On the Capacity of MRT/MRC Diversity Technique in Full-Duplex Relay System with Hardware Impairments over Rayleigh Fading Environments

This paper investigates the ergodic capacity (EC) of full-duplex (FD) relay system with maximal ratio transmission (MRT) and maximal ratio combining (MRC) techniques under the effect of hardware impairments (HI). We mathematically derive the closed-form expression of EC of the HI-FD relay system under the joint impact of HI and residual self-interference (RSI) over Rayleigh fading environments. Based on the derived expression, we can quickly obtain the EC expressions of related systems such as ideal hardware (ID) FD relay systems, HI half-duplex (HD) relay system, and ID-HD relay system. The Monte-Carlo simulation validates all analytical expressions. Numerical results indicate a strong effect of both HI and RSI on the EC of the considered HI-FD relay system. Specifically, EC reaches the capacity floor in the high signal-to-noise ratio (SNR) regime. Also, the influence of HI is more substantial when the RSI is smaller and vice versa.