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Fading relay channels: Performance limits and space-time signal design

by Rohit U. Nabar, Helmut Bölcskei, Felix W. Kneubühler - 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 ..."
Abstract - Cited by 445 (4 self) - Add to MetaCart
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 TDMA-based cooperative protocols that vary the degree of broadcasting and receive collision. The relay terminal operates in either the amplify-and-forward (AF) or decode-and-forward (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 (second-order 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 point-of-view) of a new protocol proposed in this paper. The second part of the paper is devoted to (distributed) space-time 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 co-located antennas as well as appropriate power control rules. Consequently space-time codes designed for the case of co-located multi-antenna channels can be used to realize cooperative diversity provided that appropriate power control is employed.
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On the achievable diversity-multiplexing tradeoff in half-duplex cooperative channels

by Kambiz Azarian, Hesham El Gamal, Philip Schniter - IEEE TRANS. INFORM. THEORY , 2005
"... We propose novel cooperative transmission protocols for delay-limited coherent fading channels consisting of (half-duplex and single-antenna) partners and one cell site. In our work, we differentiate between the relay, cooperative broadcast (down-link), and cooperative multiple-access (CMA) (up-lin ..."
Abstract - Cited by 311 (11 self) - Add to MetaCart
We propose novel cooperative transmission protocols for delay-limited coherent fading channels consisting of (half-duplex and single-antenna) partners and one cell site. In our work, we differentiate between the relay, cooperative broadcast (down-link), and cooperative multiple-access (CMA) (up-link) channels. The proposed protocols are evaluated using Zheng–Tse diversity–multiplexing tradeoff. For the relay channel, we investigate two classes of cooperation schemes; namely, amplify and forward (AF) protocols and decode and forward (DF) protocols. For the first class, we establish an upper bound on the achievable diversity–multiplexing tradeoff with a single relay. We then construct a new AF protocol that achieves this upper bound. The proposed algorithm is then extended to the general case with relays where it is shown to outperform the space–time coded protocol of Laneman and Wornell without requiring decoding/encoding at the relays. For the class of DF protocols, we develop a dynamic decode and forward (DDF) protocol that achieves the optimal tradeoff for multiplexing gains. Furthermore, with a single relay, the DDF protocol is shown to dominate the class of AF protocols for all multiplexing gains. The superiority of the DDF protocol is shown to be more significant in the cooperative broadcast channel. The situation is reversed in the CMA channel where we propose a new AF protocol that achieves the optimal tradeoff for all multiplexing gains. A distinguishing feature of the proposed protocols in the three scenarios is that they do not rely on orthogonal subspaces, allowing for a more efficient use of resources. In fact, using our results one can argue that the suboptimality of previously proposed protocols stems from their use of orthogonal subspaces rather than the half-duplex constraint.
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Achievable Rates in Cognitive Radio Channels

by Natasha Devroye, Patrick Mitran, Vahid Tarokh - IEEE Trans. Inf. Theory , 2006
"... Cognitive radio promises a low cost, highly flexible alternative to the classic single frequency band, single protocol wireless device. By sensing and adapting to its environment, such a device is able to fill voids in the wireless spectrum and dramatically increase spectral efficiency. In this pape ..."
Abstract - Cited by 274 (46 self) - Add to MetaCart
Cognitive radio promises a low cost, highly flexible alternative to the classic single frequency band, single protocol wireless device. By sensing and adapting to its environment, such a device is able to fill voids in the wireless spectrum and dramatically increase spectral efficiency. In this paper, the cognitive radio channel is defined as an n-transmitter, m-receiver interference channel in which sender i obtains the messages senders 1 through i − 1 plan to transmit. The two sender, two receiver case is considered. In this scenario, one user, a cognitive radio, obtains (genie assisted, or causally) knowledge of the data to be transmitted by the other user. The cognitive radio may then simultaneously transmit over the same channel, as opposed to waiting for an idle channel as in a traditional cognitive radio channel protocol. Dirty-paper coding and ideas from achievable region constructions for the interference channel are used, and an achievable region for the cognitive radio channel is computed. It is shown that in the Gaussian case, the described achievable region approaches the upper bounds provided by the 2×2 Gaussian MIMO broadcast channel, and an interference-free channel. Results are extended to the case in which the message is causally obtained.
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Distributed space-time coding in wireless relay networks,”IEEE Trans.

by Frédérique Oggier , Babak Hassibi - on Wireless Communications, , 2006
"... Abstract In this paper, we present a coding strategy for half duplex wireless relay networks, where we assume no channel knowledge at any of the transmitter, receiver or relays. The coding scheme uses distributed space-time coding, that is, the relay nodes cooperate to encode the transmitted signal ..."
Abstract - Cited by 225 (16 self) - Add to MetaCart
Abstract In this paper, we present a coding strategy for half duplex wireless relay networks, where we assume no channel knowledge at any of the transmitter, receiver or relays. The coding scheme uses distributed space-time coding, that is, the relay nodes cooperate to encode the transmitted signal so that the receiver senses a space-time codeword. It is inspired by noncoherent differential techniques. The proposed strategy is available for any number of relays nodes. It is analyzed, and shown to yield a diversity linear in the number of relays. We also study the resistance of the scheme to relay node failures, and show that a network with R relay nodes and d of them down behaves, as far as diversity is concerned, as a network with R − d nodes. Finally, our construction can be easily generalized to the case where the transmitter and receiver nodes have several antennas.
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On the feasibility of distributed beamforming in wireless networks

