Performance Analysis and Beamforming Designs of MIMO AF Relaying With Hardware Impairments

This paper investigates outage performance analysis and beamforming designs of a dual-hop multiple-input multiple output (MIMO) amplify-and-forward (AF) relay channel with hardware impairments. We derive analytical closed-form expressions of the exact outage probability with fixed-gain and variable gain relaying beamforming schemes. Moreover, asymptotic outage probability expressions are analyzed at high signal-to-noise ratio (SNR), which show that how hardware impairments and the number of relay antennas affect the system performance. We find that the outage probability in both relaying beamforming schemes has lower bounds with the increase of the SNR. Especially in the fixed gain relaying beamforming scheme, we obtain a simple floor of the outage probability that is a monotone increasing function of hardware impairments' level. To further compensate the performance loss brought by hardware impairments, we optimize the beamforming matrix for the dual-hop MIMO AF relay network by maximizing the end-to-end signal-to-noise-and-distortion ratio with the relay's power constraint. We derive optimal beamforming designs for sum-power constraint and for per-antenna power constraints. Our results show that the performance of the variable gain relaying is superior to the fixed-gain relaying, especially for the case with varying scaling factor of the relay beamforming matrix. It is also shown that more performance gains can be attained with the proposed optimal beamforming designs.