# The Meta Distributions of the SIR/SNR and Data Rate in Coexisting Sub-6GHz and Millimeter-wave Cellular Networks

## TL;DR

This paper develops a comprehensive framework using stochastic geometry to analyze the fine-grained performance metrics, including reliability and latency, of coexisting sub-6GHz and millimeter-wave cellular networks, considering different channel conditions and fading models.

## Contribution

It introduces a systematic method to characterize the meta distributions of SIR, SNR, and data rate in hybrid cellular networks with distinct sub-6GHz and mm-wave spectrums, accounting for their unique interference and noise limitations.

## Key findings

- Meta distribution of SIR/SNR derived for both channels.
- Insights into reliability and latency trade-offs in hybrid networks.
- Validation of analytical models with numerical simulations.

## Abstract

Meta distribution is a fine-grained unified performance metric that enables us to evaluate the {reliability and latency} of next generation wireless networks, in addition to the conventional coverage probability. In this paper, using stochastic geometry tools, we develop a systematic framework to characterize the meta distributions of the downlink signal-to-interference-ratio (SIR)/signal-to-noise-ratio (SNR) and data rate of a typical device in a cellular network with coexisting sub-6GHz and millimeter wave (mm-wave) spectrums. Macro base-stations (MBSs) transmit on sub-6GHz channels (which we term "microwave" channels), whereas small base-stations (SBSs) communicate with devices on mm-wave channels. The SBSs are connected to MBSs via a microwave ($\mu$wave) wireless backhaul. The $\mu$wave channels are interference limited and mm-wave channels are noise limited; therefore, we have the meta-distribution of SIR and SNR in $\mu$wave and mm-wave channels, respectively. To model the line-of-sight (LOS) nature of mm-wave channels, we use Nakagami-m fading model. To derive the meta-distribution of SIR/SNR, we characterize the conditional success probability (CSP) (or equivalently reliability) and its $b^{\mathrm{th}}$ moment for a typical device (a) when it associates to a $\mu$wave MBS for {\em direct} transmission, and (b) when it associates to a mm-wave SBS for {\em dual-hop} transmission (backhaul and access transmission). Performance metrics such as the mean and variance of the local delay (network jitter), mean of the CSP (coverage probability), and variance of the CSP are derived. Numerical results validate the analytical results. Insights are extracted related to the reliability, coverage probability, and latency of the considered network.