Impact of mobility will be increasingly important in future generation wireless services and the related challenges will need to be addressed. Sojourn time, the time duration that a mobile user stays within a cell, is a mobility-aware parameter that can significantly impact the performance of mobile users and it can also be exploited to improve resource allocation and mobility management methods in the network. In this paper, we derive the distribution and mean of the sojourn time in multi-tier cellular networks, where spatial distribution of base stations (BSs) in each tier follows an independent homogeneous Poisson point process (PPP). To obtain the sojourn time distribution in multi-tier cellular networks with maximum biased averaged received power association, we derive the linear contact distribution function and chord length distribution of each tier. We also study the relation between mean sojourn time and other mobility-related performance metrics. We show that the mean sojourn time is inversely proportional to the handoff rate, and the complementary cumulative distribution function (CCDF) of sojourn time is bounded from above by the complement of the handoff probability. Moreover, we study the impact of user velocity and network parameters on the sojourn time.
Heterogeneous cellular networks (HCNs) constitute a necessary step in the evolution of cellular networks. In this paper, we apply the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on K-tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (HIP) model, with range expansion bias (offloading bias) in each tier. Expressions for the b-th moment of the conditional success probability for both the entire network and each tier are derived, based on which the exact meta distributions and …
Based on the distinguishing features of multi-tier millimeter wave (mmWave) networks such as different transmit powers, different directivity gains from directional beamforming alignment and path loss laws for line-of-sight (LOS) and non-line-of-sight (NLOS) links, we introduce a normalization model to simplify the analysis of multi-tier mmWave cellular networks. The highlight of the model is that we convert a multi-tier mmWave cellular network into a single-tier mmWave network, where all the base stations (BSs) have the same normalized transmit power 1 and the densities of BSs scaled by LOS o…
In this paper, we study the key properties of multi-antenna two-tier networks under different system configurations. Based on stochastic geometry, we derive the expressions and approximations for the users' average data rate. Through the more tractable approximations, the theoretical analysis can be greatly simplified. We find that the differences in density and transmit power between two tiers, together with range expansion bias significantly affect the users' data rate. Besides, for the purpose of area spectral efficiency (ASE) maximization, we find that the optimal number of active users fo…
This paper studies the carrier-to-interference ratio (CIR) and carrier-to-interference-plus-noise ratio (CINR) performance at the mobile station (MS) within a multi-tier network composed of M tiers of wireless networks, with each tier modeled as the homogeneous n-dimensional (n-D, n=1,2, and 3) shotgun cellular system, where the base station (BS) distribution is given by the homogeneous Poisson point process in n-D. The CIR and CINR at the MS in a single tier network are thoroughly analyzed to simplify the analysis of the multi-tier network. For the multi-tier network with given system paramet…
In this paper we demonstrate the rate gains achieved by two-tier heterogeneous cellular networks (HetNets) with varying degrees of coordination between macrocell and microcell base stations (BSs). We show that without the presence of coordination, network densification does not provide any gain in the sum rate and rapidly decreases the mean per-user signal-to-interference-plus-noise-ratio (SINR). Our results show that coordination reduces the rate of SINR decay with increasing numbers of microcell BSs in the system. Validity of the analytically approximated mean per-user SINR over a wide range…
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 candid…
This paper derives tight performance upper and lower bounds on the downlink outage efficiency of K-tier heterogeneous cellular networks (HCNs) for general signal propagation models with Poisson distributed base stations in each tier. In particular, the proposed approach to analyze the outage metrics in a K-tier HCN allows for the use of general bounded path-loss functions and random fading processes of general distributions. Considering two specific base station (BS) association policies, it is shown that the derived performance bounds track the actual outage metrics reasonably well for a wide…
Multi-tier cellular networks are considered as an effective solution to enhance the coverage and data rate offered by cellular systems. In a multi-tier network, high power base stations (BSs) such as macro BSs are overlaid by lower power small cells such as femtocells and/or picocells. However, co-channel deployment of multiple tiers of BSs gives rise to the problem of cross-tier interference that significantly impacts the performance of wireless networks. Multicell cooperation techniques, such as coordinated multipoint (CoMP) transmission, have been proposed as a promising solution to mitigat…
In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported experimental data. The path-loss model accounts for different distributions of line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process…
