Asynchronous Massive MIMO Receiver for Pilot-Based Unsourced Random Access
In this paper we study fully asynchronous random access (RA) multiple antenna receiver in a Rayleigh block-fading AWGN channel with pure path delays. Although our approach can be used to detect users in a grant-free random access system, where each user sporadically and without waiting for a permission from a base station (BS) transmits short messages, we in particular consider the pilot-based unsourced random access (U-RA), where those messages are from a common codebook. The first and arguably the most important task of the pilot-based U-RA receiver is to detect the list of transmitted pilots. Due to the propagation through the considered channel, those pilots are received as a superposition at the BS with delays, due to the lack of perfect timing synchronization. We show that the output of the chip matched filter at the BS receiver can be seen as the superposition of two zero-padded versions of each transmitted pilot sequence. We include this observation in the compressed sensing (CS) formulation of the activity detection (AD) problem, and solve it using the multiple measurement vectors approximate message passing (MMV-AMP) algorithm and a dedicated parametrized 2-level hierarchical sparsity (P2-LHS) denoiser. Our numerical experiments show that the proposed scheme can accurately detect U-RA messages and shows excellent robustness to timing asynchronism. The proposed denoiser vastly outperforms the standard Bernoulli-Gaussian (BG) denoiser for a large range of signal-to-noise ratio (SNR) values. Furthermore, using outage rate analysis, we investigate the performance of the asynchronous U-RA receiver using a Gaussian codebook and minimum distance decoding in the data phase. Our results show that a significant gain in throughput can be achieved when users adopt rate control (RC).
