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In typical wireless heterogeneous networks (HetNets), users are clustered around known hotspots, e.g., shopping centers or schools, but such a non-uniform distribution of nodes is difficult to analyze. This paper explicitly models this scenario, with macro base stations (MBSs) modeled by a homogeneous Poisson point process (PPP), and millimeter-wave small base stations (mmWave SBSs) and users clustered around the hotspot centers, forming two Poisson cluster processes (PCPs), respectively. Fractional frequency reuse (FFR) and coordinated multi-point transmission (CoMP) are assumed since they help to limit the co-tier interference and enhance the coverage and capacity of the network. We present a distance-based approach for grouping macro user equipments (MUEs) from the cell center (CC) and cell edge (CE) regions for FFR analysis. We first derive some distance distributions, including joint distance distribution from the typical user to the cooperative open-access mmWave SBS and distance distribution from the typical user to the non-cooperative open-access mmWave SBS. We obtain expressions for various performance metrics, including association probability, signal to interference-plus-noise ratio (SINR) coverage probability, and ergodic capacity, under these conditions. Due to the complexity of the exact expressions, we derive novel approximations, using Alzer's lemma, to obtain the lower bounds on coverage and ergodic capacity, which are shown to be accurate through Monte Carlo simulation. Simulation results analyze the effect of different parameters on the network performance to give some guidance for the design of future networks. Numerical optimization of a key parameter, in terms of association probability, coverage probability, and ergodic capacity, is enabled by our analysis. [ABSTRACT FROM AUTHOR]

In order to satisfy the requirement of extremely high data rate in traffic hotspot regions, millimeter wave (mmWave) has attracted significant attention in wireless communication networks. While the coverage performance of mmWave networks based on the distribution of signal-to-interference-plus-noise ratio (SINR) has been widely studied, it provides only very limited information on the link reliability. In this paper, we provide a fine-grained performance analysis of the mmWave networks with hotspots. Specifically, we first establish a general and tractable framework to investigate the performance of mmWave networks using the Poisson cluster process integrated with several features of the mmWave band. Both open and closed association strategies are considered. To show what fraction of users in the networks achieves target reliability when the SINR is given, we derive the tier association probability and the moments of the conditional SINR distribution, based on which the exact meta distributions of SINR are given. Interestingly, in clustered mmWave networks, the widely used standard and generalized beta approximations do not work well when the blockage effect is severe. To resolve this issue, we provide a modified approximation by scaling the standard beta distribution, which is shown to be closer to the exact results. We conduct extensive simulations to study the impact of mmWave and deployment features on the performance of clustered mmWave networks. Numerical results reveal that the optimal scattering variance of mmWave base stations scales with the cluster size to maximize the number of concurrent reliable links, and increasing the antenna directivity results in more reliable communications than elevating the transmit power of mmWave base stations. [ABSTRACT FROM AUTHOR]

Device-to-Device (D2D) communication has become a promising candidate in future cellular networks to improve spectrum efficiency and energy efficiency, while reducing the latency. As the capacity of D2D user equipments (DUEs) increases, it makes DUEs caching possible, and it can offload traffic from macro base stations, perform computation-intensive and latency-critical tasks. In this paper, in-band communication is considered, and the Poisson cluster process is utilized to model and analyze the clustered D2D networks under cluster-centric caching strategy. Firstly, we use the Thomas cluster process to model cellular user equipments (CUEs) and DUEs, and give a deployment scheme of clustered D2D caching networks. Secondly, the aggregated interference of the typical D2D receiver is analyzed in the clustered D2D networks. Then the Laplace transform of the aggregated interference is analyzed, and the expressions of coverage probability, average achievable rate and cache hit probability of the typical D2D receiver are deduced. The simulation results show that we can adjust the path loss exponent, densities of DUEs and CUEs, transmitting power of CUEs, mean of simultaneously active transmitters in each cluster and Zipf exponent to improve the performance of clustered D2D caching networks. [ABSTRACT FROM AUTHOR]

Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). Despite its undisputed relevance to HetNets—corroborated by the models used in the industry—the PCP’s use in performance analysis has been limited. This is primarily because of the lack of analytical tools to characterize the performance metrics, such as the coverage probability of a user connected to the strongest BS. In this paper, we develop an analytical framework for the evaluation of the coverage probability, or equivalently the complementary cumulative density function (CCDF) of signal-to-interference-and-noise ratio (SINR), of a typical user in a $K$ -tier HetNet under a $\max $ power-based association strategy, where the BS locations of each tier follow either a Poisson point process (PPP) or a PCP. The key enabling step involves conditioning on the parent PPPs of all the PCPs, which allows us to express the coverage probability as a product of sum-product and probability generating functionals (PGFLs) of the parent PPPs. In addition to several useful insights, our analysis provides a rigorous way to study the impact of the cluster size on the ${\it SINR}$ distribution, which was not possible using the existing PPP-based models. [ABSTRACT FROM AUTHOR]

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated a variety of user and base station (BS) configurations to be considered for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models proposed by standardization bodies, such as the 3rd Generation Partnership Project (3GPP). Complementary to these simulation models, stochastic geometry-based approach, modeling the locations of the users, and the $K$ tiers of BSs as independent and homogeneous Poisson point processes (PPPs), has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based K$ -tier HetNet model is not rich enough to capture spatial coupling between user and BS locations that exists in real-world HetNet deployments and is included in 3GPP simulation models. In this paper, we demonstrate that modeling a fraction of users and arbitrary number of BS tiers alternatively with a Poisson cluster process (PCP) captures the aforementioned coupling, thus bridging the gap between the 3GPP simulation models and the PPP-based analytic model for HetNets. We further show that the downlink coverage probability of a typical user under maximum signal-to-interference-ratio ( \mathtt {SIR} ) association can be expressed in terms of the sum-product functionals over PPP, PCP, and its associated offspring point process, which are all characterized as a part of our analysis. We also show that the proposed model converges to the PPP-based HetNet model as the cluster size of the PCPs tends to infinity. Finally, we specialize our analysis based on general PCPs for Thomas and Matérn cluster processes. Special instances of the proposed model closely resemble the different configurations for BS and user locations considered in 3GPP simulations. [ABSTRACT FROM PUBLISHER]

This paper develops a new approach to the modeling and analysis of heterogeneous cellular networks (HetNets) that accurately incorporates coupling across the locations of users and base stations, which exists due to the deployment of small cell base stations (SBSs) at the places of high user density (termed user hotspots in this paper). Modeling the locations of the geographical centers of user hotspots as a homogeneous Poisson point process (PPP), we assume that the users and SBSs are clustered around each user hotspot center independently with two different distributions. The macrocell BS locations are modeled by an independent PPP. This model is consistent with the user and SBS configurations considered by 3GPP. Using this model, we study the performance of a typical user in terms of coverage probability and throughput for two association policies: 1) Policy 1, under which a typical user is served by the open-access BS that provides maximum averaged received power and 2) Policy 2, under which the typical user is served by the small cell tier if the maximum averaged received power from the open-access SBSs is greater than a certain power threshold; and macro tier otherwise. A key intermediate step in our analysis is the derivation of distance distributions from a typical user to the open-access and closed-access interfering SBSs. Our analysis demonstrates that as the number of SBSs reusing the same resource block increases, coverage probability decreases, whereas throughput increases. Therefore, contrary to the usual assumption of orthogonal channelization, it is reasonable to assign the same resource block to multiple SBSs in a given cluster as long as the coverage probability remains acceptable. This approach to HetNet modeling and analysis significantly generalizes the state-of-the-art approaches that are based on modeling the locations of BSs and users by independent PPPs. [ABSTRACT FROM PUBLISHER]

