On the Performance Gain of Hybrid Decode-Amplify-Forward Cooperative Communications

We investigate the performance of adaptive decode-forward (ADF), amplify-forward (AF), and hybrid decode-amplify-forward (HDAF) relaying protocol. Specifically, we derive the closed-form expression of symbol error probability (SEP) for these three relaying protocols. For the AF protocol, we derive a simpler and more tractable final result than previously published work. Furthermore, analyzing the high signal-to-noise ratio (SNR) regime, we derive an asymptotically tight approximation for SEP. The approximation is used to assess an important aspect between the three different relaying protocols, i.e., the SEP performance gain of HADF over the two conventional relaying schemes ADF and AF. It is shown that the performance gain of HDAF over ADF and AF significantly depends on the relative value of channel conditions between source-to-relay and relay-to-destination links. Interestingly, it is shown that HDAF has no benefit compare to the two others if the relay is located close to the source. In contrast, the performance gains of HDAF over the ADF and AF scheme are remarkably large as the relay moves nearby the destination. Specifically, the numerical results given as well as our analysis indicate that for QPSK modulation, HDAF outperforms ADF and AF with a performance improvement by 5 dB and 6 dB, respectively.