On Capacity and Optimal Scheduling for the Half-Duplex Multiple-Relay Channel

We study the half-duplex multiple-relay channel (HD-MRC) where every node can either transmit or listen but cannot do both at the same time. We obtain a capacity upper bound based on a max-flow min-cut argument and achievable transmission rates based on the decode-forward (DF) coding strategy, for both the discrete memoryless HD-MRC and the phase-fading HD-MRC. We discover that both the upper bound and the achievable rates are functions of the transmit/listen state (a description of which nodes transmit and which receive). More precisely, they are functions of the time fraction of the different states, which we term a schedule. We formulate the optimal scheduling problem to find an optimal schedule that maximizes the DF rate. The optimal scheduling problem turns out to be a maximin optimization, for which we propose an algorithmic solution. We demonstrate our approach on a four-node multiple-relay channel, obtaining closed-form solutions in certain scenarios. Furthermore, we show that for the received signal-to-noise ratio degraded phase-fading HD-MRC, the optimal scheduling problem can be simplified to a max optimization.Comment: Author's final version (to appear in IEEE Transactions on Information Theory

Transmit Signal and Bandwidth Optimization in Multiple-Antenna Relay Channels

Transmit signal and bandwidth optimization is considered in multiple-antenna relay channels. Assuming all terminals have channel state information, the cut-set capacity upper bound and decode-and-forward rate under full-duplex relaying are evaluated by formulating them as convex optimization problems. For half-duplex relays, bandwidth allocation and transmit signals are optimized jointly. Moreover, achievable rates based on the compress-and-forward transmission strategy are presented using rate-distortion and Wyner-Ziv compression schemes. It is observed that when the relay is close to the source, decode-and-forward is almost optimal, whereas compress-and-forward achieves good performance when the relay is close to the destination.Comment: 16 pages, 10 figure

Multi-Antenna Cooperative Wireless Systems: A Diversity-Multiplexing Tradeoff Perspective

We consider a general multiple antenna 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 (half-duplex or full-duplex), and the network geometry (clustered or non-clustered). We first study the multiple antenna relay channel with a full-duplex 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 decode-and-forward (DF), and compress-and-forward (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 is increased, whereas CF continues to perform optimally. We also study the multiple antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the half-duplex relay DMT. We next study the multiple-access 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 idealistic assumption of full-duplex relays and a clustered network, this virtual multi-input multi-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains to be in effect.Comment: version 1: 58 pages, 15 figures, Submitted to IEEE Transactions on Information Theory, version 2: Final version, to appear IEEE IT, title changed, extra figures adde

Half-Duplex Relaying for the Multiuser Channel

This work focuses on studying the half-duplex (HD) relaying in the Multiple Access Relay Channel (MARC) and the Compound Multiple Access Channel with a Relay (cMACr). A generalized Quantize-and-Forward (GQF) has been proposed to establish the achievable rate regions. Such scheme is developed based on the variation of the Quantize-and-Forward (QF) scheme and single block with two slots coding structure. The results in this paper can also be considered as a significant extension of the achievable rate region of Half-Duplex Relay Channel (HDRC). Furthermore, the rate regions based on GQF scheme is extended to the Gaussian channel case. The scheme performance is shown through some numerical examples.Comment: 7 pages, 4 figures, conference pape

Asymptotic Capacity of Large Fading Relay Networks with Random Node Failures

To understand the network response to large-scale physical attacks, we investigate the asymptotic capacity of a half-duplex fading relay network with random node failures when the number of relays $N$ is infinitely large. In this paper, a simplified independent attack model is assumed where each relay node fails with a certain probability. The noncoherent relaying scheme is considered, which corresponds to the case of zero forward-link channel state information (CSI) at the relays. Accordingly, the whole relay network can be shown equivalent to a Rayleigh fading channel, where we derive the $\epsilon$-outage capacity upper bound according to the multiple access (MAC) cut-set, and the $\epsilon$-outage achievable rates for both the amplify-and-forward (AF) and decode-and-forward (DF) strategies. Furthermore, we show that the DF strategy is asymptotically optimal as the outage probability $\epsilon$ goes to zero, with the AF strategy strictly suboptimal over all signal to noise ratio (SNR) regimes. Regarding the rate loss due to random attacks, the AF strategy suffers a less portion of rate loss than the DF strategy in the high SNR regime, while the DF strategy demonstrates more robust performance in the low SNR regime.Comment: 24 pages, 5 figures, submitted to IEEE Transactions on Communication