# Intelligent Reflecting Surface: Practical Phase Shift Model and Beamforming Optimization

## TL;DR

This paper introduces a practical phase shift model for intelligent reflecting surfaces in wireless systems, accounting for phase-dependent amplitude variations, and proposes an optimization method that significantly improves system performance over ideal models.

## Contribution

The paper presents a realistic phase shift model for IRS elements and develops a low-complexity joint beamforming optimization method based on this model.

## Key findings

- Joint beamforming optimization yields substantial performance gains.
- The practical phase shift model outperforms the ideal model in simulations.
- Proposed method effectively enhances achievable rate in IRS-assisted systems.

## Abstract

Intelligent reflecting surface (IRS) that enables the control of the wireless propagation environment has been looked upon as a promising technology for boosting the spectrum and energy efficiency in future wireless communication systems. Prior works on IRS are mainly based on the ideal phase shift model assuming the full signal reflection by each of the elements regardless of its phase shift, which, however, is practically difficult to realize. In contrast, we propose in this paper a practical phase shift model that captures the phase-dependent amplitude variation in the element-wise reflection coefficient. Applying this new model to an IRS-aided wireless system, we formulate a problem to maximize its achievable rate by jointly optimizing the transmit beamforming and the IRS reflect beamforming. The formulated problem is non-convex and difficult to be optimally solved in general, for which we propose a low-complexity suboptimal solution based on the alternating optimization (AO) technique. Simulation results unveil a substantial performance gain achieved by the joint beamforming optimization based on the proposed phase shift model as compared to the conventional ideal model.