Modeling and Analyzing Millimeter Wave Cellular Systems (1605.04283v1)

Abstract: We provide a comprehensive overview of mathematical models and analytical techniques for millimeter wave (mmWave) cellular systems. The two fundamental physical differences from conventional Sub-6GHz cellular systems are (i) vulnerability to blocking, and (ii) the need for significant directionality at the transmitter and/or receiver, which is achieved through the use of large antenna arrays of small individual elements. We overview and compare models for both of these factors, and present a baseline analytical approach based on stochastic geometry that allows the computation of the statistical distributions of the downlink signal-to-interference-plus-noise ratio (SINR) and also the per link data rate, which depends on the SINR as well as the average load. There are many implications of the models and analysis: (a) mmWave systems are significantly more noise-limited than at Sub-6GHz for most parameter configurations; (b) initial access is much more difficult in mmWave; (c) self-backhauling is more viable than in Sub-6GHz systems which makes ultra-dense deployments more viable, but this leads to increasingly interference-limited behavior; and (d) in sharp contrast to Sub-6GHz systems cellular operators can mutually benefit by sharing their spectrum licenses despite the uncontrolled interference that results from doing so. We conclude by outlining several important extensions of the baseline model, many of which are promising avenues for future research.

• The paper provides a rigorous mathematical framework using stochastic geometry to model mmWave systems and derive SINR and rate distributions.
• The analysis highlights the impact of blocking and directional beamforming on performance, revealing differences between noise-limited and interference-limited regimes.
• The study discusses challenges in initial access and benefits like self-backhauling and spectrum sharing for optimal mmWave cellular deployments.

Analysis of Millimeter Wave Cellular Systems

The paper "Modeling and Analyzing Millimeter Wave Cellular Systems" by Jeffrey G. Andrews et al., provides a comprehensive mathematical foundation for understanding the characteristics of Millimeter Wave (mmWave) cellular systems and the implications of their deployment.

The core contributions of the paper hinge upon the two fundamental physical differences distinguishing mmWave systems from traditional Sub-6GHz networks: sensitivity to blocking and the requisite directionality at both the transmitter and the receiver achieved through large antenna arrays.

Mathematical Modeling of mmWave Systems

The paper adopts a stochastic geometric approach to model mmWave cellular systems, allowing for the computation of distributions related to the downlink signal-to-interference-plus-noise ratio (SINR) and the per-link data rate. Here are some key modeling aspects considered:

1. Base Station Locations: The base stations are modeled as a homogeneous Poisson Point Process (PPP) distributed on a plane, assuming all BSs are outdoors.
2. User Locations: Users are also modeled as a homogeneous PPP, associating with the BS that offers the smallest path loss.
3. Blocking Effects: Blocking is crucial at mmWave frequencies and is modeled through various approaches. The paper particularly emphasizes the LOS ball model and the random shape theory model.
4. Directionality: Achieved via analog beamforming, the directional gains are modeled using a step function approximation for tractable analysis.
5. Path Loss: Different path loss exponents and parameters are used for LOS and NLOS links.

SINR and Rate Distribution

The SINR coverage probability is derived in the paper, accounting for:

• The Nakagami fading model for small-scale fading.
• The segmentation of base stations into LOS and NLOS sub-processes based on the distance-dependent LOS probability.
• The random nature of beamforming gains.

The SINR coverage probability is extended to the rate coverage by incorporating user load distributions, exploiting round-robin scheduling for simplification.

Key Findings and Implications

• Noise-Limited vs. Interference-Limited Regimes: The paper explores when mmWave systems will be predominantly noise-limited due to high directionality and blocking effects. For instance, systems operating at higher frequencies like 73 GHz with larger bandwidths exhibit more noise-limited behavior compared to systems at 28 GHz.
• Initial Access: The analysis highlights the challenge of initial access in mmWave systems due to the need for beam alignment. The expected low-SNR before beamforming makes initial access procedures more complex compared to Sub-6GHz systems.
• Self-Backhauling: The relatively noise-limited nature of mmWave interference channels facilitates the feasibility of self-backhauling, making ultra-dense deployments more viable.
• Spectrum Sharing: The paper discusses how cellular operators can benefit mutually from sharing spectrum licenses despite the potential for interference, a contrast to Sub-6GHz where spectrum sharing often leads to detrimental interference.

Extensions and Future Work

Several extensions to the baseline model are critical for practical deployments:

• Uplink Modeling: The extension to the uplink SINR and rate coverage considering user scheduling and power control.
• Joint Coverage with Sub-6GHz Systems: Considering the coexistence of Sub-6GHz macrocells which aid mmWave cells in control signaling and in covering areas where mmWave signals cannot penetrate.
• Outdoor-to-Indoor Coverage: Acknowledging the penetration losses through building materials and modeling the coverage dynamics for indoor users.
• Advanced MIMO Techniques: Extending the analysis to consider hybrid beamforming, multi-user MIMO, and massive MIMO approaches respecting the hardware constraints of mmWave systems.

Conclusion

The paper sets a mathematical groundwork that is vital for the design and analysis of mmWave cellular systems. It carefully balances complexity with tractability and lays the foundation for multiple avenues of future research crucial for the practical deployment of mmWave technologies in next-generation networks.