. Surveys & Tutorials, vol. 14, pp. 836 – 857, 2012.

[39] L. Wang, L. Kong, S. X. Ng, and L. Hanzo, “Code-rate-optimizeddifferentially modulated near-capacity cooperation,” in IEEE Trans.Commun., vol. 59, pp. 2185 – 2195, Aug. 2011.

[40] W. T. Webb, L. Hanzo, and R. Steele, “Bandwidth efficient QAMschemes for Rayleigh fading channels,” IEE Proceedings I, Communi-cations, Speech and Vision, vol. 138, pp. 169–175, June 1991.

[41] H. Rohling and V. Engels, “Differential amplitude phase shift keying(DAPSK) - a new modulation method for DTVB,” Proc. InternationalBroadcasting Convention, pp. 102–108, 1995.

[42] F. Adachi and M. Sawahashi, “Decision feedback differential detectionof differentially encoded 16APSK signals,” IEEE Trans. Commun.,vol. 44, pp. 416–418, Apr. 1996.

[43] B. M. Hochwald and W. Sweldens, “Differential unitary space-timemodulation,” IEEE Trans. Commun., vol. 48, no. 12, pp. 2041–2052,2000.

[44] B. L. Hughes, “Differential space-time modulation,” IEEE Trans. Inf.Theory, vol. 46, pp. 2567–2578.

[45] G. Wang, Y. Zhang, and M. Amin, “Differential distributed space-timemodulation for cooperative networks,” IEEE Trans. Wireless Commun.,vol. 5, pp. 3097–3108, Nov. 2006.

[46] Y. Jing and H. Jafarkhani, “Distributed differential space-time codingfor wireless relay networks,” IEEE Trans. Commun., vol. 56, pp. 1092–1100, July 2008.

[47] F. Oggier and E. Lequeu, “Differential distributed cayley space-timecodes,” IEEE Trans. Wireless Commun., vol. 8, pp. 3808–3814, July2009.

[48] S. Yiu, R. Schober, and L. Lampe, “Differential distributed space-time block coding,” IEEE Pacific Rim Conference on Communications,Computers and Signal Processing, pp. 53–56, 2005.

[49] V. Tarokh and H. Jafarkhani, “A differential detection scheme fortransmit diversity,” IEEE J. Sel. Areas Commun., vol. 18, no. 7,pp. 1169–1174, 2000.

[50] A. Shokrollahi, B. Hassibi, B. M. Hochwald, and W. Sweldens,“Representation theory for high-rate multiple-antenna code design,”IEEE Trans. Inf. Theory, vol. 47, no. 6, pp. 2335–2367, 2001.

[51] B. Hassibi and B. M. Hochwald, “Cayley differential unitary space-time codes,” IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1485–1503,2002.

[52] L. Z. Zheng and D. N. C. Tse, “Communication on the grassmannmanifold: a geometric approach to the noncoherent multiple-antennachannel,” IEEE Trans. Inf. Theory, vol. 48, pp. 359–383, Feb. 2002.

[53] S. H. Nam, C. S. Hwang, J. Chung, and V. Tarokh, “Differential spacetime block codes using QAM for four transmit antennas,” in IEEEInternational Conference on Communications, vol. 2, pp. 952–956,June 2004.

[54] Y. Zhu and H. Jafarkhani, “Differential modulation based on quasi-orthogonal codes,” IEEE Trans. Wireless Commun., vol. 4, no. 6,pp. 3005–3017, 2005.

[55] F. Oggier, “Cyclic algebras for noncoherent differential space-timecoding,” IEEE Trans. Inf. Theory, vol. 53, pp. 3053–3065, September2007.

[56] I. Stewart, Galois Theory. London, UK: Chapman and Hall, 1989.[57] G. Wang, , Y. Zhang, and M. Amin, “Differential distributed space-time

modulation for cooperative networks,” IEEE Trans. Wireless Commun.,vol. 5, pp. 3097 – 3108, Nov. 2006.

[58] S. Yiu, R. Schober, and L. Lampe, “Distributed space-time blockcoding,” IEEE Trans. Commun., vol. 54, pp. 1195 – 1206, 2006.

