Spectral efficiency of cell-free massive MIMO with LSFD receiver under spatially correlated Rayleigh fading channels

This paper investigates the uplink spectral efficiency of distributed cell-free (CF) massive multiple-input multiple-output (mMIMO) networks with correlated Rayleigh fading channels based on three different channel estimation schemes. Specifically, each access point (AP) first uses embedded pilots to estimate the channels of all users based on minimum mean-squared error (MMSE) estimation. Given the high computational cost of MMSE estimation, the low-complexity element-wise MMSE (EW-MMSE) channel estimator and the least-squares (LS) channel estimator without prior statistical information are also analyzed. To reduce non-coherent and coherent interference during uplink payload data transmission, simple centralized decoding (SCD) and large-scale fading decoding (LSFD) are examined. Then, the closed-form expressions for uplink spectral efficiency (SE) using MMSE, EW-MMSE, and LS estimators are developed for maximum ratio (MR) combining under LSFD, where each AP may have any number of antennas. The sum SE maximization problem with uplink power control is formulated. Since the maximization problem is non-convex and challenging, a block coordinate descent approach based on the weighted MMSE method is used to get the optimal local solution. Numerical studies demonstrate that LSFD and efficient uplink power control can considerably increase SE in distributed CF mMIMO networks.