# A Normalization Model for Analyzing Multi-Tier Millimeter Wave Cellular Networks

## TL;DR

This paper introduces a normalization model that simplifies the analysis of multi-tier millimeter wave cellular networks by converting them into a single-tier model, enabling easier computation of coverage probability and revealing an optimal beam width for maximizing coverage.

## Contribution

The paper presents a novel normalization model that transforms multi-tier mmWave networks into a single-tier framework, simplifying analysis and providing new insights into beamforming optimization.

## Key findings

- Normalization model simplifies network analysis.
- Coverage probability expressions derived for general and perfect alignment cases.
- Optimal beam width exists to maximize coverage probability.

## Abstract

Based on the distinguishing features of multi-tier millimeter wave (mmWave) networks such as different transmit powers, different directivity gains from directional beamforming alignment and path loss laws for line-of-sight (LOS) and non-line-of-sight (NLOS) links, we introduce a normalization model to simplify the analysis of multi-tier mmWave cellular networks. The highlight of the model is that we convert a multi-tier mmWave cellular network into a single-tier mmWave network, where all the base stations (BSs) have the same normalized transmit power 1 and the densities of BSs scaled by LOS or NLOS scaling factors respectively follow piecewise constant function which has multiple demarcation points. On this basis, expressions for computing the coverage probability are obtained in general case with beamforming alignment errors and the special case with perfect beamforming alignment in the communication. According to corresponding numerical exploration, we conclude that the normalization model for multi-tier mmWave cellular networks fully meets requirements of network performance analysis, and it is simpler and clearer than the untransformed model. Besides, an unexpected but sensible finding is that there is an optimal beam width that maximizes coverage probability in the case with beamforming alignment errors.