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Cooperative Communications With OutageOptimal Opportunistic Relaying
"... Abstract — In this paper, we present simple opportunistic relaying with decodeandforward (DaF) and amplifyandforward (AaF) strategies under an aggregate power constraint. In particular, we consider distributed relayselection algorithms requiring only local channel knowledge. We show that opport ..."
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Cited by 95 (7 self)
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Abstract — In this paper, we present simple opportunistic relaying with decodeandforward (DaF) and amplifyandforward (AaF) strategies under an aggregate power constraint. In particular, we consider distributed relayselection algorithms requiring only local channel knowledge. We show that opportunistic DaF relaying is outageoptimal, that is, it is equivalent in outage behavior to the optimal DaF strategy that employs all potential relays. We further show that opportunistic AaF relaying is outageoptimal among singlerelay selection methods and significantly outperforms an AaF strategy based on equalpower multiplerelay transmissions with local channel knowledge. These findings reveal that cooperation offers diversity benefits even when cooperative relays choose not to transmit but rather choose to cooperatively listen; they act as passive relays and give priority to the transmission of a single opportunistic relay. Numerical and simulation results are presented to verify our analysis. Index Terms — Cooperative diversity, fading relay channel, outage probability, wireless networks. I.
Network beamforming using relays with perfect channel information
 IEEE Trans. Inform. Theory
, 2009
"... This paper is on beamforming in wireless relay networks with perfect channel information at relays, the receiver, and the transmitter if there is a direct link between the transmitter and receiver. It is assumed that every node in the network has its own power constraint. A twostep amplifyandforw ..."
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Cited by 87 (10 self)
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This paper is on beamforming in wireless relay networks with perfect channel information at relays, the receiver, and the transmitter if there is a direct link between the transmitter and receiver. It is assumed that every node in the network has its own power constraint. A twostep amplifyandforward protocol is used, in which the transmitter and relays not only use match filters to form a beam at the receiver but also adaptively adjust their transmit powers according to the channel strength information. For a network with any number of relays and no direct link, the optimal power control is solved analytically. The complexity of finding the exact solution is linear in the number of relays. Our results show that the transmitter should always use its maximal power and the optimal power used at a relay is not a binary function. It can take any value between zero and its maximum transmit power. Also, surprisingly, this value depends on the quality of all other channels in addition to the relay’s own channels. Despite this coupling fact, distributive strategies are proposed in which, with the aid of a lowrate broadcast from the receiver, a relay needs only its own channel information to implement the optimal power control. Simulated performance shows that network beamforming achieves the maximal diversity and outperforms other existing schemes. ∗This work was supported in part by ARO under the MultiUniversity Research Initiative (MURI) grant #W911NF0410224. 1 Then, beamforming in networks with a direct link are considered. We show that when the direct link exists during the first step only, the optimal power control at the transmitter and relays is the same as that of networks with no direct link. For networks with a direct link during the second step only and both steps, recursive numerical algorithms are proposed to solve the power control problem. Simulation shows that by adjusting the transmitter and relays ’ powers adaptively, network performance is significantly improved. 1
Distributed beamforming for relay networks based on secondorder statistics of the channel state information
 IEEE Trans. Signal Process
, 2008
"... Abstract—In this paper, the problem of distributed beamforming is considered for a wireless network which consists of a transmitter, a receiver, and relay nodes. For such a network, assuming that the secondorder statistics of the channel coefficients are available, we study two different beamform ..."
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Cited by 68 (4 self)
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Abstract—In this paper, the problem of distributed beamforming is considered for a wireless network which consists of a transmitter, a receiver, and relay nodes. For such a network, assuming that the secondorder statistics of the channel coefficients are available, we study two different beamforming design approaches. As the first approach, we design the beamformer through minimization of the total transmit power subject to the receiver quality of service constraint. We show that this approach yields a closedform solution. In the second approach, the beamforming weights are obtained through maximizing the receiver signaltonoise ratio (SNR) subject to two different types of power constraints, namely the total transmit power constraint and individual relay power constraints. We show that the total power constraint leads to a closedform solution while the individual relay power constraints result in a quadratic programming opti
Distributed spacetime coding for twoway wireless,” caltech
, 2007
"... Abstract — We consider distributed spacetime coding for twoway wireless relay networks, where communication between two terminals is assisted by relay nodes. We compare existing and new protocols that operate over 2, 3 or 4 times slots. Particularly, a new class of relaying protocols, termed as par ..."
