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Cooperative diversity in wireless networks: efficient protocols and outage behavior
 IEEE TRANS. INFORM. THEORY
, 2004
"... We develop and analyze lowcomplexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals’ relaying signals for one another. We outline several strategies ..."
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Cited by 1940 (31 self)
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We develop and analyze lowcomplexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals’ relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplifyandforward and decodeandforward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signaltonoise ratio (SNR) regime. Except for fixed decodeandforward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., secondorder diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to halfduplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks—wherever space constraints preclude the use of physical arrays—the performance characterizations reveal that large power or energy savings result from the use of these protocols.
Cooperative strategies and capacity theorems for relay networks
 IEEE Trans. Inform. Theory
, 2005
"... Abstract—Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decodeandforward the source message to the destination, or they compressandforward their channel outputs to the destination. The decodeandforward scheme is a va ..."
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Cited by 733 (19 self)
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Abstract—Coding strategies that exploit node cooperation are developed for relay networks. Two basic schemes are studied: the relays decodeandforward the source message to the destination, or they compressandforward their channel outputs to the destination. The decodeandforward scheme is a variant of multihopping, but in addition to having the relays successively decode the message, the transmitters cooperate and each receiver uses several or all of its past channel output blocks to decode. For the compressandforward scheme, the relays take advantage of the statistical dependence between their channel outputs and the destination’s channel output. The strategies are applied to wireless channels, and it is shown that decodeandforward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides with the rate of a distributed antenna array with full cooperation even though the transmitting antennas are not colocated. The capacity results generalize broadly, including to multiantenna transmission with Rayleigh fading, singlebounce fading, certain quasistatic fading problems, cases where partial channel knowledge is available at the transmitters, and cases where local user cooperation is permitted. The results further extend to multisource and multidestination networks such as multiaccess and broadcast relay channels. Index Terms—Antenna arrays, capacity, coding, multiuser channels, relay channels. I.
Fading relay channels: Performance limits and spacetime signal design
 IEEE J. SELECT. AREAS COMMUN
, 2004
"... Cooperative diversity is a transmission technique where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay ch ..."
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Cited by 436 (4 self)
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Cooperative diversity is a transmission technique where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay channel where the source, destination and relay terminals are each equipped with single antenna transceivers. We consider three different TDMAbased cooperative protocols that vary the degree of broadcasting and receive collision. The relay terminal operates in either the amplifyandforward (AF) or decodeandforward (DF) modes. For each protocol, we study the ergodic and outage capacity behavior (assuming Gaussian code books) under the AF and DF modes of relaying. We analyze the spatial diversity performance of the various protocols and find that full spatial diversity (secondorder in this case) is achieved by certain protocols provided that appropriate power control is employed. Our analysis unifies previous results reported in the literature and establishes the superiority (both from a capacity as well as a diversity pointofview) of a new protocol proposed in this paper. The second part of the paper is devoted to (distributed) spacetime code design for fading relay channels operating in the AF mode. We show that the corresponding code design criteria consist of the traditional rank and determinant criteria for the case of colocated antennas as well as appropriate power control rules. Consequently spacetime codes designed for the case of colocated multiantenna channels can be used to realize cooperative diversity provided that appropriate power control is employed.
Capacity bounds and power allocation for wireless relay channels
 IEEE TRANS. INF. THEORY
, 2005
"... We consider threenode wireless relay channels in a Rayleighfading environment. Assuming transmitter channel state information (CSI), we study upper bounds and lower bounds on the outage capacity and the ergodic capacity. Our studies take into account practical constraints on the transmission/rece ..."
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Cited by 317 (6 self)
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We consider threenode wireless relay channels in a Rayleighfading environment. Assuming transmitter channel state information (CSI), we study upper bounds and lower bounds on the outage capacity and the ergodic capacity. Our studies take into account practical constraints on the transmission/reception duplexing at the relay node and on the synchronization between the source node and the relay node. We also explore power allocation. Compared to the direct transmission and traditional multihop protocols, our results reveal that optimum relay channel signaling can significantly outperform multihop protocols, and that power allocation has a significant impact on the performance.
On the capacity of large Gaussian relay networks
 IEEE TRANS. INF. THEORY
, 2005
"... The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cutset arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and ..."
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Cited by 149 (6 self)
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The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cutset arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cutset upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source–channel coding problem, and it is well known that the source–channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance—it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include certain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source–destination pair, capacity grows with the logarithm of the number of nodes.
Gaussian Orthogonal Relay Channels: Optimal Resource Allocation and Capacity
 IEEE Trans. on Information Theory
, 2005
"... Abstract—A Gaussian orthogonal relay model is investigated, where the source transmits to the relay and destination in channel 1, and the relay transmits to the destination in channel 2, with channels 1 and 2 being orthogonalized in the time–frequency plane in order to satisfy practical constraints. ..."
