Tight performance bounds for two-way opportunistic amplify-and-forward wireless relaying networks with TDBC protocols

Based on amplify-and-forward network coding (AFNC) protocol, the outage probability and ergodic capacity of two-way network coding opportunistic relaying (TWOR-AFNC) systems are investigated as well as the corresponding closed-form solutions. For the TWOR-AFNC systems, it is investigated under two scenarios, namely, the TWOR-AFNC systems without direct link (TWOR-AFNC-Nodir) and the TWOR-AFNC systems with direct link (TWOR-AFNC-Dir). First, we investigate TWOR-AFNC-Nodir systems by employing the approximate analysis in high SNR, and obtain closed-form solutions to the cumulative distribution function (CDF) and the probability density function (PDF) of the instantaneous end-to-end signal-to-noise ratio (SNR) with very simple expressions. The derived simple expressions are given by defining an equivalent variable ωeq-k(θ), 2 ≤ θ ≤ 3. When θ = 2, the derived results are the tight lower bounds to CDF and PDF. The sequent simulation demonstrates that the derived tight lower bounds are also very effective over the entire SNR region though which the results are derived in high SNR approximation. Then, with the derived tight closed-form lower bound solutions (θ = 2) in TWOR-AFNC-Nodir systems, we investigate TWOR-AFNC-Dir systems as well as the overall comparison of the outage probability and the ergodic capacity between the two system models. The comparison analysis performed over path loss model basis shows that, in urban environment, due to utilizing the direct link the TWOR-AFNC-Dir outperform considerably the TWOR-AF-Nodir systems. However, when the value of path loss exponent is relatively large, the achievable gain is very small and the direct link can be omitted. In this case, the TWOR-AFNC-Dir model can be displaced by TWOR-AFNC-Nodir model having lower implementation complexity.