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Quantized Precoding for Maximizing Sum Rate in MU-MIMO Systems with Constrained Fronthaul

Yasaman Khorsandmanesh, Alva Kosasih, Emil Björnson, Joakim Jaldén

TL;DR

A novel sum rate maximization framework that directly incorporates the quantizer's constraints into the precoding design and a heuristic quantization-aware precoding method with comparable complexity to the baseline but superior performance.

Abstract

This paper studies a downlink multi-user multiple-input multiple-output (MU-MIMO) system, where the precoding matrix is computed at a baseband unit (BBU) and then transmitted to the remote antenna array over a limited-capacity digital fronthaul. The limited bit resolution of the fronthaul introduces quantization effects that are explicitly modeled. We propose a novel sum rate maximization framework that directly incorporates the quantizer's constraints into the precoding design. The resulting maximization problem, a non-convex mixed-integer program, is addressed using a new iterative algorithm inspired by the weighted minimum mean square error (WMMSE) methodology. The precoding optimization subproblem is reformulated as an integer least-squares problem and solved using a novel sphere decoding (SD) algorithm. Additionally, a low-complexity expectation propagation (EP)-based method is introduced to enable the practical implementation of quantized precoding in MU-massive MIMO (MU-mMIMO) systems. Furthermore, numerical evaluations demonstrate that the proposed precoding schemes outperform conventional approaches that optimize infinite-resolution precoding followed by element-wise quantization. We also propose a heuristic quantization-aware precoding method with comparable complexity to the baseline but superior performance. In particular, the EP-based approach offers near-optimal performance with substantial complexity reduction, making it well-suited for real-time MU-mMIMO applications.

Quantized Precoding for Maximizing Sum Rate in MU-MIMO Systems with Constrained Fronthaul

TL;DR

A novel sum rate maximization framework that directly incorporates the quantizer's constraints into the precoding design and a heuristic quantization-aware precoding method with comparable complexity to the baseline but superior performance.

Abstract

This paper studies a downlink multi-user multiple-input multiple-output (MU-MIMO) system, where the precoding matrix is computed at a baseband unit (BBU) and then transmitted to the remote antenna array over a limited-capacity digital fronthaul. The limited bit resolution of the fronthaul introduces quantization effects that are explicitly modeled. We propose a novel sum rate maximization framework that directly incorporates the quantizer's constraints into the precoding design. The resulting maximization problem, a non-convex mixed-integer program, is addressed using a new iterative algorithm inspired by the weighted minimum mean square error (WMMSE) methodology. The precoding optimization subproblem is reformulated as an integer least-squares problem and solved using a novel sphere decoding (SD) algorithm. Additionally, a low-complexity expectation propagation (EP)-based method is introduced to enable the practical implementation of quantized precoding in MU-massive MIMO (MU-mMIMO) systems. Furthermore, numerical evaluations demonstrate that the proposed precoding schemes outperform conventional approaches that optimize infinite-resolution precoding followed by element-wise quantization. We also propose a heuristic quantization-aware precoding method with comparable complexity to the baseline but superior performance. In particular, the EP-based approach offers near-optimal performance with substantial complexity reduction, making it well-suited for real-time MU-mMIMO applications.
Paper Structure (25 sections, 1 theorem, 26 equations, 8 figures, 2 tables, 3 algorithms)

This paper contains 25 sections, 1 theorem, 26 equations, 8 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Prior Work
  3. Contributions
  4. Notation and Preliminaries
  5. System model
  6. Limited-Capacity Fronthaul Model
  7. Downlink Communications
  8. Channel Estimation and Uplink Quantization
  9. Problem Formulation
  10. Proposed WMMSE Algorithm and Optimized Quantized Precoding
  11. Sphere Decoding-Based Precoding
  12. Heuristic Expectation Propagation-Based Precoding
  13. Maximum A Posteriori Problem
  14. The EP Algorithm
  15. Alternative Precoding Schemes
  16. ...and 10 more sections

Key Result

Proposition 1

By defining the auxiliary weight $d_k \geq 0$, the sum rate maximization problem $\mathbb{P}_1$ is equivalent to the weighted sum MMSE problem where $\boldsymbol{\beta} = [\beta_1,\ldots,\beta_K]^\mathrm{T}$ is a vector containing all receiver gains and $\boldsymbol{d} = [d_1,\ldots,d_K]^\mathrm{T}$ is a vector containing all the UE weights in the weighted MSE. Problem $\mathbb{P}_2$ is equivalen

Figures (8)

  • Figure 1: Downlink MU-MIMO system with constrained fronthaul capacity.
  • Figure 2: Normalized histogram of $\boldsymbol{c} - \boldsymbol{G}\boldsymbol{p}$ overlaid with a fitted normal distribution with zero mean and standard deviation $\sigma = 0.03$. The setup assumes $M = 16$ ULA BS antennas serving $K = 4$ single-antenna UEs at an SNR of 25 dB. The channel follows the Rician fading model described in Section \ref{['sec:numericalchannelModel']}.
  • Figure 3: The average sum rate and objective function \ref{['eq:wmmse']} evolution when running the proposed WMMSE algorithm using the proposed SD-based and EP-based methods.
  • Figure 4: The average sum rate versus the SNR for different precoding schemes, assuming $M=4 \times 4$, $K=4$, and $L=8$.
  • Figure 5: The average sum rate versus the BS antennas $M$ for various precoding schemes, assuming $\text{SNR} = 20$ dB, $K=4$ UEs and $L=8$ quantization levels.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Remark 1
  • Proposition 1
  • Remark 2