On the Stability Region of Cooperative Relay Networks with Fading States

This paper considers an amplify-and-forward re- lay network and determines its maximum stable throughput. Amplify-and-forward (and other forwarding schemes) form the core mechanism for enabling cooperative communication in wireless networks, and thus determining stabilizing policies for such networks is an important problem. The interaction between nodes in this network is described in terms of continuous-valued signals instead of discrete "packets". Hence, the stabilit y analysis for relay networks is by no means a straightforward extension of that in packet-based networks. I. I NTRODUCTION Relaying is central to wireless mesh and ad hoc networks. There is no "network" without multi-hop communication, and thus, understanding the role and impact of different relayi ng techniques on networks is of critical importance. There are multiple possible forwarding strategies that could be used by each relay node in the network, with the most popular ones being decode-and-forward, amplify-and-forward and quantize- and-forward. Note that the forwarding strategy used and the resulting network capacity are inherently coupled, and it i s not obvious which of the above forwarding strategies, if any, is information theoretically optimal for a particular netw ork topology. For a few settings, amplify-and-forward has been shown to be better than decode-and-forward (1), and for a few others, partial decode-and-forward has been shown to be optimal (2). Other than purely information-theoretic rate calculation s, there are practical reasons for the use of amplify-and/or- quantize-and-forward strategy. Decoding a packet at the relay requires an entire receive chain (demodulation and decod- ing) to be implemented at the relay, along with an entire transmit chain (re-encode, remodulate and retransmit). An amplify/quantize-and-forward relay can bypass this chain, processing the received signal directly to obtain the relay output. This simplification greatly impacts the cost, energ y usage and size of the relays, and therefore, it is not surpris ing that the majority of the relays used in practice today are bas ed on amplify-and-forward strategies. The forwarding strategy used at the relay has repercus- sions beyond the physical layer. For all strategies other than decode-and-forward relaying, there is no discrete-valued "packet" traversing the network. In essence, when the re- lays/intermediate nodes in a network choose not to decode d