# Meta Distribution of SIR in Dual-Hop Internet-of-Things (IoT) Networks

## TL;DR

This paper analyzes the detailed distribution of the SIR in dual-hop IoT networks, providing new insights into network performance metrics like coverage and delay through the meta distribution approach.

## Contribution

It introduces a novel analysis of the meta distribution of SIR in dual-hop IoT networks, deriving explicit expressions for moments and special cases considering relay association biases.

## Key findings

- Meta distribution offers a fine-grained view of network performance.
- Increasing relay density impacts the mean local delay.
- Derived expressions for success probability and delay metrics.

## Abstract

This paper characterizes the meta distribution of the downlink signal-to-interference ratio (SIR) attained at a typical Internet-of-Things (IoT) device in a dual-hop IoT network. The IoT device associates with either a serving macro base station (MBS) for direct transmissions or associates with a decode and forward (DF) relay for dual-hop transmissions, depending on the biased received signal power criterion. In contrast to the conventional success probability, the meta distribution is the distribution of the conditional success probability (CSP), which is conditioned on the locations of the wireless transmitters. The meta distribution is a fine-grained performance metric that captures important network performance metrics such as the coverage probability and the mean local delay as its special cases. Specifically, we derive the moments of the CSP in order to calculate analytic expressions for the meta distribution. Further, we derive mathematical expressions for special cases such as the mean local delay, variance of the CSP, and success probability of a typical IoT device and typical relay with different offloading biases. We take in consideration in our analysis the association probabilities of IoT devices. Finally, we investigate the impact of increasing the relay density on the mean local delay using numerical results.