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Cited by 37 (6 self)
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Abstract — We consider distributed spacetime coding for twoway wireless relay networks, where communication between two terminals is assisted by relay nodes. We compare existing and new protocols that operate over 2, 3 or 4 times slots. Particularly, a new class of relaying protocols, termed as partial decodeandforward (PDF), is proposed for the 2 time slots transmission. We show that the proposed amplify and ( forward (AF) ) protocols achieve the diversity order of min{N,T}, where N is the number of relays, P is the total power of the network, and T is the number of symbols transmitted during each time slot. When linear dispersion (LD) codes with random unitary matrices are used, the proposed PDF protocols resemble random linear network coding, where the former operates on unitary group and the latter works on finite field. I.
Distributed Differential SpaceTime Coding for Wireless Relay Networks
"... Distributed spacetime coding is a cooperative transmission scheme proposed for wireless relay networks. With this scheme, antennas of the distributive relays work as transmit antennas of the sender and generate a spacetime code at the receiver. When the transmit power is infinitely large, it achie ..."
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Cited by 36 (7 self)
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Distributed spacetime coding is a cooperative transmission scheme proposed for wireless relay networks. With this scheme, antennas of the distributive relays work as transmit antennas of the sender and generate a spacetime code at the receiver. When the transmit power is infinitely large, it achieves the maximum diversity. Although the scheme needs no channel information at relays, it requires full channel information at the receiver. In this paper, based on distributed spacetime coding, we propose a differential transmission scheme, which requires channel information at neither relays nor the receiver. As distributed spacetime coding can be seen as the counterpart of spacetime coding in the network setting, this scheme is the counterpart of differential spacetime coding. Compared to distributed coherent spacetime coding, the differential scheme is 3dB worse. In addition, we show that Alamouti, square real orthogonal, and Sp(2) codes, which are originally proposed for multipleantenna systems, can be used differentially in networks with corresponding numbers of relays.
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.
A family of distributed spacetime trellis codes with asynchronous cooperative diversity
 in International Symposium on Inform. Processing in Sensor Networks
, 2005
"... Abstract — In current cooperative communication schemes, to achieve cooperative diversity, synchronization between terminals is usually assumed, which may not be practical since each terminal has its own local oscillator. In this paper, we first present a necessary and sufficient condition for the s ..."
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Cited by 30 (3 self)
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Abstract — In current cooperative communication schemes, to achieve cooperative diversity, synchronization between terminals is usually assumed, which may not be practical since each terminal has its own local oscillator. In this paper, we first present a necessary and sufficient condition for the spacetime trellis codes based on the stack construction proposed by Hammons and El Gamal to possess the full cooperative diversity order without the synchronization assumption. The condition is that the binary generator metrices of the trellis codes are shift full rank (SFR) matrices, i.e., have full row rank no matter the shifts of their row vectors, where a row corresponds to a terminal (or transmit antenna) and the length of a row vector is the memory size of the corresponding trellis code on the corresponding terminal. We then present a simple construction of SFR for any number of rows, whose number of columns, however, grows exponentially with the number of rows. We finally present some systematic SFR matrix constructions including shortest, i.e., square, SFR matrices. I.
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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Multigroup ML Decodable Collocated and Distributed Space Time Block Codes
"... In this paper, collocated and distributed spacetime block codes (DSTBCs) which admit multigroup maximum likelihood (ML) decoding are studied. First the collocated case is considered and the problem of constructing spacetime block codes (STBCs) which optimally tradeoff rate and ML decoding complexi ..."
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Cited by 26 (18 self)
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In this paper, collocated and distributed spacetime block codes (DSTBCs) which admit multigroup maximum likelihood (ML) decoding are studied. First the collocated case is considered and the problem of constructing spacetime block codes (STBCs) which optimally tradeoff rate and ML decoding complexity is posed. Recently, sufficient conditions for multigroup ML decodability have been provided in the literature and codes meeting these sufficient conditions were called Clifford Unitary Weight (CUW) STBCs. An algebraic framework based on extended Clifford algebras is proposed to study CUW STBCs and using this framework, the optimal tradeoff between rate and ML decoding complexity of CUW STBCs is obtained for few specific cases. Code constructions meeting this tradeoff optimally are also provided. The paper then focuses on multigroup ML decodable DSTBCs for application in synchronous wireless relay networks and three constructions of fourgroup ML decodable DSTBCs are provided. Finally, the OFDM based Alamouti spacetime coded scheme proposed by LiXia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Fourgroup decodable DSTBCs applicable in the proposed OFDM based transmission scheme are also given.