Multi-IRS-Aided Millimeter-Wave Multi-User MISO Systems for Power Minimization Using Generalized Benders Decomposition

Difficulties in controlling IRSs to form the optimized passive beamforming have rarely been considered in intelligent reflecting surface (IRS)-aided systems, which are summarized as follows: 1) sending the optimized passive precoding vectors to the IRS controller incurs significant control overheads; 2) implementing the optimized passive precoding needs to set massive modes in the IRS control circuit. To address these issues, we investigate codebook-based passive beamforming for multi-IRS-aided millimeter-wave (mmWave) multi-user multiple-input single-output (MU-MISO) systems, where the control overheads are reduced to several scalars and the number of modes set in the IRS control circuit is reduced to that of codewords. Moreover, we formulate a joint passive and active precoding problem in the multi-IRS-aided mmWave MU-MISO system as a mixed-integer nonlinear programming (MINLP) problem, and then develop a generalized Benders decomposition (GBD)-based joint passive and active precoding algorithm. The proposed algorithm offers near-optimal performance ( $\ge99.9$ %) with significantly-reduced computational complexity. Simulation results show that the proposed algorithm achieves energy savings of up to 50% and 95%, compared to the benchmark by the maximum ratio transmission and that without IRSs, respectively. In addition, the energy savings increase with the number of reflecting elements packed on each IRS as well as that of codewords.

I. Introduction

Emerging bandwidth-demanding services such as augmented/virtual reality put great a strain on wireless systems [1]. Millimeter-wave (mmWave) communications spanning a wide frequency range can provide a data rate of Gbps, which have been widely studied [2], [3]. Compared to signals at sub-6GHz frequencies [1], one differentiating factor in mmWave signals is the ten-fold decrease in wavelength. The decrease in wavelength enables packing massive mmWave antennas into small form factors [2]. From the Friis free-space equation [4], however, the penetration loss at mmWave frequencies is more excessive than that at sub-6GHz frequencies, and therefore, mmWave signals are more sensitive to blockages than sub-6GHz signals [5], [6].