  We consider a cell-free massive multiple-input multiple-output (MIMO) system
with multi-antenna access points and user equipments (UEs) over Weichselberger
Rician fading channels with random phase-shifts. More specifically, we
investigate the uplink spectral efficiency (SE) for two pragmatic processing
schemes: 1) the fully centralized processing scheme with global minimum mean
square error (MMSE) or maximum ratio (MR) combining; 2) the large-scale fading
decoding (LSFD) scheme with local MMSE or MR combining. To improve the system
SE performance, we propose a practical uplink precoding scheme based on only
the eigenbasis of the UE-side correlation matrices. Moreover, we derive novel
closed-form SE expressions for characterizing the LSFD scheme with the MR
combining. Numerical results validate the accuracy of our derived expressions
and show that the proposed precoding scheme can significantly improve the SE
performance compared with the scenario without any precoding scheme.
