[Paper Review] Coverage Analysis of Two-Tier HetNets for Co-Channel, Orthogonal, and Partial Spectrum Sharing under Fractional Load Conditions

Praful D. Mankar, Goutam Das+1 more|arXiv (Cornell University)|Sep 19, 2016

Advanced MIMO Systems Optimization3 citations

TL;DR

This paper proposes a composite stochastic geometry model using Poisson point processes (PPP) for macro base stations (MBSs) and Poisson cluster processes (PCP) for femto access points (FAPs) to analyze coverage probability in two-tier heterogeneous networks (HetNets) under fractional load. It evaluates co-channel, orthogonal, and partial spectrum sharing modes, showing that cognitive channel access at FAPs significantly improves coverage by reducing inter-tier interference, with partial sharing offering the best performance under realistic clustered deployment and load conditions.

ABSTRACT

In heterogeneous networks, the random deployment of femto access points (FAPs) and macro base stations (MBSs) with uncoordinated channel access impose huge inter-tier interferences. In real-life networks, the process of MBSs deployment exhibits the homogeneity, however the FAPs have the behavioral characteristic of clusters formation like in malls, apartments, offices, etc. Therefore, the composite modeling of the MBSs and the FAPs using Poisson point process and Poisson cluster process is employed for the evaluation of coverage probability. The scenario of the real-time traffic for macro-tier and the best-effort traffic for femto-tier is considered. Cognition is introduced in the clustered FAPs to control the inter-tier interference. Furthermore, the impact of macro-tier load is analyzed by exploiting the inherent coupling between coverage probability and activity factor of an MBS. Further, we study the effect of co-channel, orthogonal, and partial spectrum sharing modes on the coverage for given parameters like load condition, FAPs/MBSs density, etc. We provide simulation validation for the derived expressions of coverage and present an comparative analysis for the mentioned spectrum sharing modes.

Motivation & Objective

• To address the challenge of inter-tier interference in two-tier HetNets caused by random and clustered deployment of femto access points (FAPs) and macro base stations (MBSs).
• To model the heterogeneous deployment behavior—homogeneous for MBSs and clustered for FAPs—using Poisson point process (PPP) and Poisson cluster process (PCP), respectively.
• To evaluate the impact of different spectrum sharing modes—co-channel, orthogonal, and partial sharing—on coverage probability under fractional load conditions.
• To introduce cognitive channel access at the FAP level using local information to mitigate inter-tier interference without requiring global macro-level coordination.
• To establish a quantitative link between MBS activity factor and coverage probability, enabling analysis under realistic traffic load variations.

Proposed method

• Model MBSs using a homogeneous Poisson point process (PPP) to reflect their uniform, ubiquitous deployment for coverage.
• Model FAPs using a Poisson cluster process (PCP) to capture their clustered deployment behavior in residential, commercial, and office environments.
• Derive the Laplace transform of aggregate interference from FAPs to macro users using the probability generating functional (PGFL) of PCP and moment generating function (MGF) of Poisson-distributed cluster sizes.
• Incorporate fractional load conditions by relating the MBS activity factor to the coverage probability through a coupling model, enabling analysis under dynamic traffic load.
• Apply cognitive channel access at FAPs by modeling spectrum access as a function of local interference conditions, reducing co-channel interference to macro users.
• Use stochastic geometry and Laplace transform techniques to derive closed-form approximations for coverage probability under co-channel, orthogonal, and partial spectrum sharing modes.

Experimental results

Research questions

• RQ1 How does the composite PPP-PCP model improve the accuracy of coverage probability analysis in two-tier HetNets compared to traditional PPP-only models?
• RQ2 What is the impact of FAP clustering on inter-tier interference and coverage probability in macro-femto networks under fractional load?
• RQ3 How do co-channel, orthogonal, and partial spectrum sharing modes compare in terms of coverage performance under realistic deployment and load conditions?
• RQ4 To what extent can cognitive channel access at the FAP level reduce inter-tier interference without requiring global network coordination?
• RQ5 How does the MBS activity factor influence coverage probability, and how can this coupling be leveraged for load-aware network optimization?

Key findings

• The composite PPP-PCP model provides a more accurate representation of real-world HetNet deployments, where MBSs are uniformly distributed and FAPs form clusters in high-traffic areas.
• Cognitive channel access at FAPs significantly improves macro-tier coverage by reducing inter-tier interference, especially under high FAP density and partial spectrum sharing.
• Partial spectrum sharing achieves the highest coverage probability across all tested load and density conditions, outperforming co-channel and orthogonal sharing due to better interference management.
• The derived coverage probability expressions are validated via simulation, showing close agreement with theoretical approximations under various network parameters.
• The coupling between MBS activity factor and coverage probability enables dynamic load-aware optimization, with coverage decreasing as MBS load increases due to higher interference levels.
• The approximation method using Jensen’s inequality and exponential bounds on the Laplace transform of interference yields tractable and accurate results, enabling practical deployment insights.