by R. Mudumbai, Student Member, G. Barriac, U. Madhow - IEEE Trans. on Wireless Commun , 2007
"... Abstract — Energy efficient communication is a fundamental problem in wireless ad-hoc and sensor networks. In this paper, we explore the feasibility of a distributed beamforming approach to this problem, with a cluster of distributed transmitters emulating a centralized antenna array so as to transm ..."
Abstract - Cited by 92 (16 self) - Add to MetaCart
Abstract — Energy efficient communication is a fundamental problem in wireless ad-hoc and sensor networks. In this paper, we explore the feasibility of a distributed beamforming approach to this problem, with a cluster of distributed transmitters emulating a centralized antenna array so as to transmit a common message signal coherently to a distant Base Station. The potential SNR gains from beamforming are well-known. However, realizing these gains requires synchronization of the individual carrier signals in phase and frequency. In this paper we show that a large fraction of the beamforming gains can be realised even with imperfect synchronization corresponding to phase errors with moderately large variance. We present a master-slave architecture where a designated master transmitter coordinates the synchronization of other (slave) transmitters for beamforming. We observe that the transmitters can achieve distributed beamforming with minimal coordination with the Base Station using channel reciprocity. Thus, inexpensive local coordination with a master transmitter makes the expensive communication with a distant Base Station receiver more efficient. However, the duplexing constraints of the wireless channel place a fundamental limitation on the achievable accuracy of synchronization. We present a stochastic analysis that demonstrates the robustness of beamforming gains with imperfect synchronization, and demonstrate a tradeoff between synchronization overhead and beamforming gains. We also present simulation results for the phase errors that validate the analysis. Index Terms — Distributed beamforming, synchronization, wireless networks, sensor networks, space-time communication.
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Outage analysis of coded cooperation

by Todd E. Hunter, Shahab Sanayei, Aria Nosratinia - 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 ..."
Abstract - Cited by 89 (0 self) - Add to MetaCart
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 decode-and-forward 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 decode-and-forward, despite their superficial similarities. We also apply our analysis to space-time 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.
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Network beamforming using relays with perfect channel information

by Yindi Jing, Hamid Jafarkhani - 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 two-step amplify-and-forw ..."
Abstract - Cited by 87 (10 self) - Add to MetaCart
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 two-step amplify-and-forward 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 low-rate 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 Multi-University Research Initiative (MURI) grant #W911NF-04-1-0224. 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
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High-Performance Cooperative Demodulation With Decode-and-Forward Relays

by Tairan Wang, Alfonso Cano, Georgios B. Giannakis, J. Nicholas Laneman , 2007
"... Cooperative communication systems using various relay strategies can achieve spatial diversity gains, enhance coverage, and potentially increase capacity. For the practically attractive decode-and-forward (DF) relay strategy, we derive a high-performance low-complexity coherent demodulator at the d ..."
Abstract - Cited by 82 (6 self) - Add to MetaCart
Cooperative communication systems using various relay strategies can achieve spatial diversity gains, enhance coverage, and potentially increase capacity. For the practically attractive decode-and-forward (DF) relay strategy, we derive a high-performance low-complexity coherent demodulator at the destination in the form of a weighted combiner. The weights are selected adaptively to account for the quality of both source-relay-destination and source-destination links. Analysis proves that the novel coherent demodulator can achieve the maximum possible diversity, regardless of the underlying constellation. Its error performance tightly bounds that of maximum-likelihood (ML) demodulation, which provably quantifies the diversity gain of ML detection with DF relaying. Simulations corroborate the analysis and compare the performance of the novel decoder with existing diversity-achieving strategies including analog amplify-and-forward and selective-relaying.

Optimal space-time codes for the MIMO amplify-and-forward cooperative channel

by Sheng Yang, Jean-claude Belfiore - IEEE Trans. Inf. Theory , 2007
"... In this work, we extend the non-orthogonal amplify-and-forward (NAF) cooperative diversity scheme to the MIMO channel. A family of space-time block codes for a half-duplex MIMO NAF fading cooperative channel with N relays is constructed. The code construction is based on the non-vanishing determinan ..."
Abstract - Cited by 77 (9 self) - Add to MetaCart
In this work, we extend the non-orthogonal amplify-and-forward (NAF) cooperative diversity scheme to the MIMO channel. A family of space-time block codes for a half-duplex MIMO NAF fading cooperative channel with N relays is constructed. The code construction is based on the non-vanishing determinant (NVD) criterion and is shown to achieve the optimal diversity-multiplexing tradeoff (DMT) of the channel. We provide a general explicit algebraic construction, followed by some examples. In particular, in the single-relay case, it is proved that the Golden code and the 4×4 Perfect code are optimal for the single-antenna and two-antenna case, respectively. Simulation results reveal that a significant gain (up to 10 dB) can be obtained with the proposed codes, especially in the single-antenna case.
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Symmetric Feedback Capacity of the Gaussian Interference Channel to Within One Bit

by Changho Suh, David Tse
"... We characterize the symmetric capacity of the two-user Gaussian interference channel with feedback to within 1 bit/s/Hz. The result makes use of a deterministic model to provide insights into the Gaussian channel. We derive a new outer bound to show that a proposed scheme can achieve the symmetric ..."
Abstract - Cited by 67 (5 self) - Add to MetaCart
We characterize the symmetric capacity of the two-user Gaussian interference channel with feedback to within 1 bit/s/Hz. The result makes use of a deterministic model to provide insights into the Gaussian channel. We derive a new outer bound to show that a proposed scheme can achieve the symmetric capacity to within one bit for all channel parameters. From this result, we show that feedback provides unbounded gain, i.e., the gain becomes arbitrarily large for certain channel parameters. It is a surprising result because feedback has been so far known to provide no gain in memoryless point-to-point channels and only power gain (bounded gain) in the multiple access channels.