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User-Centric Association and Feedback Bit Allocation for FDD Cell-Free Massive MIMO

Kwangjae Lee, Jung Hoon Lee, Wan Choi

TL;DR

The paper tackles downlink CSI acquisition for FDD CF-mMIMO under limited uplink feedback by proposing a user-centric UE-AP association and adaptive feedback bit allocation that respect per-AP budgets. It leverages a Saleh-Valenzuela multipath channel model and introduces a tailored codebook structure to quantize path gains, formulating a long-term optimization problem (P$_{AP}$1) and tractable alternatives. A two-stage solution to (P$_{AP}$3)—first (P$_{AP}$3a) with equal per-UE allocations and then (P$_{AP}$3b) via a convex Lagrangian/KKT method—yields closed-form bit allocations per path, while UE-side (P$_{UE}$2-$k$) refines the per-path splits to maximize per-user rate under the same budget. Numerical results show the proposed scheme surpasses conventional equal-allocation and existing baselines, demonstrating improved sum rates under realistic feedback budgets and network scales, with implications for practical 6G CF-mMIMO deployments.

Abstract

In this paper, we introduce a novel approach to user-centric association and feedback bit allocation for the downlink of a cell-free massive MIMO (CF-mMIMO) system, operating under limited feedback constraints. In CF-mMIMO systems employing frequency division duplexing, each access point (AP) relies on channel information provided by its associated user equipments (UEs) for beamforming design. Since the uplink control channel is typically shared among UEs, we take account of each AP's total feedback budget, which is distributed among its associated UEs. By employing the Saleh-Valenzuela multi-resolvable path channel model with different average path gains, we first identify necessary feedback information for each UE, along with an appropriate codebook structure. This structure facilitates adaptive quantization of multiple paths based on their dominance. We then formulate a joint optimization problem addressing user-centric UE-AP association and feedback bit allocation. To address this challenge, we analyze the impact of feedback bit allocation and derive our proposed scheme from the solution of an alternative optimization problem aimed at devising long-term policies, explicitly considering the effects of feedback bit allocation. Numerical results show that our proposed scheme effectively enhances the performance of conventional approaches in CF-mMIMO systems.

User-Centric Association and Feedback Bit Allocation for FDD Cell-Free Massive MIMO

TL;DR

The paper tackles downlink CSI acquisition for FDD CF-mMIMO under limited uplink feedback by proposing a user-centric UE-AP association and adaptive feedback bit allocation that respect per-AP budgets. It leverages a Saleh-Valenzuela multipath channel model and introduces a tailored codebook structure to quantize path gains, formulating a long-term optimization problem (P1) and tractable alternatives. A two-stage solution to (P3)—first (P3a) with equal per-UE allocations and then (P3b) via a convex Lagrangian/KKT method—yields closed-form bit allocations per path, while UE-side (P2-) refines the per-path splits to maximize per-user rate under the same budget. Numerical results show the proposed scheme surpasses conventional equal-allocation and existing baselines, demonstrating improved sum rates under realistic feedback budgets and network scales, with implications for practical 6G CF-mMIMO deployments.

Abstract

In this paper, we introduce a novel approach to user-centric association and feedback bit allocation for the downlink of a cell-free massive MIMO (CF-mMIMO) system, operating under limited feedback constraints. In CF-mMIMO systems employing frequency division duplexing, each access point (AP) relies on channel information provided by its associated user equipments (UEs) for beamforming design. Since the uplink control channel is typically shared among UEs, we take account of each AP's total feedback budget, which is distributed among its associated UEs. By employing the Saleh-Valenzuela multi-resolvable path channel model with different average path gains, we first identify necessary feedback information for each UE, along with an appropriate codebook structure. This structure facilitates adaptive quantization of multiple paths based on their dominance. We then formulate a joint optimization problem addressing user-centric UE-AP association and feedback bit allocation. To address this challenge, we analyze the impact of feedback bit allocation and derive our proposed scheme from the solution of an alternative optimization problem aimed at devising long-term policies, explicitly considering the effects of feedback bit allocation. Numerical results show that our proposed scheme effectively enhances the performance of conventional approaches in CF-mMIMO systems.
Paper Structure (25 sections, 3 theorems, 47 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 25 sections, 3 theorems, 47 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. System Model Overview
  4. Detailed Setups
  5. User-Centric UE-AP Association
  6. Channel Model and Limited Feedback Environment
  7. ZF Beamforming and Achievable Rate
  8. Problem Description
  9. Identification of Feedback Information and Codebook Structure
  10. Identification of Feedback Information
  11. Codebook Structure
  12. Each UE's Feedback Bit Splitting and Reconstructed Channels from Feedback Information
  13. Effects of Channel Quantization and Alternative Optimization Problems
  14. The Effects of Feedback Bit Splitting on the Quantized Channel via Rate-Distortion Quantizer
  15. The Effects of Quantization Errors on the Achievable Rate
  16. ...and 10 more sections

Key Result

Lemma 1

(The rate-distortion for Gaussian sources Cover1999) When compressing a memoryless source of a Gaussian random variable $X$ with variance $\sigma_X^2$ into $\hat{X}$, the minimum (compressing) rate $R$ to achieve the distortion $D \triangleq \mathbb{E}[(X-\hat{X})^2]$ is

Figures (3)

  • Figure 1: An illustration of our system model. Distributed APs are connected to the CPU via backhaul links, forming a CF-mMIMO system. The feedback links for each AP are shared among its associated UEs.
  • Figure 2: Achievable sum rates of various schemes in our CF-mMIMO scenario with respect to (a) the transmit SNR and (b) each AP's feedback budget.
  • Figure 3: Achievable sum rates of various schemes in our CF-mMIMO scenario with respect to (a) the total number of APs, (b) the total number of UEs, (c) the maximum number of streams available at each AP.

Theorems & Definitions (8)

  • Remark 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5