This paper investigates the performance of millimeter wave (mmWave) communications in clustered device-to-device (D2D) networks. The locations of D2D transceivers are modeled as a Poisson Cluster Process. In each cluster, devices are equipped with multiple antennas, and the active D2D transmitter (D2D-Tx) utilizes mmWave to serve one of the proximate D2D receivers. Specifically, we introduce three user association strategies: 1) uniformly distributed D2D-Tx model; 2) nearest D2D-Tx model; and 3) closest line-of-site (LOS) D2D-Tx model. To characterize the performance of the considered scenarios, we derive new analytical expressions for the coverage probability and area spectral efficiency (ASE). Additionally, in order to efficiently illustrating the general trends of our system, a closed-form lower bound for the special case interfered by intra-cluster LOS links is derived. We provide Monte Carlo simulations to corroborate the theoretical results and show that: 1) the coverage probability is mainly affected by the intra-cluster interference with LOS links; 2) there exists an optimum number of simultaneously active D2D-Txs in each cluster for maximizing ASE; and 3) the closest LOS model outperforms the other two scenarios but at the cost of extra system overhead. [ABSTRACT FROM PUBLISHER]

In heterogeneous networks, the random deployment of femto access points (FAPs) and macro base stations (MBSs) with uncoordinated channel access imposes huge intertier interferences. In real-life networks, the process of MBSs’ deployment exhibits the homogeneity; however the FAPs have the behavioral characteristic of clusters formation, such as in malls, apartments, or offices. Therefore, the composite modeling of the MBSs and the FAPs using Poisson point process and Poisson cluster process is employed for the evaluation of coverage probability. The scenario of the real-time traffic for macrotier and the best-effort traffic for femto-tier is considered. Cognition is introduced in the clustered FAPs to control the intertier interference. Furthermore, the impact of the macrotier load is analyzed by exploiting the inherent coupling between coverage probability and activity factor of an MBS. Further, we study the effect of co-channel, orthogonal, and partial spectrum sharing modes on the coverage for given parameters, such as load condition and FAPs/MBSs density. We provide simulation validation for the derived expressions of coverage and present a comparative analysis for the mentioned spectrum sharing modes. [ABSTRACT FROM AUTHOR]

One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations. This assumption is not quite accurate, especially for user-centric capacity-driven small cell deployments where low-power BSs are deployed in the areas of high user density, thus inducing a natural correlation in the BS and user locations. In order to capture this correlation, we enrich the existing $K$ -tier Poisson point process (PPP) HetNet model by considering user locations as Poisson Cluster Process with the BSs at the cluster centers. In particular, we provide the formal analysis of the downlink coverage probability in terms of a general density function describing the locations of users around the BSs. The derived results are specialized for two cases of interest: 1) Thomas cluster process, where the locations of the users around BSs are Gaussian distributed and 2) Matérn cluster process, where the users are uniformly distributed inside a disc of a given radius. Tight closed-form bounds for the coverage probability in these two cases are also derived. Our results demonstrate that the coverage probability decreases as the size of user clusters around BSs increases, ultimately collapsing to the result obtained under the assumption of PPP distribution of users independent of the BS locations when the cluster size goes to infinity. Using these results, we also handle mixed user distributions consisting of two types of users: 1) uniformly distributed and 2) clustered around certain tiers. [ABSTRACT FROM PUBLISHER]

Device-to-device (D2D) communication enables direct communication between proximate devices thereby improving the overall spectrum utilization and offloading traffic from cellular networks. This paper develops a new spatial model for D2D networks in which the device locations are modeled as a Poisson cluster process. Using this model, we study the performance of a typical D2D receiver in terms of coverage probability under two realistic content availability setups: 1) content of interest for a typical device is available at a device chosen uniformly at random from the same cluster, which we term uniform content availability, and 2) content of interest is available at the k^th closest device from the typical device inside the same cluster, which we term $k$-closest content availability. Using these coverage probability results, we also characterize the area spectral efficiency (ASE) of the whole network for the two setups. A key intermediate step in this analysis is the derivation of the distributions of distances from a typical device to both the intra- and inter-cluster devices. Our analysis reveals that an optimum number of D2D transmitters must be simultaneously activated per cluster in order to maximize ASE. This can be interpreted as the classical tradeoff between more aggressive frequency reuse and higher interference power. The optimum number of simultaneously transmitting devices and the resulting ASE increase as the content is made available closer to the receivers. Our analysis also quantifies the best and worst case performance of clustered D2D networks both in terms of coverage and ASE. [ABSTRACT FROM PUBLISHER]

