Differential modulations for multinode cooperative communications

This paper proposes and analyzes differential modulation schemes for two cooperation protocols in multinode cooperative wireless networks; namely, multinode differential amplify-and-forward scheme (DiffAF) and multinode differential decode-and-forward scheme (DiffDF). In the DiffAF scheme, with knowledge of long-term average of received signals from all communication links, the destination efficiently combines signals from direct and all multiple-relay links to improve communication reliability. In the DiffDF scheme, by utilizing a decision threshold at each relay-destination link, the destination efficiently combines signals from the direct link and each relay link. whose signal amplitude is larger than the threshold. For the DiffAF scheme, an exact bit error rate (BER) formulation based on optimum combining is provided for differential M-ary phase shift keying (DMPSK) modulation, and it serves as a performance benchmark of the proposed DiffAF scheme. In addition, BER upper bounds, BER lower bounds, and simple BER approximations are derived. Then, optimum power allocation is provided to further improve performance of the DiffAF scheme. Based on the tight BER approximation, the optimum power allocation can be simply obtained through a single dimensional search. In case of the DiffDF scheme, the performance of DMPSK modulation is analyzed. First, a BER formulation for DMPSK modulation is derived. Next, an approximate BER formulation of the DiffDF scheme is obtained, and a tractable BER lower bound is derived to provide further insights. Then, the performance of the DiffDF scheme is enhanced by jointly optimizing power allocation and decision thresholds with an aim to minimize the BER. Finally, simulation results under the two proposed cooperation protocols are given to validate their merit and support the theoretical analysis.