A scaling law approach to wireless relay networks

There has been significant recent progress in understanding approximately optimal relaying strategies for wireless networks, such as quantize-map-and-forward, noisy network coding, amplify-and-forward, etc. While one can construct specific instances of networks, with specific topology and channel configurations, where each one of these strategies can provide significant gains over simple strategies such as routing and direct transmission, it is not clear how much gain these more sophisticated strategies can provide in generic setups. In this paper, we follow a scaling law approach and assume that nodes are randomly distributed over the network area and the channels between them are governed by a path-loss model. This approach has been used to demonstrate the benefits of sophisticated cooperation in networks with multiple unicast flows both in the high and the low SNR regimes. However, for a single unicast flow, we show that more sophisticated relaying can not provide significant gain over simple multi-hop or direct transmission both in the high and the low-SNR regimes, if the nodes are uniformly distributed over the network area. More sophisticated relaying is needed in networks where nodes are clustered in the low to moderate SNR regimes. We propose a cluster decode-and-forward strategy that is scaling optimal.