Differential modulation with threshold-based decision combining for cooperative communications

Differential modulation is widely known as a practical alternative that provides a good tradeoff between receiver complexity and performance. However, the available differential schemes for wireless relay networks require perfect synchronization and/or provide limited transmission rates. This paper proposes a threshold-based differential decode-and-forward cooperative scheme that not only alleviates the problems of synchronization and rate limitation, but also efficiently exploits the cooperative relay channels via the use of a predetermined decision threshold. In the proposed scheme, the source information is forwarded by the relay only if it is correctly decoded. The properly designed threshold enables the destination to decide whether the received signal from the relay contains information such that the received signals from the source and the relay can be efficiently combined and jointly decoded. Bit error rate (BER) performance analysis of the proposed scheme is analyzed in the case of differential M-ary PSK signals. The analysis focuses on the case when the relay is able to judge whether each decoded symbol is corrected or not. The obtained BER performance in this case serves as a performance benchmark, and the proposed differential decode-and-forward scheme can achieve it in an ideal situation that the error propagation at the relay can be negligible. A tight BER approximation is first derived, and then BER upper bound and lower bound are determined. Based on the tight BER approximation, joint optimum decision threshold and power allocation are numerically evaluated. Both analytical and simulation results reveal that the decision threshold and the power allocation depend on qualities of the communication channels. Interestingly, when the link quality between relay and destination is very good, the effect of the threshold dominates the effect of the power allocation at high signal-to-noise ratio. Extensive simulation results are provided to validate the merit of the proposed scheme and confirm the theoretical analysis.