Distributed power allocation in multi-user multi-channel cellular relay networks

In this paper, we consider the amplify-and-forward relaying transmission in the downlink of a multi-channel cellular network with one base station and multiple relay-destination pairs. Spatial reuse of the relaying slot by allowing simultaneous transmissions from the relays is adopted to avoid the spectral loss incurred by the half-duplex relays. The relays are modeled as rational agents engaging in a non-cooperative game. In order to maximize its individual rate, each relay node iteratively allocates its power across different subchannels based on local information, while treating the signals from the other users as additive noise. First, we propose a distributed algorithm based on best response that is applicable in any signal to interference plus noise ratio (SINR) regions. Then, by focusing on the low SINR region, we propose a modified iterative water-filling algorithm. The existence of Nash equilibrium (NE) is guaranteed and the sufficient condition to reach a NE iteratively is determined. Next, we consider medium to high SINR regions and propose a distributed algorithm based on the sub-optimal response, which can be shown to reduce to the classic Gaussian interference channel model, for which analytical sufficient conditions for the convergence to the unique NE can be readily obtained. Finally, we extend the analysis to a general network topology wherein the users having different channel conditions coexist. The results show that, in low SINR regions, the proposed modified iterative water-filling algorithm yields a higher average sum rate than two simplified algorithms, i.e., the equal power allocation scheme and the conventional time-division based protocol, while in medium to high SINR regions, the sub-optimal-response based algorithm outperforms these two simplified algorithms in terms of the average sum rate