Joint Activity-Delay Detection and Channel Estimation for Asynchronous Massive Random Access: A Free Probability Theory Approach

TL;DR

This paper develops novel algorithms for joint activity detection, delay estimation, and channel estimation in asynchronous massive random access systems, leveraging free probability theory to improve efficiency and accuracy.

Contribution

It introduces a free probability AMP (FPAMP) algorithm that reduces computational complexity while effectively handling non-i.i.d. pilot matrices in asynchronous scenarios.

Findings

FPAMP reduces computational cost by 40%.

Both algorithms outperform existing baselines.

Proposed methods effectively handle asynchronous delays.

Abstract

Grant-free random access (RA) has been recognized as a promising solution to support massive connectivity due to the removal of the uplink grant request procedures. While most endeavours assume perfect synchronization among users and the base station, this paper investigates asynchronous grant-free massive RA, and develop efficient algorithms for joint user activity detection, synchronization delay detection, and channel estimation. Considering the sparsity on user activity, we formulate a sparse signal recovery problem and propose to utilize the framework of orthogonal approximate message passing (OAMP) to deal with the non-independent and identically distributed (i.i.d.) Gaussian pilot matrices caused by the synchronization delays. In particular, an OAMP-based algorithm is developed to fully harness the common sparsity among received pilot signals from multiple base station antennas. To reduce the computational complexity, we further propose a free probability AMP (FPAMP)-based algorithm, which exploits the rectangular free cumulants to make the cost-effective AMP framework compatible to general pilot matrices. Simulation results demonstrate that the two proposed algorithms outperform various baselines, and the FPAMP-based algorithm reduces 40% of the computations while maintaining comparable detection/estimation accuracy with the OAMP-based algorithm.