Abstract-Millimeter wave (mmWave) holds promise as a carrier frequency for fifth generation cellular networks. Because mmWave signals are sensitive to blockage, prior models for cellular networks operated in the ultra high frequency (UHF) band do not apply to analyze mmWave cellular networks directly. Leveraging concepts from stochastic geometry, this paper proposes a general framework to evaluate the coverage and rate performance in mmWave cellular networks. Using a distancedependent line-of-site (LOS) probability function, the locations of the LOS and non-LOS base stations are modeled as two independent non-homogeneous Poisson point processes, to which different path loss laws are applied. Based on the proposed framework, expressions for the signal-to-noise-and-interference ratio (SINR) and rate coverage probability are derived. The mmWave coverage and rate performance are examined as a function of the antenna geometry and base station density. The case of dense networks is further analyzed by applying a simplified system model, in which the LOS region of a user is approximated as a fixed LOS ball. The results show that dense mmWave networks can achieve comparable coverage and much higher data rates than conventional UHF cellular systems, despite the presence of blockages. The results suggest that the cell size to achieve the optimal SINR scales with the average size of the area that is LOS to a user.

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 Sub6GHz 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.

Large-scale blockages like buildings affect the performance of urban cellular networks, especially at higher frequencies. Unfortunately, such blockage effects are either neglected or characterized by oversimplified models in the analysis of cellular networks. Leveraging concepts from random shape theory, this paper proposes a mathematical framework to model random blockages and analyze their impact on cellular network performance. Random buildings are modeled as a process of rectangles with random sizes and orientations whose centers form a Poisson point process on the plane. The distribution of the number of blockages in a link is proven to be Poisson random variable with parameter dependent on the length of the link. A path loss model that incorporates the blockage effects is proposed, which matches experimental trends observed in prior work. The model is applied to analyze the performance of cellular networks in urban areas with the presence of buildings, in terms of connectivity, coverage probability, and average rate. Analytic results show while buildings may block the desired signal, they may still have a positive impact on network performance since they can block significantly more interference.

Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complicated, making evaluation of different communication strategies challenging in both analysis and simulation. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper proposes to analyze downlink performance in a fixedsize cell, which is inscribed within a weighted Voronoi cell in a Poisson field of interferers. A nearest out-of-cell interferer, out-ofcell interferers outside a guard region, and cross-tier interference are included in the interference calculations. Bounding the interference power as a function of distance from the cell center, the total interference is characterized through its Laplace transform. An equivalent marked process is proposed for the out-of-cell interference under additional assumptions. To facilitate simplified calculations, the interference distribution is approximated using the Gamma distribution with second order moment matching. The Gamma approximation simplifies calculation of the success probability and average rate, incorporates small-scale and largescale fading, and works with co-tier and cross-tier interference. Simulations show that the proposed model provides a flexible way to characterize outage probability and rate as a function of the distance to the cell edge.

Abstract-Ad hoc networks provide an on-demand, infrastructure-free means to communicate between soldiers in war zones, aid workers in disaster areas, or consumers in device-to-device (D2D) applications. Unfortunately, ad hoc networks are limited by interference due to nearby transmissions. Millimeter-wave (mmWave) devices offer several potential advantages for ad hoc networks including reduced interference due to directional antennas and building blockages, not to mention huge bandwidth channels for large data rates.. This paper uses a stochastic geometry approach to characterize the oneway and two-way signal-to-interference ratio distribution of a mmWave ad hoc network with directional antennas, random blockages, and ALOHA channel access. The interference-tonoise ratio shows that a fundamental limitation of an ad hoc network, interference, may still be an issue. The performance of mmWave ad hoc networks is bounded by the transmission capacity and area spectral efficiency. The results show that mmWave networks can support much higher densities and larger spectral efficiencies, even in the presence of blockage, compared with lower frequency communication for certain link distances. Due to the increased bandwidth, the rate coverage of mmWave can be much greater than lower frequency devices.

This paper proposes a stochastic geometry framework to analyze the SINR and rate performance in a large-scale uplink massive MIMO network. Based on the model, expressions are derived for spatial average SINR distributions over user and base station distributions with maximum ratio combining (MRC) and zero-forcing (ZF) receivers. We show that using massive MIMO, the uplink SINR in certain urban marco-cell scenarios is limited by interference. In the interference-limited regime, the results reveal that for MRC receivers, a super-linear (polynomial) scaling law between the number of base station antennas and scheduled users per cell preserves the uplink SIR distribution, while a linear scaling applies to ZF receivers. ZF receivers are shown to outperform MRC receivers in the SIR coverage, and the performance gap is quantified in terms of the difference in the number of antennas to achieve the same SIR distribution. Numerical results verify the analysis. It is found that the optimal compensation fraction in fractional power control to optimize rate is generally different for MRC and ZF receivers. Besides, simulations show that the scaling results derived from the proposed framework apply to the networks where base stations are distributed according to a hexagonal lattice.

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The millimeter wave (mmWave) spectrum is a strong candidate carrier frequency for access channels in fifth generation cellular networks. Unfortunately, the human body heavily attenuates mmWave signals. This paper evaluates the impact of self-body blocking (the blocking of the direct link by the handset user's body) in mmWave cellular networks using a stochastic geometric network model. A mathematical model for self-body blocking is proposed, allowing for position changes, and used to compute signal-to-interference-plus-noise ratio (SINR) distributions with two possible user association rules. The results characterize how self-body blocking impacts the SINR coverage. Even including self-body blocking, mmWave cellular systems can still outperform convention systems at lower frequencies, in terms of the achievable rate, due to the larger bandwidth.