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In this work, we consider a selective Detect-and-Forward (a symbol based decode-and-forward) (DetF) multi-relay two-way network employing differential MPSK with regularized Weighted Decision Feedback Differential Coherent (WDFDC) receivers. Regularized WDFDC receivers based on a regularized linear predictor (RLP) were proposed for one-way relay networks where it was shown to mitigate the performance loss due to decision feedback error propagation and intermittent transmission between relay nodes and the destination.This paper introduces regularized WDFDC receivers for two way selective DetF relay networks, employing various protocols with and without network coding, and using multiple relays. For each protocol, an optimal destination threshold is derived to decide if a relay transmits or remains silent. Furthermore, analytical performance bounds, providing insights to the effects that cause degradation, are also derived. Extensive simulation results demonstrate that the use of network coding achieves higher bandwidth efficiency, but suffers an error rate performance loss. Diversity gains can be achieved when the number of relays increases. However, repeated transmissions from the same relay do not yield extra diversity gains.

Bidirectional selective Detect-and-Forward (DetF) multi-relay systems with regularized WDFDC receivers