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Interference Minimization in Beyond-Diagonal RIS-assisted MIMO Interference Channels

Ignacio Santamaria, Mohammad Soleymani, Eduard Jorswieck, Jesus Gutierrez

TL;DR

The paper tackles interference in $K$-user MIMO interference channels aided by a beyond-diagonal RIS (BD-RIS). It introduces a two-stage framework: Stage I passively designs a BD-RIS with a symmetric unitary matrix to minimize interference leakage (IL), and Stage II designs the users’ active precoders to cope with residual interference under criteria such as min-IL, max-SINR, or max-SR. The authors propose a geodesic manifold optimization on the unitary group leveraging Takagi factorization for fully-connected BD-RIS, plus a relax-then-project (RtP) suboptimal method and a group-connected extension to reduce complexity; they also analyze an unconstrained BD-RIS IL-zero condition. Simulations show that max-SR precoding yields substantial gains (e.g., >20% sum-rate improvement) especially for moderate BD-RIS sizes and high transmit power, and demonstrate that when IL can be suppressed below noise, the system approaches parallel MIMO channels. The work highlights BD-RIS deployment and architecture as key levers for practical interference management in future 6G networks, with notable gains from joint BD-RIS and precoder optimization and scalable group-connected designs.

Abstract

This paper proposes a two-stage approach for passive and active beamforming in multiple-input multiple-output (MIMO) interference channels (ICs) assisted by a beyond-diagonal reconfigurable intelligent surface (BD-RIS). In the first stage, the passive BD-RIS is designed to minimize the aggregate interference power at all receivers, a cost function called interference leakage (IL). To this end, we propose an optimization algorithm in the manifold of unitary matrices and a suboptimal but computationally efficient solution. In the second stage, users' active precoders are designed under different criteria such as minimizing the IL (min-IL), maximizing the signal-to-interference-plus-noise ratio (max-SINR), or maximizing the sum rate (max-SR). The residual interference not cancelled by the BD-RIS is treated as noise by the precoders. Our simulation results show that the max-SR precoders provide more than 20% sum rate improvement compared to other designs, especially when the BD-RIS has a moderate number of elements ($M<20$) and users transmit with high power, in which case the residual interference is still significant.

Interference Minimization in Beyond-Diagonal RIS-assisted MIMO Interference Channels

TL;DR

The paper tackles interference in -user MIMO interference channels aided by a beyond-diagonal RIS (BD-RIS). It introduces a two-stage framework: Stage I passively designs a BD-RIS with a symmetric unitary matrix to minimize interference leakage (IL), and Stage II designs the users’ active precoders to cope with residual interference under criteria such as min-IL, max-SINR, or max-SR. The authors propose a geodesic manifold optimization on the unitary group leveraging Takagi factorization for fully-connected BD-RIS, plus a relax-then-project (RtP) suboptimal method and a group-connected extension to reduce complexity; they also analyze an unconstrained BD-RIS IL-zero condition. Simulations show that max-SR precoding yields substantial gains (e.g., >20% sum-rate improvement) especially for moderate BD-RIS sizes and high transmit power, and demonstrate that when IL can be suppressed below noise, the system approaches parallel MIMO channels. The work highlights BD-RIS deployment and architecture as key levers for practical interference management in future 6G networks, with notable gains from joint BD-RIS and precoder optimization and scalable group-connected designs.

Abstract

This paper proposes a two-stage approach for passive and active beamforming in multiple-input multiple-output (MIMO) interference channels (ICs) assisted by a beyond-diagonal reconfigurable intelligent surface (BD-RIS). In the first stage, the passive BD-RIS is designed to minimize the aggregate interference power at all receivers, a cost function called interference leakage (IL). To this end, we propose an optimization algorithm in the manifold of unitary matrices and a suboptimal but computationally efficient solution. In the second stage, users' active precoders are designed under different criteria such as minimizing the IL (min-IL), maximizing the signal-to-interference-plus-noise ratio (max-SINR), or maximizing the sum rate (max-SR). The residual interference not cancelled by the BD-RIS is treated as noise by the precoders. Our simulation results show that the max-SR precoders provide more than 20% sum rate improvement compared to other designs, especially when the BD-RIS has a moderate number of elements () and users transmit with high power, in which case the residual interference is still significant.

Paper Structure

This paper contains 34 sections, 3 theorems, 36 equations, 8 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Related work on BD-RIS optimization
  4. Motivation
  5. Contributions
  6. Paper outline and notations
  7. BD-RIS-assisted MIMO IC
  8. Signal model
  9. Proposed two-stage optimization framework
  10. Stage I: BD-RIS design to minimize interference
  11. Problem statement
  12. Unconstrained BD-RIS
  13. Manifold optimization algorithm
  14. Computational complexity
  15. A relax-then-project suboptimal solution
  16. ...and 19 more sections

Key Result

Lemma 1

Consider a genericMeaning that all channels are independent of each other and their entries are also independently drawn from a continuous distribution.$K$-user MIMO-IC $(N_{T_k} \times N_{R_k}, d_k)^K$ assisted by an unconstrained BD-RIS, $\bm{\Theta}$, optimized to minimize the IL cost function in

Figures (8)

  • Figure 1: BD-RIS-assisted $K$-user MIMO IC. Dashed lines represent the direct Tx-Rx links; solid lines represent the channels through the BD-RIS.
  • Figure 2: Simulation setup for the RIS-assisted MIMO-IC.
  • Figure 3: $\Delta{\text{INR}}$ in dB as a function of the position of a BD-RIS with $M=40$ elements in a $(3 \times 3,2)^3$ MIMO-IC.
  • Figure 4: Convergence of the MO iterative algorithm for a fully-connected BD-RIS with $M=40$ elements. Each curve shows the convergence for a different random initialization.
  • Figure 5: Run time of the MO and RtP algorithms for the group-connected BD-RIS architecture vs. $M$ (total number of BD-RIS elements).
  • ...and 3 more figures

Theorems & Definitions (7)

  • Lemma 1
  • proof
  • Remark 1
  • Remark 2
  • Lemma 2: soleymani2022improper
  • Lemma 3: soleymani2024optimization
  • Remark 3