  In this paper, we investigate the capacity of the Gaussian two-hop
full-duplex (FD) relay channel with residual 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 residual
self-interference. We adopt the worst-case linear self-interference model with
respect to the channel capacity, and model the residual self-interference as a
Gaussian random variable whose variance depends on the amplitude of the
transmit symbol of 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 of 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 residual
self-interference is zero and infinite, respectively. Our numerical results
show that significant performance gains are achieved with the proposed
capacity-achieving coding scheme compared to the achievable rates of
conventional HD relaying and/or conventional FD relaying.