[59] Y. Jing and H. Jafarkhani, “Distributed differential space-time codingfor wireless relay networks,” IEEE Trans. Commun., vol. 56, pp. 1092– 1100, 2008.

[60] G. S. Rajan and B. S. Rajan, “Algebraic distributed differential space-time codes with low decoding complexity,” IEEE Trans. WirelessCommun., vol. 7, pp. 3962 – 3971, Oct. 2008.

[61] F. Oggier and E. Lequeu, “Differential distributed cayley space-timecodes,” IEEE Trans. Wireless Commun., vol. 8, pp. 3808 – 3814, 2009.

[62] Z. Gao and H. Q. L. K. J. R. Liu, “Differential space-time networkcoding for multi-source cooperative communications,” IEEE Trans.Commun., vol. 59, pp. 3146 – 3157, Nov. 2011.

[63] Q. Huo, L. Song, Y. Li, and B. Jiao, “A distributed differential space-time coding scheme with analog network coding in two-way relaynetworks,” IEEE Trans. Signal Process., vol. 60, pp. 4998 – 5004,Sept. 2012.

[64] P. Dayal, M. Brehler, and M. K. Varanasi, “Leveraging coherent space-time codes for noncoherent communication via training,” IEEE Trans.Inf. Theory, vol. 50, pp. 2058–2080, Sept. 2004.

[65] G. Farhadi and N. Beaulieu, “Fixed relaying versus selective relayingin multi-hop diversity transmission systems,” IEEE Trans. Commun.,vol. 58, pp. 956–965, Mar. 2010.

[66] W. W. Peterson and D. T. Brown, “Cyclic codes for error detection,”Proc. Institute of Radio Engineers, vol. 49, pp. 228–235, Jan. 1961.

[67] T. Himsoon, W. Su, and K. J. R. Liu, “Differential transmissionfor amplify-and-forward cooperative communications,” IEEE SignalProcess. Lett., vol. 12, pp. 597–600, Sept. 2005.

[68] L. Wang and L. Hanzo, “The amplify-and-forward cooperative up-link using multiple-symbol differential sphere-detection,” IEEE SignalProc. Lett., vol. 16, pp. 913–916, Oct. 2009.

[69] V. Pauli and L. Lampe, “Multiple-symbol differential sphere decodingfor unitary space-time modulation,” IEEE Global TelecommunicationsConference, vol. 3, p. 6, Nov. 2005.

[70] Y. Liang and V. V. Veeravalli, “Capacity of noncoherent time-selectiverayleigh-fading channels,” IEEE Trans. Inf. Theory, vol. 50, pp. 3095–3110, Dec. 2004.

[71] U. Fincke and M. Pohst, “Improved methods for calculating vectors ofshort length in a lattice, including a complexity analysis,” Mathematicsof Computation, vol. 44, pp. 463–471, April 1985.


[72] E. Viterbo and J. Boutros, “A universal lattice code decoder for fadingchannels,” IEEE Trans. Inf. Theory, vol. 45, pp. 1639–1642, July 1999.

[73] L. Lampe, R. Schober, V. Pauli, and C. Windpassinger, “Multiple-symbol differential sphere decoding,” IEEE Trans. Commun., vol. 12,pp. 1981–1985, Dec. 2005.

[74] D. Divsalar and M. K. Simon, “Multiple-symbol differential detectionof MPSK,” IEEE Trans. Commun., vol. 38, pp. 300–308, Mar. 1990.

[75] D. Divsalar and M. K. Simon, “Maximum-likelihood differentialdetection of uncoded and trellis-coded amplitude phase modulationover awgn and fading channels–metrics and performance,” IEEE Trans.Commun., vol. 42, pp. 76–89, Jan. 1994.

[76] R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge UniversityPress, 1985.

[77] M. O. Damen, K. Abed-Meraim, and J. C. Belfiore, “Generalisedsphere decoder for asymmetrical space-time communication architec-ture,” Electronics Letters, vol. 36, pp. 166–167, Jan. 2000.

[78] T. Cui and C. Tellambura, “An efficient generalized sphere decoder forrank-deficient MIMO systems,” IEEE Commun. Lett., vol. 9, pp. 423–425, May 2005.