This paper proposes a centralized decision making framework at the macro base station (MBS) for device to device (D2D) communication underlaying a two-tier cellular network. We consider a D2D pair in the presence of an MBS and a femto access point, each serving a user, with quality of service constraints for all users. Our proposed solution encompasses mode selection (choosing between cellular or reuse or dedicated mode), resource allocation (in cellular and dedicated mode) and power control (in reuse mode) within a single framework. The framework prioritizes D2D dedicated mode if the D2D pair…
Multi-tier architecture improves the spatial reuse of radio spectrum in cellular networks, but it introduces complicated heterogeneity in the spatial distribution of transmitters, which brings new challenges in interference analysis. In this work, we present a stochastic geometric model to evaluate the uplink interference in a two-tier network considering multi-type users and base stations. Each type of tier-1 users and tier-2 base stations are modeled as independent homogeneous Poisson point processes, and tier-2 users are modeled as locally non-homogeneous clustered Poisson point processes c…
Next generation cellular networks will consist of multiple tiers of cells and users associated with different network tiers may have different priorities (e.g., macrocell-picocell-femtocell networks with macro tier prioritized over pico tier, which is again prioritized over femto tier). Designing efficient joint power and admission control (JPAC) algorithms for such networks under a co-channel deployment (i.e., underlay) scenario is of significant importance. Feasibility checking of a given target signal-to-noise-plus-interference ratio (SINR) vector is generally the most significant contribut…
Caching popular contents at base stations (BSs) of a heterogeneous cellular network (HCN) avoids frequent information passage from content providers to the network edge, thereby reducing latency and alleviating traffic congestion in backhaul links. In general, the optimal strategies for content placement in HCNs remain largely unknown and deriving them forms the theme of this paper. To this end, we adopt the popular random HCN model where $K$ tiers of BSs are modelled as independent Poisson point processes distributed in the plane with different densities. Further, the random caching scheme is…
We characterize the ergodic spectral efficiency of a non-cooperative and a cooperative type of K-tier heterogeneous networks with limited feedback. In the non-cooperative case, a multi-antenna base station (BS) serves a single-antenna user using maximum-ratio transmission based on limited feedback. In the cooperative case, a BS coordination set is formed by using dynamic clustering across the tiers, wherein the intra-cluster interference is mitigated by using multi-cell zero-forcing also based on limited feedback. Modeling the network based on stochastic geometry, we derive analytical expressi…
Heterogeneous cellular networks (HetNets) are to be deployed for future wireless communication to meet the ever-increasing mobile traffic demand. However, the dense and random deployment of small cells and their uncoordinated operation raise important concerns about energy efficiency. Base station (BS) cooperation is set to play a key role in managing interference in the HetNets. In this paper, we consider BS cooperation in the downlink HetNets where BSs from different tiers within the respective cooperative clusters jointly transmit the same data to a typical user, and further optimize the en…
In two-tier networks -- comprising a conventional cellular network overlaid with shorter range hotspots (e.g. femtocells, distributed antennas, or wired relays) -- with universal frequency reuse, the near-far effect from cross-tier interference creates dead spots where reliable coverage cannot be guaranteed to users in either tier. Equipping the macrocell and femtocells with multiple antennas enhances robustness against the near-far problem. This work derives the maximum number of simultaneously transmitting multiple antenna femtocells meeting a per-tier outage probability constraint. Coverage…
Caching popular contents at base stations (BSs) is a promising way to unleash the potential of cellular heterogeneous networks (HetNets), where backhaul has become a bottleneck. In this paper, we compare a cache-enabled HetNet where a tier of multi-antenna macro BSs is overlaid by a tier of helper nodes having caches but no backhaul with a conventional HetNet where the macro BSs tier is overlaid by a tier of pico BSs with limited-capacity backhaul. We resort stochastic geometry theory to derive the area spectral efficiencies (ASEs) of these two kinds of HetNets and obtain the closed-form expre…
This paper investigates the downlink performance of K-tier heteregeneous cellular networks (HCNs) under general settings. First, Gaussian approximation bounds for the standardized aggregate wireless interference (AWI) in dense K-tier HCNs are obtained for when base stations (BSs) in each tier are distributed over the plane according to a spatial and general Poisson point process. The Kolmogorov-Smirnov (KS) distance is used to measure deviations of the distribution of the standardized AWI from the standard normal distribution. An explicit and analytical expression bounding the KS distance betw…
In this paper, the outage performance of a two-tier heterogeneous mmWave cellular networks employing joint spatial division and multiplexing (JSDM) is investigated. It is assumed that macro base stations (BSs) equipped with a large number of antennas and pico BSs equipped with single antenna serve users simultaneously. The two-tier BSs and users are distributed according to independent Poisson point processes (PPPs). Theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) outage probability of the typical user is first provided. The all SINR outage probability of the two tie…
