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 diversity-multiplexing tradeoff (DMT). We examine several projections of this most general problem taking into account the network geometry (clustered or non-clustered), the processing capability of the relays (half-duplex or full-duplex) and the number of antennas the nodes have. We first study 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. We provide communication strategies that achieve the best DMT of this relay system. We extend our work to cover cooperative systems with multiple sources and multiple destinations and show that the same limitation is still in effect. We next study the relay channel with multiple antenna nodes for full-duplex relays 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 proves to be a more robust strategy. As having a full-duplex relay is an idealistic assumption, we also study the multiple antenna relay channel with half-duplex relays. 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. We also study the multiple-access relay channel (MARC) as a subproblem of the most general network, and evaluate how CF works in MARC. Our results show that CF is a robust strategy, which performs well in different relay networks and multiple antenna scenarios. This material is based upon work partially supported by the National Science Foundation under Grant No. 0093163. The material in this paper was presented in part at the 40th Annual Conference on Information Sciences and Systems, CISS, 2006, and at the IEEE International Symposium on Information Theory, Seattle, WA, July 2006. The authors are with Electrical and Computer Engineering Department, Polytechnic University, Brooklyn, NY 11201 USA (e-mail: [email protected]; [email protected]). SUBMITTED TO IEEE TRANSACTIONS ON INFORMATION THEORY 2 Index Terms cooperation, diversity-multiplexing tradeoff, fading channels, multiple-input multiple output (MIMO), relay channel, wireless networks. SUBMITTED TO IEEE TRANSACTIONS ON INFORMATION THEORY 3