  In this paper, we investigate a cell-free massive MIMO 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) based on a two-layer decoding structure with maximum ratio (MR) or local
minimum mean-square error (MMSE) combining applied in the first layer and
optimal large-scale fading decoding method implemented in the second layer,
respectively. To maximize the weighted sum SE, an uplink precoding structure
based on an Iteratively Weighted sum-MMSE (I-WMMSE) algorithm using only
channel statistics is proposed. Furthermore, with MR combining applied in the
first layer, we derive novel achievable SE expressions and optimal precoding
structures in closed-form. Numerical results validate our proposed results and
show that the I-WMMSE precoding can achieve excellent sum SE performance.