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 tha…
In this paper, we propose a novel and effective approach to optimizing the load balancing in a millimeter wave (mmWave) cellular heterogeneous network (HetNet) with a macro-tier and a micro-tier. The unique characteristics of mmWave transmission are incorporated into the network by adopting the Poisson point process (PPP) for base station (BS) location, the line-of-sight (LoS) ball model for mmWave links, the sectored antenna model for key antenna array characteristics, and Nakagami-$m$ fading for wireless channels. To reduce the load of macro-tier BSs, we consider a bias factor $A_{s}$ in the…
We model and analyze heterogeneous cellular networks with multiple antenna BSs (multi-antenna HetNets) with K classes or tiers of base stations (BSs), which may differ in terms of transmit power, deployment density, number of transmit antennas, number of users served, transmission scheme, and path loss exponent. We show that the cell selection rules in multi-antenna HetNets may differ significantly from the single-antenna HetNets due to the possible differences in multi-antenna transmission schemes across tiers. While it is challenging to derive exact cell selection rules even for maximizing s…
This paper derives Gaussian approximation bounds for the standardized aggregate wireless interference (AWI) in the downlink of K-tier heterogeneous cellular networks when base stations in each tier are distributed over the plane according to a (possibly non-homogeneous) Poisson process. The proposed methodology is general enough to account for general bounded path-loss models and fading statistics. The deviations of the distribution of the standardized AWI from the standard normal distribution are measured in terms of the Kolmogorov-Smirnov distance. An explicit expression bounding the Kolmogo…
In this paper, we focus on one of the representative 5G network scenarios, namely multi-tier heterogeneous cellular networks. User association is investigated in order to reduce the down-link co-channel interference. Firstly, in order to analyze the multi-tier heterogeneous cellular networks where the base stations in different tiers usually adopt different transmission powers, we propose a Transmission Power Normalization Model (TPNM), which is able to convert a multi-tier cellular network into a single-tier network, such that all base stations have the same normalized transmission power. The…
In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BS…
We address the user association problem in multi-tier in-band full-duplex (FD) networks. Specifically, we consider the case of decoupled user association (DUA) in which users (UEs) are not necessarily served by the same base station (BS) for uplink (UL) and downlink (DL) transmissions. Instead, UEs can simultaneously associate to different BSs based on two independent weighted path-loss user association criteria for UL and DL. We use stochastic geometry to develop a comprehensive modeling framework for the proposed system model where BSs and UEs are spatially distributed according to independe…
While network densification is considered an important solution to cater the ever-increasing capacity demand, its effect on the handover (HO) rate is overlooked. In dense 5G networks, HO delays may neutralize or even negate the gains offered by network densification. Hence, user mobility imposes a nontrivial challenge to harvest capacity gains via network densification. In this paper, we propose a velocity-aware HO management scheme for two-tier downlink cellular network to mitigate the HO effect on the foreseen densification throughput gains. The proposed HO scheme sacrifices the best BS conn…
In this paper, we consider the downlink signal-to-interference-plus-noise ratio (SINR) analysis in a heterogeneous cellular network with K tiers. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain BS density, transmission power, random shadow fading factors with arbitrary distribution, arbitrary path-loss exponent and a certain bias towards admitting the mobile-station (MS). The MS associates with the BS that has the maximum SINR under the open access cell association scheme. For such a general setting, we provide an anal…
In heterogeneous cellular scenarios with macrocells, femtocells or picocells users may suffer from significant co-channel cross-tier interference. To manage this interference 3GPP introduced almost blank subframe (ABSF), a subframe in which the interferer tier is not allowed to transmit data. Vulnerable users thus get a chance to be scheduled in ABSFs with reduced cross-tier interference. We analyze downlink scenarios using stochastic geometry and formulate a condition for the required number of ABSFs based on base station placement statistics and user throughput requirement. The result is a s…
Heterogeneous base stations (e.g. picocells, microcells, femtocells and distributed antennas) will become increasingly essential for cellular network capacity and coverage. Up until now, little basic research has been done on the fundamentals of managing so much infrastructure -- much of it unplanned -- together with the carefully planned macro-cellular network. Inter-cell coordination is in principle an effective way of ensuring different infrastructure components behave in a way that increases, rather than decreases, the key quality of service (QoS) metrics. The success of such coordination …
