The Ginibre Point Process as a Model for Wireless Networks with Repulsion (1401.3677v1)

Abstract: The spatial structure of transmitters in wireless networks plays a key role in evaluating the mutual interference and hence the performance. Although the Poisson point process (PPP) has been widely used to model the spatial configuration of wireless networks, it is not suitable for networks with repulsion. The Ginibre point process (GPP) is one of the main examples of determinantal point processes that can be used to model random phenomena where repulsion is observed. Considering the accuracy, tractability and practicability tradeoffs, we introduce and promote the $\beta$-GPP, an intermediate class between the PPP and the GPP, as a model for wireless networks when the nodes exhibit repulsion. To show that the model leads to analytically tractable results in several cases of interest, we derive the mean and variance of the interference using two different approaches: the Palm measure approach and the reduced second moment approach, and then provide approximations of the interference distribution by three known probability density functions. Besides, to show that the model is relevant for cellular systems, we derive the coverage probability of the typical user and also find that the fitted $\beta$-GPP can closely model the deployment of actual base stations in terms of the coverage probability and other statistics.

• The paper introduces the β-Ginibre Point Process as an analytical tool bridging PPP and DPP for modeling repulsive wireless node placements.
• It derives precise expressions for interference metrics using dual methodologies, enhancing the prediction of network performance.
• Comparative analysis shows the β-GPP closely fits real cellular deployments, outperforming traditional models in spatial accuracy.

The Ginibre Point Process as a Model for Wireless Networks with Repulsion

This paper investigates the use of the Ginibre Point Process (GPP), a member of determinantal point processes (DPPs), as a model for wireless networks where node locations exhibit repulsion, contrary to the independence assumption inherent in the Poisson Point Process (PPP). Unlike other models that account for repulsion but suffer from analytical intractability, the GPP offers a compromise by maintaining analytical tractability alongside better capturing spatial dependencies in node distributions.

Summary of Key Findings

• Introducing the $\beta$-Ginibre Point Process: The paper proposes the $\beta$-GPP, an intermediate process between the PPP and the GPP, tuned by a parameter $\beta$. As $\beta \to 0$, the process converges to a PPP, making it adaptable to various extents of repulsion in wireless networks.
• Analytical Results: The authors derive expressions for critical metrics like mean and variance of interference, which are instrumental in assessing the performance of wireless networks. Two distinct methodologies—Palm measure approach and reduced second moment approach—are employed to validate these results.
• Comparison and Validation: Comparisons with the PPP and the Matérn hard-core processes reveal that the $\beta$-GPP provides a better model for networks demonstrating node repulsion. Empirically, the GPP fits closely with the spatial occurrence of base stations in real-world cellular networks, showing a strong correlation not achievable with traditional models.
• Practical Application: The paper includes a fitting exercise on real-world base station distributions, demonstrating urban deployments as more regular ($\beta \approx 1$) compared to rural ones (with lower $\beta$).

Theoretical and Practical Implications

The theoretical advancement through the introduction of the $\beta$-GPP and its development in both mean and variance analysis for interference significantly contributes to the stochastic geometry framework. It provides a scalable framework extending the practical applicability of DPPs in modeling wireless network topologies.

Practically, the ability to fit the $\beta$-GPP to real network configurations implies its utility in optimizing network layouts, enhancing coverage probability predictions, and guiding infrastructure development, especially in areas with limitations against dense deployments.

Future Prospects

The framework outlined for utilizing the GPP points towards several avenues for future research:

1. Parameter Optimization: Extending the $\beta$-tuning approach to achieve dynamic adaptation based on real-time network conditions could enhance network adaptability and performance.
2. Multi-tier and Cognitive Networks: Investigating the applicability of the $\beta$-GPP model in multi-tier networks, such as those including pico or femtocells, or in cognitive radio networks where spectrum sharing involves varied communicative intensities and behaviors.
3. Network Performance Metrics: Further exploration can be conducted to corroborate other performance metrics within this model, like spectral efficiency, outage probability, and energy efficiency.

This paper delivers a significant contribution to the field of wireless communication by leveraging stochastic geometry and determinantal point processes to create a robust, flexible, and analytically tractable model for wireless networks characterized by node repulsion. This lays a foundation that addresses existing limitations of current models while fostering more accurate and predictive network performance assessments.