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Low-Cost Physical-Layer Security Design for IRS-Assisted mMIMO Systems with One-Bit DACs

Weijie Xiong, Jian Yang, Jingran Lin, Hongli Liu, Zhiling Xiao, Qiang Li

TL;DR

Two algorithms are proposed that transform the SRM problem into an unconstrained optimization over a product Riemannian manifold, eliminating auxiliary variables and enabling faster convergence with a slight trade-off in secrecy performance, and are proven to converge to Karush-Kuhn-Tucker points.

Abstract

Integrating massive multiple-input multiple-output (mMIMO) systems with intelligent reflecting surfaces (IRS) presents a promising paradigm for enhancing physical-layer security (PLS) in wireless communications. However, deploying high-resolution quantizers in large-scale mMIMO arrays, along with numerous IRS elements, leads to substantial hardware complexity. To address these challenges, this paper proposes a cost-effective PLS design for IRS-assisted mMIMO systems by employing one-bit digital-to-analog converters (DACs). The focus is on jointly optimizing one-bit quantized precoding at the transmitter and constant-modulus phase shifts at the IRS to maximize the secrecy rate. This leads to a highly non-convex fractional secrecy rate maximization (SRM) problem. To efficiently solve this problem, two algorithms are proposed: (1) the WMMSE-PDD algorithm, which reformulates the SRM problem into a sequence of non-fractional programs with auxiliary variables using the weighted minimum mean-square error (WMMSE) method and solves them via the penalty dual decomposition (PDD) approach, achieving superior secrecy performance; and (2) the exact penalty product Riemannian gradient descent (EPPRGD) algorithm, which transforms the SRM problem into an unconstrained optimization over a product Riemannian manifold, eliminating auxiliary variables and enabling faster convergence with a slight trade-off in secrecy performance. Both algorithms provide analytical solutions at each iteration and are proven to converge to Karush-Kuhn-Tucker (KKT) points. Simulation results confirm the effectiveness of the proposed methods and highlight their respective advantages.

Low-Cost Physical-Layer Security Design for IRS-Assisted mMIMO Systems with One-Bit DACs

TL;DR

Two algorithms are proposed that transform the SRM problem into an unconstrained optimization over a product Riemannian manifold, eliminating auxiliary variables and enabling faster convergence with a slight trade-off in secrecy performance, and are proven to converge to Karush-Kuhn-Tucker points.

Abstract

Integrating massive multiple-input multiple-output (mMIMO) systems with intelligent reflecting surfaces (IRS) presents a promising paradigm for enhancing physical-layer security (PLS) in wireless communications. However, deploying high-resolution quantizers in large-scale mMIMO arrays, along with numerous IRS elements, leads to substantial hardware complexity. To address these challenges, this paper proposes a cost-effective PLS design for IRS-assisted mMIMO systems by employing one-bit digital-to-analog converters (DACs). The focus is on jointly optimizing one-bit quantized precoding at the transmitter and constant-modulus phase shifts at the IRS to maximize the secrecy rate. This leads to a highly non-convex fractional secrecy rate maximization (SRM) problem. To efficiently solve this problem, two algorithms are proposed: (1) the WMMSE-PDD algorithm, which reformulates the SRM problem into a sequence of non-fractional programs with auxiliary variables using the weighted minimum mean-square error (WMMSE) method and solves them via the penalty dual decomposition (PDD) approach, achieving superior secrecy performance; and (2) the exact penalty product Riemannian gradient descent (EPPRGD) algorithm, which transforms the SRM problem into an unconstrained optimization over a product Riemannian manifold, eliminating auxiliary variables and enabling faster convergence with a slight trade-off in secrecy performance. Both algorithms provide analytical solutions at each iteration and are proven to converge to Karush-Kuhn-Tucker (KKT) points. Simulation results confirm the effectiveness of the proposed methods and highlight their respective advantages.
Paper Structure (35 sections, 9 theorems, 79 equations, 10 figures, 2 tables, 2 algorithms)

This paper contains 35 sections, 9 theorems, 79 equations, 10 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Proposed WMMSE-PDD Algorithm
  4. Smoothing of the One-Bit Constraint (\ref{['cons1orig2']})
  5. Problem Transformation by WMMSE method
  6. Realization of the PDD-based Algorithm
  7. Update $w_b$ and $w_e$
  8. Update $\bf v$
  9. Update $\bf x$
  10. Update $\bm \theta$
  11. Update $\bf t$
  12. Update $\bm \phi$
  13. Overview of the WMMSE-PDD Algorithm
  14. Analysis of computation complexity
  15. Analysis of Convergence
  16. ...and 20 more sections

Key Result

Lemma 3.1

Let $\mathcal{X} =\bigl\{\pm\sqrt{\tfrac{1}{2M}}\pm j\sqrt{\tfrac{1}{2M}}\bigr\}$, and let $\mathbf x\in\mathbb C^{M}$. Then, the following statements are equivalent,

Figures (10)

  • Figure 1: The structure of the proposed PDD-based algorithm.
  • Figure 2: Convergence performance of the WMMSE-PDD algorithm.
  • Figure 3: Convergence performance of the EPPRGD algorithm.
  • Figure 4: Comparison of empirical runtime among architectures on the first twenty randomly generated channels.
  • Figure 5: Comparison of secrecy rates among architectures as the number of antennas at Alice ($M$) increases from 32 to 1024.
  • ...and 5 more figures

Theorems & Definitions (9)

  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • Lemma 3.4
  • Theorem 3.1
  • Theorem 3.2
  • Lemma 4.1
  • Theorem 4.1
  • Theorem 4.2