Comprehensive Throughput Analysis of Unslotted ALOHA for Low-Power Wide-Area Networks

Abstract

Unslotted ALOHA has been often employed by several low-power wide-area networks (LPWANs) for Internet of Things (IoT) as a random access (RA) protocol. This work analyzes the performance of unslotted ALOHA systems in terms of throughput and RA delay, and investigates their optimization. Our analysis consists of: 1) two- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heterogeneous</i> user case, whose backoff rate and packet length are different; 2) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">homogeneous</i> user case, whose backoff rate and packet length are identical; and 3) homogeneous users of infinite population model. In the two-user case, we investigate the throughput region of unslotted ALOHA by using a multiobjective optimization problem (MOOP) and derive the Laplace Stieltjes transform (LST) of the probability density function (PDF) of RA delay. For <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> -homogeneous user case, we show how the throughput behaves according to the population size, packet length, and backoff rate. Our work may provide a comprehensive analytical framework for unslotted ALOHA systems.