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Active and Passive Beamforming Designs for SER Minimization in RIS-Assisted MIMO Systems

Trinh Van Chien, Bui Trong Duc, Ho Viet Duc Luong, Huynh Thi Thanh Binh, Hien Quoc Ngo, Symeon Chatzinotas

TL;DR

This work tackles the problem of minimizing average symbol error rate (SER) in RIS-assisted MIMO downlinks by deriving a closed-form per-user SER under modulated signaling and mutual interference, framed as a non-convex NP-hard optimization over active beamforming vectors and RIS phase shifts. It introduces an improved differential evolution (DE) algorithm with local search and SHADE-style parameter adaptation to jointly design active and passive beamformers, validated against Monte Carlo simulations. The results show that the proposed joint optimization outperforms benchmarks across various user counts, RIS sizes, and channel conditions, demonstrating significant SER reductions and robustness to CSI imperfections. The approach provides a scalable, model-agnostic path to enhance reliability in RIS-enabled 6G networks by exploiting both active transmit beamforming and RIS phase control.

Abstract

This research exploits the applications of reconfigurable intelligent surface (RIS)-assisted multiple input multiple output (MIMO) systems, specifically addressing the enhancement of communication reliability with modulated signals. Specifically, we first derive the analytical downlink symbol error rate (SER) of each user as a multivariate function of both the phase-shift and beamforming vectors. The analytical SER enables us to obtain insights into the synergistic dynamics between the RIS and MIMO communication. We then introduce a novel average SER minimization problem subject to the practical constraints of the transmitted power budget and phase shift coefficients, which is NP-hard. By incorporating the differential evolution (DE) algorithm as a pivotal tool for optimizing the intricate active and passive beamforming variables in RIS-assisted communication systems, the non-convexity of the considered SER optimization problem can be effectively handled. Furthermore, an efficient local search is incorporated into the DE algorithm to overcome the local optimum, and hence offer low SER and high communication reliability. Monte Carlo simulations validate the analytical results and the proposed optimization framework, indicating that the joint active and passive beamforming design is superior to the other benchmarks.

Active and Passive Beamforming Designs for SER Minimization in RIS-Assisted MIMO Systems

TL;DR

This work tackles the problem of minimizing average symbol error rate (SER) in RIS-assisted MIMO downlinks by deriving a closed-form per-user SER under modulated signaling and mutual interference, framed as a non-convex NP-hard optimization over active beamforming vectors and RIS phase shifts. It introduces an improved differential evolution (DE) algorithm with local search and SHADE-style parameter adaptation to jointly design active and passive beamformers, validated against Monte Carlo simulations. The results show that the proposed joint optimization outperforms benchmarks across various user counts, RIS sizes, and channel conditions, demonstrating significant SER reductions and robustness to CSI imperfections. The approach provides a scalable, model-agnostic path to enhance reliability in RIS-enabled 6G networks by exploiting both active transmit beamforming and RIS phase control.

Abstract

This research exploits the applications of reconfigurable intelligent surface (RIS)-assisted multiple input multiple output (MIMO) systems, specifically addressing the enhancement of communication reliability with modulated signals. Specifically, we first derive the analytical downlink symbol error rate (SER) of each user as a multivariate function of both the phase-shift and beamforming vectors. The analytical SER enables us to obtain insights into the synergistic dynamics between the RIS and MIMO communication. We then introduce a novel average SER minimization problem subject to the practical constraints of the transmitted power budget and phase shift coefficients, which is NP-hard. By incorporating the differential evolution (DE) algorithm as a pivotal tool for optimizing the intricate active and passive beamforming variables in RIS-assisted communication systems, the non-convexity of the considered SER optimization problem can be effectively handled. Furthermore, an efficient local search is incorporated into the DE algorithm to overcome the local optimum, and hence offer low SER and high communication reliability. Monte Carlo simulations validate the analytical results and the proposed optimization framework, indicating that the joint active and passive beamforming design is superior to the other benchmarks.
Paper Structure (23 sections, 5 theorems, 69 equations, 13 figures, 1 table, 1 algorithm)

This paper contains 23 sections, 5 theorems, 69 equations, 13 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. RIS-Assisted System Model and Downlink Symbol Error Rate
  3. Downlink Data Transmission
  4. Analysis of Symbol Error Rate
  5. Symbol Error Rate Analysis with Linear Beamforming Techniques
  6. Active and Passive Beamforming Designs for Symbol Error Rate Optimization
  7. Joint Active and Passive Beamforming Design
  8. Passive Beamforming Design with Linear Precoding
  9. Improved Differential Evolution-based Active and Passive Beamforming Designs
  10. Improved Different Evolution with Local Search
  11. Solution representation and population initialization
  12. Mutation
  13. Crossover
  14. Selection
  15. Local search
  16. ...and 8 more sections

Key Result

Lemma 1

The analytical downlink SER of user $k$ is where the signal-to-interference-and-noise ratio of user $k$, denoted by $\mathsf{SINR}_k(\{ \mathbf{w}_k \}, \pmb{\Phi})$, is driven based on the received signal in eq:rk as and $\mathrm{erfc}(\cdot)$ is the complementary error function defined as ${ \operatorname{erfc}(z) = 1 - \operatorname{erf}(z) = \frac{2}{\sqrt{\pi}} \int_{z}^{\infty} e^{-t^2}\op

Figures (13)

  • Figure 1: The considered RIS-assisted MIMO system model where a BS serves multiple users.
  • Figure 2: An example of 16-QAM with the Voronoi regions of the constellation points.
  • Figure 3: Followchart of the joint active and passive beamforming designs by the improved DE algorithm with a local search.
  • Figure 4: An individual with $N = 4$, $M = 2$, and $K = 2$.
  • Figure 5: SER of a RIS-assisted multiuser MIMO system with the different number of users in the network.
  • ...and 8 more figures

Theorems & Definitions (13)

  • Lemma 1
  • proof
  • Corollary 1
  • proof
  • Lemma 2
  • proof
  • Remark 1
  • Example 1
  • Theorem 1
  • proof
  • ...and 3 more