In this paper, a comprehensive study of the the downlink performance in a heterogeneous cellular network (or hetnet) is conducted. A general hetnet model is considered consisting of an arbitrary number of open-access and closed-access tier of base stations (BSs) arranged according to independent homogeneous Poisson point processes. The BSs of each tier have a constant transmission power, random fading coefficient with an arbitrary distribution and arbitrary path-loss exponent of the power-law path-loss model. For such a system, analytical characterizations for the coverage probability and aver…
This paper considers a device-to-device (D2D) underlaid cellular network where an uplink cellular user communicates with the base station while multiple direct D2D links share the uplink spectrum. This paper proposes a random network model based on stochastic geometry and develops centralized and distributed power control algorithms. The goal of the proposed power control algorithms is two-fold: ensure the cellular users have sufficient coverage probability by limiting the interference created by underlaid D2D users, while also attempting to support as many D2D links as possible. For the distr…
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 stochas…
Interference management techniques are critical to the performance of heterogeneous cellular networks, which will have dense and overlapping coverage areas, and experience high levels of interference. Fractional frequency reuse (FFR) is an attractive interference management technique due to its low complexity and overhead, and significant coverage improvement for low-percentile (cell-edge) users. Instead of relying on system simulations based on deterministic access point locations, this paper instead proposes an analytical model for evaluating Strict FFR and Soft Frequency Reuse (SFR) deploym…
The 5G cellular wireless systems will have a multi-tier architecture consisting of macrocells, different types of licensed small cells and D2D networks to serve users with different quality-of-service (QoS) requirements in a spectrum efficient manner. Distributed resource allocation and interference management is one of the fundamental research challenges for such multi-tier heterogeneous networks. In this chapter, we consider the radio resource allocation problem in a multi-tier orthogonal frequency division multiple access (OFDMA)-based cellular (e.g., 5G LTE-A) network. In particular, we pr…
Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of condition…
For small cell technology to significantly increase the capacity of tower-based cellular networks, mobile users will need to be actively pushed onto the more lightly loaded tiers (corresponding to, e.g., pico and femtocells), even if they offer a lower instantaneous SINR than the macrocell base station (BS). Optimizing a function of the long-term rates for each user requires (in general) a massive utility maximization problem over all the SINRs and BS loads. On the other hand, an actual implementation will likely resort to a simple biasing approach where a BS in tier j is treated as having its…
Backward compatibility is an essential ingredient for the success of new technologies. In the context of in-band full-duplex (FD) communication, FD base stations (BSs) should support half-duplex (HD) users' equipment (UEs) without sacrificing the foreseen FD gains. This paper presents flexible and tractable modeling framework for multi-tier cellular networks with FD BSs and FD/HD UEs. The presented model is based on stochastic geometry and accounts for the intrinsic vulnerability of uplink transmissions. The results show that FD UEs are not necessarily required to harvest rate gains from FD BS…
Multi-tier cellular communication networks constitute a promising approach to expand the coverage of cellular networks and enable them to offer higher data rates. In this paper, an uplink two-tier communication network is studied, in which macro users, femto users and femto access points are geometrically located inside the coverage area of a macro base station according to Poisson point processes. Each femtocell is assumed to have a fixed backhaul constraint that puts a limit on the maximum number of femto and macro users it can service. Under this backhaul constraint, the network adopts a sp…
In this article, a network model incorporating both line-of-sight (LOS) and non-line-of-sight (NLOS) transmissions is proposed to investigate impacts of blockages in urban areas on heterogeneous network coverage performance. Results show that co-existence of NLOS and LOS transmissions has a significant impact on network performance. We find in urban areas, that deploying more BSs in different tiers is better than merely deploying all BSs in the same tier in terms of coverage probability.
One of key 5G scenarios is that device-to-device (D2D) and massive multiple-input multiple-output (MIMO) will be co-existed. However, interference in the uplink D2D underlaid massive MIMO cellular networks needs to be coordinated, due to the vast cellular and D2D transmissions. To this end, this paper introduces a spatially dynamic power control solution for mitigating the cellular-to-D2D and D2D-to-cellular interference. In particular, the proposed D2D power control policy is rather flexible including the special cases of no D2D links or using maximum transmit power. Under the considered powe…
We propose a new model for heterogeneous cellular networks that incorporates dependencies between the layers. In particular, it places lower-tier base stations at locations that are poorly covered by the macrocells, and it includes a small-cell model for the case where the goal is to enhance network capacity.
