Uplink Precoding Design for Cell-Free Massive MIMO with Iteratively Weighted MMSE

In this paper, we investigate a cell-free massive multiple-input multiple-output system with both access points and user equipments equipped with multiple antennas over the Weichselberger Rayleigh fading channel. We study the uplink spectral efficiency (SE) for the fully centralized processing scheme and large-scale fading decoding (LSFD) scheme. To further improve the SE performance, we design the uplink precoding schemes based on the weighted sum SE maximization. Since the weighted sum SE maximization problem is not jointly over all optimization variables, two efficient uplink precoding schemes based on Iteratively Weighted sum-Minimum Mean Square Error (I-WMMSE) algorithms, which rely on the iterative minimization of weighted Mean Square Error (MSE), are proposed for two processing schemes investigated. Furthermore, with maximum ratio combining applied in the LSFD scheme, we derive novel closed-form achievable SE expressions and optimal precoding schemes. Numerical results validate the proposed results and show that the I-WMMSE precoding schemes can achieve excellent sum SE performance with a large number of UE antennas.