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A Unified Activity Detection Framework for Massive Access: Beyond the Block-Fading Paradigm

Jianan Bai, Erik G. Larsson

TL;DR

A framework for low-dimensional approximation of the channel to capture its variations over time and frequency is developed, and this framework is used to implement robust activity detection algorithms.

Abstract

The wireless channel changes continuously with time and frequency and the block-fading assumption, which is popular in many theoretical analyses, never holds true in practical scenarios. This discrepancy is critical for user activity detection in grant-free random access, where joint processing across multiple coherence blocks is undesirable, especially when the environment becomes more dynamic. In this paper, we develop a framework for low-dimensional approximation of the channel to capture its variations over time and frequency, and use this framework to implement robust activity detection algorithms. Furthermore, we investigate how to efficiently estimate the principal subspace that defines the low-dimensional approximation. We also examine pilot hopping as a way of exploiting time and frequency diversity in scenarios with limited channel coherence, and extend our algorithms to this case. Through numerical examples, we demonstrate a substantial performance improvement achieved by our proposed framework.

A Unified Activity Detection Framework for Massive Access: Beyond the Block-Fading Paradigm

TL;DR

A framework for low-dimensional approximation of the channel to capture its variations over time and frequency is developed, and this framework is used to implement robust activity detection algorithms.

Abstract

The wireless channel changes continuously with time and frequency and the block-fading assumption, which is popular in many theoretical analyses, never holds true in practical scenarios. This discrepancy is critical for user activity detection in grant-free random access, where joint processing across multiple coherence blocks is undesirable, especially when the environment becomes more dynamic. In this paper, we develop a framework for low-dimensional approximation of the channel to capture its variations over time and frequency, and use this framework to implement robust activity detection algorithms. Furthermore, we investigate how to efficiently estimate the principal subspace that defines the low-dimensional approximation. We also examine pilot hopping as a way of exploiting time and frequency diversity in scenarios with limited channel coherence, and extend our algorithms to this case. Through numerical examples, we demonstrate a substantial performance improvement achieved by our proposed framework.

Paper Structure

This paper contains 26 sections, 35 equations, 14 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Contributions and Organization of the Paper
  3. Notation
  4. System Model
  5. Activity Detection with Dimensionality-Reduced Channel Variations
  6. Existing Low-Dimensional Models
  7. A Viewpoint from Low-Rank Covariance Approximation
  8. Covariance-Based Activity Detection
  9. Learning the Low-Dimensional Structure
  10. Extension: Pilot Hopping
  11. Pilot Hopping in Covariance-Based Activity Detection
  12. Hopping Pattern Design
  13. The Complete Framework
  14. Numerical Results
  15. Generation of Channels
  16. ...and 11 more sections

Figures (14)

  • Figure 1: Pilot hopping as integrating a special structure in pilots.
  • Figure 2: Pilot hopping system as a bipartite graph.
  • Figure 3: The complete activity detection framework.
  • Figure 4: The mapping from $(t_l,f_l)$ to $l$ for $T=F=4$ and $P_\textup{time} = P_\textup{freq} = 2$.
  • Figure 5: Detection performance with different hopping schemes.
  • ...and 9 more figures

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4