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Multi-Group Multicasting Systems Using Multiple RISs

Hyeongtaek Lee, Seungsik Moon, Youngjoo Lee, Jaeky Oh, Jaehoon Chung, Junil Choi

TL;DR

This work tackles inter-group interference in downlink multi-group multicasting aided by multiple distributed RISs. It introduces two complementary beamforming strategies: a BD-based approach that completely cancels inter-group interference at the cost of high complexity, and an MTZF method that uses representative-group channels with a loss-minimizing RIS design to achieve much lower complexity while remaining effective. The BD strategy relies on SVD-based null-space projections and SDR-driven RIS optimization to maximize the minimum group rate, while MTZF leverages Neumann-series approximations and a closed-form RIS update to minimize the loss from interference nulling. Numerical results show MTZF outperforms BD in moderate to low BS antenna regimes and that both schemes significantly improve performance over a single-RIS baseline, demonstrating the practical benefits of distributed RISs with group-specific RIS operations for scalable multi-group multicasting.

Abstract

In this paper, practical utilization of multiple distributed reconfigurable intelligent surfaces (RISs), which are able to conduct group-specific operations, for multi-group multicasting systems is investigated. To tackle the inter-group interference issue in the multi-group multicasting systems, the block diagonalization (BD)-based beamforming is considered first. Without any inter-group interference after the BD operation, the multiple distributed RISs are operated to maximize the minimum rate for each group. Since the computational complexity of the BD-based beamforming can be too high, a multicasting tailored zero-forcing (MTZF) beamforming technique is proposed to efficiently suppress the inter-group interference, and the novel design for the multiple RISs that makes up for the inevitable loss of MTZF beamforming is also described. Effective closed-form solutions for the loss minimizing RIS operations are obtained with basic linear operations, making the proposed MTZF beamforming-based RIS design highly practical. Numerical results show that the BD-based approach has ability to achieve high sum-rate, but it is useful only when the base station deploys large antenna arrays. Even with the small number of antennas, the MTZF beamforming-based approach outperforms the other schemes in terms of the sum-rate while the technique requires low computational complexity. The results also prove that the proposed techniques can work with the minimum rate requirement for each group.

Multi-Group Multicasting Systems Using Multiple RISs

TL;DR

This work tackles inter-group interference in downlink multi-group multicasting aided by multiple distributed RISs. It introduces two complementary beamforming strategies: a BD-based approach that completely cancels inter-group interference at the cost of high complexity, and an MTZF method that uses representative-group channels with a loss-minimizing RIS design to achieve much lower complexity while remaining effective. The BD strategy relies on SVD-based null-space projections and SDR-driven RIS optimization to maximize the minimum group rate, while MTZF leverages Neumann-series approximations and a closed-form RIS update to minimize the loss from interference nulling. Numerical results show MTZF outperforms BD in moderate to low BS antenna regimes and that both schemes significantly improve performance over a single-RIS baseline, demonstrating the practical benefits of distributed RISs with group-specific RIS operations for scalable multi-group multicasting.

Abstract

In this paper, practical utilization of multiple distributed reconfigurable intelligent surfaces (RISs), which are able to conduct group-specific operations, for multi-group multicasting systems is investigated. To tackle the inter-group interference issue in the multi-group multicasting systems, the block diagonalization (BD)-based beamforming is considered first. Without any inter-group interference after the BD operation, the multiple distributed RISs are operated to maximize the minimum rate for each group. Since the computational complexity of the BD-based beamforming can be too high, a multicasting tailored zero-forcing (MTZF) beamforming technique is proposed to efficiently suppress the inter-group interference, and the novel design for the multiple RISs that makes up for the inevitable loss of MTZF beamforming is also described. Effective closed-form solutions for the loss minimizing RIS operations are obtained with basic linear operations, making the proposed MTZF beamforming-based RIS design highly practical. Numerical results show that the BD-based approach has ability to achieve high sum-rate, but it is useful only when the base station deploys large antenna arrays. Even with the small number of antennas, the MTZF beamforming-based approach outperforms the other schemes in terms of the sum-rate while the technique requires low computational complexity. The results also prove that the proposed techniques can work with the minimum rate requirement for each group.
Paper Structure (13 sections, 1 theorem, 36 equations, 8 figures, 1 table, 2 algorithms)

This paper contains 13 sections, 1 theorem, 36 equations, 8 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. BD-based Beamforming with Minimum Rate Maximizing RISs Design
  4. BD-Based Beamforming Technique
  5. Minimum Rate Maximizing Multiple RISs Design
  6. Algorithm Description and Complexity Analysis
  7. MTZF Beamforming with Loss Minimizing RISs Design
  8. Proposed MTZF Beamforming Technique
  9. Low-Complexity Approximation of MTZF Beamforming Vectors without Matrix Inversion
  10. Proposed Loss Minimizing Multiple RISs Design
  11. Algorithm Description and Complexity Analysis
  12. Numerical Results
  13. Conclusion

Key Result

Lemma 1

For any complex number $\alpha$ and complex vector $\boldsymbol{\beta}$, the optimal solution of $\boldsymbol{\theta}$ that maximizes $\left\vert \alpha+\boldsymbol{\theta}^\mathrm{H} \boldsymbol{\beta} \right\vert$ with unit-norm constraint on the elements of $\boldsymbol{\theta}$ is given by $e^{j

Figures (8)

  • Figure 1: Conceptual figure of multi-group multicasting communication system utilizing multiple distributed RISs.
  • Figure 2: Positions of BS and each group's center with distributed RISs when $G=4$.
  • Figure 3: Average sum-rate performance according to $P_\mathrm{T}$ with $N=2 \times 8$, $G=3$, and $K_g=4$. The solid lines are the case of $M_g=8\times 3$, and $M_g=8\times 4$ is considered for the dashed lines.
  • Figure 4: Average sum-rate performance according to $P_\mathrm{T}$ with $M_g=8\times 3$, $G=3$, and $K_g=4$. The solid lines are the case of $N=2\times 8$, and $N=3\times 8$ is considered for the dashed lines.
  • Figure 5: Average sum-rate performance according to $N$ with $M_g=8\times 3$, $G=3$, $K_g=4$, and $P_\mathrm{T}=$30 dBm.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Lemma 1
  • proof