[79] J. Jalden and B. Ottersten, “On the complexity of sphere decodingin digital communications,” IEEE Trans. Signal Process., vol. 53,pp. 1474–1484, 2005.

[80] J. Akhtman and L. Hanzo, “An optimized-hierarchy-aided maximumlikelihood detector for MIMO-OFDM,” IEEE 63rd Vehicular Technol-ogy Conference, VTC 2006-Spring, vol. 3, pp. 1526–1530, 2006.

[81] I. Motedayen-Aval, A. Krishnamoorthy, and A. Anastasopoulos, “Op-timal joint detection/estimation in fading channels with polynomialcomplexity,” IEEE Trans. Inf. Theory, vol. 53, pp. 209–223, 2007.

[82] V. Pauli, L. Lampe, R. Schober, and K. Fukuda, “Multiple-symboldifferential detection based on combinatorial geometry,” IEEE Trans.Commun., vol. 56, pp. 1596–1600, 2008.

[83] L. Hanzo, S. X. Ng, W. Webb, and T. Keller, Quadrature AmplitudeModulation: From Basics to Adaptive Trellis-Coded, Turbo-Equalisedand Space-Time Coded OFDM, CDMA and MC-CDMA Systems.Wiley-Blackwell, 2004.

[84] V. Engels and H. Rohling, “Multilevel differential modulation tech-niques (64-dapsk) for multicarrier transmission systems,” EuropeanTrans. Telecommunications, vol. 6, pp. 633–640, Nov. 1995.

[85] H. Rohling and V. Engels, “Differential amplitude phase shift keying(DAPSK) a new modulation method for DVBT,” International Broad-casting Convention, pp. 102–108, Sept. 1995.

[86] A. Song, G. Wang, W. Su, and X. G. Xia, “Unitary space-time codesfrom Alamouti’s scheme with APSK signals,” IEEE Trans. WirelessCommun., vol. 3, pp. 2374–2384, Nov. 2004.

[87] C. S. Hwang, S. H. Nam, J. Chung, and V. Tarokh, “Differential spacetime block codes using nonconstant modulus constellations,” IEEETrans. Signal Process., vol. 51, no. 11, pp. 2955–2964, 2003.

[88] F. Adachi and M. Sawahashi, “Performance analysis of various 16level modulation schemes under Rayleigh fading,” Electronics Letters,vol. 28, pp. 1579–1581, Aug. 1992.

[89] M. Machida, S. Handa, and S. Oshita, “Multiple-symbol differentialdetection of APSK based on MAP criterion,” IEEE Global Telecom-munications Conference, vol. 5, pp. 2740–2744, Nov. 1998.

[90] V. Pauli, L. Lampe, and R. Schober, ““Turbo DPSK” using softmultiple-symbol differential sphere decoding,” IEEE Trans. Inf. The-ory, vol. 52, no. 4, pp. 1385–1398, 2006.

[91] K. Ishibashi, H. Ochiai, and R. Kohno, “Low-complexity bit-interleaved coded DAPSK for Rayleigh-fading channels,” IEEE J. Sel.Areas Commun., vol. 23, pp. 1728–1738, Sept. 2005.

[92] A. Ashikhmin, G. Kramer, and S. ten Brink, “Extrinsic informationtransfer functions: model and erasure channel properties,” IEEE Trans.Inf. Theory, vol. 50, pp. 2657–2673, Nov. 2004.

[93] L. Lampe and R. Fischer, “Comparison and optimization of differen-tially encoded transmission on fading channels,” in Proc. 3rd Int. Symp.Power-Line Communications (ISPLC), 1999.

[94] T. Weber, A. Sklavos, and M. Meurer, “Imperfect channel-state in-formation in MIMO transmission,” IEEE Trans. Commun., vol. 54,pp. 543–552, Mar. 2006.

[95] H. V. Poor and G. W. Wornell, Wireless Communications: SignalProcessing Perspectives. Prentice Hall PTR, 1998.

[96] S. K. Cheung and R. Schober, “Differential spatial multiplexing,” IEEETrans. Wireless Commun., vol. 5, pp. 2127–2135, Aug. 2006.