A two-tier heterogeneous cellular network (HCN) with intra-tier and inter-tier dependence is studied. The macro cell deployment follows a Poisson point process (PPP) and two different clustered point processes are used to model the cache-enabled small cells. Under this model, we derive approximate expressions in terms of finite integrals for the average delivery rate considering inter-tier and intra-tier dependence. On top of the fact that cache size drastically improves the performance of small cells in terms of average delivery rate, we show that rate splitting of limited-backhaul induces no…
Energy harvesting in cellular networks is an emerging technique to enhance the sustainability of power-constrained wireless devices. This paper considers the co-channel deployment of a macrocell overlaid with small cells. The small cell base stations (SBSs) harvest energy from environmental sources whereas the macrocell base station (MBS) uses conventional power supply. Given a stochastic energy arrival process for the SBSs, we derive a power control policy for the downlink transmission of both MBS and SBSs such that they can achieve their objectives (e.g., maintain the signal-to-interference-…
In a Poisson Point Process (PPP) network model, in which the locations of Base Stations (BSs) are randomly distributed according to a Spatial Poisson Process, has been recently used as a tractable stochastic model to analyse the performance of downlink Heterogeneous Cellular Networks (HCNs). The HCN is modelled as a multi-tier cellular network where each tier is characterised by the transmission power level, propagation path loss exponent and density of BSs. The current works on HCN enabling Intercell Interference Coordination (ICIC) technique usually deal with Strict Frequency Reuse (FR) or S…
This tutorial is intended as an accessible but rigorous first reference for someone interested in learning how to model and analyze cellular network performance using stochastic geometry. In particular, we focus on computing the signal-to-interference-plus-noise ratio (SINR) distribution, which can be characterized by the coverage probability (the SINR CCDF) or the outage probability (its CDF). We model base stations (BSs) in the network as a realization of a homogeneous Poisson point process of density $λ$, and compute the SINR for three main cases: the downlink, uplink, and finally the multi…
The heterogeneity in cellular networks that comprise multiple base stations types imposes new challenges in network planning and deployment of future generation of cellular networks. The Radio Resource Management (RRM) techniques, such as dynamic sharing of the available resources and advanced user association strategies, determine the overall network capacity and efficiency. This paper evaluates the downlink performance of a two tier heterogeneous network (consisting of macro and femto tiers) in terms of rate distribution, i.e. the percentage of users that achieve certain rate in the system. …
In heterogeneous cellular networks (HCNs), the interference received at a user is correlated over time slots since it comes from the same set of randomly located BSs. This results in the correlations of link successes, thus affecting network performance. Under the assumptions of a K-tier Poisson network, strongest-candidate based BS association, and independent Rayleigh fading, we first quantify the correlation coefficients of interference. We observe that the interference correlation is independent of the number of tiers, BS density, SIR threshold, and transmit power. Then, we study the corre…
In this paper, we first introduce a generalized modeling and analysis framework to explore the fundamental interactions between user association, coverage probability and link rate in a millimeter wave (mmWave) heterogeneous cellular network (HetNet) in which there are multiple tiers of the ultra-high-frequency (UHF) macrocell and small cell base stations (BSs) and a single tier of mmWave small cell BSs. A generalized user association scheme that can cover many path-loss-based user association schemes is proposed and its related probabilistic properties that facilitate the derivations of the c…
This work does the statistical quality-of-service (QoS) analysis of a block-fading device-to-device (D2D) link in a multi-tier cellular network that consists of a macro-BS (BSMC) and a micro-BS (BSmC) which both operate in full-duplex (FD) mode. For the D2D link under consideration, we first formulate the mode selection problem-whereby D2D pair could either communicate directly, or, through the BSmC, or, through the BSMC-as a ternary hypothesis testing problem. Next, to compute the effective capacity (EC) for the given D2D link, we assume that the channel state information (CSI) is not availab…
Employing multi-tier networks is among the most promising approaches to address the rapid growth of the data demand in cellular networks. In this paper, we study a two-tier uplink cellular network consisting of femtocells and a macrocell. Femto base stations, and femto and macro users are assumed to be spatially deployed based on independent Poisson point processes. We consider an open access assignment policy, where each macro user based on the ratio between its distances from its nearest femto access point (FAP) and from the macro base station (MBS) is assigned to either of them. By tuning t…
