Energy Efficiency of Massive Random Access in MIMO Quasi-Static Rayleigh Fading Channels with Finite Blocklength

TL;DR

This paper analyzes the energy efficiency of massive random access in MIMO Rayleigh fading channels with finite blocklength, deriving bounds and studying the impact of channel state information on performance.

Contribution

It provides new achievability and converse bounds for energy-per-bit in massive MIMO random access, considering scenarios with and without channel state information.

Findings

Achievability and converse bounds are within 2.5-4 dB gap.

Performance gap with known and unknown number of active users is small.

Spectral efficiency scales linearly with the number of antennas under CSIR.

Abstract

This paper considers the massive random access problem in MIMO quasi-static Rayleigh fading channels. Specifically, we derive achievability and converse bounds on the minimum energy-per-bit required for each active user to transmit $J$ bits with blocklength $n$ and power $P$ under a per-user probability of error (PUPE) constraint, in the cases with and without \emph{a priori} channel state information at the receiver (CSIR and no-CSI). In the case of no-CSI, we consider both the settings with and without knowing the number $K_a$ of active users. The achievability bounds rely on the design of the ``good region''. Numerical evaluation shows the gap between achievability and converse bounds is less than $2.5$ dB in the CSIR case and less than $4$ dB in the no-CSI case in most considered regimes. When the distribution of $K_a$ is known, the performance gap between the cases with and without knowing the value of $K_a$ is small. For example, in the setup with blocklength $n=1000$, payload $J=100$, error requirement $\epsilon=0.001$, and $L=128$ receive antennas, compared to the case with known $K_a$, the extra required energy-per-bit when $K_a$ is unknown and distributed as $K_a\sim\text{Binom}(K,0.4)$ is less than $0.3$ dB on the converse side and $1.1$ dB on the achievability side. The spectral efficiency grows approximately linearly with $L$ in the CSIR case, whereas the growth rate decreases with no-CSI. Moreover, we study the performance of a pilot-assisted scheme, which is suboptimal especially when $K_a$ is large. Building on non-asymptotic results, when all users are active and $J=\Theta(1)$, we obtain scaling laws as follows: when $L=\Theta \left(n^2\right)$ and $P=\Theta\left(\frac{1}{n^2}\right)$, one can reliably serve $K=\mathcal{O}(n^2)$ users with no-CSI; under mild conditions with CSIR, the PUPE requirement is satisfied if and only if $\frac{nL\ln KP}{K}=\Omega\left(1\right)$.