Impact of channel estimation error on zero-forcing-based multiple-input-multiple-output two-way relaying

In this study, the authors investigate the impact of channel estimation error (CEE) on the performance of a multiple-input–multiple-output (MIMO) two-way relay system under Rayleigh fading. Herein, transmit/receive zero-forcing (ZF) is employed at the two source nodes, whereas analogue network coding is used at the relay node. Fundamentally, for making use of transmit/receive ZF, all nodes must be aware of channel state information (CSI). As perfect CSI may not always be available in practical scenarios, the CEE does exist in the considered system. By taking the imperfect CSI into account, they enucleate that the residual self-interference and additional noise pertaining to the CEE have effect of reducing end-to-end signal-to-noise ratios (SNRs) at the two source nodes. Based on the statistical characterisations of these post-processing SNRs, they carry out the overall system outage probability analysis. Further, they investigate the asymptotic outage behaviour to deduce the achievable diversity order. They substantiate that the diversity order may reduce to zero under severe impact of CEE. In addition, they derive a closed-form expression of ergodic sum-rate of the considered system with CEE. Numerical and simulation investigations are conducted to support all the theoretical findings using various values of CEE and antenna configurations.