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On the Performance of RIS-Aided Spatial Modulation for Downlink Transmission

Xusheng Zhu, Qingqing Wu, Wen Chen

TL;DR

The paper studies downlink RIS-assisted transmit spatial modulation (RIS-SM) with three detectors (ML, TSML, GD) and derives performance expressions under CLT-driven channel modeling. It provides closed-form or GCQ-based expressions for the conditional/unconditional pair error probability, ABEP via a union bound, and ergodic capacity approximations for the RIS-SM system, validated by Monte Carlo simulations. Key findings show that the greedy detector closely approaches ML performance with much lower complexity, while the TSML detector can fail under certain conditions; increasing RIS elements improves CLT accuracy and ABEP behavior, and RIS phase errors degrade performance. The work offers practical insights into RIS-SM design, highlighting phase-control accuracy and detector choice as critical design levers, and presents tractable analytical tools for system optimization in downlink RIS-enabled networks.

Abstract

In this study, we explore the performance of a reconfigurable reflecting surface (RIS)-assisted transmit spatial modulation (SM) system for downlink transmission, wherein the deployment of RIS serves the purpose of blind area coverage within the channel. At the receiving end, we present three detectors, i.e., maximum likelihood (ML) detector, two-stage ML detection, and greedy detector to recover the transmitted signal. By utilizing the ML detector, we initially derive the conditional pair error probability expression for the proposed scheme. Subsequently, we leverage the central limit theorem (CLT) to obtain the probability density function of the combined channel. Following this, the Gaussian-Chebyshev quadrature method is applied to derive a closed-form expression for the unconditional pair error probability and establish the union tight upper bound for the average bit error probability (ABEP). Furthermore, we derive a closed-form expression for the ergodic capacity of the proposed RIS-SM scheme. Monte Carlo simulations are conducted not only to assess the complexity and reliability of the three detection algorithms but also to validate the results obtained through theoretical derivation results.

On the Performance of RIS-Aided Spatial Modulation for Downlink Transmission

TL;DR

The paper studies downlink RIS-assisted transmit spatial modulation (RIS-SM) with three detectors (ML, TSML, GD) and derives performance expressions under CLT-driven channel modeling. It provides closed-form or GCQ-based expressions for the conditional/unconditional pair error probability, ABEP via a union bound, and ergodic capacity approximations for the RIS-SM system, validated by Monte Carlo simulations. Key findings show that the greedy detector closely approaches ML performance with much lower complexity, while the TSML detector can fail under certain conditions; increasing RIS elements improves CLT accuracy and ABEP behavior, and RIS phase errors degrade performance. The work offers practical insights into RIS-SM design, highlighting phase-control accuracy and detector choice as critical design levers, and presents tractable analytical tools for system optimization in downlink RIS-enabled networks.

Abstract

In this study, we explore the performance of a reconfigurable reflecting surface (RIS)-assisted transmit spatial modulation (SM) system for downlink transmission, wherein the deployment of RIS serves the purpose of blind area coverage within the channel. At the receiving end, we present three detectors, i.e., maximum likelihood (ML) detector, two-stage ML detection, and greedy detector to recover the transmitted signal. By utilizing the ML detector, we initially derive the conditional pair error probability expression for the proposed scheme. Subsequently, we leverage the central limit theorem (CLT) to obtain the probability density function of the combined channel. Following this, the Gaussian-Chebyshev quadrature method is applied to derive a closed-form expression for the unconditional pair error probability and establish the union tight upper bound for the average bit error probability (ABEP). Furthermore, we derive a closed-form expression for the ergodic capacity of the proposed RIS-SM scheme. Monte Carlo simulations are conducted not only to assess the complexity and reliability of the three detection algorithms but also to validate the results obtained through theoretical derivation results.
Paper Structure (24 sections, 5 theorems, 89 equations, 10 figures, 1 table)

This paper contains 24 sections, 5 theorems, 89 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Model of RIS-SM Scheme
  4. Signal Detection of RIS-SM Scheme
  5. ML Detector
  6. TSML Detector
  7. GD
  8. Performance Analysis
  9. CPEP
  10. UPEP
  11. Correct transmit antenna detection $\hat{n}_t = n_t$
  12. Erroneous transmit antenna detection $\hat{n}_t \neq n_t$
  13. ABEP
  14. Ergodic Capacity Analysis
  15. Simulation and Analytical Results
  16. ...and 9 more sections

Key Result

Theorem 1

The distribution of variable $\xi$ can be described as where the mean and variance can be denoted as $\mu_\xi=\frac{L\pi}{4}$ and $\sigma_\xi^2=\frac{L(16-\pi^2)}{16}$, respectively.

Figures (10)

  • Figure 1: The RIS-assisted SM system model.
  • Figure 2: Complexity analysis of different detectors.
  • Figure 3: The received power with respect to different transmit antennas.
  • Figure 4: Comparison of ABEP performance with different detectors.
  • Figure 5: Verification of the CLT-based analytical ABEP results.
  • ...and 5 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Theorem 2
  • Lemma 1
  • Lemma 2
  • Theorem 3