On the Outage Probability of MIMO Full-Duplex Relaying: Impact of Antenna Correlation and Imperfect CSI

Abstract

This paper analyzes the performance of multiple-input multiple-output (MIMO) full-duplex (FD) relaying systems, where the source and destination nodes are equipped with single antenna and communicate via a dual-hop amplify-and-forward (AF) relay with multiple receive and transmit antennas. The system performance due to practical wireless transmission impairments of spatial fading correlation and imperfect channel state information (CSI) is investigated. At the relay, the loopback self-interference (LI) is mitigated by using the receive zero-forcing (ZF) precoding scheme, then steering the signal to the destination by using a maximum and ratio transmission (MRT) technique. To this end, new exact closed-form expressions for the outage probability are derived, where the case of arbitrary, exponential, and no correlations are considered. Meanwhile, for better system performance insights, simpler outage probability lower bound expressions are also included, through which the achievable diversity order of the receive ZF/MRT scheme is shown to be $\text{min}(N_{R}-1, N_{T})$ , where $N_{R}$ and $N_{T}$ are the number of relay receive and transmit antennas, respectively. Numerical results sustained by Monte Carlo simulations show the exactness and tightness of the proposed closed-form exact and lower bound expressions, respectively. In addition, it is seen that the outage probability performance of FD relaying outperforms that of the conventional half-duplex (HD) relaying at low to medium signal-to-noise ratio (SNR). However, at high SNR, the performance of HD relaying outperforms that of the FD relaying. Furthermore, in the presence of channel estimation errors, an outage probability error floor is seen at high SNR. Therefore, for optimum outage performance, hybrid relaying modes that switches between HD and FD relaying modes is proposed.