Differential modulation for multi-node amplify-and-forward wireless relay networks

In this paper, we propose a multi-node differential amplify-and-forward scheme for cooperative communications. The proposed scheme efficiently combines signals from the direct and multiple relay links to improve communication reliability. Bit-error-rate (BER) analysis for M-ary differential phase shift keying is provided as performance measure of the proposed scheme, and optimum power allocation is investigated. While the exact BER formulation of the proposed scheme is not available currently, we provide as a performance benchmark a tight BER formulation based on optimum combining weights. A simple BER upper bound and a tight BER approximation show that the proposed scheme can achieve the full diversity which equals to the number of cooperating nodes. We further provide simple BER approximation in order to provide analytical result on power allocation scheme. A closed-form optimum power allocation based on the tight simple BER approximation is obtained for single-relay scenario. An approximate optimum power allocation scheme is provided for multi-relay systems. The provided BER formulations are shown to closely match to the simulation results. Moreover, simulation results show that the optimum power allocation scheme achieves up to 2 dB performance gain over the equal power allocation scheme