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In this paper, we study the uplink (UL) and downlink (DL) spectral efficiency (SE) of a cell-free
massive multiple input-multiple-output (MIMO) system over Rician fading channels. The phase of the
line-of-sight (LoS) path is modeled as a uniformly distributed random variable to take the phase-shifts
due to mobility and phase noise into account. Considering the availability of prior information at the
access points (APs), the regularized zero forcing (RZF) is developed and compared with phase-aware
minimum mean square error (MMSE), non-aware linear MMSE (LMMSE), and least-square (LS)
estimators are derived. The MMSE estimator requires perfectly estimated phase knowledge whereas
the LMMSE and LS are derived without it. In the UL, a two-layer decoding method is investigated in
order to mitigate both coherent and non-coherent interference. Closed form UL SE expressions with
phase-aware proposed RZF, and existing MMSE, LMMSE, and LS estimators are derived for
maximum-ratio (MR) combining in the first layer and optimal large-scale fading decoding (LSFD) in
the second layer. In the DL, two different transmission modes are studied: coherent and non-coherent.
Closed-form DL SE expressions for both transmission modes with RZF precoding are derived.
Numerical results show that the RZF-LSFD improves the UL SE performance and coherent
transmission mode performs much better than non-coherent transmission in the DL. Besides, the
performance loss due to the lack of phase information depends on the pilot length and it is small when
the pilot contamination is low.