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Multipleantenna cooperative wireless systems: A diversity multiplexing tradeoff perspective
, 2007
"... We consider a general multipleantenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity–multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (halfduplex o ..."
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Cited by 70 (3 self)
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We consider a general multipleantenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity–multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (halfduplex or fullduplex), and the network geometry (clustered or nonclustered). We first study the multipleantenna relay channel with a fullduplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decodeandforward (DF), and compressandforward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link are increased, whereas CF continues to perform optimally. We also study the multipleantenna relay channel with a halfduplex relay. We show that the halfduplex DMT behavior can significantly be different from the fullduplex case. We find that CF is DMT optimal for halfduplex relaying as well, and is the first protocol known to achieve the halfduplex relay DMT. We next study the multipleaccess relay channel (MARC) DMT. Finally, we investigate a system with a single source–destination pair and multiple relays, each node with a single antenna, and show that even under the ideal assumption of fullduplex relays and a clustered network, this virtual multipleinput multipleoutput (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains in effect.
DMT optimality of LRaided linear decoders for a general class of channels, lattice designs, and system models
 IEEE TRANS. INFOM. THEORY
, 2010
"... The work identifies the first general, explicit, and nonrandom MIMO encoderdecoder structures that guarantee optimality with respect to the diversitymultiplexing tradeoff (DMT), without employing a computationally expensive maximumlikelihood (ML) receiver. Specifically, the work establishes the ..."
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Cited by 33 (4 self)
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The work identifies the first general, explicit, and nonrandom MIMO encoderdecoder structures that guarantee optimality with respect to the diversitymultiplexing tradeoff (DMT), without employing a computationally expensive maximumlikelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their latticereduction (LR)aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular latticecode applied. As a special case, it is established that the LLLbased LRaided linear implementation of the MMSEGDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worstcase complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in rate. The results’ generality lends them applicable to a plethora of pertinent communication scenarios such as quasistatic MIMO, MIMOOFDM, ISI, cooperativerelaying, and MIMOARQ channels, in all of which the DMT optimality of the LRaided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding.
DMG Tradeoff and optimal codes for a class of AF and DF cooperative communication protocols,” submitted to the IEEE Trans. Inform. Theory, available at: http://arxiv.org/pdf/cs.IT/0611156.
, 2007
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Multiantenna cooperative wireless systems: A diversity multiplexing tradeoff perspective
 IEEE Trans. Inform. Theory
, 2007
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Impact of Imperfect Channel Estimation on the Performance of AmplifyandForward Relaying
"... Abstract—In this paper, we investigate the error rate performance of amplifyandforward (AF) relaying with imperfect channel estimation. We consider a singlerelay scenario with orthogonal and nonorthogonal AF (OAF and NAF) cooperative protocols. Two pilotsymbolassisted receiver architectures ar ..."
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Cited by 23 (1 self)
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Abstract—In this paper, we investigate the error rate performance of amplifyandforward (AF) relaying with imperfect channel estimation. We consider a singlerelay scenario with orthogonal and nonorthogonal AF (OAF and NAF) cooperative protocols. Two pilotsymbolassisted receiver architectures are studied: In the mismatchedcoherent receiver, the complex fading channel coefficients (i.e., both phase and amplitude) are estimated based on a linear minimummeansquarederror estimation approach and fed to a coherent suboptimal maximum likelihood decoder as if the channels were perfectly known. In the partiallycoherent receiver, channel amplitude is ignored and phase is estimated by a phase locked loop. For both receiver types, we analyze the achievable diversity orders for cooperative protocols under consideration and quantify the impact of channel estimation through the derivation of pairwise error probability. Our performance analysis reveals that a second order diversity order is obtained for the considered singlerelay scenario indicating that full diversity is extracted. Our simulation results demonstrate that the performance degradation due to channel estimation with respect to the genie bound (i.e., perfect channel state information) is as small as 1.1dB based on the employed detector. Performance results further show that partiallycoherent receiver presents a similar performance to mismatchedreceiver for sufficiently large loop SNRs although channel amplitude is completely ignored. Index Terms—Transmission technology, cooperative diversity, spacetime coding.
A tutorial on the optimization of amplifyandforward MIMO relay systems
 IEEE J. Select. Areas Commun
, 2012
"... Abstract—The remarkable promise of multipleinput multipleoutput (MIMO) wireless channels has motivated an intense research activity to characterize the theoretical and practical issues associated with the design of transmit (source) and receive (destination) processing matrices under different op ..."
