# User-Centric Cell-Free Massive Multiple-Input-Multiple-Output System with Noisy Channel Gain Estimation and Line of Sight: A Beckmann Distribution Approach

## TL;DR

This paper introduces a new method using the Beckmann distribution to model signal behavior in user-centric cell-free systems with noisy channel estimates and line of sight.

## Contribution

The first use of the Beckmann distribution to model effective channel gain in user-centric cell-free systems with noisy CSI and LoS.

## Key findings

- The Beckmann distribution accurately models the effective channel gain envelope in UC CF systems.
- The Beckmann PDF can derive SINR PDF and CDF for UC CF systems.
- The effective gain follows a Beckmann distribution regardless of the AP-UE channel gain distribution.

## Abstract

This paper analyzes for the first time how the Beckmann distribution can be used to characterize the random variable that represents the envelope of the effective channel gain experienced by the k-th user equipment (UE) of a user-centric (UC) cell-free (CF) system in a scenario with noisy channel state information (CSI) estimation and line of sight (LoS). Additionally, it is shown how the Beckmann probability density function (PDF) can be used to derive the PDF and the cumulative density function (CDF) of the instantaneous signal-to-interference-plus-noise ratio (SINR) of the UC CF k-th UE, followed by applications in the ergodic capacity (EC) and outage probability (OP) expression derivations. It is shown that, regardless of the type of distribution considered for the channel gain between each access point (AP) and UE links, the effective gain presents a Beckmann distribution.