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Joint Hybrid Precoding and Multi-IRS Optimization for mmWave MU-MISO Communication Network

Fardad Rahkheir, Soroush Akhlaghi

TL;DR

This work tackles the challenging problem of jointly optimizing hybrid precoding and multi-IRS beamforming in a mmWave MU-MISO system employing the Alamouti code at the BS. By reformulating the multiplicative couplings into rank-constrained matrices $\mathbf{Q}$ and $\mathbf{W}$ and applying inner approximation with majorization-minimization, the authors solve the first subproblem to configure IRS phases and the fully digital-to-hybrid precoder mapping. A subsequent modified block coordinate descent (MBCD) optimizes the HP analog/digital precoders by minimizing the Euclidean distance to the fully digital design, with a robust SDP-based approach and DC relaxations for rank constraints. Simulation results show notable rate gains over multiple benchmarks and demonstrate enhanced coverage when two IRSs are deployed, highlighting the practical value of the proposed joint design in mitigating mmWave propagation challenges. Overall, the framework achieves near-fully digital performance while reducing hardware complexity and providing scalable benefits with additional IRSs.

Abstract

This paper attempts to jointly optimize the hybrid precoding (HP) and intelligent reflecting surfaces (IRS) beamforming matrices in a multi-IRS-aided mmWave communication network, utilizing the Alamouti scheme at the base station (BS). Considering the overall signal-to-noise ratio (SNR) as the objective function, the underlying problem is cast as an optimization problem, which is shown to be non-convex in general. To tackle the problem, noting that the unknown matrices contribute multiplicatively to the objective function, they are reformulated into two new matrices with rank constraints. Then, using the so-called inner approximation (IA) technique in conjunction with majorization-minimization (MM) approaches, these new matrices are solved iteratively. From one of these matrices, the IRS beamforming matrices can be effectively extracted. Meanwhile, HP precoding matrices can be solved separately through a new optimization problem aimed at minimizing the Euclidean distance between the fully digital (FD) precoder and HP analog/digital precoders. This is achieved through the use of a modified block coordinate descent (MBCD) algorithm. Simulation results demonstrate that the proposed algorithm outperforms various benchmark schemes in terms of achieving a higher achievable rate.

Joint Hybrid Precoding and Multi-IRS Optimization for mmWave MU-MISO Communication Network

TL;DR

This work tackles the challenging problem of jointly optimizing hybrid precoding and multi-IRS beamforming in a mmWave MU-MISO system employing the Alamouti code at the BS. By reformulating the multiplicative couplings into rank-constrained matrices and and applying inner approximation with majorization-minimization, the authors solve the first subproblem to configure IRS phases and the fully digital-to-hybrid precoder mapping. A subsequent modified block coordinate descent (MBCD) optimizes the HP analog/digital precoders by minimizing the Euclidean distance to the fully digital design, with a robust SDP-based approach and DC relaxations for rank constraints. Simulation results show notable rate gains over multiple benchmarks and demonstrate enhanced coverage when two IRSs are deployed, highlighting the practical value of the proposed joint design in mitigating mmWave propagation challenges. Overall, the framework achieves near-fully digital performance while reducing hardware complexity and providing scalable benefits with additional IRSs.

Abstract

This paper attempts to jointly optimize the hybrid precoding (HP) and intelligent reflecting surfaces (IRS) beamforming matrices in a multi-IRS-aided mmWave communication network, utilizing the Alamouti scheme at the base station (BS). Considering the overall signal-to-noise ratio (SNR) as the objective function, the underlying problem is cast as an optimization problem, which is shown to be non-convex in general. To tackle the problem, noting that the unknown matrices contribute multiplicatively to the objective function, they are reformulated into two new matrices with rank constraints. Then, using the so-called inner approximation (IA) technique in conjunction with majorization-minimization (MM) approaches, these new matrices are solved iteratively. From one of these matrices, the IRS beamforming matrices can be effectively extracted. Meanwhile, HP precoding matrices can be solved separately through a new optimization problem aimed at minimizing the Euclidean distance between the fully digital (FD) precoder and HP analog/digital precoders. This is achieved through the use of a modified block coordinate descent (MBCD) algorithm. Simulation results demonstrate that the proposed algorithm outperforms various benchmark schemes in terms of achieving a higher achievable rate.

Paper Structure

This paper contains 13 sections, 66 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Problem Formulation
  4. First Sub-problem
  5. Second Subproblem
  6. Digital Precoding Design
  7. Analog Precoding Design
  8. Complexity Analysis
  9. Simulation Results
  10. Conclusion
  11. Calculate SNR of 2 Single User antenna
  12. Proof of $\mathbf{X}^H \mathbf{A} \mathbf{X} = \mathbf{A} \odot (\mathbf{x} \mathbf{x}^H)$
  13. Evaluate the $\tilde{S}_1(\mathbf{Q}^{(i)}, \mathbf{W}^{(i)})$

Figures (7)

  • Figure 1: Double IRS-aided MU-MISO mmWave communication system with Alamouti scheme.
  • Figure 2: Main scenario of double IRS-aided MU-MISO mmWave communication utilizing the Alamouti Scheme.
  • Figure 3: Convergence of the proposed algorithm.
  • Figure 4: Comparison of the Achievable Rate of the Proposed algorithm with benchmark Schemes.
  • Figure 5: Performance Analysis of the Proposed Scheme with Increasing Reflecting Elements of IRSs and Changing User locations.
  • ...and 2 more figures