Tight upper bound ergodic capacity of an AF full-duplex physical-layer network coding system

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In this paper, we present a two-way relay channel (TWRC) network that utilizes a full-duplex physical layer network coding (FD-PLNC) scheme in conjunction with amplify-and-forward (AF) relaying and orthogonal frequency-division multiplexing (OFDM). In order to cope with the self-interference (SI) induced by the FD mode of operation, a self-interference cancellation (SIC) scheme is utilized at each node in the proposed system. The performance of the proposed system is thoroughly investigated in the presence of residual SI by deriving a closed-form expression for the distribution of the tight upper bound end-to-end (E2E) signal to interference and noise ratio (SINR). Furthermore, an exact closed-form expression for the tight upper bound ergodic capacity is derived and used to evaluate the E2E upper bound ergodic capacity of the proposed AF-FD-PLNC system. The obtained results demonstrate the ergodic capacity gain of the proposed AF-FD-PLNC over the ergodic capacity of traditional AF half-duplex (HD) PLNC systems. In particular, the proposed AF-FD-PLNC can increase the ergodic capacity of AF-HD-PLNC by a factor of 2 when the SNR is higher than 25 dB and the SI to noise ratio is less than 0 dB.