Two-Way Incremental Relaying With Symbol-Based Network Coding: Performance Analysis and Optimal Thresholds

In this paper, we investigate the signal-to-noise ratio-based incremental relaying scheme for a two-way relay channel (TWRC) with symbol-based network coding. Under the assumption of error propagation from the relay to the destination, we analyze the performance of the system in terms of the end-to-end symbol error rate (SER), the average spectral efficiency (ASE), the outage probability, the asymptotic behavior, and the diversity order for M-ary phase-shift keying modulation. All of these performance measures depend on a single threshold employed by the destination. By optimizing this threshold with respect to two different performance measures, we attain two different incremental relaying schemes: 1) the SER-optimal scheme that minimizes the end-to-end SER and 2) the ASE-constrained scheme that minimizes the end-to-end SER under an ASE constraint for the TWRC. In all cases, we derive closed-form expressions for the performance measures and the optimal thresholds. The asymptotic analysis of the system shows that both the SER-optimal and ASE-constrained schemes achieve the full diversity gain at both transceivers. Moreover, both of the schemes are optimal in the sense of the asymptotic ASE. We also propose a class of thresholds that are independent of the network geometry and asymptotically perform the same as the optimal thresholds.