[97] H.-J. Su and E. Geraniotis, “Maximum signal-to-noise ratio arrayprocessing for space-time coded systems,” IEEE Trans. Commun.,vol. 50, pp. 1419–1422, Sept. 2002.

[98] L. Wang and L. Hanzo, “Differential interference suppression forSDMA-OFDM based on joint multiple-symbol filtering and detection,”IEEE Trans. Veh. Technol., vol. 60, pp. 4656–4662, Nov. 2011.

[99] J. Yang, F. Yang, H.-S. Xi, W. Guo, and Y. Sheng, “Robust adaptivemodified newton algorithm for generalized eigendecomposition and itsapplication,” EURASIP J. Advances in Signal Processing, vol. 2007,pp. 1–10, June 2007.

[100] C.-C. Lo and S.-L. Su, “Combining of forward and backward multiple-symbol differential sphere decoding for turbo coded system,” IEEEVehicular Technology Conference (VTC’10-Spring), May 2010.

[101] A. M. Rabiei and N. C. Beaulieu, “Frequency offset invariant multiplesymbol differential detection of mpsk,” IEEE Trans. Commun., vol. 59,pp. 652 – 657, Mar. 2011.

[102] L. Li, L. Wang, and L. Hanzo, “Differential interference suppressionaided three-stage concatenated successive relaying,” IEEE Trans. Com-mun., vol. 60, pp. 2146 – 2155, Aug. 2012.

[103] S. Ibi, T. Matsumoto, R. Thoma, S. Sampei, and N. Morinaga, “Exitchart-aided adaptive coding for multilevel bicm with turbo equalizationin frequency-selective mimo channels,” IEEE Trans. Veh. Technol.,vol. 56, pp. 3757–3769, Nov. 2007.

Li Wang (S’09-M’10) was born in Chengdu, China,in 1982. He received his BEng degree in InformationEngineering from Chengdu University of Technol-ogy (CDUT), Chengdu, China, in 2005 and hisMSc degree with distinction in Radio FrequencyCommunication Systems from the University ofSouthampton, UK, in 2006. Between October 2006and January 2010 he was pursuing his PhD degree inthe Communications Group, School of Electronicsand Computer Science, University of Southamp-ton, and meanwhile he participated in the Delivery

Efficiency Core Research Programme of the Virtual Centre of Excellencein Mobile and Personal Communications (Mobile VCE). Upon completionof his PhD in January 2010 he conducted research as a Senior ResearchFellow in the School of Electronics and Computer Science at the Universityof Southampton. During this period he was involved in Project #7 of theIndian-UK Advanced Technology Centre (IU-ATC): advanced air interfacetechnique for MIMO-OFDM and cooperative communications. In March 2012he joined the R&D center of Huawei Technologies in Stockholm, Sweden,working as Senior Engineer of Baseband Algorithm Architecture. He haspublished over 30 research papers in IEEE/IET journals and conferences,and he also co-authored one John Wiley/IEEE Press book. He has broadresearch interests in the field of wireless communications, including PHYlayer modeling, link adaptation, cross-layer system design, multi-carriertransmission, MIMO techniques, CoMP, channel coding, multi-user detection,non-coherent transmission techniques, advanced iterative receiver design andadaptive filter.

Li Li received the B.Eng. degree in informationengineering from the University of Electronic Sci-ence and Technology of China (UESTC), Chengdu,China, in 2006 and the M.Sc. degree with distinc-tion in wireless communications from the Univer-sity of Southampton, Southampton, U.K., in 2009.He is currently working towards the Ph.D. degreewith the Research Group of Communications, Sig-nal Processing and Control, School of Electronicsand Computer Science, University of Southampton,Southampton, U.K., and participating in the Euro-

pean Union Concerto project. His research interests include channel coding,iterative detection, non-coherent transmission technologies, cooperative com-munications, interference suppression techniques and network coding.


