Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Activity Detection for Massive Connectivity in Cell-free Networks with Unknown Large-scale Fading, Channel Statistics, Noise Variance, and Activity Probability: A Bayesian Approach

Hao Zhang, Qingfeng Lin, Yang Li, Lei Cheng, Yik-Chung Wu

TL;DR

This work tackles activity detection in cell-free massive connectivity under unknown large-scale fading, small-scale fading statistics, noise variance, and activity probability. It introduces a Bayesian model with a sparsity-enhancing generalized hyperbolic (GH) prior that couples per-user activity across all APs via a shared latent variable, enabling activity consistency without precise system parameters. Two inference engines are developed: a MAP estimator and a variational inference algorithm (GHVI) that account for uncertainty and learn hyperparameters from data. Across simulations, the proposed methods outperform covariance-based and AMP-based baselines, especially when system parameters are imperfect or unknown, demonstrating robust, parameter-free detection suitable for dense IoT deployments.

Abstract

Activity detection is an important task in the next generation grant-free multiple access. While there are a number of existing algorithms designed for this purpose, they mostly require precise information about the network, such as large-scale fading coefficients, small-scale fading channel statistics, noise variance at the access points, and user activity probability. Acquiring these information would take a significant overhead and their estimated values might not be accurate. This problem is even more severe in cell-free networks as there are many of these parameters to be acquired. Therefore, this paper sets out to investigate the activity detection problem without the above-mentioned information. In order to handle so many unknown parameters, this paper employs the Bayesian approach, where the unknown variables are endowed with prior distributions which effectively act as regularizations. Together with the likelihood function, a maximum a posteriori (MAP) estimator and a variational inference algorithm are derived. Extensive simulations demonstrate that the proposed methods, even without the knowledge of these system parameters, perform better than existing state-of-the-art methods, such as covariance-based and approximate message passing methods.

Activity Detection for Massive Connectivity in Cell-free Networks with Unknown Large-scale Fading, Channel Statistics, Noise Variance, and Activity Probability: A Bayesian Approach

TL;DR

This work tackles activity detection in cell-free massive connectivity under unknown large-scale fading, small-scale fading statistics, noise variance, and activity probability. It introduces a Bayesian model with a sparsity-enhancing generalized hyperbolic (GH) prior that couples per-user activity across all APs via a shared latent variable, enabling activity consistency without precise system parameters. Two inference engines are developed: a MAP estimator and a variational inference algorithm (GHVI) that account for uncertainty and learn hyperparameters from data. Across simulations, the proposed methods outperform covariance-based and AMP-based baselines, especially when system parameters are imperfect or unknown, demonstrating robust, parameter-free detection suitable for dense IoT deployments.

Abstract

Activity detection is an important task in the next generation grant-free multiple access. While there are a number of existing algorithms designed for this purpose, they mostly require precise information about the network, such as large-scale fading coefficients, small-scale fading channel statistics, noise variance at the access points, and user activity probability. Acquiring these information would take a significant overhead and their estimated values might not be accurate. This problem is even more severe in cell-free networks as there are many of these parameters to be acquired. Therefore, this paper sets out to investigate the activity detection problem without the above-mentioned information. In order to handle so many unknown parameters, this paper employs the Bayesian approach, where the unknown variables are endowed with prior distributions which effectively act as regularizations. Together with the likelihood function, a maximum a posteriori (MAP) estimator and a variational inference algorithm are derived. Extensive simulations demonstrate that the proposed methods, even without the knowledge of these system parameters, perform better than existing state-of-the-art methods, such as covariance-based and approximate message passing methods.
Paper Structure (25 sections, 43 equations, 9 figures, 2 tables, 2 algorithms)

This paper contains 25 sections, 43 equations, 9 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Two Maximum Likelihood Estimators
  3. Encoding Prior Knowledge with Probabilistic Modeling
  4. Sparsity-enhancing Prior for Combined Activity Status and Large-scale Fading
  5. Modeling of Small-scale Fading Prior
  6. Modeling Unknown Noise Precision
  7. Posterior Distribution and the MAP Algorithm
  8. Bayesian Variational Inference
  9. Convergence Property
  10. Sparsity and Large-scale Fading Learning
  11. Hyper-parameter Settings in Priors
  12. Uncertainty Utilization in GHVI
  13. Algorithm Time Complexity
  14. Simulation Results and Discussions
  15. Simulation Setting
  16. ...and 10 more sections

Figures (9)

  • Figure 1: Cell-free network model.
  • Figure 2: Marginal probability density function of GH prior with different values of hyper-parameters.
  • Figure 3: PMD versus PFA in cell-free system.
  • Figure 4: PMD=PFA versus the pilot sequence lengths.
  • Figure 5: PMD versus PFA in cell-free system when assumptions A1-A4 are violated.
  • ...and 4 more figures