Stochastic Geometry Modeling and Analysis of Multi-Tier Millimeter Wave Cellular Networks (1410.3577v1)

Abstract: In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported experimental data. The path-loss model accounts for different distributions of line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying on a noise-limited approximation for typical millimeter wave network deployments, simple and exact integral as well as approximated and closed-form formulas for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. The proposed mathematical framework is applicable to cell association criteria based on the smallest path-loss and on the highest received power. It accounts for beamforming alignment errors and for multi-tier cellular network deployments. Numerical results confirm that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, both in terms of coverage probability and average rate.

• The paper introduces a novel analytical framework using stochastic geometry to model empirical path-loss and blockage effects in mmWave cellular networks.
• It derives precise expressions for coverage probability and average rate under a noise-limited assumption validated by Monte Carlo simulations.
• The study highlights that adequate beamforming gain and deployment density are crucial for mmWave networks to outperform traditional μWave systems.

Stochastic Geometry Modeling and Analysis of Multi-Tier Millimeter Wave Cellular Networks

The paper presented introduces an analytical framework for evaluating millimeter wave (mmWave) cellular networks using stochastic geometry. This framework is notable due to its incorporation of empirical path-loss and blockage models, which reflect realistic conditions more accurately than conventional models often used in $\mu$Wave communications. By employing a Poisson point process (PPP) to model the spatial distribution of base stations (BSs) and assuming a noise-limited system, the authors derive precise expressions for both coverage probability and average rate performance metrics. The noise-limited assumption is particularly relevant for mmWave systems due to the large bandwidths and significant path-loss, aspects that differentiate them from traditional microwave-based cellular networks.

The framework delineates the performance differences between association strategies, namely the smallest path-loss and the highest received power criteria, offering flexibility to consider variations in network deployments and environmental impacts. Moreover, it accounts for complex aspects such as beamforming alignment errors and multi-tier network structures—a reflection of the heterogeneous nature of modern and future network deployments. The robustness of the framework is affirmed through Monte Carlo simulations that validate the noise-limited model for typical network densities, enhancing confidence in its practical applicability.

The results underscore that mmWave networks, given adequate density, can surpass $\mu$Wave systems in both coverage probability and average rate. However, this superiority hinges on the presence of a sufficient beamforming gain, mitigating the high path-loss inherent to high-frequency transmissions. The empirical path-loss and blockage models were derived from extensive channel measurement studies, making the findings particularly relevant for real-world implementations where such environmental and propagation characteristics are significant.

In terms of numerical results, the paper provides clear evidence supporting the applicability of the proposed framework. Specifically, the framework's accuracy remains high under realistic network conditions, as substantiated by simulation results even when interference is considered, illustrating the tractability and fidelity of a noise-limited approximation for mmWave systems. The paper also offers insights into the spatial distribution and link state characteristics of mmWave links, emphasizing their dependency on the deployment density and propagation conditions.

This paper opens numerous avenues for future research, particularly in refining multi-tier and heterogeneous network models. The propagation models detailed here could be extrapolated or adapted for emerging network paradigms, such as ultra-dense networks and vehicular or drone-based communications, where mmWave technologies are primed to be influential. In practice, the ability to accurately forecast coverage and rate performance using tractable mathematical models is invaluable for network designers aiming to optimize deployment strategies for new mmWave-based infrastructure.

The comprehensive nature of this framework offers a solid foundation for further research into optimizing beamforming techniques, mitigating the effects of blocking and shadowing, and enhancing network protocols to better accommodate the nuances of mmWave propagation. Such efforts could substantially impact the ongoing development of 5G and future 6G cellular networks, where mmWave frequencies are anticipated to play a pivotal role.