In this paper, a novel Poisson hole process (PHP) modeling of wireless networks is proposed. We consider a more general hole shape, i.e. circular sector holes in a random direction, to capture the spatial separation between tiers in a millimeter wave (mmWave) heterogeneous cellular network (HCN). In this case, small cell BSs (SBSs) and macrocell BSs (MBSs) are distributed as a PHP and Poisson point process (PPP). Due to fundamental propagation differences between mmWave and microwave frequencies, we incorporate blockage and directional beamforming in the network model. Using tools from stochastic geometry, the evaluation of the coverage performance in a two-tier mmWave HCN is provided. Since the exact formulation of distance distribution, association probability and coverage probability based on PHP modeling of SBSs is not known, fairly accurate expressions for them are derived and validated by simulation results. Moreover, some interesting facts about the effect of holes on coverage probability and the relation between proposed hole configuration and prior models with circular holes is discovered. It turns out that the analysis based on the proposed PHP model can provide a more general study than prior works and the proposed approaches are more accurate for two-tier HCNs than independent PPP-based analysis.
Heterogeneous cellular network (HCN) is modeled as a multi-tiered cellular network where the base stations (BSs) of each tier are randomly distributed and have a particular transmit power and spatial density. A general model for HCNs assumes K independent tiers of Poisson point process (PPP) distributed BSs, which is the most simplified model in the literature. Some tractable models for SINR distribution in a general K-tier downlink HCN have been developed in @cite_7 , @cite_8 , @cite_11 . Employing similar approaches from stochastic geometry used in microwave frequency and incorporating the distinguishing features of mmWave frequency, in @cite_12 heterogeneous downlink mmWave cellular networks was studied.
@cite_11 @cite_12 @cite_7 @cite_8
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In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association policies. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a particular transmit power, path loss exponent, spatial density, and bias towards admitting mobile users. For example, as compared to macrocells, picocells would usually have lower transmit power, higher path loss exponent (lower antennas), higher spatial density (many picocells per macrocell), and a positive bias so that macrocell users are actively encouraged to use the more lightly loaded picocells. In the present paper we implicitly assume all base stations have full queues; future work should relax this. For this model, we derive the outage probability of a typical user in the whole network or a certain tier, which is equivalently the downlink SINR cumulative distribution function. The results are accurate for all SINRs, and their expressions admit quite simple closed-forms in some plausible special cases. We also derive the average ergodic rate of the typical user, and the minimum average user throughput - the smallest value among the average user throughputs supported by one cell in each tier. We observe that neither the number of BSs or tiers changes the outage probability or average ergodic rate in an interference-limited full-loaded HCN with unbiased cell association (no biasing), and observe how biasing alters the various metrics. 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. Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given , adding more tiers and or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR. We develop a tractable, flexible, and accurate model for downlink heterogeneous cellular networks. It consists of K tiers of randomly-located base stations (BSs), where each tier may differ in terms of the average transmit power, the supported data rate and the BS density. This allows elements spanning traditional, micro, pico, and femtocell BSs to be simultaneously considered. Assuming a mobile user connects to its strongest BS, we derive its Signal-to-Interference-Ratio (SIR) distribution and use that to find the coverage (equivalently outage) probability over the entire network. We verify the accuracy of these analytical results through empirical comparisons with an actual 4G macro-cell network.