Compared to the standard success (coverage) probability, the meta distribution of the signal-to-interference ratio (SIR) provides much more fine-grained information about the network performance. We consider general heterogeneous cellular networks (HCNs) with base station tiers modeled by arbitrary stationary and ergodic non-Poisson point processes. The exact analysis of non-Poisson network models is notoriously difficult, even in terms of the standard success probability, let alone the meta distribution. Hence we propose a simple approach to approximate the SIR meta distribution for non-Poiss…
Heterogeneous cellular networks (HCNs) usually exhibit spatial separation amongst base stations (BSs) of different types (termed tiers in this paper). For instance, operators will usually not deploy a picocell in close proximity to a macrocell, thus inducing separation amongst the locations of pico and macrocells. This separation has recently been captured by modeling the small cell locations by a Poisson Hole Process (PHP) with the hole centers being the locations of the macrocells. Due to the presence of exclusion zones, the analysis of the resulting model is significantly more complex compa…
Handover rate is one of the most import metrics to instruct mobility management and resource management in wireless cellular networks. In the literature, the mathematical expression of handover rate has been derived for homogeneous cellular network by both regular hexagon coverage model and stochastic geometry model, but there has not been any reliable result for heterogeneous cellular networks (HCNs). Recently, stochastic geometry modeling has been shown to model well the real deployment of HCNs and has been extensively used to analyze HCNs. In this paper, we give an effective handover analys…
In this work, the problem of cross-tier interference in a two-tiered (macro-cell and cognitive small-cells) network, under the complete spectrum sharing paradigm, is studied. A new orthogonal precoder transmit scheme for the small base stations, called multi-user Vandermonde-subspace frequency division multiplexing (MU-VFDM), is proposed. MU-VFDM allows several cognitive small base stations to coexist with legacy macro-cell receivers, by nulling the small- to macro-cell cross-tier interference, without any cooperation between the two tiers. This cleverly designed cascaded precoder structure, n…
In this paper, we provide joint subcarrier assignment and power allocation schemes for quality-of-service (QoS)-constrained energy-efficiency (EE) optimization in the downlink of an orthogonal frequency division multiple access (OFDMA)-based two-tier heterogeneous cellular network (HCN). Considering underlay transmission, where spectrum-efficiency (SE) is fully exploited, the EE solution involves tackling a complex mixed-combinatorial and non-convex optimization problem. With appropriate decomposition of the original problem and leveraging on the quasi-concavity of the EE function, we propose …
In this paper, we provide an analytical framework to analyze heterogeneous downlink mmWave cellular networks consisting of K tiers of randomly located base stations (BSs) where each tier operates in a mmWave 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 mmWave communications such as directional beamforming and having different path loss laws for line-of-sight (LOS) and non-line-of-sight (NLOS) links are incorporated into the coverage analysis by assuming …
In order to improve the uplink performance of future cellular networks, the idea to decouple the downlink (DL) and uplink (UL) association has recently been shown to provide significant gain in terms of both coverage and rate performance. However, all the work is limited to SISO network. Therefore, to study the gain provided by the DL and UL decoupling in multi-antenna base stations (BSs) setup, we study a two tier heterogeneous network consisting of multi-antenna BSs, and single antenna user equipments (UEs). We use maximal ratio combining (MRC) as a linear receiver at the BSs and using tools…
The use of unmanned aerial vehicles (UAVs) operating as aerial base stations (BSs) has emerged as a promising solution especially in scenarios requiring rapid deployments (e.g., in the cases of crowded hotspots, sporting events, emergencies, natural disasters) in order to assist the ground BSs. In this paper, an analytical framework is provided to analyze the signal-to-interference-plus-noise ratio (SINR) coverage probability of unmanned aerial vehicle (UAV) assisted cellular networks with clustered user equipments (UEs). Locations of UAVs and ground BSs are modeled as Poison point processes (…
We consider a hierarchical network that consists of mobile users, a two-tiered cellular network (namely small cells and macro cells) and central routers, each of which follows a Poisson point process (PPP). In this scenario, small cells with limited-capacity backhaul are able to cache content under a given set of randomized caching policies and storage constraints. Moreover, we consider three different content popularity models, namely fixed content popularity, distance-dependent and load-dependent, in order to model the spatio-temporal behavior of users' content request patterns. We derive ex…
