FD Cell-Free Massive MIMO Systems With Downlink Pilots: Analysis and Optimization

We consider a full duplex (FD) massive multiple-input multiple-output (mMIMO) cell-free (CF) system, where a large number of multi-antenna FD access points (APs) jointly serve multiple FD user equipments (UEs). The APs transmit precoded downlink pilots for the UEs to estimate the effective downlink channel. For this system, we derive closed-form uplink and downlink spectral efficiency (SE) expressions by considering i) radio-frequency (RF) impairments at the APs and UEs; ii) dynamic resolution analog-to-digital converter/digital-to-analog converter (ADC/DAC) architecture at the APs and low-resolution ADC/DACs at the UEs; and iii) spatially-correlated Rician channels. We then maximize the non-convex global energy efficiency metric by using the block minorization-maximization technique, which decomposes the main optimization into multiple convex surrogate sub-problems. We analytically show that the SE gain obtained with downlink training is limited for practical CF systems with RF and ADC/DAC impairments, Rician channel and pilot contamination. We also extensively investigate the impact of FD interferences on the downlink training gain.