[Paper Review] An Effective Handover Analysis for the Randomly Distributed Heterogeneous Cellular Networks

Bin Fang, Wuyang Zhou|arXiv (Cornell University)|Jan 7, 2015

Advanced MIMO Systems Optimization3 citations

TL;DR

This paper proposes a stochastic geometry-based analytical framework to compute the handover rate in randomly deployed heterogeneous cellular networks (HCNs), focusing on multi-tier architectures. By modeling base station locations as Poisson point processes and applying an infinitesimal method, it derives closed-form expressions for instantaneous handover rates that depend on user speed and network parameters, with results validated via simulation across multiple mobility models.

ABSTRACT

Handover rate is one of the most import metrics to instruct mobility management and resource management in wireless cellular networks. In the literature, the mathematical expression of handover rate has been derived for homogeneous cellular network by both regular hexagon coverage model and stochastic geometry model, but there has not been any reliable result for heterogeneous cellular networks (HCNs). Recently, stochastic geometry modeling has been shown to model well the real deployment of HCNs and has been extensively used to analyze HCNs. In this paper, we give an effective handover analysis for HCNs by stochastic geometry modeling, derive the mathematical expression of handover rate by employing an infinitesimal method for a generalized multi-tier scenario, discuss the result by deriving some meaningful corollaries, and validate the analysis by computer simulation with multiple walking models. By our analysis, we find that in HCNs the handover rate is related to many factors like the base stations' densities and transmitting powers, user's velocity distribution, bias factor, pass loss factor and etc. Although our analysis focuses on the scenario of multi-tier HCNs, the analytical framework can be easily extended for more complex scenarios, and may shed some light for future study.

Motivation & Objective

• To address the lack of reliable, generalized mathematical expressions for handover rates in heterogeneous cellular networks (HCNs), particularly due to random base station (BS) deployments and varying transmit powers.
• To develop a tractable analytical framework for computing handover rates—both horizontal and vertical—in multi-tier HCNs with arbitrary BS densities, transmit powers, and path loss exponents.
• To demonstrate that handover rate depends only on user speed distribution and not direction, enabling application to all memoryless mobility models.
• To validate the analytical results through extensive computer simulations using multiple walking models, ensuring accuracy under realistic mobility conditions.
• To provide a foundation for future work on mobility and resource management in 5G and beyond networks by offering a scalable, extendable analytical model.

Proposed method

• Models the locations of BSs in each tier as independent homogeneous Poisson Point Processes (PPPs), enabling stochastic geometry-based analysis of random network topologies.
• Applies an infinitesimal method to derive the instantaneous handover rate experienced by a typical user equipment (UE) moving at a given speed, based on geometric probability of crossing cell boundaries.
• Derives closed-form expressions for handover rates between any two tiers by integrating over the joint distribution of distances and angles between the UE and BSs in different tiers.
• Introduces bias factors and path loss exponents to model real-world deployment scenarios where BSs in different tiers have varying coverage ranges and signal strengths.
• Uses the derived instantaneous handover rate expression and averages it over the user’s speed distribution to obtain the overall expected handover rate.
• Validates the analytical results through Monte Carlo simulations using various mobility models, including random walk and random waypoint, across multiple network configurations.

Experimental results

Research questions

• RQ1 How can the handover rate in a multi-tier heterogeneous cellular network be analytically modeled when BSs are randomly deployed and have different transmit powers?
• RQ2 What is the dependence of the handover rate on key system parameters such as BS density, transmit power, path loss exponent, and user velocity?
• RQ3 Does the handover rate depend on the direction of user movement, or is it solely determined by speed, as suggested by the memoryless mobility assumption?
• RQ4 How do vertical handovers (between different tiers) compare in frequency to horizontal handovers (within the same tier), and what factors influence this ratio?
• RQ5 Can the proposed analytical framework be extended to more complex HCN scenarios beyond the multi-tier model?

Key findings

• The instantaneous handover rate depends only on the user’s instantaneous speed and is independent of the direction of movement, validating the applicability of the model to all memoryless mobility models.
• The derived handover rate expression is a closed-form function of BS densities, transmit powers, path loss exponents, bias factors, and user speed distribution.
• Simulation results confirm the accuracy of the analytical model across various mobility patterns, with close agreement between theoretical predictions and simulated handover rates.
• The total handover rate increases with higher user velocity and greater BS density in the network, particularly in the second tier, with a more than 200% increase observed when density doubles.
• Vertical handover rates are significantly influenced by bias factors and path loss exponents; increasing the bias of a lower-tier BS can reduce its handover rate by up to 60% due to extended coverage.
• The forward and reverse handover rates between two tiers are symmetric when the system parameters are reciprocal, confirming the theoretical symmetry in the derived expressions.