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Robust Analysis of Full-Duplex Two-Way Space Shift Keying With RIS Systems

Xusheng Zhu, Wen Chen, Qingqing Wu, Wen Fang, Chaoying Huang, Jun Li

TL;DR

This work analyzes a RIS-assisted full-duplex two-way space shift keying system under imperfect CSI, modeling channels with correlation and estimation errors and deploying RISs near each user to overcome blocked direct links. It develops a ML-based detector framework and derives closed-form ABEP expressions using Gaussian-Chebyshev quadrature, along with upper bounds, asymptotic ABEP, outage probability, and throughput, all validated by Monte Carlo simulations. The analysis leverages CLT to approximate the combined channel statistics and reveals how the number of RIS elements and residual self-interference influence performance, showing FD can outperform HD at high SNR when LI is small or RIS size is large. The results provide practical insights into robustness against CSI imperfections and quantify the trade-offs between pilot overhead, RIS scale, and reliability in RIS-assisted FD-SSK networks, with potential extensions to hybrid RIS and spectral-reliability optimization.

Abstract

Reconfigurable intelligent surface (RIS)-assisted index modulation system schemes are considered a promising technology for sixth-generation (6G) wireless communication systems, which can enhance various system capabilities such as coverage and reliability. However, obtaining perfect channel state information (CSI) is challenging due to the lack of a radio frequency chain in RIS. In this paper, we investigate the RIS-assisted full-duplex (FD) two-way space shift keying (SSK) system under imperfect CSI, where the signal emissions are augmented by deploying RISs in the vicinity of two FD users. The maximum likelihood detector is utilized to recover the transmit antenna index. With this in mind, we derive closed-form average bit error probability (ABEP) expression based on the Gaussian-Chebyshev quadrature (GCQ) method and provide the upper bound and asymptotic ABEP expressions in the presence of channel estimation errors. To gain more insights, we also derive the outage probability and provide the throughput of the proposed scheme with imperfect CSI. The correctness of the analytical derivation results is confirmed via Monte Carlo simulations. It is demonstrated that increasing the number of elements of RIS can significantly improve the ABEP performance of the FD system over the half-duplex (HD) system. Furthermore, in the high SNR region, the ABEP performance of the FD system is better than that of the HD system.

Robust Analysis of Full-Duplex Two-Way Space Shift Keying With RIS Systems

TL;DR

This work analyzes a RIS-assisted full-duplex two-way space shift keying system under imperfect CSI, modeling channels with correlation and estimation errors and deploying RISs near each user to overcome blocked direct links. It develops a ML-based detector framework and derives closed-form ABEP expressions using Gaussian-Chebyshev quadrature, along with upper bounds, asymptotic ABEP, outage probability, and throughput, all validated by Monte Carlo simulations. The analysis leverages CLT to approximate the combined channel statistics and reveals how the number of RIS elements and residual self-interference influence performance, showing FD can outperform HD at high SNR when LI is small or RIS size is large. The results provide practical insights into robustness against CSI imperfections and quantify the trade-offs between pilot overhead, RIS scale, and reliability in RIS-assisted FD-SSK networks, with potential extensions to hybrid RIS and spectral-reliability optimization.

Abstract

Reconfigurable intelligent surface (RIS)-assisted index modulation system schemes are considered a promising technology for sixth-generation (6G) wireless communication systems, which can enhance various system capabilities such as coverage and reliability. However, obtaining perfect channel state information (CSI) is challenging due to the lack of a radio frequency chain in RIS. In this paper, we investigate the RIS-assisted full-duplex (FD) two-way space shift keying (SSK) system under imperfect CSI, where the signal emissions are augmented by deploying RISs in the vicinity of two FD users. The maximum likelihood detector is utilized to recover the transmit antenna index. With this in mind, we derive closed-form average bit error probability (ABEP) expression based on the Gaussian-Chebyshev quadrature (GCQ) method and provide the upper bound and asymptotic ABEP expressions in the presence of channel estimation errors. To gain more insights, we also derive the outage probability and provide the throughput of the proposed scheme with imperfect CSI. The correctness of the analytical derivation results is confirmed via Monte Carlo simulations. It is demonstrated that increasing the number of elements of RIS can significantly improve the ABEP performance of the FD system over the half-duplex (HD) system. Furthermore, in the high SNR region, the ABEP performance of the FD system is better than that of the HD system.
Paper Structure (15 sections, 1 theorem, 63 equations, 11 figures, 1 table)

This paper contains 15 sections, 1 theorem, 63 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Performance Analysis
  4. Pairwise Error Probability (PEP)
  5. GCQ Method
  6. Upper bound
  7. Asymptotic PEP
  8. Average Bit Error Probability (ABEP)
  9. Outage Probability
  10. Asymptotic Outage Probability
  11. Throughput
  12. Simulation and Analytical Results
  13. Verification
  14. System Performance Under Various Parameters
  15. Conclusions

Key Result

Theorem 1

The expectation and variance of $b_{n,\hat{l}}e^{j(\vartheta_{n,l}-\vartheta_{n,\hat{l}})}$ are respectively given by Proof: Without loss of generality, we make $x = \vartheta_{n,l}, y = \vartheta_{n,\hat{l}}$, and $z = \nu_n$. Then, the PDF of $X$ and $Y$ can be expressed respectively as $f_X(x)=\frac{1}{2\pi}, f_Y(y)=\frac{1}{2\pi}, x,y\in[-\pi,\pi].$ As a result, the PDF of the variable $z$ c

Figures (11)

  • Figure 1: System model.
  • Figure 2: The integral region varies with the variable $z$.
  • Figure 3: Verification of GCQ method.
  • Figure 4: Verification of correctness of analytical derivation.
  • Figure 5: Impact of fixed $\sigma_e^2$ on the proposed systems.
  • ...and 6 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Remark 1
  • Remark 2