Unsourced Random Access in MIMO Quasi-Static Rayleigh Fading Channels: Finite Blocklength and Scaling Law Analyses
Year: 2025
Type: article
Abstract: This paper considers the unsourced random access (URA) problem with a random and unknown number of active users in multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channels. We derive non-asymptotic achievability bounds on the probability of incorrectly estimating the number of active users, and provide scaling laws on the gap between the estimated and true numbers of active users. We prove that the error probability reaches a plateau as the powerPand blocklengthnincrease, whereas it decays exponentially with the numberLof receive antennas and eventually vanishes. Then, we explore the fundamental limits of URA by deriving non-asymptotic achievability bounds and converse bounds (including two single-user converse bounds and one multi-user ensemble converse bound) on the minimum energy-per-bit required by each active user to transmitJbits with blocklengthnunder misdetection and false-alarm constraints. Numerical results show that the extra required energy-per-bit due to the uncertainty in the number${\mathrm {K}}_{a}$of active users decreases asLand$\mathbb {E}[{\mathrm {K}}_{a}]$increase and the error requirement becomes milder. In the non-asymptotic regime, using codewords distributed on a sphere outperforms Gaussian random coding. Existing schemes are shown to exhibit a large gap to our bounds when the number of active users is large, calling for more advanced schemes that perform energy-efficiently in this case. In the asymptotic regime with$n\to \infty $, we establish scaling laws on the minimum requiredPandLto reliably support${\mathrm {K}}_{a}$active users as functions ofn, which highlight the potential of MIMO in enabling low-cost communication and indicate that it is possible for the minimum requiredPandLto remain on the same order when the number of active users increases but stays below a threshold.
Authors: Junyuan Gao, Yongpeng Wu, Giuseppe Caire, Wei Yang, H. Vincent Poor, Wenjun Zhang
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6959853598