On Channel Estimation for Rician Fading with the Phase-Shift in Cell-Free Massive MIMO System

Channel estimation (CE) is a crucial phase in wireless communication systems, especially in cell-free (CF) massive multiple input multiple output (M-MIMO) since it is a dynamic wireless network. Therefore, this work is introduced to study CE for the CF M-MIMO system in the uplink phase, wherein the performance of different estimators are evaluated, discussed, and compared in various situations. We assume the scenario in which each access point has prior knowledge of the channel statistics. The phase-aware-minimum mean square error (PA-MMSE) estimator, the non-phase-aware-MMSE (NPA-MMSE) estimator, and the least-squares estimator are the three estimators which are exploited in this work. Besides, we consider the Rician fading channel in which the line-of-sight path is realized with a phase-shift that models the users' mobility where the considered phase-shift follows a uniform distribution. On the other hand, the mean-squared error metric is employed in order to evaluate the performance of each estimator, where an analytical and simulated result is provided for the PA-MMSE estimator and the NPA-MMSE estimator in order to assert our numerical results.