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324
Cooperative strategies and capacity theorems for relay networks
 IEEE TRANS. INFORM. THEORY
, 2005
"... 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 ..."
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Cited by 739 (19 self)
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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.
Optimal design of nonregenerative MIMO wireless relays
 IEEE Trans. Wireless Commun
, 2007
"... Abstract — Given a multipleantenna source and a multipleantenna destination, a multipleantenna relay between the source and the destination is desirable under useful circumstances. A nonregenerative multipleantenna relay, also called nonregenerative MIMO (multiinput multioutput) relay, is de ..."
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Cited by 160 (10 self)
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Abstract — Given a multipleantenna source and a multipleantenna destination, a multipleantenna relay between the source and the destination is desirable under useful circumstances. A nonregenerative multipleantenna relay, also called nonregenerative MIMO (multiinput multioutput) relay, is designed to optimize the capacity between the source and the destination. Without a direct link between the source and the destination, the optimal canonical coordinates of the relay matrix are first established, and the optimal power allocations along these coordinates are then found. The system capacity with the optimal relay matrix is shown to be significantly higher than those with heuristic relay matrices. When a direct link is present, upper and lower bounds of the optimal system capacity are discussed. Index Terms — Multipleantenna relay, MIMO relay, nonregenerative relay, capacity analysis, optimal canonical coordinates, optimal power allocation. I.
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 146 (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.
Bounds on capacity and minimum energyperbit for AWGN relay channels
 IEEE TRANS. INF. THEORY
, 2006
"... Upper and lower bounds on the capacity and minimum energyperbit for general additive white Gaussian noise (AWGN) and frequencydivision AWGN (FDAWGN) relay channel models are established. First, the maxflow mincut bound and the generalized blockMarkov coding scheme are used to derive upper an ..."
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Cited by 108 (2 self)
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Upper and lower bounds on the capacity and minimum energyperbit for general additive white Gaussian noise (AWGN) and frequencydivision AWGN (FDAWGN) relay channel models are established. First, the maxflow mincut bound and the generalized blockMarkov coding scheme are used to derive upper and lower bounds on capacity. These bounds are never tight for the general AWGN model and are tight only under certain conditions for the FDAWGN model. Two coding schemes that do not require the relay to decode any part of the message are then investigated. First, it is shown that the “sideinformation coding scheme ” can outperform the blockMarkov coding scheme. It is also shown that the achievable rate of the sideinformation coding scheme can be improved via time sharing. In the second scheme, the relaying functions are restricted to be linear. The problem is reduced to a “singleletter ” nonconvex optimization problem for the FDAWGN model. The paper also establishes a relationship between the minimum energyperbit and capacity of the AWGN relay channel. This relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energyperbit that do not differ by more than a factor of 1 45 for the FDAWGN relay channel model and 1 7 for the general AWGN model.
Joint optimization of relay strategies and resource allocations in cooperative cellular networks
 in Proceedings of the Conference on Information Sciences and Systems (CISS
, 2006
"... Abstract — This paper considers a wireless cooperative cellular data network with a base station and many subscribers in which the subscribers have the ability to relay information for each other to improve the overall network performance. For a wireless network operating in a frequencyselective fa ..."
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Cited by 103 (2 self)
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Abstract — This paper considers a wireless cooperative cellular data network with a base station and many subscribers in which the subscribers have the ability to relay information for each other to improve the overall network performance. For a wireless network operating in a frequencyselective fading environment, the choices of relay node, relay strategy, and the allocation of power and bandwidth for each user are important design parameters. The design challenge is compounded further by the need to take user traffic demands into consideration. This paper proposes a utility maximization framework for such a network. We show that for a cellular system employing orthogonal frequencydivision multipleaccess (OFDMA), the optimization of physicallayer transmission strategies can be done efficiently by introducing a set of pricing variables. The proposed solution incorporates both user traffic demand and the physical channel realization in a crosslayer design that not only allocates power and bandwidth optimally for each user, but also selects the best relay node and best relay strategy (i.e. decodeandforward vs. amplifyandforward) for each sourcedestination pair. I.
