Hop-by-Hop ZF Beamforming for MIMO Full-Duplex Relaying With Co-Channel Interference

In this paper, a comprehensive design and analysis of multiple-input multiple-output (MIMO) full-duplex (FD) relaying systems in a multi-cell environment is investigated, where a multi-antenna amplify-and-forward FD relay station serves multiple half-duplex (HD) multi-antenna users. The pivotal obstacles of loopback self-interference (LI) and multiple co-channel interferers (CCI) at the relay and destination when employing FD relaying in cellular networks are addressed. In contrast to the HD relaying mode, the CCI in the FD relaying mode is predicted to double since the uplink and downlink communications are simultaneously scheduled via the same channel. In this paper, the optimal layout of transmit (receive) precoding (decoding) weight vectors which maximizes the overall signal-to-interference-plus-noise ratio is constructed by a suitable optimization problem, and then a closed-form sub-optimal formula based on null space projection is presented. The proposed hop-by-hop rank-1 zero-forcing (ZF) beamforming vectors are based on added ZF constraints used to suppress the LI and CCI channels at the relay and destination, i.e., the source and relay perform transmit ZF beamforming, while the relay and destination employ receive ZF combining. To this end, unified accurate expressions for the outage probability and ergodic capacity are derived in closed form. In addition, simpler tight lower bound formulas for the outage probability and ergodic capacity are presented. Moreover, the asymptotic approximations for outage probability are considered to gain insights into system behavior in terms of the diversity order and array gain. Numerical and simulation results show the accuracy of the presented exact analytical expressions and the tightness of the lower bound expressions. The case of hop-by-hop maximum-ratio transmission/maximal-ratio combining beamforming is included for comparison purposes. Furthermore, our results show that while multi-antenna terminals improve the system performance, the detrimental effect of CCI on FD relaying is clearly seen. Therefore, our findings unveil that MIMO FD relaying could significantly improve the system performance compared to its conventional MIMO HD relaying counterpart.