[Paper Review] Generalized Carrier to Interference Ratio Analysis for the Shotgun Cellular System in Multiple Dimensions

Prasanna Madhusudhanan, Juan G. Restrepo+3 more|arXiv (Cornell University)|Feb 21, 2010

Advanced MIMO Systems Optimization25 references4 citations

TL;DR

This paper presents a generalized analytical framework for the signal-to-interference-plus-noise ratio (SINR) in shotgun cellular systems (SCSs) with base stations distributed via non-homogeneous Poisson point processes in one, two, or three dimensions. It derives semi-analytical coverage probability expressions under arbitrary fading and path-loss models, revealing that in interference-limited, homogeneous scenarios with power-law path loss, the SINR distribution is invariant to fading type and base station density.

ABSTRACT

In this paper, we analyze the signal-to-interference-plus-noise ratio (SINR) performance at a mobile station (MS) in a random cellular network. The cellular network is formed by base-stations (BSs) placed in a one, two or three dimensional space according to a possibly non-homogeneous Poisson point process, which is a generalization of the so-called shotgun cellular system. We develop a sequence of equivalence relations for the SCSs and use them to derive semi-analytical expressions for the coverage probability at the MS when the transmissions from each BS may be affected by random fading with arbitrary distributions as well as attenuation following arbitrary path-loss models. For homogeneous Poisson point processes in the interference-limited case with power-law path-loss model, we show that the SINR distribution is the same for all fading distributions and is not a function of the base station density. In addition, the influence of random transmission powers, power control, multiple channel reuse groups on the downlink performance are also discussed. The techniques developed for the analysis of SINR have applications beyond cellular networks and can be used in similar studies for cognitive radio networks, femtocell networks and other heterogeneous and multi-tier networks.

Motivation & Objective

• To analyze the SINR performance in random cellular networks with base stations distributed via Poisson point processes in 1D, 2D, or 3D space.
• To develop a general framework for coverage probability under arbitrary fading distributions and path-loss models.
• To investigate the impact of network parameters such as transmission power randomness, power control, and channel reuse on downlink performance.
• To establish analytical invariance properties of SINR distribution under specific conditions, particularly in interference-limited, homogeneous networks.
• To extend the applicability of the analysis to heterogeneous and multi-tier networks, including cognitive radio and femtocell systems.

Proposed method

• Modeling base station locations using non-homogeneous Poisson point processes across one, two, or three spatial dimensions.
• Deriving equivalence relations for shotgun cellular systems to simplify the SINR analysis across different network dimensions.
• Using stochastic geometry techniques to express the coverage probability in semi-analytical form, incorporating arbitrary fading and path-loss models.
• Applying Laplace transform methods to characterize the distribution of interference power from spatially random base stations.
• Establishing conditions under which the SINR distribution becomes independent of fading distribution and base station density in interference-limited scenarios.
• Extending the framework to include effects of random transmission powers, power control, and multiple channel reuse groups in downlink analysis.

Experimental results

Research questions

• RQ1 How does the coverage probability in a shotgun cellular system vary with spatial dimensionality (1D, 2D, 3D) under general point process models?
• RQ2 What is the impact of arbitrary fading distributions and path-loss models on the SINR distribution and coverage probability?
• RQ3 Under what conditions does the SINR distribution become independent of the fading distribution and base station density?
• RQ4 How do random transmission powers and power control mechanisms affect downlink performance in interference-limited networks?
• RQ5 To what extent can the derived analytical framework be generalized to other network types such as cognitive radio or multi-tier heterogeneous networks?

Key findings

• In interference-limited, homogeneous Poisson networks with power-law path loss, the SINR distribution is invariant to the fading distribution and does not depend on base station density.
• The derived coverage probability expressions are semi-analytical and applicable to arbitrary fading and path-loss models, enabling precise performance evaluation.
• The equivalence relations developed for SCSs allow consistent SINR analysis across different spatial dimensions, simplifying cross-dimensional comparisons.
• Random transmission powers and power control mechanisms significantly influence downlink coverage, with performance gains observed under optimal power control strategies.
• The framework's generality allows direct application to cognitive radio networks, femtocell deployments, and multi-tier heterogeneous networks.
• The analytical results reveal that in high-interference regimes, the network's spatial dimension and path-loss exponent dominate performance, while fading characteristics become negligible in determining SINR distribution.