Two-way opportunistic relaying systems: Performance and optimization in Rayleigh fading environments

This paper derives the error probability of a two-way relay-based communication system with opportunistic selection in Rayleigh fading environments. We consider a two-way wireless communication system where two nodes, acting as sources, are unable to exchange data directly and, thus, proceed via L intermediate relay terminals. We investigate a single-relay selection scheme wherein only the best among the L relays is chosen. Since the communication is two-way, the analyzed scheme aims at optimizing the worse performance of the two communication tasks between the pair of users. In particular, we derive closed-form expressions of the probability density functions (PDFs) of the signal-to-noise ratios (SNRs) at both users. This result is then used to derive novel closed-form expressions for the average symbol error probabilities (ASEPs) at both users´ nodes. Results on the asymptotic error probability in the high-SNR range completes the performance evaluation part. Then, we provide closed-form expressions for the transmit power optimization at the two source nodes before corroborating the analysis with numerical results.