Chao Xu (S’09) received the B.Eng. degree fromBeijing University of Posts and Telecommunica-tions, Beijing, China, and the B.Sc.(Eng) (first-classhonors) from Queen Mary, University of London,London, UK, in 2008, both in TelecommunicationsEnginneering with Management and both througha Sino-UK joint degree program. He received theM.Sc. degree (with distinction) in radio frequencycommunication systems from the University ofSouthampton, Southampton, UK, in 2009. He iscurrently working towards the PhD degree with

the Research Group of Commmunications, Signal Processing and Control,School of Electronics and Computer Science, University of Southampton. Hisresearch interests include reduced-complexity multiple-input-multiple-outputdesign, noncoherent spacetime modulation detection, extrinsic-information-transfer-chart-aided turbo detection, and cooperative communications.

Mr. Xu was awarded the 2009 Best M.Sc. Student in Broadband and MobileCommunication Networks by the IEEE Communications Society (UnitedKingdom and Republic of Ireland Chapter), and the 2013 Chinese GovernmentAward for Outstanding Self-Financed Students Abroad.

Dr. Dandan Liang (S’09) received her B.Eng.degree (First class) in electronic science and tech-nology from the PLA Information Engineering Uni-versity, Zhengzhou, China, in 2008. She received herM.Sc. degree (First class) in radio frequency com-munication systems and Ph.D. degree in wirelesscommunications from the University of Southamp-ton, UK, in 2009 and 2013, respectively. Her re-search interests include adaptive coded modulation,coded modulation, non/coherent modulation detec-tion, iterative detection, networking coding, cooper-

ative communications as well as wireless-optical fiber communications.

Dr Soon Xin Ng (S’99-M’03-SM’08) received theB.Eng. degree (First class) in electronics engineeringand the Ph.D. degree in wireless communicationsfrom the University of Southampton, Southampton,U.K., in 1999 and 2002, respectively. From 2003 to2006, he was a postdoctoral research fellow workingon collaborative European research projects knownas SCOUT, NEWCOM and PHOENIX. Since Au-gust 2006, he has been a member of academicstaff in the School of Electronics and ComputerScience, University of Southampton. He is involved

in the OPTIMIX and CONCERTO European projects as well as the IU-ATCand UC4G projects. He is currently a senior lecturer at the University ofSouthampton.

His research interests include adaptive coded modulation, coded modula-tion, channel coding, space-time coding, joint source and channel coding,iterative detection, OFDM, MIMO, cooperative communications, distributedcoding, quantum error correction codes and joint wireless-and-optical-fibercommunications. He has published over 160 papers and co-authored two JohnWiley/IEEE Press books in this field. He is a Senior Member of the IEEE,a Chartered Engineer and a Fellow of the Higher Education Academy in theUK.

Lajos Hanzo FREng, FIEEE, FIET, Fellow ofEURASIP, DSc received his degree in electronicsin 1976 and his doctorate in 1983. In 2009 he wasawarded the honorary doctorate “Doctor HonorisCausa” by the Technical University of Budapest.During his 35-year career in telecommunications hehas held various research and academic posts inHungary, Germany and the UK. Since 1986 he hasbeen with the School of Electronics and ComputerScience, University of Southampton, UK, wherehe holds the chair in telecommunications. He has

successfully supervised 80 PhD students, co-authored 20 John Wiley/IEEEPress books on mobile radio communications totalling in excess of 10 000pages, published 1300 research entries at IEEE Xplore, acted both as TPCand General Chair of IEEE conferences, presented keynote lectures and hasbeen awarded a number of distinctions. Currently he is directing a 100-strongacademic research team, working on a range of research projects in the field ofwireless multimedia communications sponsored by industry, the Engineeringand Physical Sciences Research Council (EPSRC) UK, the European ISTProgramme and the Mobile Virtual Centre of Excellence (VCE), UK. He isan enthusiastic supporter of industrial and academic liaison and he offers arange of industrial courses. He is also a Governor of the IEEE VTS. During2008 - 2012 he was the Editor-in-Chief of the IEEE Press and a ChairedProfessor also at Tsinghua University, Beijing. His research is funded bythe European Research Council’s Senior Research Fellow Grant. For furtherinformation on research in progress and associated publications please referto http://www-mobile.ecs.soton.ac.uk.

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