Spatially Correlated Rayleigh Fading for Cell-Free Massive MIMO Systems

In this paper, we present the detailed rate analysis for cell-free massive multiple-input multiple-output (MIMO) systems over spatially correlated Rayleigh fading channels. Taking the realistic impairment effects of spatial channel correlation, pilot contamination, and channel estimation errors into account, the lower-bounds of the achievable rates for both the uplink and downlink are derived with the low-complexity linear processing such as matched filter and conjugate beamforming, which enable us to take cognizance of the impacts of transmitted power, and the number of access points (APs). Based on the derived rate results, the asymptotic performance analysis is then carried out. Besides, we propose the sophisticated max-min power allocation strategies taking the actual requirements into consideration to provide uniformly good service to all users. However, the objective functions of the two optimization problems are both non-concave. Fortunately, the former for uplink can be characterized as geometric programming (GP), whilst the latter for downlink merging the efficient tools of second-order-cone programming (SOCP). Lastly, the numerical results are shown to verify our analytical results and the effectiveness of the proposed max-min fairness algorithms.