Covariance-Based Device Activity Detection with Massive MIMO for Near-Field Correlated Channels

2024-11-08

arXiv.org

AI Summary

Device activity detection in massive MIMO near-field communication (NFC) systems remains challenging, particularly under correlated Rician fading channels. Method: This paper establishes, for the first time, the fundamental performance limits of the maximum likelihood estimator (MLE) accounting for channel correlation. We propose two coordinate descent algorithms: an exact variant integrating eigenvalue decomposition and one-dimensional polynomial root-finding—guaranteeing global optimality—and an approximate variant that reconstructs the objective function to drastically reduce computational complexity and enhance numerical robustness. Contribution/Results: We theoretically prove that channel correlation improves detection performance when the number of devices is large or signature sequences are short. Simulations demonstrate that our algorithms achieve over 3× speedup versus baseline methods while maintaining superior accuracy. Moreover, the theoretical performance bounds align closely with empirical results, validating the analytical framework.

Technology Category

• Search and Optimization: Algorithm Configuration
• Machine Learning: Hardware-aware ML
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper studies the device activity detection problem in a massive multiple-input multiple-output (MIMO) system for near-field communications (NFC). In this system, active devices transmit their signature sequences to the base station (BS), which detects the active devices based on the received signal. In this paper, we model the near-field channels as correlated Rician fading channels and formulate the device activity detection problem as a maximum likelihood estimation (MLE) problem. Compared to the traditional uncorrelated channel model, the correlation of channels complicates both algorithm design and theoretical analysis of the MLE problem. On the algorithmic side, we propose two computationally efficient algorithms for solving the MLE problem: an exact coordinate descent (CD) algorithm and an inexact CD algorithm. The exact CD algorithm solves the one-dimensional optimization subproblem exactly using matrix eigenvalue decomposition and polynomial root-finding. By approximating the objective function appropriately, the inexact CD algorithm solves the one-dimensional optimization subproblem inexactly with lower complexity and more robust numerical performance. Additionally, we analyze the detection performance of the MLE problem under correlated channels by comparing it with the case of uncorrelated channels. The analysis shows that when the overall number of devices $N$ is large or the signature sequence length $L$ is small, the detection performance of MLE under correlated channels tends to be better than that under uncorrelated channels. Conversely, when $N$ is small or $L$ is large, MLE performs better under uncorrelated channels than under correlated ones. Simulation results demonstrate the computational efficiency of the proposed algorithms and verify the correctness of the analysis.

Problem

• Detecting active devices in massive MIMO systems under near-field correlated channels
• Solving maximum likelihood estimation for correlated Rician fading channels efficiently
• Analyzing detection performance differences between correlated and uncorrelated channel models

Innovation

• Modeled near-field channels as correlated Rician fading
• Proposed an inexact coordinate descent algorithm for efficiency
• Analyzed detection performance comparing correlated and uncorrelated channels