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 the view of the signal-to-interference-and-noise-ratio 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 with 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.
Meanwhile, starting with @cite_18 , modeling and analyzing cellular networks using stochastic geometry has become a popular and accepted approach to understanding their performance trends. Most relevant to this study, mmWave networks were analyzed assuming a Poisson point process (PPP) for the base station (BS) distribution in @cite_15 @cite_19 @cite_22 . In @cite_15 a line-of-sight (LOS) ball model was considered for blockage modeling where BSs inside the LOS ball were considered to be in LOS whereas any BS outside of the LOS ball was treated as NLOS. In @cite_19 , this blocking model was modified by adding a LOS probability within the LOS ball, and this approach was shown to reflect several realistic blockage scenarios. Therefore we consider the same approach in this paper. Decoupled association in a mixed sub-6GHz and mmWave deployment was very recently considered in @cite_30 from a resource allocation perspective. However, there is no complete or analytical study to our knowledge on downlink-uplink decoupling for mmWave networks or the mmWave-sub-6GHz hybrid network considered in this paper.
@cite_30 @cite_18 @cite_22 @cite_19 @cite_15
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In this paper, we investigate the downlink performance of dense cellular networks with elevated base stations (BSs) using a channel model that incorporates line-of-sight (LOS) non-line-of-sight (NLOS) propagation into both small-scale and large-scale fading. Modeling LOS fading with Nakagami- @math fading, we provide a unified framework based on stochastic geometry that encompasses both closest and strongest BS association. This paper is particularized to two distance-dependent LOS NLOS models of practical interest. Considering the effect of LOS propagation alone, we derive closed-form expressions for the coverage probability with Nakagami- @math fading, showing that the performance for strongest BS association is the same as in the case of Rayleigh fading, whereas for closest BS association it monotonically increases with the shape parameter @math . Then, focusing on the effect of elevated BSs, we show that network densification eventually leads to near-universal outage even for moderately low BS densities: in particular, the maximum area spectral efficiency is proportional to the inverse of the square of the BS height. Deploying sub-6-GHz network together with millimeter wave (mm-wave) is a promising solution to simultaneously achieve sufficient coverage and high data rate. In heterogeneous networks, the traditional coupled access, i.e., users are constrained to be associated with the same base station in both downlink and uplink, is no longer optimal, and the concept of downlink and uplink decoupling (DUDe) has recently been proposed. In this paper, we analyze the coverage probability and area throughput for both the downlink and uplink of sub-6-GHz mm-wave cellular networks with decoupled access. Compared with the existing works, we take uplink power control and mm-wave interference into account. Using the tools from stochastic geometry, the expressions of signal-to-interference-plus-noise ratio coverage probability, user-perceived rate coverage probability and the area throughput are derived. The impact of decoupled access and different small cells (SCells) is investigated. In particular, analytical results reveal that with decoupled access, UEs are more likely to be associated with SCells in uplink when the network is sparse, and the uplink traffic will be offloaded from sub-6-GHz SCells to mm-wave SCells when the network is dense. Moreover, the dense deployment of mm-wave SCells rather than sub-6-GHz SCells is more reasonable, and the DUDe is a key factor in improving the performance of dense cellular networks with multi-band. The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. In this paper, different spatial stochastic models (the Poisson point process (PPP), the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice) are used to model the structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting. One is fitting by the method of maximum pseudolikelihood. As for the fitted models, it is not sufficient to distinguish them conclusively by some classical statistics. We propose the coverage probability as the criterion for the goodness-of-fit. In terms of coverage, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately. Furthermore, we introduce a novel metric, the deployment gain, and we demonstrate how it can be used to estimate the coverage performance and average rate achieved by a data set. In this paper, we provide an analytical framework to analyze heterogeneous downlink millimeter-wave (mm-wave) cellular networks consisting of @math tiers of randomly located base stations (BSs), where each tier operates in an mm-wave frequency band. Signal-to-interference-plus-noise ratio (SINR) coverage probability is derived for the entire network using tools from stochastic geometry. The distinguishing features of mm-wave communications, such as directional beamforming, and having different path loss laws for line-of-sight and non-line-of-sight links are incorporated into the coverage analysis by assuming averaged biased-received power association and Nakagami fading. By using the noise-limited assumption for mm-wave networks, a simpler expression requiring the computation of only one numerical integral for coverage probability is obtained. Also, the effect of beamforming alignment errors on the coverage probability analysis is investigated to get insight on the performance in practical scenarios. Downlink rate coverage probability is derived as well to get more insights on the performance of the network. Moreover, the effect of deploying low-power smaller cells and the impact of biasing factor on energy efficiency is analyzed. Finally, a hybrid cellular network operating in both mm-wave and @math -wave frequency bands is addressed.