Spectral efficiency comparison analysis of wireless transmission schemes for two-way network coding opportunistic relaying systems

The spectrum efficiency of two-way opportunistic relaying with amplify-and-forward network coding systems (OR-TW-AFNC) is investigated in detail. In general, it is believed that there are three transmission schemes for two-way opportunistic relaying, i.e., two slots, three slots, and four slots schemes. By using the appropriate approximate mathematical manipulation, we obtain the closed-form analytical expressions to the average sum rates of the three transmission schemes. The comparison analysis shows that the spectral efficiencies of the three two-way opportunistic relaying systems are determined by the practical channel state and signal-to-noise ratio (SNR) region. Under certain channel gains and SNR region, the three slots schemes can outperform the two slots ones, especially in low SNR. This is due to the fact that the three slots scheme utilizes the signal from direct link. At the same time, the comparison numerical results validate the derivations, effectively.