In this letter, the performance of opportunistic-based two-way relaying with beamforming over Nakagami-m fading channels is investigated. We provide an approximate expression for the cumulative distribution function of the end-to-end signal-to-noise ratio to derive the closed-form lower bounds for the outage probability and average bit error probability as well as the closed-form upper bound for the ergodic capacity. Simulation results demonstrate the tightness of the derived bounds.

In this letter, a dual-hop wireless communication network with opportunistic amplify and forward (O-AF) relay is investigated over independent and non-identically distributed Nakagami-m fading channels. Employing Maclaurin series expansion around zero to derive the approximate probability density function of the normalized instantaneous signal-to-noise ratio (SNR), the asymptotic symbol error rate (SER) and outage probability expressions are presented. Simulation results indicate that the derived expressions well match the results of Monte-Carlo simulations at medium and high SNR regions. By comparing the O-AF with all AF relaying analyzed previously, it can be concluded that the former has significantly better performance than the latter in many cases.

This letter investigates the performance of amplify-and-forward relaying systems using maximum ratio transmission at the source. A closed-form expression for the outage probability and a closed-form lower bound for the average bit error probability of the system are derived. Also, the approximate expressions for the outage probability and average bit error probability in the high signal-to-noise ratio regime are given, based on which the optimal power allocation strategies to minimize the outage probability and average bit error probability are developed. Furthermore, numerical results illustrate that optimizing the allocation of power can improve the system performance, especially in the high signal-to-noise ratio regime.