  We consider a practical cell-free massive multiple-input-multiple-output
(MIMO) system with multi-antenna access points (APs) and spatially correlated
Rician fading channels. The significant phase-shift of the line-of-sight
component induced by the user equipment movement is modeled randomly.
Furthermore, we investigate the uplink spectral efficiency (SE) with maximum
ratio (MR)/local minimum mean squared error (L-MMSE) combining and optimal
large-scale fading decoding based on the phase-aware MMSE, phase-aware
element-wise MMSE and linear MMSE (LMMSE) estimators. Then new closed-form SE
expressions with MR combining are derived. Numerical results validate our
derived expressions and show that the SE benefits from the spatial correlation.
It is important to observe that the performance gap between L-MMSE and MR
combining increases with the number of antennas per AP and the SE of the LMMSE
estimator is lower than that of other estimators due to the lack of
phase-shifts knowledge.
