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Mutual Information Optimization for SIM-Based Holographic MIMO Systems

Nemanja Stefan Perović, Le-Nam Tran

TL;DR

The paper tackles MI optimization for SIM-based HMIMO systems with discrete signaling by replacing the intractable MI objective with the tractable channel cutoff rate $R_0$. It develops an alternating projected gradient method (APGM) that jointly optimizes transmit precoding $ ext{P}$ and the unit-modulus phase shifts of the transmit and receive SIM layers in a layer-by-layer fashion, using per-layer step sizes and line searches. Gradients for $ ext{P}$, $oldsymbol{ heta}$, and $oldsymbol{ u}$ are derived, with projections enforcing the unit-modulus constraints; the approach achieves significant CR improvements that translate into MI gains, and even modest digital precoding substantially boosts MI. The results validate CR as a practical proxy for MI optimization in SIM-based HMIMO and point to promising applications in integrated sensing and communication as well as potential optimality benchmarking.

Abstract

In the context of emerging stacked intelligent metasurface (SIM)-based holographic MIMO (HMIMO) systems, a fundamental problem is to study the mutual information (MI) between transmitted and received signals to establish their capacity. However, direct optimization or analytical evaluation of the MI, particularly for discrete signaling, is often intractable. To address this challenge, we adopt the channel cutoff rate (CR) as an alternative optimization metric for the MI maximization. In this regard, we propose an alternating projected gradient method (APGM), which optimizes the CR of a SIM-based HMIMO system by adjusting signal precoding and the phase shifts across the transmit and receive SIMs on a layer-by-layer basis. Simulation results indicate that the proposed algorithm significantly enhances the CR, achieving substantial gains, compared to the case with random SIM phase shifts, that are proportional to those observed for the corresponding MI. This justifies the effectiveness of using the channel CR for the MI optimization. Moreover, we demonstrate that the integration of digital precoding, even on a modest scale, has a significant impact on the ultimate performance of SIM-aided systems.

Mutual Information Optimization for SIM-Based Holographic MIMO Systems

TL;DR

The paper tackles MI optimization for SIM-based HMIMO systems with discrete signaling by replacing the intractable MI objective with the tractable channel cutoff rate . It develops an alternating projected gradient method (APGM) that jointly optimizes transmit precoding and the unit-modulus phase shifts of the transmit and receive SIM layers in a layer-by-layer fashion, using per-layer step sizes and line searches. Gradients for , , and are derived, with projections enforcing the unit-modulus constraints; the approach achieves significant CR improvements that translate into MI gains, and even modest digital precoding substantially boosts MI. The results validate CR as a practical proxy for MI optimization in SIM-based HMIMO and point to promising applications in integrated sensing and communication as well as potential optimality benchmarking.

Abstract

In the context of emerging stacked intelligent metasurface (SIM)-based holographic MIMO (HMIMO) systems, a fundamental problem is to study the mutual information (MI) between transmitted and received signals to establish their capacity. However, direct optimization or analytical evaluation of the MI, particularly for discrete signaling, is often intractable. To address this challenge, we adopt the channel cutoff rate (CR) as an alternative optimization metric for the MI maximization. In this regard, we propose an alternating projected gradient method (APGM), which optimizes the CR of a SIM-based HMIMO system by adjusting signal precoding and the phase shifts across the transmit and receive SIMs on a layer-by-layer basis. Simulation results indicate that the proposed algorithm significantly enhances the CR, achieving substantial gains, compared to the case with random SIM phase shifts, that are proportional to those observed for the corresponding MI. This justifies the effectiveness of using the channel CR for the MI optimization. Moreover, we demonstrate that the integration of digital precoding, even on a modest scale, has a significant impact on the ultimate performance of SIM-aided systems.
Paper Structure (7 sections, 1 theorem, 20 equations, 2 figures, 1 algorithm)

This paper contains 7 sections, 1 theorem, 20 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Problem Formulation
  4. Proposed Optimization Method
  5. Computational Complexity
  6. Simulation Results
  7. Conclusion

Key Result

Theorem 1

The gradients of $f(\mathbf{P},\boldsymbol{\phi},\boldsymbol{\psi})$ with respect to $\mathbf{P}^{*}$, $\boldsymbol{\phi}^{l*}$ and $\boldsymbol{\psi}^{k*}$ are given by where where $\boldsymbol{\Theta}^{m:n}=(\mathbf{W}^{m})^{H}(\boldsymbol{\mathbf{\Phi}}^{m})^{H}\cdots(\mathbf{W}^{n})^{H}(\boldsymbol{\mathbf{\Phi}}^{n})^{H}$ and $\boldsymbol{\Upsilon}^{m:n}=(\mathbf{\Psi}^{m})^{H}(\mathbf{U}^{

Figures (2)

  • Figure 1: CR and MI of the proposed APGM algorithm.
  • Figure 2: MI of the considered system with (w/-) and without (w/o) signal precoding ($M=4$).

Theorems & Definitions (1)

  • Theorem 1