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.

Abstract-Millimeter wave (mmWave) cellular systems will require high gain directional antennas and dense base station (BS) deployments to overcome high near field path loss and poor diffraction. As a desirable side effect, high gain antennas offer interference isolation, providing an opportunity to incorporate self-backhauling-BSs backhauling among themselves in a mesh architecture without significant loss in throughput-to enable the requisite large BS densities. The use of directional antennas and resource sharing between access and backhaul links leads to coverage and rate trends that differ significantly from conventional ultra high frequency (UHF) cellular systems. In this paper, we propose a general and tractable mmWave cellular model capturing these key trends and characterize the associated rate distribution. The developed model and analysis is validated using actual building locations from dense urban settings and empirically-derived path loss models. The analysis shows that in sharp contrast to the interference-limited nature of UHF cellular networks, the spectral efficiency of mmWave networks (besides total rate) also increases with BS density particularly at the cell edge. Increasing the system bandwidth, although boosting median and peak rates, does not significantly influence the cell edge rate. With self-backhauling, different combinations of the wired backhaul fraction (i.e. the fraction of BSs with a wired connection) and BS density are shown to guarantee the same median rate (QoS).

Millimeter wave (mmWave) links will offer high capacity but are poor at penetrating into or diffracting around solid objects. Thus, we consider a hybrid cellular network with traditional sub 6 GHz macrocells coexisting with denser mmWave small cells, where a mobile user can connect to either opportunistically. We develop a general analytical model to characterize and derive the uplink and downlink cell association in view of the SINR and rate coverage probabilities in such a mixed deployment. We offer extensive validation of these analytical results (which rely on several simplifying assumptions) with simulation results. Using the analytical results, different decoupled uplink and downlink cell association strategies are investigated and their superiority is shown compared to the traditional coupled approach.Finally, small cell biasing in mmWave is studied, and we show that unprecedented biasing values are desirable due to the wide bandwidth. is with OFCOM, UK. M. Dohler (mischa.dohler@kcl.ac.uk) is with the Centre for Telecommunications Research (CTR), King's College London, UK. I. INTRODUCTIONTwo key capacity-increasing techniques for future cellular networks including 5G will be network densification and the use of higher frequency bands, such as millimeter wave (mmWave) [1], [2]. The main challenges to using mmWave frequencies are their high near-field pathloss (due to small effective antenna aperture) and very poor penetration into buildings. However, it is increasingly believed these challenges can be overcome, at least for outdoor-to-outdoor cellular networks, using high gain steerable antennas in a dense enough network with sufficient scattering[3]- [11]. Further, recent studies have shown that with such highly directional transmissions and sensitivity to blockage, a positive side effect is that interference is greatly reduced, and so in many or most cases, mmWave networks will be noise rather than interference-limited [10]- [13].Nevertheless, it is unrealistic to expect universal coverage with mmWave, especially indoors, and so a likely deployment scenario is that mmWave will co-exist with a traditional sub-6GHz cellular network. The mmWave small cells will be used opportunistically when a connection is possible, with the sub-6GHz base stations providing universal coverage, for both control signaling and for data when a mmWave connection is not available. The goal of this paper is to model and analyze such a hybrid network, considering in particular how user equipments (UEs) should associate with the two types of BSs in the uplink (UL) and downlink (DL). A. Related WorkDownlink and uplink associations are typically coupled, i.e. a UE connects to the same BS in the DL and UL. In the context of a heterogeneous network, downlink-uplink decoupling (DUDe) has been recently shown to significantly improve the network capacity (especially in the UL) by considering different association criteria for the UL and DL [14]. DUDe has been discussed in [2], [15], [16] as an interesting component for future cellular netw...

Large antenna arrays will be needed in future millimeter wave (mmWave) cellular networks, enabling a large number of different possible antenna architectures and multiple-input multiple-output (MIMO) techniques. It is still unclear which MIMO technique is most desirable as a function of different network parameters. This paper, therefore, compares the coverage and rate performance of hybrid beamforming enabled multi-user (MU) MIMO and single-user spatial multiplexing (SM) with single-user analog beamforming (SU-BF). A stochastic geometry model for coverage and rate analysis is proposed for MU-MIMO mmWave cellular networks, taking into account important mmWave-specific hardware constraints for hybrid analog/digital precoders and combiners, and a blockagedependent channel model which is sparse in angular domain. The analytical results highlight the coverage, rate and power consumption tradeoffs in multiuser mmWave networks. With perfect channel state information at the transmitter and round robin scheduling, MU-MIMO is usually a better choice than SM or SU-BF in mmWave cellular networks. This observation, however, neglects any overhead due to channel acquisition or computational complexity. Incorporating the impact of such overheads, our results can be re-interpreted so as to quantify the minimum allowable efficiency of MU-MIMO to provide higher rates than SM or SU-BF.Index Terms-Millimeter wave networks, hybrid beamforming, stochastic geometry, multiuser MIMO.

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