Performance Analysis and Power Control of Cell-Free Massive MIMO over Non-Reciprocal Channels

In this paper, we investigate the important impacts of imperfect channel state information (CSI) and pilot contamination of cell-free (CF) multiple-input multiple-output (MIMO) systems over non-reciprocal channels with large-scale fading precoding (LSFP). We derive analytical lower bounds of spectral efficiency (SE) for a physically inspired channel nonreciprocity (NRC) model where the NRC variables vary slowly in time. By using our derived closed-form expressions, we study the influence of NRC on the max-min power control scheme. The analysis shows that the achievable downlink SE is only sensitive to the access points (APs) side phase non-reciprocity under pilot contamination and conjugate beamforming, hence the corresponding calibration can be simplified with practical feasibility. Simulation results illustrate that when considering any power control scheme, pilot contamination and NRC both reduce the SE performance while the former shows a greater effect. However, different power control schemes show different sensitivity to NRC. More precisely, the max-min scheme loses its superiority compared to the equal power scheme as the NRC increases. Our results are new and different from the extent CF power control schemes which consider perfect NRC.