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Cited by 19 (7 self)
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Abstract—The remarkable promise of multipleinput multipleoutput (MIMO) wireless channels has motivated an intense research activity to characterize the theoretical and practical issues associated with the design of transmit (source) and receive (destination) processing matrices under different operating conditions. This activity was primarily focused on pointtopoint (singlehop) communications but more recently there has been an extensive work on twohop or multihop settings in which single or multiple relays are used to deliver the information from the source to the destination. The aim of this tutorial is to provide an uptodate overview of the fundamental results and practical implementation issues in designing amplifyandforward MIMO relay systems. Index Terms—Tutorial, MIMO, optimization, transceiver design, amplifyandforward, nonregenerative relay, power allocation, majorization theory, qualityofservice requirements, singlehop, twohop, multihop, oneway, twoway, multiple relays, perfect channel state information, robust design. I.
The amplifyandforward halfduplex cooperative system: Pairwise error probability and precoder design
 Ph.D. Thesis  Wessam Mesbah McMaster  Electrical & Computer Engineering
, 2007
"... AbstractIn this paper, an exact asymptotic pairwise error probability (PEP) is derived for a halfduplex cooperative system employing an amplifyandforward (AF) protocol. When compared with the PEP of a traditional multipleinput multipleoutput (MIMO) system, the "diversity gain" for th ..."
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Cited by 17 (1 self)
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AbstractIn this paper, an exact asymptotic pairwise error probability (PEP) is derived for a halfduplex cooperative system employing an amplifyandforward (AF) protocol. When compared with the PEP of a traditional multipleinput multipleoutput (MIMO) system, the "diversity gain" for the cooperative system is no longer just a simple exponential function of the signaltonoise ratio (SNR), rather, it involves the logarithm of the SNR. The term diversity gain function is used to designate this characteristic of the PEP. The coding gain, on the other hand, is found similar to that for the MIMO system and is proportional to the determinant of the autocorrelation of the error matrix. Based on our analysis and observations, we propose a design of unitary precoder for the cooperative system to achieve the full diversity gain function. For the case of a 4QAM signal being transmitted, we further optimize the coding gain, and arrive at a closedform optimum precoder. Simulations indicate that our proposed precoder designs greatly improve the performance of the cooperative system. Index TermsCooperative system, halfduplex, amplifyandforward (AF), pairwise error probability, diversity gain function, precoder.
DiversityMultiplexing Tradeoff in MultipleRelay Network–Part I: Proposed Scheme and SingleAntenna Networks
"... Abstract—This paper studies the setup of a multiplerelay network in which K halfduplex multipleantenna relays assist in the transmission between a/several multipleantenna source(s) and a multipleantenna destination. Each two nodes are assumed to be either connected through a quasistatic Raylei ..."
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Cited by 16 (3 self)
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Abstract—This paper studies the setup of a multiplerelay network in which K halfduplex multipleantenna relays assist in the transmission between a/several multipleantenna source(s) and a multipleantenna destination. Each two nodes are assumed to be either connected through a quasistatic Rayleigh fading channel, or disconnected. This paper is comprised of two parts. In this part of the paper, we propose a new scheme, which we call random sequential (RS), based on the amplifyandforward relaying. We derive diversitymultiplexing tradeoff (DMT) of the proposed RS scheme for general singleantenna multiplerelay networks. As a result, we show that for singleantenna twohop multipleaccess multiplerelay (K> 1) networks (without direct link between the source(s) and the destination), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple access single relay setup, we show that the RS scheme reduces to the naive amplifyandforward relaying and is not optimum in terms of DMT, while the dynamic decodeandforward scheme is shown to be optimum for this scenario 1. I.
An algebraic coding scheme for wireless relay networks with multipleantenna nodes
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2008
"... We consider the problem of coding over a halfduplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas, whereas each relay is a small device with only a single antenna. Since, in this scenario, requiring the relays to decode r ..."
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Cited by 14 (4 self)
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We consider the problem of coding over a halfduplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas, whereas each relay is a small device with only a single antenna. Since, in this scenario, requiring the relays to decode results in severe rate hits, we propose a full rate strategy where the relays do a simple operation before forwarding the signal, based on the idea of distributed spacetime coding. Our scheme relies on division algebras, an algebraic object which allows the design of fully diverse matrices. The code construction is applicable to systems with any number of transmit/receive antennas and relays, and has better performance than random code constructions, with much less encoding complexity. Finally, the robustness of the proposed distributed spacetime codes to node failures is considered.