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Capacity Maximization for RIS-assisted Multi-user MISO Communication Systems

M. S. S. Manasa, Kali Krishna Kota, Praful D. Mankar, Harpreet S. Dhillon

TL;DR

An RIS-enabled MU-MISO downlink is addressed by maximizing the capacity through maximizing the effective rank of the weighted channel covariance $\mathbf{H}\mathbf{R}_x\mathbf{H}^H$. A gradient-descent method optimizes RIS phase shifts $\boldsymbol{\theta}$ while low-complex MRT or MMSE precoding with water-filling designs the input covariance $\mathbf{R}_x$, with a key finding that MRT and MMSE become equivalent when the effective rank is maximized and the RIS has many elements. Numerical results show notable spectral-efficiency gains and convergence between MRT and MMSE as $N$ increases, highlighting the practical impact of RIS-driven rank conditioning on capacity and receiver design. The work delivers a low-complexity transmit strategy that leverages RIS to orthogonalize channel paths, enabling near-optimal performance in large-scale RIS deployments.

Abstract

We consider a multi-user multiple input single output (MU-MISO) system assisted by a reconfigurable intelligent surface (RIS). For such a system, we aim to optimally select the RIS phase shifts and precoding vectors for maximizing the effective rank of the weighted channel covariance matrix which in turn improves the channel capacity. For a low-complex transmitter design, we employ maximum ratio transmission (MRT) and minimum-mean square error (MMSE) precoding schemes along with water-filling algorithm-based power allocation. Further, we show that MRT and MMSE exhibit equivalent performance and become optimal when the channel effective rank is maximized by optimally configuring the RIS consisting of a large number of elements.

Capacity Maximization for RIS-assisted Multi-user MISO Communication Systems

TL;DR

An RIS-enabled MU-MISO downlink is addressed by maximizing the capacity through maximizing the effective rank of the weighted channel covariance . A gradient-descent method optimizes RIS phase shifts while low-complex MRT or MMSE precoding with water-filling designs the input covariance , with a key finding that MRT and MMSE become equivalent when the effective rank is maximized and the RIS has many elements. Numerical results show notable spectral-efficiency gains and convergence between MRT and MMSE as increases, highlighting the practical impact of RIS-driven rank conditioning on capacity and receiver design. The work delivers a low-complexity transmit strategy that leverages RIS to orthogonalize channel paths, enabling near-optimal performance in large-scale RIS deployments.

Abstract

We consider a multi-user multiple input single output (MU-MISO) system assisted by a reconfigurable intelligent surface (RIS). For such a system, we aim to optimally select the RIS phase shifts and precoding vectors for maximizing the effective rank of the weighted channel covariance matrix which in turn improves the channel capacity. For a low-complex transmitter design, we employ maximum ratio transmission (MRT) and minimum-mean square error (MMSE) precoding schemes along with water-filling algorithm-based power allocation. Further, we show that MRT and MMSE exhibit equivalent performance and become optimal when the channel effective rank is maximized by optimally configuring the RIS consisting of a large number of elements.
Paper Structure (9 sections, 1 theorem, 25 equations, 4 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 25 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Optimal RIS Configuration and Precoding
  4. Design of phase shifts
  5. Design of input covariance matrix
  6. MRT
  7. MMSE
  8. Numerical analysis
  9. Conclusion

Key Result

Lemma 1

MRT scheme provides capacity equal to that of the MMSE scheme when the effective rank of the weighted channel covariance matrix $\mathbf{HR}_x\mathbf{H}^H$ is maximized by optimally configuring RIS with infinitely large number of elements.

Figures (4)

  • Figure 1: Illustration of RIS-aided MU-MISO Downlink System.
  • Figure 2: SE v/s SNR.
  • Figure 3: Top: SE vs. $N$. Bottom: Effective Rank vs. $N$.
  • Figure 4: SE vs. $N$.

Theorems & Definitions (4)

  • Definition 1
  • Lemma 1
  • proof
  • Remark 1