[Paper Review] Serving Distance and Coverage in a Closed Access PHP-Based Heterogeneous Cellular Network

Zeinab Yazdanshenasan, Harpreet S. Dhillon+1 more|arXiv (Cornell University)|Apr 10, 2017

Advanced MIMO Systems Optimization8 references7 citations

TL;DR

This paper proposes a tractable analytical framework for downlink coverage in a two-tier closed-access heterogeneous cellular network using a Poisson Hole Process (PHP) to model small cell deployment around macrocells with exclusion zones. It derives tight bounds on serving distance and coverage probability, significantly improving accuracy over prior approximations by preserving local interference structure while simplifying far-field interference.

ABSTRACT

Heterogeneous cellular networks (HCNs) usually exhibit spatial separation amongst base stations (BSs) of different types (termed tiers in this paper). For instance, operators will usually not deploy a picocell in close proximity to a macrocell, thus inducing separation amongst the locations of pico and macrocells. This separation has recently been captured by modeling the small cell locations by a Poisson Hole Process (PHP) with the hole centers being the locations of the macrocells. Due to the presence of exclusion zones, the analysis of the resulting model is significantly more complex compared to the more popular Poisson Point Process (PPP) based models. In this paper, we derive a tight bound on the distribution of the distance of a typical user to the closest point of a PHP. Since the exact distribution of this distance is not known, it is often approximated in the literature. For this model, we then provide tight characterization of the downlink coverage probability for a typical user in a two-tier closed-access HCN under two cases: (i) typical user is served by the closest macrocell, and (ii) typical user is served by its closest small cell. The proposed approach can be extended to analyze other relevant cases of interest, e.g., coverage in a PHP-based open access HCN.

Motivation & Objective

• To address the lack of accurate analytical models for serving distance and coverage in heterogeneous cellular networks with inter-tier spatial separation.
• To overcome the limitations of existing approximations (e.g., PPP, Weibull fitting) that fail across broad system parameter ranges.
• To develop a rigorous framework for coverage probability in closed-access PHP-based HCNs by precisely modeling interference from both tiers.
• To provide a foundation for extending analysis to open-access scenarios, which are more complex due to joint cell selection.

Proposed method

• Model macrocell locations as a homogeneous Poisson Point Process (PPP) and small cell locations as a Poisson Hole Process (PHP), where holes of radius D are carved around each macrocell.
• Derive a tight bound on the distribution of the distance from a typical user to the closest PHP point, preserving local neighborhood structure for accuracy.
• Use stochastic geometry tools to compute the Laplace transform of interference from both macro and small cells, accounting for exclusion zones.
• Develop lower and upper bounds on the coverage probability conditioned on serving distances to the closest macrocell and small cell.
• Apply the generalized approach from prior work on shot-noise analysis to maintain accuracy while enabling tractability.
• Decondition over serving distances using derived distributions to obtain the overall coverage probability.

Experimental results

Research questions

• RQ1 How can the serving distance distribution to the closest small cell be accurately characterized in a PHP-based HCN with exclusion zones?
• RQ2 What is the coverage probability for a typical user served by its closest small cell in a closed-access two-tier HCN with PHP-based small cell deployment?
• RQ3 How does the coverage probability change when the typical user is served by its closest macrocell instead?
• RQ4 What is the impact of exclusion zones on interference modeling and coverage performance in PHP-based HCNs compared to standard PPP models?
• RQ5 Can tight analytical bounds on coverage probability be derived without relying on curve-fitting or density-based approximations?

Key findings

• The proposed bound on the serving distance to the closest PHP point is remarkably tight across a wide range of system parameters, significantly outperforming existing approximations.
• The coverage probability for a user served by its closest small cell is bounded using a novel interference model that accounts for exclusion zones and conditional serving distances.
• The lower bound on coverage probability incorporates the effective interference from both the closest macrocell and the interferers in the small cell tier outside the serving range.
• The upper bound on coverage probability accounts for the reduced interference from small cells due to hole-induced exclusion, leading to a more accurate interference estimate.
• The derived bounds are shown to be tight through numerical comparisons, validating their use in place of less accurate approximations.
• The framework enables accurate analysis of closed-access HCNs and provides a stepping stone for open-access scenarios, which remain a focus of future work.