Optimal Power Allocation and Capacity of Full-Duplex AF Relaying under Residual Self-Interference

This paper investigates the optimal power allocation scheme and corresponding capacity limit of a full-duplex (FD) dual-hop amplify-and-forward relay system under residual self-interference whose variance is proportional to the λ'th power of the transmitted power (0 ≤ λ ≤ 1). At first, the related optimization problems are shown to be quasiconcave under both per-node and sum power constraints. Given the non-linearity of the derivative, bisection is then proposed to obtain the optimal power strategies. The capacity and optimal schemes are then analyzed in different high power regions. Specifically, we apply the dominant balance method to show that full power at the relay is suboptimal when its power constraint approaches a large value. Following a similar approach, we then show that the multiplexing gain of the FD scheme with the optimal allocation is 1/[1 + λ]. Comparisons between the half-duplex and FD systems are finally carried out, where analytical and simulation results reveal that the FD system is superior in high source power regions with either fixed or large power constraints at the relay.