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WMMSE-Based Joint Transceiver Design for Multi-RIS Assisted Cell-free Networks Using Hybrid CSI

Xuesong Pan, Zhong Zheng, Xueqing Huang, Zesong Fei

TL;DR

This paper tackles uplink multi-user MIMO in multi-RIS assisted cell-free networks under fronthaul limitations by leveraging a hybrid CSI, two-layer detection scheme. It develops a WMMSE-based joint design that optimizes the CPU’s weighted combining matrices, UEs’ transmit precoders, and RIS phase shifts, decomposed into WCM, TPM, and PSM subproblems. To mitigate overhead, an asymptotic alternating optimization framework based on operator-valued free probability replaces Monte Carlo expectations with Cauchy-transform expressions that depend only on long-term channel statistics. Numerical results confirm fast convergence and substantial rate gains from joint optimization and RIS deployment, while significantly reducing information exchange compared to fully centralized schemes.

Abstract

In this paper, we consider cell-free communication systems with several access points (APs) serving terrestrial users (UEs) simultaneously. To enhance the uplink multi-user multiple-input multiple-output communications, we adopt a hybrid-CSI-based two-layer distributed multi-user detection scheme comprising the local minimum mean-squared error (MMSE) detection at APs and the one-shot weighted combining at the central processing unit (CPU). Furthermore, to improve the propagation environment, we introduce multiple reconfigurable intelligent surfaces (RISs) to assist the transmissions from UEs to APs. Aiming to maximize the weighted sum rate, we formulate the weighted sum-MMSE (WMMSE) problem, where the UEs' beamforming matrices, the CPU's weighted combining matrix, and the RISs' phase-shifting matrices are alternately optimized. Considering the limited fronthaul capacity constraint in cell-free networks, we resort to the operator-valued free probability theory to derive the asymptotic alternating optimization (AO) algorithm to solve the WMMSE problem, which only depends on long-term channel statistics and thus reduces the interaction overhead. Numerical results demonstrate that the asymptotic AO algorithm can achieve a high communication rate as well as reduce the interaction overhead.

WMMSE-Based Joint Transceiver Design for Multi-RIS Assisted Cell-free Networks Using Hybrid CSI

TL;DR

This paper tackles uplink multi-user MIMO in multi-RIS assisted cell-free networks under fronthaul limitations by leveraging a hybrid CSI, two-layer detection scheme. It develops a WMMSE-based joint design that optimizes the CPU’s weighted combining matrices, UEs’ transmit precoders, and RIS phase shifts, decomposed into WCM, TPM, and PSM subproblems. To mitigate overhead, an asymptotic alternating optimization framework based on operator-valued free probability replaces Monte Carlo expectations with Cauchy-transform expressions that depend only on long-term channel statistics. Numerical results confirm fast convergence and substantial rate gains from joint optimization and RIS deployment, while significantly reducing information exchange compared to fully centralized schemes.

Abstract

In this paper, we consider cell-free communication systems with several access points (APs) serving terrestrial users (UEs) simultaneously. To enhance the uplink multi-user multiple-input multiple-output communications, we adopt a hybrid-CSI-based two-layer distributed multi-user detection scheme comprising the local minimum mean-squared error (MMSE) detection at APs and the one-shot weighted combining at the central processing unit (CPU). Furthermore, to improve the propagation environment, we introduce multiple reconfigurable intelligent surfaces (RISs) to assist the transmissions from UEs to APs. Aiming to maximize the weighted sum rate, we formulate the weighted sum-MMSE (WMMSE) problem, where the UEs' beamforming matrices, the CPU's weighted combining matrix, and the RISs' phase-shifting matrices are alternately optimized. Considering the limited fronthaul capacity constraint in cell-free networks, we resort to the operator-valued free probability theory to derive the asymptotic alternating optimization (AO) algorithm to solve the WMMSE problem, which only depends on long-term channel statistics and thus reduces the interaction overhead. Numerical results demonstrate that the asymptotic AO algorithm can achieve a high communication rate as well as reduce the interaction overhead.

Paper Structure

This paper contains 25 sections, 2 theorems, 75 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. System Model and Uplink Signal Detection Architecture
  5. Signal Model
  6. Channel Model
  7. Two-layer Signal Detection Scheme
  8. Joint Optimization for Weighted Combining Matrix, Transmit Precoding Matrices, and Phase-Shifting Matrices
  9. The WCM sub-problem
  10. The update of weight matrix variables
  11. The TPM sub-problem
  12. The PSM sub-problem
  13. Operator-Valued Free Probability Theory for Asymptotic AO Algorithm Design
  14. Optimization of $\mathbf{A}^{(i+1)}$ for given $\mathbf{W}^{(i)}$ and $\mathbf{\Theta}^{(i)}$
  15. Optimization of $\mathbf{V}^{(i+1)}$ for given $\mathbf{A}^{(i+1)}$, $\mathbf{W}^{(i)}$ and $\mathbf{\Theta}^{(i)}$
  16. ...and 10 more sections

Key Result

Proposition 1

The definition of the Cauchy transform $\mathcal{G}_{\mathbf{\Xi},\mathbf{B}_{l}}(z)$, with $z\in\mathbb{C}^+$, is given as follows where $\mathbf{\Xi}\in\mathbb{C}^{T_t\times T_t}$ is a nonnegative definite matrix with uniformly bounded spectral norm and the matrix ${\bf{\Omega}}(z)$ is defined as The matrix-valued functions $\bm{\Upsilon}(z)$, $\bm{\Gamma}(z)$, $\bm{\widetilde{\Gamma}}(z)$ an

Figures (6)

  • Figure 1: RIS-assisted CF networks with capacity-limited fronthaul links.
  • Figure 2: Sum-rate versus the number of APs with varying numbers of RIS's passive reflecting antennas and transmitting antennas per UE, where $N=2$, $K=2$ and $R=8$. The solid lines represent theoretical results and the markers represent Monte Carlo simulation results.
  • Figure 3: Sum-rate versus the number of iterations with varying numbers of UEs, where $L=4$, $K=2$, $R=8$, $T=4$ and $L_k=32$ for $k=1,\dots,K$. The solid lines represent theoretical results and the markers represent Monte Carlo simulation results.
  • Figure 4: Sum-rate versus the number of transmitting antennas, where $N=4$, $L=8$, $K=4$, $R=8$ and $L_k=32$ for $k=1,\dots,K$.
  • Figure 5: Sum-rate comparison in the NLoS-dominated environment ($\kappa=0$) and the LoS-dominated environment ($\kappa=10$), where $N=4$, $L=4$, $K=2$, $R=4$, $T=2$ and $L_k=32$ for $k=1,\dots,K$.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • Definition 1