Robust Optimization of Instantaneous Beamforming and Quasi-static Phase Shifts in an IRS-assisted Multi-Cell Network

TL;DR

This paper develops robust optimization techniques for beamforming and phase shifts in IRS-assisted multi-cell networks, accounting for practical issues like channel estimation errors and interference, leading to significant performance improvements.

Contribution

It introduces a robust joint design framework for instantaneous beamforming and quasi-static phase shifts under imperfect CSIT and inter-cell interference, with closed-form solutions and an iterative algorithm.

Findings

Closed-form robust beamforming designs for any phase shifts.

An iterative algorithm for phase shift optimization with KKT points.

Significant performance gains over existing methods.

Abstract

The impacts of channel estimation errors, inter-cell interference, phase adjustment cost, and computation cost on an intelligent reflecting surface (IRS)-assisted system are severe in practice but have been ignored for simplicity in most existing works. In this paper, we investigate a multi-antenna base station (BS) serving a single-antenna user with the help of a multi-element IRS in a multi-cell network with inter-cell interference. We consider imperfect channel state information (CSI) at the BS, i.e., imperfect CSIT, and focus on the robust optimization of the BS's instantaneous CSI-adaptive beamforming and the IRS's quasi-static phase shifts in two scenarios. In the scenario of coding over many slots, we formulate a robust optimization problem to maximize the user's ergodic rate. In the scenario of coding within each slot, we formulate a robust optimization problem to maximize the user's average goodput under the successful transmission probability constraints. The robust optimization problems are challenging two-timescale stochastic non-convex problems. In both scenarios, we obtain closed-form robust beamforming designs for any given phase shifts and more tractable stochastic non-convex approximate problems only for the phase shifts. Besides, we propose an iterative algorithm to obtain a Karush-Kuhn-Tucker (KKT) point of each of the stochastic problems for the phase shifts. It is worth noting that the proposed methods offer closed-form robust instantaneous CSI-adaptive beamforming designs which can promptly adapt to rapid CSI changes over slots and robust quasi-static phase shift designs of low computation and phase adjustment costs in the presence of imperfect CSIT and inter-cell interference. Numerical results further demonstrate the notable gains of the proposed robust joint designs over existing ones and reveal the practical values of the proposed solutions.