Optimal SNR-based selection relaying scheme in multi-relay cooperative networks with distributed space–time coding

Error propagation from the relay to the destination is a major drawback of digital relaying protocols that substantially diminishes the cooperative diversity gain of the system. Appropriately designed selection relaying schemes can effectively mitigate this phenomenon and improve the diversity order, especially when the source-relay channel state information (CSI) is not available at the destination. In this study, the authors investigate the SNR-based selection relaying scheme in a multi-relay cooperative network that employs the distributed space-time coding (DSTC) strategy. The authors present a closed-form expression for the end-to-end bit error probability (BEP) of the system. It is demonstrated that the orthogonality of the space-time coded signals transmitted by the relays is not preserved under the error propagation from the relays to the destination and this gives rise to intersymbol interference at the destination. The SNR loss and intersymbol interference caused by the error propagation substantially diminish the diversity order of the system. The error propagation can be effectively mitigated by employing appropriate thresholds at the relays. The authors derive a closed-form expression for the optimal threshold that minimises the end-to-end BEP of the system. The authors also analyse the asymptotic behaviour of the BEP and demonstrate that by employing the optimal threshold the full diversity order is achieved. Furthermore, the authors propose a class of thresholds that are independent of the network geometry and also provide full diversity order. By employing these thresholds, each relay node can decide to forward or remain silent independent of other relay nodes.