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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, the authors 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.
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