This paper develops a comprehensive analytical framework with foundations in stochastic geometry to characterize the performance of cluster-centric content placement in a cache-enabled device-to-device (D2D) network. Different from device-centric content placement, cluster-centric placement focuses on placing content in each cluster, such that the collective performance of all the devices in each cluster is optimized. Modeling the locations of the devices by a Poisson cluster process, we define and analyze the performance for three general cases: 1) k -Tx case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at the k{\mathrm{ th}} closest device to the cluster center; 2) \ell $ -Rx case: the receiver of interest is the \ell {\mathrm{ th}} closest device to the cluster center and its content of interest is available at a device chosen uniformly at random from the same cluster; and 3) baseline case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at a device chosen independently and uniformly at random from the same cluster. Easy-to-use expressions for the key performance metrics, such as coverage probability and area spectral efficiency of the whole network, are derived for all three cases. Our analysis concretely demonstrates significant improvement in the network performance when the device on which content is cached or device requesting content from cache is biased to lie closer to the cluster center compared with the baseline case. Based on this insight, we develop and analyze a new generative model for cluster-centric D2D networks that allows to study the effect of intra-cluster interfering devices that are more likely to lie closer to the cluster center. [ABSTRACT FROM AUTHOR]

Due to its tractability, a multitier model of mutually independent Poisson point processes (PPPs) for heterogeneous cellular networks (HCNs) has recently been attracting much attention. However, in reality, the locations of the BSs, within each tier and across tiers, are not fully independent. Accordingly, in this paper, we propose two HCN models with inter-tier dependence (Case 1) and intra-tier dependence (Case 2), respectively. In Case 1, the macro-base station (MBS) and the pico-base station (PBS) deployments follow a Poisson point process (PPP) and a Poisson hole process (PHP), respectively. Under this setup and conditioning on a fixed serving distance (distance between a user and its nearest serving BS), we derive bounds on the outage probabilities of both macro and pico users. We also use a fitted Poisson cluster process to approximate the PHP, which is shown to provide a good approximation of the interference and outage statistics. In Case 2, the MBSs and the PBSs follow a PPP and an independent Matern cluster process, respectively. Explicit expressions of the interference and the outage probability are derived first for fixed serving distance and second with random distance, and we derive the outage performance, the per-user capacity, and the area spectral efficiency (ASE) for both cases. It turns out that the proposed Case 2 model is a more appropriate and accurate model for a HCN with hotspot regions than the multitier independent PPP model since the latter underestimates some key performance metrics, such as the per-user capacity and the ASE, by a factor of 1.5 to 2. Overall, the two models proposed provide good tradeoffs between the accuracy, tractability, and practicability. [ABSTRACT FROM PUBLISHER]

Future mobile networks are visualized as networks that consist of more than one type of base station to cope with rising user demands. Such networks are referred to as heterogeneous networks. There have been various attempts at modeling and optimization of such networks using spatial point processes, some of which are alluded to (later) in this paper. We model a heterogeneous network consisting of two types of base stations by using a particular Poisson cluster process model. The main contributions are two-fold. First, a complete description of the interference in heterogeneous networks is derived in the form of its Laplace functional. Second, using an asymptotic convergence result which was shown in our previous work, we derive the expressions for the mean and variance of the distribution to which the interference converges. The utility of this framework is discussed for both the contributions. [ABSTRACT FROM PUBLISHER]