# Communication Through a Large Reflecting Surface With Phase Errors

## TL;DR

This paper analyzes the impact of phase errors in large reflecting surfaces used for wireless communication, showing that performance remains robust despite imperfections and modeling the channel as Nakagami fading.

## Contribution

It introduces a theoretical framework for understanding phase errors in large reflecting surfaces and models the resulting channel as Nakagami fading, aiding system design.

## Key findings

- Performance is robust against phase errors.
- The composite channel can be modeled as Nakagami fading.
- Theoretical analysis matches numerical simulations.

## Abstract

Assume the communication between a source and a destination is supported by a large reflecting surface (LRS), which consists of an array of reflector elements with adjustable reflection phases. By knowing the phase shifts induced by the composite propagation channels through the LRS, the phases of the reflectors can be configured such that the signals combine coherently at the destination, which improves the communication performance. However, perfect phase estimation or high-precision configuration of the reflection phases is unfeasible. In this paper, we study the transmission through an LRS with phase errors that have a generic distribution. We show that the LRS-based composite channel is equivalent to a point-to-point Nakagami fading channel. This equivalent representation allows for theoretical analysis of the performance and can help the system designer study the interplay between performance, the distribution of phase errors, and the number of reflectors. Numerical evaluation of the error probability for a limited number of reflectors confirms the theoretical prediction and shows that the performance is remarkably robust against the phase errors.