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.
Consider a cognitive radio network with two types of users: primary users (PUs) and cognitive users (CUs), whose locations follow two independent Poisson point processes. The cognitive users follow the policy that a cognitive transmitter is active only when it is outside the primary user exclusion regions. We found that under this setup the active cognitive users form a point process called the Poisson hole process. Due to the interaction between the primary users and the cognitive users through exclusion regions, an exact calculation of the interference and the outage probability seems unfeasible. Instead, two different approaches are taken to tackle this problem. First, bounds for the interference (in the form of Laplace transforms) and the outage probability are derived, and second, it is shown how to use a Poisson cluster process to model the interference in this kind of network. Furthermore, the bipolar network model with different exclusion region settings is analyzed. Over the last decade, the growing amount of uplink (UL) and downlink (DL) mobile data traffic has been characterized by substantial asymmetry and time variations. Dynamic time-division duplex (TDD) has the capability to accommodate to the traffic asymmetry by adapting the UL DL configuration to the current traffic demands. In this work, we study a two-tier heterogeneous cellular network (HCN) where the macro tier and small cell tier operate according to a dynamic TDD scheme on orthogonal frequency bands. To offload the network infrastructure, mobile users in proximity can engage in device-to-device (D2D) communications, whose activity is determined by a carrier sensing multiple access (CSMA) scheme to protect the ongoing infrastructure-based and D2D transmissions. We present an analytical framework for evaluating the network performance in terms of load-aware coverage probability and network throughput. The proposed framework allows quantification of the effect on the coverage probability of the most important TDD system parameters, such as the UL DL configuration, the base station density, and the bias factor. In addition, we evaluate how the bandwidth partition and the D2D network access scheme affect the total network throughput. Through the study of the tradeoff between coverage probability and D2D user activity, we provide guidelines for the optimal design of D2D network access.