  Full-duplex (FD) is an attractive technology that can significantly boost the
throughput of wireless communications. However, it is limited by the severe
self-interference (SI) from the transmitter to the local receiver. In this
paper, we propose a new SI cancellation (SIC) scheme based on reconfigurable
intelligent surface (RIS), where small RISs are deployed inside FD devices to
enhance SIC capability and system capacity under frequencyselective fading
channels. The novel scheme can not only address the challenges associated with
SIC but also improve the overall performance. We first analyze the near-field
behavior of the RIS and then formulate an optimization problem to maximize the
SIC capability by controlling the reflection coefficients (RCs) of the RIS and
allocating the transmit power of the device. The problem is solved with
alternate optimization (AO) algorithm in three cases: ideal case, where both
the amplitude and phase of each RIS unit cell can be controlled independently
and continuously, continuous phases, where the phase of each RIS unit cell can
be controlled independently, while the amplitude is fixed to one, and discrete
phases, where the RC of each RIS unit cell can only take discrete values and
these discrete values are equally spaced on the unit circle. For the ideal
case, the closed-form solution to RC is derived with Karush-Kuhn-Tucker (KKT)
conditions. Based on Riemannian conjugate gradient (RCG) algorithm, we optimize
the RC for the case of continuous phases and then extend the solution to the
case of discrete phases by the nearest point projection (NPP) method.
Simulation results are given to validate the performance of our proposed SIC
scheme.
