Distributed Power Allocation in Multi-User Multi-Channel Relay Networks

In this paper, we consider a wireless amplify-and-forward relay network with multiple source-relay-destination pairs transmitting concurrently over parallel channels and investigate the distributed power allocation problem within the framework of non-cooperative game theory. In order to combat the interference effect, each source node iteratively maximizes its own rate based on local information by allocating its power across different subchannels, subject to its power constraint, while treating the signals from the other users as additive noise. First, by focusing on the low signal to interference plus noise ratio (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 is determined. Then, we consider medium and high SINR regions and propose distributed algorithms based on both best (or optimal) and sub-optimal responses. The proposed algorithm based on the sub-optimal response is mathematically tractable and easier to compute, and exhibits a negligible performance loss, compared to the best-response based algorithm. Furthermore, the sub-optimal-response algorithm can be reduced to the classic Gaussian interference channel model, for which analytical sufficient conditions for the convergence to the unique NE can be readily obtained. 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 and high SINR regions, both the best-response and sub-optimal-response based algorithms outperform these two simplified algorithms in terms of the average sum rate.