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Cited by 61 (3 self)
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Abstract—A Gaussian orthogonal relay model is investigated, where the source transmits to the relay and destination in channel 1, and the relay transmits to the destination in channel 2, with channels 1 and 2 being orthogonalized in the time–frequency plane in order to satisfy practical constraints. The total available channel resource (time and bandwidth) is split into the two orthogonal channels, and the resource allocation to the two channels is considered to be a design parameter that needs to be optimized. The main focus of the analysis is on the case where the sourcetorelay link is better than the sourcetodestination link, which is the usual scenario encountered in practice. A lower bound on the capacity (achievable rate) is derived, and optimized over the parameter, which represents the fraction of the resource assigned to channel 1. It is shown that the lower bound achieves the maxflow mincut upper bound at the optimizing, the common value thus being the capacity of the channel at the optimizing. Furthermore, it is shown that when the relaytodestination signaltonoise ratio (SNR) is less than a certain threshold, the capacity at the optimizing is also the maximum capacity of the channel over all possible resource allocation parameters. Finally, the achievable rates for optimal and equal resource allocations are compared, and it is shown that optimizing the resource allocation yields significant performance gains. Index Terms—Achievable rate, decodeandforward relay, parallel relay channel. I.
Capacity theorems for wireless relay channels
 in 41th Allerton Conf. on Commun., Control and Computing
, 2003
"... An achievable rate region for memoryless relay networks is developed based on an existing region for additive white Gaussian noise (AWGN) channels. It is shown that multi–hopping achieves the information–theoretic capacity of wireless relay networks if the relays are in a region near the source term ..."
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Cited by 58 (4 self)
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An achievable rate region for memoryless relay networks is developed based on an existing region for additive white Gaussian noise (AWGN) channels. It is shown that multi–hopping achieves the information–theoretic capacity of wireless relay networks if the relays are in a region near the source terminal, and if phase information is available at the receivers only. 1
Bandwidth and power allocation for cooperative strategies in Gaussian relay networks
 in Proc. 38th Asilomar Conf. Signal, System Computers
, 2004
"... Achievable rates with amplifyandforward (AF) and decodeandforward (DF) cooperative strategies are examined for relay networks. Motivated by sensor network applications, powerconstrained networks with large bandwidth resources and a large number of nodes are considered. It is shown that AF strat ..."
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Cited by 42 (2 self)
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Achievable rates with amplifyandforward (AF) and decodeandforward (DF) cooperative strategies are examined for relay networks. Motivated by sensor network applications, powerconstrained networks with large bandwidth resources and a large number of nodes are considered. It is shown that AF strategies do not necessarily benefit from the large available bandwidth. Rather, transmitting in the optimum AF bandwidth allows the network to operate in the linear regime where the achieved rate increases linearly with the available network power. The optimum power allocation among the AF relays is presented next. The solution, which can be viewed as a form of maximum ratio combining, indicates the favorable relay positions. Motivated by the large bandwidth resources, orthogonal node transmissions are also considered. While the above result for the optimum bandwidth still holds, the relay power solution in this case can be viewed as a form of waterfilling. The above results can be contrasted to the decodeandforward (DF) solution. In a network with unconstrained bandwidth, the DF strategy will operate in the wideband regime to minimize the energy cost per information bit. The wideband DF strategy is shown to require a different choice of relays. Thus, in general, in a large scale network, a choice of a coding strategy goes beyond determining a coding scheme at a node; it also determines the operating bandwidth as well as the set of relay nodes and best distribution of the relay power. Index Terms Twohop cooperative strategies, optimum relay powers, antenna arrays, relay channels. I.
Forwarding Strategies for Gaussian ParallelRelay Networks
, 2004
"... This paper investigates reliable and unreliable forwarding strategies in a parallelrelay network. We consider the problem that maximizes the achievable rate under the total power constraint that allows for the power allocation among the nodes. We approach this problem by solving its dual with the ..."
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Cited by 37 (1 self)
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This paper investigates reliable and unreliable forwarding strategies in a parallelrelay network. We consider the problem that maximizes the achievable rate under the total power constraint that allows for the power allocation among the nodes. We approach this problem by solving its dual with the objective to communicate to the destination at rate using minimum transmitted power. Motivated by applications in sensor networks, we assume large bandwidth resources allowing orthogonal transmissions at the nodes. In such a network, the energy cost per information bit [1] during the reliable forwarding is minimized by operating in the wideband regime. For the wideband decodeandforward (DF) strategy, we present the optimum parallelrelay solution by identifying the best choice of relay nodes and the optimum power allocation among them. We demonstrate that the data should be sent over a single relay route through one relay that is in the “best ” position in the network. On the other hand, as observed in [2], the benefit of unreliable amplifyandforward (AF) strategy diminishes in the wideband regime. We characterize the optimum bandwidth for AF that minimizes the total energy cost per information bit for our network model. We show that transmitting in the optimum bandwidth allows the network to operate in the linear regime where the achieved rate increases linearly with transmit power. We then identify the best subset of AF relay nodes and characterize the optimum power allocation per dimension among relays, for a given source power and bandwidth. Based on this analysis, we compare the energyefficiency of DF and AF in a onerelay network and show the regions where each strategy is optimal.