Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Decentralized Cooperative Beamforming for BDRIS-Assisted Cell-Free MIMO OFDM Systems

Konstantinos D. Katsanos, George C. Alexandropoulos

TL;DR

The paper tackles high-rate, wideband downlink in a cell-free MIMO-OFDM system aided by multiple shared Beyond Diagonal RISs (BDRISs) and develops a decentralized cooperative beamforming framework to maximize the sum-rate under imperfect CSI.A Dynamic Group-Connected (DGC) RIS architecture is proposed to add frequency-dependent control, and a consensus-based stochastic successive concave approximation (CSD-SCA) algorithm enables each BS to optimize its local precoding and RIS parameters while agreeing on shared RIS configurations.Key contributions include closed-form precoder updates, gradient-tracked RIS capacitor optimization via Dykstra-like projections, LSAP-based RIS permutation optimization, and adaptive network weights that accelerate consensus, all with proven convergence under standard assumptions.Numerical results show that DGC-BDRISs closely approach fully connected RIS performance, outperform noncooperative and diagonal RIS benchmarks, and offer robust performance against imperfect CSI, highlighting practical benefits for scalable, high-capacity wireless deployments.

Abstract

In this paper, a wideband cell-free multi-stream multi-user Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) system is considered operating within a smart wireless environment enabled by multiple Beyond Diagonal Reconfigurable Intelligent Surfaces (BDRISs). A novel decentralized active and passive beamforming framework, robust to imperfect channel state availability and with minimal cooperation among the system's multiple Base Stations (BSs) for deciding the final configurations of the shared BDRISs, is proposed, which aims to substantially reduce the overhead inherent in centralized solutions necessitating a central processing unit of high computational power. By considering a Dynamic Group-Connected (DGC) BDRIS architecture with frequency-selective responses per unit element, we formulate the system's sum-rate maximization problem with respect to the tunable capacitances and permutation matrices of the BDRISs as well as the precoding matrices of the BSs, which is solved via successive concave approximation and alternating projections as well as consensus-based updates for the BDRISs' design. Through extensive simulation results, it is showcased that the proposed robust decentralized cooperative approach with diverse BDRIS architectures outperforms non-cooperation benchmarks. It is also demonstrated that the considered DGC BDRIS architecture is able to provide sum-rate performance gains sufficiently close to the more complex fully-connected BDRIS structure.

Decentralized Cooperative Beamforming for BDRIS-Assisted Cell-Free MIMO OFDM Systems

TL;DR

The paper tackles high-rate, wideband downlink in a cell-free MIMO-OFDM system aided by multiple shared Beyond Diagonal RISs (BDRISs) and develops a decentralized cooperative beamforming framework to maximize the sum-rate under imperfect CSI.A Dynamic Group-Connected (DGC) RIS architecture is proposed to add frequency-dependent control, and a consensus-based stochastic successive concave approximation (CSD-SCA) algorithm enables each BS to optimize its local precoding and RIS parameters while agreeing on shared RIS configurations.Key contributions include closed-form precoder updates, gradient-tracked RIS capacitor optimization via Dykstra-like projections, LSAP-based RIS permutation optimization, and adaptive network weights that accelerate consensus, all with proven convergence under standard assumptions.Numerical results show that DGC-BDRISs closely approach fully connected RIS performance, outperform noncooperative and diagonal RIS benchmarks, and offer robust performance against imperfect CSI, highlighting practical benefits for scalable, high-capacity wireless deployments.

Abstract

In this paper, a wideband cell-free multi-stream multi-user Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) system is considered operating within a smart wireless environment enabled by multiple Beyond Diagonal Reconfigurable Intelligent Surfaces (BDRISs). A novel decentralized active and passive beamforming framework, robust to imperfect channel state availability and with minimal cooperation among the system's multiple Base Stations (BSs) for deciding the final configurations of the shared BDRISs, is proposed, which aims to substantially reduce the overhead inherent in centralized solutions necessitating a central processing unit of high computational power. By considering a Dynamic Group-Connected (DGC) BDRIS architecture with frequency-selective responses per unit element, we formulate the system's sum-rate maximization problem with respect to the tunable capacitances and permutation matrices of the BDRISs as well as the precoding matrices of the BSs, which is solved via successive concave approximation and alternating projections as well as consensus-based updates for the BDRISs' design. Through extensive simulation results, it is showcased that the proposed robust decentralized cooperative approach with diverse BDRIS architectures outperforms non-cooperation benchmarks. It is also demonstrated that the considered DGC BDRIS architecture is able to provide sum-rate performance gains sufficiently close to the more complex fully-connected BDRIS structure.
Paper Structure (20 sections, 4 theorems, 49 equations, 6 figures, 2 algorithms)

This paper contains 20 sections, 4 theorems, 49 equations, 6 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. BDRIS Architecture and Frequency-Dependent Response
  5. Received Signal Model
  6. System Design Objective
  7. Distributed Sum-Rate Maximization
  8. Precoding Optimization at Each $b$-th BS
  9. BDRIS Phase Configuration Optimization at Each $b$-th BS
  10. RIS Permutation Matrix Optimization at Each $b$-th BS
  11. Overall Decentralized Cooperative Solution
  12. Convergence and Complexity Analysis
  13. Adaptive Weights for $\boldsymbol{\mathbf{V}}_{\rm net}^t$
  14. Numerical Results and Discussion
  15. Simulation Setup
  16. ...and 5 more sections

Key Result

Lemma 1

Let the following matrix definitions: $\boldsymbol{\mathbf{T}}_{u,k} \triangleq \boldsymbol{\mathbf{S}}_{u,u,k}\boldsymbol{\mathbf{S}}_{u,u,k}^{\rm H} + \boldsymbol{\mathbf{P}}_{u,k}$, $\boldsymbol{\mathbf{L}}_{u,k} \triangleq \boldsymbol{\mathbf{I}}_{N_s} - \boldsymbol{\mathbf{S}}_{u,u,k}^{\rm H}\b

Figures (6)

  • Figure 1: The $xy$-plane of the simulated in $3$D cell-free MIMO system including $B=4$ BSs and $R=2$ shared BDRISs. Each node's coordinates include the distances $x$, $y$, and $z$ along the corresponding axes. The positions of the UEs have been randomly selected from two clusters, each with $U=4$ UEs, with the setting $y_{cl}=57.5\,m$.
  • Figure 2: Convergence behavior of the achievable sum rate with Algorithm \ref{['alg:OP_Overall_Distr_Alg']} for different transmit power levels $P^{\max}$, considering $M=64$ unit elements for each one of the deployed BDRISs.
  • Figure 3: Consensus error for the BDRIS parameters $\widetilde{\boldsymbol{\mathbf{C}}}$ and $\widetilde{\boldsymbol{\mathbf{Q}}}_p$ with respect to the number of iterations in Algorithm \ref{['alg:OP_Overall_Distr_Alg']}, considering both static and adaptive weights for the network graph matrix $\boldsymbol{\mathbf{V}}_{\rm net}$, $P^{\max} = 35$ dBm, and $M=64$ unit elements per metasurface.
  • Figure 4: Average achievable sum-rate performance versus the transmit power $P^{\max}$ of each BS, considering $R=2$ BDRISs of $M=64$ unit elements with different architectures.
  • Figure 5: Average achievable sum rate as a function of the common number $M$ of unit elements at each BDRIS, considering the transmit power $P^{\max}=30$ dBm and different metasurface architectures.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Theorem 1
  • Corollary 1
  • Theorem 2