Three-phase two-way relaying with imperfect channel estimation and asymmetric traffic requirements: performance analysis and optimization

We study the effect of imperfect channel estimation (ICE) and asymmetric traffic requirements (ATRs) on the performance of bidirectional relaying with a direct link by employing three-phase analog network coding under Nakagami-m fading. Under such a realistic scenario, a tight lower bound on the overall outage probability is derived in closed-form, while a useful expression is presented for the asymptotically low outage regime. We also deduce the tight closed-form expression for the ergodic sum-rate. Furthermore, we formulate and solve analytically three optimization problems viz., relay power allocation under fixed location of the relay, relay position with fixed relay power allocation, and joint optimization of relay power allocation and location. Our results reveal that for given ICE, the optimal relay location offers significant system performance enhancement under ATRs, whilst the optimal relay power allocation has a more noticeable impact under symmetric traffic. It is also shown that the joint optimization of relay power allocation and location can further enhance the system performance, regardless of ATRs and ICE. Above all, based on the direct link quality, we show that the considered scheme outperforms its two-phase counterpart, even in the low signal-to-noise ratio regime.