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Achievable Rate Optimization for Stacked Intelligent Metasurface-Assisted Holographic MIMO Communications

Anastasios Papazafeiropoulos, Jiancheng An, Pandelis Kourtessis, Tharmalingam Ratnarajah, Symeon Chatzinotas

TL;DR

This work investigates achievable-rate optimization for SIM-assisted HMIMO systems by jointly designing the transmit covariance ${\mathbf{Q}}$ and the unit-modulus phase shifts at transmitter and receiver SIMs. A simultaneous projected gradient method is proposed to update ${\mathbf{Q}}$, ${\boldsymbol{\phi}}_{l}$, and ${\boldsymbol{\psi}}_{k}$ together, with closed-form complex-valued gradients and projection operators ensuring feasibility; convergence is guaranteed by a Lipschitz-gradient constant $\Lambda$ and a backtracking line search. The paper demonstrates that the proposed algorithm attains the same maximum rate as alternating optimization (AO) benchmarks but with significantly fewer iterations and lower per-iteration complexity, highlighting substantial gains over single-RIS and conventional MIMO setups. Overall, the results support SIMs as a practical wave-domain processing platform for HMIMO, enabling near-digital performance with potentially reduced hardware costs.

Abstract

Stacked intelligent metasurfaces (SIM) is a revolutionary technology, which can outperform its single-layer counterparts by performing advanced signal processing relying on wave propagation. In this work, we exploit SIM to enable transmit precoding and receiver combining in holographic multiple-input multiple-output (HMIMO) communications, and we study the achievable rate by formulating a joint optimization problem of the SIM phase shifts at both sides of the transceiver and the covariance matrix of the transmitted signal. Notably, we propose its solution by means of an iterative optimization algorithm that relies on the projected gradient method, and accounts for all optimization parameters simultaneously. We also obtain the step size guaranteeing the convergence of the proposed algorithm. Simulation results provide fundamental insights such the performance improvements compared to the single-RIS counterpart and conventional MIMO system. Remarkably, the proposed algorithm results in the same achievable rate as the alternating optimization (AO) benchmark but with a less number of iterations.

Achievable Rate Optimization for Stacked Intelligent Metasurface-Assisted Holographic MIMO Communications

TL;DR

This work investigates achievable-rate optimization for SIM-assisted HMIMO systems by jointly designing the transmit covariance and the unit-modulus phase shifts at transmitter and receiver SIMs. A simultaneous projected gradient method is proposed to update , , and together, with closed-form complex-valued gradients and projection operators ensuring feasibility; convergence is guaranteed by a Lipschitz-gradient constant and a backtracking line search. The paper demonstrates that the proposed algorithm attains the same maximum rate as alternating optimization (AO) benchmarks but with significantly fewer iterations and lower per-iteration complexity, highlighting substantial gains over single-RIS and conventional MIMO setups. Overall, the results support SIMs as a practical wave-domain processing platform for HMIMO, enabling near-digital performance with potentially reduced hardware costs.

Abstract

Stacked intelligent metasurfaces (SIM) is a revolutionary technology, which can outperform its single-layer counterparts by performing advanced signal processing relying on wave propagation. In this work, we exploit SIM to enable transmit precoding and receiver combining in holographic multiple-input multiple-output (HMIMO) communications, and we study the achievable rate by formulating a joint optimization problem of the SIM phase shifts at both sides of the transceiver and the covariance matrix of the transmitted signal. Notably, we propose its solution by means of an iterative optimization algorithm that relies on the projected gradient method, and accounts for all optimization parameters simultaneously. We also obtain the step size guaranteeing the convergence of the proposed algorithm. Simulation results provide fundamental insights such the performance improvements compared to the single-RIS counterpart and conventional MIMO system. Remarkably, the proposed algorithm results in the same achievable rate as the alternating optimization (AO) benchmark but with a less number of iterations.
Paper Structure (18 sections, 4 theorems, 76 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 18 sections, 4 theorems, 76 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Channel Model
  5. Problem Formulation
  6. Achievable Rate Optimization
  7. Proposed Algorithm
  8. Complex-Valued Gradients of $f({\mathbf{Q}},{\bm{\phi}}_{l},{\bm{\psi}}_{k})$
  9. Projection Operations of Algorithm \ref{['Algoa1']}
  10. Convergence and Complexity Analyses
  11. Convergence Analysis
  12. Complexity Analysis
  13. Numerical Results
  14. Conclusion
  15. Proof of Lemma \ref{['lemmaGradient']}
  16. ...and 3 more sections

Key Result

Lemma 1

The gradients of $f({\mathbf{Q}},{\bm{\phi}}_{l},{\bm{\psi}}_{k})$ with respect to ${\mathbf{Q}}^{*}$, ${\bm{\phi}}_{l}^{*}$, and ${\bm{\psi}}_{k}^{*}$ are given by where

Figures (5)

  • Figure 1: A SIM-assisted HMIMO system.
  • Figure 2: Convergence of the proposed algorithm and dependence on the initialization.
  • Figure 3: Achievable rate versus the number of transmit metasurfaces layers $L$ for $K =2$ layers of receive metasurfaces. Impact of phase shifts optimization of the SIMs.
  • Figure 4: Achievable rate versus the number of transmit metasurfaces layers $L$ while varying the number of receiver metasurface layers $K$.
  • Figure 5: Impact of the numbers of meta-atoms per transmit layer and transmit antennas.

Theorems & Definitions (15)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Lemma 1
  • proof
  • Definition 1
  • Proposition 1
  • ...and 5 more