Capacity Bounds and User Identification Costs in Rayleigh-Fading Many-Access Channel

TL;DR

This paper analyzes the capacity and user identification costs in a Rayleigh-fading many-access channel, proposing bounds and practical strategies for active user discovery in massive IoT scenarios.

Contribution

It introduces a Rayleigh-fading model for MnAC, derives capacity bounds, and evaluates a practical group testing method for active user detection.

Findings

N-COMP GT scales similarly to the lower bound on user identification cost.

Required channel uses grow with the number of users at a rate close to theoretical bounds.

In low SNR, N-COMP GT is within a factor of two of the lower bound for large populations.

Abstract

Many-access channel (MnAC) model allows the number of users in the system and the number of active users to scale as a function of the blocklength and as such is suited for dynamic communication systems with massive number of users such as the Internet of Things. Existing MnAC models assume a priori knowledge of channel gains which is impractical since acquiring Channel State Information (CSI) for massive number of users can overwhelm the available radio resources. This paper incorporates Rayleigh fading effects to the MnAC model and derives an upper bound on the symmetric message-length capacity of the Rayleigh-fading Gaussian MnAC. Furthermore, a lower bound on the minimum number of channel uses for discovering the active users is established. In addition, the performance of Noisy Combinatorial Orthogonal Matching Pursuit (N-COMP) based group testing (GT) is studied as a practical strategy for active device discovery. Simulations show that, for a given SNR, as the number of users increase, the required number of channel uses for N-COMP GT scales approximately the same way as the lower bound on minimum user identification cost. Moreover, in the low SNR regime, for sufficiently large population sizes, the number of channel uses required by N-COMP GT was observed to be within a factor of two of the lower bound when the expected number of active users scales sub-linearly with the total population size.