# Fundamental limits of many-user MAC with finite payloads and fading

## TL;DR

This paper investigates the fundamental limits of many-user wireless multiple-access channels with finite payloads and fading, revealing the potential for near-perfect interference cancellation below a critical user density and challenging traditional solutions.

## Contribution

It introduces a PUPE-based analysis of many-user MACs with fading, deriving energy-spectral efficiency bounds and highlighting the suboptimality of standard methods like orthogonalization.

## Key findings

- Almost perfect multi-user interference cancellation below a critical user density.
- Standard solutions like orthogonalization are suboptimal in this setting.
- Finite energy-per-bit communication is achievable with PUPE criterion.

## Abstract

Consider a (multiple-access) wireless communication system where users are connected to a unique base station over a shared-spectrum radio links. Each user has a fixed number $k$ of bits to send to the base station, and his signal gets attenuated by a random channel gain (quasi-static fading). In this paper we consider the many-user asymptotics of Chen-Chen-Guo'2017, where the number of users grows linearly with the blocklength. Differently, though, we adopt a per-user probability of error (PUPE) criterion (as opposed to classical joint-error probability criterion). Under PUPE the finite energy-per-bit communication is possible, and we are able to derive bounds on the tradeoff between energy and spectral efficiencies. We reconfirm the curious behaviour (previously observed for non-fading MAC) of the possibility of almost perfect multi-user interference (MUI) cancellation for user densities below a critical threshold. Further, we demonstrate the suboptimality of standard solutions such as orthogonalization (i.e., TDMA/FDMA) and treating interference as noise (i.e. pseudo-random CDMA without multi-user detection). Notably, the problem treated here can be seen as a variant of support recovery in compressed sensing for the unusual definition of sparsity with one non-zero entry per each contiguous section of $2^k$ coordinates. This identifies our problem with that of the sparse regression codes (SPARCs) and hence our results can be equivalently understood in the context of SPARCs with sections of length $2^{100}$. Finally, we discuss the relation of the almost perfect MUI cancellation property and the replica-method predictions.