On Power Allocation and Relay Selection for a Two-Way Amplify-and-Forward Relaying System

In this paper, we investigate power allocation and relay selection problems for a two-way amplify-and-forward (AF) relaying system. We first derive asymptotic overall symbol error probabilities (AOSEPs) for the case of one relay cooperating with two sources with respect to the second-order channel statistics for both M-ary quadrature amplitude modulation (M-QAM) and M-ary phase-shift keying (M-PSK), and then present the corresponding optimal power allocation and relay selection schemes that minimize the AOSEPs. To achieve the full diversity order, we further propose alternative power allocation and relay selection methods by simply replacing the statistical channel information of the first scheme with instantaneous one. The diversity order of the second scheme is then verified by deriving the lower and upper bounds of the corresponding asymptotic overall outage probability. Computer simulation results are also given to support the analytical results.