# Performance of Cell-Free Massive MIMO with Rician Fading and Phase Shifts

## TL;DR

This paper analyzes the spectral efficiency of cell-free massive MIMO systems with Rician fading, considering phase shifts due to mobility and noise, and compares different estimators and transmission modes.

## Contribution

It derives closed-form spectral efficiency expressions for various estimators and transmission modes in Rician fading, accounting for phase noise and mobility effects.

## Key findings

- LSFD enhances uplink spectral efficiency.
- Coherent transmission outperforms non-coherent in downlink.
- Performance loss from phase ignorance is small with low pilot contamination.

## Abstract

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 with 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 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 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 MR precoding are derived for the three estimators. Numerical results show that the 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.