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Analytical Modeling of Uplink Cellular Networks (1203.1304v3)

Published 6 Mar 2012 in cs.IT, cs.NI, math.IT, and math.PR

Abstract: Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wyner-type model, or via complex system level simulations that often do not provide insight into why various trends are observed. This paper proposes a novel middle way using point processes that is both accurate and also results in easy-to-evaluate integral expressions based on the Laplace transform of the interference. We assume mobiles and base stations are randomly placed in the network with each mobile pairing up to its closest base station. Compared to related recent work on downlink analysis, the proposed uplink model differs in two key features. First, dependence is considered between user and base station point processes to make sure each base station serves a single mobile in the given resource block. Second, per-mobile power control is included, which further couples the transmission of mobiles due to location-dependent channel inversion. Nevertheless, we succeed in deriving the coverage (equivalently outage) probability of a typical link in the network. This model can be used to address a wide variety of system design questions in the future. In this paper we focus on the implications for power control and see that partial channel inversion should be used at low signal-to-interference-plus-noise ratio (SINR), while full power transmission is optimal at higher SINR.

Citations (458)

Summary

  • The paper introduces a tractable analytical model that uses Poisson point processes and the Laplace transform to derive uplink coverage probability.
  • It compares multiple network scenarios—PPP-Rayleigh, PPP-Uniform, and grid models—to validate the analytical approximations against simulations.
  • It offers practical insights for system design, particularly the trade-offs of fractional power control in balancing cell-edge performance and interference.

Analytical Modeling of Uplink Cellular Networks

The paper by Novlan, Dhillon, and Andrews presents an analytical model for uplink cellular networks utilizing stochastic geometry and point process theory. Traditional approaches to uplink analysis often employ oversimplified models like the Wyner model, which fail to account for the spatial variability and complexity of interference between user devices. This work introduces a novel framework that bridges the gap between simplicity and accuracy, facilitating the derivation of the complete SINR distribution.

Key Contributions

The authors propose a tractable model leveraging Poisson Point Processes (PPP) to analyze uplink performance. This model accounts for the random placement of mobile users and base stations, incorporating fractional power control schemes. By treating the distance between user devices and base stations as random variables following certain distributions, they succeeded in deriving analytical expressions for crucial performance metrics like coverage probability and average rate.

One of the significant contributions outlined in the paper is the derivation of the uplink coverage probability through the Laplace transform of interference. The use of stochastic geometry allows the model to extend beyond the Wyner model, offering more realistic insights into networks where interference isn't spatially averaged or deterministically modeled.

Analytical Insights

The model highlights several scenarios:

  • PPP-Rayleigh: Assumes Rayleigh distribution for distances, suitable for irregular cell topologies.
  • PPP-Uniform: Considers uniform distribution, approximating hexagonal grid deployments.
  • Grid Model: Benchmarked against simulations of traditional grid models to validate the analytical approximations.

These scenarios facilitate understanding of how different network layouts affect uplink performance. The authors demonstrate that their model aligns closely with simulated results and even with empirical data from urban deployments.

Practical Implications and System Design

The framework permits detailed examination of fractional power control—a key mechanism in uplink transmission aimed at mitigating interference and managing power consumption. This power control model, parameterized by a factor ε, provides insights into how transmit power reductions improve cell-edge user experience at the potential cost of increased interference for others. System designers can leverage these insights to balance power utilization with coverage enhancement, particularly crucial in battery-constrained environments.

The paper also presents a comparison between uplink and downlink coverage, emphasizing the significance of deploying unified models in performance evaluation, thereby assisting in the development of improved handoff strategies and capacity planning.

Future Directions

This work paves the way for further research in heterogeneous network scenarios where multiple access point types coexist and interact. Studies can expand on these models to understand how topology and heterogeneity affect interference and overall network performance, exploring more complex user-behavior models or more granular cell constructs.

In conclusion, this paper provides a robust analytical basis for uplink performance analysis in cellular networks, suitable for guiding both theoretical exploration and practical optimization in modern broadband communication systems.