On channel estimation and spectral efficiency for cell-free massive MIMO with multi-antenna access points considering spatially correlated channels

Channel estimation (CE) and spectral efficiency (SE) are two processes that have a major influence on system performance, especially in a more practical channel scenario with spatially correlated Rayleigh fading. During this work, we address the uplink phase CE process and the SE for spatially correlated Rayleigh fading in a cell-free (CF) massive multiple-input multiple-output (M-MIMO) network and in the conventional M-MIMO network operating under the time-division duplex protocol. Since practical channels are correlated spatially with Rayleigh fading; thereby, this work addresses spatially correlated Rayleigh fading channels in both networks using a combination of the exponential correlation model with large-scale variation across the array. Moreover, this work addresses the correlated and uncorrelated channels, where the correlated one is investigated using two array arrangements, namely, a uniform linear array (ULA) and a uniform planar array (UPA). For the two networks, the CE and SE are addressed using the minimum mean square error (MMSE) estimator and the MMSE combining vector, respectively. We propose a novel array design for CF M-MIMO using the Kronecker product of a ULA arrangement, where each access point has a UPA arrangement. In other words, we propose the covariance matrix generated by the UPA arrangement for CF M-MIMO using the Kronecker product of the covariance matrix generated by the ULA arrangement for CF M-MIMO. Numerical results are presented to validate our theoretical expressions, where we evaluate the performance of the MMSE estimator and MMSE combining vector, respectively, using the normalized mean square error metric and the quantity of information effectively transmitted per second.