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Massive Unsourced Random Access for Near-Field Communications

Xinyu Xie, Yongpeng Wu, Jianping An, Derrick Wing Kwan Ng, Chengwen Xing, Wenjun Zhang

TL;DR

Simulations reveal that via exploiting the channel sparsity, the proposed URA scheme achieves high spectral efficiency and surpasses existing multi-slot-based schemes.

Abstract

This paper investigates the unsourced random access (URA) problem with a massive multiple-input multiple-output receiver that serves wireless devices in the near-field of radiation. We employ an uncoupled transmission protocol without appending redundancies to the slot-wise encoded messages. To exploit the channel sparsity for block length reduction while facing the collapsed sparse structure in the angular domain of near-field channels, we propose a sparse channel sampling method that divides the angle-distance (polar) domain based on the maximum permissible coherence. Decoding starts with retrieving active codewords and channels from each slot. We address the issue by leveraging the structured channel sparsity in the spatial and polar domains and propose a novel turbo-based recovery algorithm. Furthermore, we investigate an off-grid compressed sensing method to refine discretely estimated channel parameters over the continuum that improves the detection performance. Afterward, without the assistance of redundancies, we recouple the separated messages according to the similarity of the users' channel information and propose a modified K-medoids method to handle the constraints and collisions involved in channel clustering. Simulations reveal that via exploiting the channel sparsity, the proposed URA scheme achieves high spectral efficiency and surpasses existing multi-slot-based schemes. Moreover, with more measurements provided by the overcomplete channel sampling, the near-field-suited scheme outperforms its counterpart of the far-field.

Massive Unsourced Random Access for Near-Field Communications

TL;DR

Simulations reveal that via exploiting the channel sparsity, the proposed URA scheme achieves high spectral efficiency and surpasses existing multi-slot-based schemes.

Abstract

This paper investigates the unsourced random access (URA) problem with a massive multiple-input multiple-output receiver that serves wireless devices in the near-field of radiation. We employ an uncoupled transmission protocol without appending redundancies to the slot-wise encoded messages. To exploit the channel sparsity for block length reduction while facing the collapsed sparse structure in the angular domain of near-field channels, we propose a sparse channel sampling method that divides the angle-distance (polar) domain based on the maximum permissible coherence. Decoding starts with retrieving active codewords and channels from each slot. We address the issue by leveraging the structured channel sparsity in the spatial and polar domains and propose a novel turbo-based recovery algorithm. Furthermore, we investigate an off-grid compressed sensing method to refine discretely estimated channel parameters over the continuum that improves the detection performance. Afterward, without the assistance of redundancies, we recouple the separated messages according to the similarity of the users' channel information and propose a modified K-medoids method to handle the constraints and collisions involved in channel clustering. Simulations reveal that via exploiting the channel sparsity, the proposed URA scheme achieves high spectral efficiency and surpasses existing multi-slot-based schemes. Moreover, with more measurements provided by the overcomplete channel sampling, the near-field-suited scheme outperforms its counterpart of the far-field.
Paper Structure (27 sections, 2 theorems, 33 equations, 8 figures, 3 algorithms)

This paper contains 27 sections, 2 theorems, 33 equations, 8 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. System Depiction
  4. Signal Model
  5. Channel Model
  6. Sparse Domain Channel Representation
  7. Limitation of Angular Domain Sampling in the Near-Field
  8. Promoting Near-Field Channel Sparsity via Angle-Distance Sampling
  9. 2D-CS-Based Codeword Activity Detection and Channel Estimation
  10. Problem Formulation
  11. Proposed Tubro-CoSaMP Algorithm for Signal Reconstruction
  12. Complexity Analysis
  13. Convergence Guarantee
  14. Enhanced Signal Reconstruction via Off-Grid CS
  15. Complexity and Convergence Analysis
  16. ...and 12 more sections

Key Result

Theorem 1

Let $\mathbf{X}$ be a $R$-sparse matrix and $\widehat{\mathbf{X}}$ is the $R$-sparse approximation of $\mathbf{X}$. Let $\mathbf{Y} = \mathbf{AXB}^{T} + \mathbf{W} \in \mathbb{C}^{N \times M}$ where each entry of $\mathbf{W}$ is generated independently from the distribution $\mathcal{CN}( 0, \sigma^

Figures (8)

  • Figure 1: Schematic of the UCS scheme for URA, where the box marked "$\mathbf{A}$" represents the common codebook.
  • Figure 2: An illustration of the angular domain channel representation in near- and far-field conditions. The considered carrier frequency is $3$ GHz, $M = 128$, $L = 3$, $( \theta_{1}, \theta_{2}, \theta_{3} ) = ( -\sqrt{3} / 2, 0.01, \sqrt{2} / 2 )$, and $( g_{1}, g_{2}, g_{3} )$ are drawn independently from a complex Gaussian distribution of zero mean and unit variance. The communication distance is set to be $1$ km for the far-field channel and $10$ m for the near-field channel. The maximum amplitude of the channel coefficients is normalized to one.
  • Figure 3: Detection error performance of various channel sampling algorithms versus SNR with $K_{\mathrm{a}} = 100$, $M = 128$, and $N = 50$.
  • Figure 4: JADCE performance of proposed algorithms with $K_{\mathrm{a}} = 100$ and $M = 128$. (a) Detection error rate versus SNR under different values of $N$; (b) NMSE versus SNR under different values of $N$; (c) Average number of iterations until convergence versus SNR with $N = 50$.
  • Figure 5: JADCE performance of various algorithms with $K_{\mathrm{a}} = 100$, $M = 128$; (a) Detection error rate versus block length $N$ when $\mathrm{SNR} = 0$ dB; (b) NMSE versus block length $N$ when $\mathrm{SNR} = 0$ dB; (c) Detection error rate versus SNR when $N = 50$; (d) NMSE versus SNR when $N = 50$; (e) Detection error rate versus SNR when $N = 100$; (d) NMSE versus SNR when $N = 100$.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • Corollary 1: Theorem 3.2 in RV06