Outage analysis of coded cooperation
 IEEE Trans. Inform. Theory
, 2006
"... We examine the outage capacity of of coded cooperation. Coded cooperation is a wireless user cooperation protocol that integrates cooperative signaling with channel coding. Each user’s code word is partitioned into two subsets that are transmitted from the user’s and the partner’s antennas, respecti ..."
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Cited by 89 (0 self)
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We examine the outage capacity of of coded cooperation. Coded cooperation is a wireless user cooperation protocol that integrates cooperative signaling with channel coding. Each user’s code word is partitioned into two subsets that are transmitted from the user’s and the partner’s antennas, respectively. A notable outcome of this research is that, unlike the decodeandforward protocol that was shown by Laneman to have diversity of one, coded cooperation achieves diversity order in the number of cooperating users. Thus we show that coded cooperation is fundamentally distinct from decodeandforward, despite their superficial similarities. We also apply our analysis to spacetime cooperation and study the effects of cooperation resource allocation. Numerical evaluation of outage expressions show that coded cooperation has a performance advantage across a wide range of SNR over several other cooperation protocols. I.
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.
Opportunistic cooperation by dynamic resource allocation
 IEEE TRANS. WIRELESS COMMUN
, 2007
"... We consider a Rayleigh fading wireless relay channel where communication is constrained by delay and average power limitations. Assuming partial channel state information at the transmitters and perfect channel state information at the receivers, we first study the delaylimited capacity of this sy ..."
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Cited by 68 (4 self)
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We consider a Rayleigh fading wireless relay channel where communication is constrained by delay and average power limitations. Assuming partial channel state information at the transmitters and perfect channel state information at the receivers, we first study the delaylimited capacity of this system and show that, contrary to a single sourcesingle destination case, a nonzero delaylimited capacity is achievable. We introduce opportunistic decodeandforward (ODF) protocol which utilizes the relay depending on the channel state. Opportunistic cooperation significantly improves the delaylimited capacity of the system and performs very close to the cutset bound. We also consider the system performance in terms of minimum outage probability. We show that ODF provides performance close to the cutset bound from the outage probability perspective as well. Our results emphasize the importance of feedback for cooperative systems that have delay sensitive applications.
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.
Resource Allocation for Wireless Fading Relay Channels: MaxMin Solution
, 2007
"... Resource allocation is investigated for fading relay channels under separate power constraints at the source and relay nodes. As a basic informationtheoretic model for fading relay channels, the parallel relay channel is first studied, which consists of multiple independent threeterminal relay ch ..."
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Cited by 56 (5 self)
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Resource allocation is investigated for fading relay channels under separate power constraints at the source and relay nodes. As a basic informationtheoretic model for fading relay channels, the parallel relay channel is first studied, which consists of multiple independent threeterminal relay channels as subchannels. Lower and upper bounds on the capacity are derived, and are shown to match, and thus establish the capacity for the parallel relay channel with degraded subchannels. This capacity theorem is further demonstrated via the Gaussian parallel relay channel with degraded subchannels, for which the synchronized and asynchronized capacities are obtained. The capacity achieving power allocation at the source and relay nodes among the subchannels is partially characterized for the synchronized case and fully characterized for the asynchronized case. The fading relay channel is then studied, which is based on the threeterminal relay channel with each communication link being corrupted by a multiplicative fading gain coefficient as well as an additive Gaussian noise term. For each link, the fading state information is assumed to be known at both the transmitter and the receiver. The source and relay nodes are allowed to allocate their power adaptively according to the instantaneous channel state information. The source and relay nodes are assumed to be subject to separate power constraints. For both the fullduplex and halfduplex cases, power allocations that maximize the achievable rates are obtained. In the halfduplex case, the power allocation needs to be jointly optimized with the channel resource (time and bandwidth) allocation between the two orthogonal channels over which the relay node transmits and receives. Capacities are established for fading relay channels that satisfy certain conditions.