Capacity of the Gaussian Two-Hop Full-Duplex Relay Channel with Self-Interference

In this paper, we investigate the capacity of the Gaussian two-hop full-duplex (FD) relay channel with self-interference. This channel is comprised of a source, an FD relay, and a destination, where a direct source-destination link does not exist and the FD relay is impaired by self-interference. We model the self-interference as an additive Gaussian random variable whose variance is proportional to the amplitude of the transmit symbol at the relay. For this channel, we derive the capacity and propose an explicit capacity-achieving coding scheme. Thereby, we show that the optimal input distribution at the source is Gaussian and its variance depends on the amplitude of the transmit symbol at the relay. On the other hand, the optimal input distribution at the relay is discrete or Gaussian, where the latter case occurs only when the relay-destination link is the bottleneck link. The derived capacity converges to the capacity of the two-hop ideal FD relay channel without self-interference and to the capacity of the two-hop half-duplex (HD) relay channel in the limiting cases when the self-interference is zero and infinite, respectively. Our numerical results show that significant performance gains are achieved using the proposed capacity-achieving coding scheme compared to the achievable rates of conventional FD relaying and HD relaying.