Tier HetNet Research Articles

On the Deployment of Small Cells in 3D HetNets With Multi-Antenna Base Stations

With the dense deployment of small cells, the impact of height difference between base stations (BSs) and user equipment (UE) on the performance of heterogeneous networks (HetNets) becomes significant. The traditional two-dimensional models are no longer sufficient to capture the three-dimensional (3D) features of dense HetNets. On the other hand, deploying multiple antennas on BSs is a promising approach to improve network capacity. In this paper, we propose a 3D model for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -tier HetNet with multi-antenna BSs, where different tiers share the same frequency band but may differ in BS height, BS density, number of antennas per BS, BS transmit power, association bias, and path loss exponent. We analytically derive the per-tier association probability under both the strongest received signal and the closest BS cell-association strategies. Based on that, we derive the expressions for the downlink ergodic rate, area spectral efficiency (ASE) and energy efficiency. The numerical results reveal that in the presence of macrocell BSs, for low to medium small-cell BS (SBS) densities, the closest BS cell-association strategy leads to low ergodic rate, ASE and energy efficiency regardless of the SBS height; while at very high SBS densities, under both cell-association strategies, SBSs should be deployed at the same height as UE to achieve high ergodic rate, ASE and energy efficiency. Moreover, we find that for a given SBS height, there exists an optimal combination of SBS density and number of antennas per SBS that maximizes the system energy efficiency.

Distributed User Association and Resource Allocation Algorithms for Three Tier HetNets

In this article, we consider joint optimization of user association and resource allocation in three tier HetNets. We formulate the objective of minimizing the resources required to clear a given set of files, as a linear program. We show that the optimal user association is determined by a rate-biasing rule, where a bias value is associated with each BS. We show that each rate-bias value crucially only takes values from a finite set which we characterize. We present a complete analytical solution along with new structural results. Using these results, we present efficient distributed algorithms for optimal control of three tier HetNets. The method involves a 1D search for a resource variable at the macro-level, and 2D search at the pico-level for a resource variable and a bias value. We apply our results to a variety of hierarchical network examples.

Nearest Distance Based Downlink Rate Modeling in Hyper-dense Heterogeneous Wireless Cell Networks

Different kinds of low transmit power, flexible cell extension and hyper dense base stations (BSs) overlaying on the well established macro cells, forming the hyper-dense multilayer heterogeneous wireless cell networks (HetNets), where the BSs in each tier are characterized by the differences in BSs transmit power, path loss exponent, tier-biasing factor and BSs spatial density, is the promising technology for 5th generation mobile networks and to support hot spots and cell edge coverage. The HetNets downlink rate modeling is one of the key and challenge problems for the random deployment characteristics of BSs in lower layer. In this paper, a three tier HetNets, which includes macro tier, Pico tier and Femto tier, is first modeled with the spatial point process in stochastic geometry theory; then, considering the BSs low transmit power, flexible cell extension and hyper BSs spatial density, a tractable downlink rate model based on the nearest distance and bias accepted factor is proposed, which adopt stochastic geometry theory and is easy to compute; last, the proposed downlink rate model is validated by numerical examples to confirm that the flexible cell extension BSs deployment in complex high traffic area with different path loss exponent is an effective scheme to improve quality of service.

Performance analysis of two tier HetNets with massive MIMO enabled wireless backhauling

Dense deployment of small cells escalates the network capacity, making it a candidate technology for the future wireless network. However, backhauling of such a large number of small cells becomes a major challenge in its successful deployment. In this paper, a framework for massive MIMO enabled wireless backhauling in a two-tier heterogeneous network is developed. The framework considers massive MIMO enabled macro base station and in-band full-duplex (IBFD) small cell base station. Massive MIMO system provides high spectral efficiency and high energy efficiency. Besides, due to IBFD capability, the small cells can utilize the same frequency band to communicate over the access link and the backhaul link simultaneously. Tools from the stochastic geometry are utilized to model and derive the analytical expressions of coverage probability and area spectral efficiency (ASE). Furthermore, a trade-off between ASE and coverage probability is observed. All the analytical results are verified by simulation. Simulation results show that massive MIMO and IBFD communication may be useful technologies from the backhauling perspective in the dense small cell network. It is observed that the proposed framework provides 42.30% improvement in the coverage performance over the other existing framework for rate threshold of 1 bps/Hz. Furthermore, optimal performance for the proposed model can be achieved by tuning of bandwidth allocation factor.

Analysis of Packet Throughput in Spatiotemporal HetNets with Scheduling and Various Traffic Loads

Recently, research attempts have been made to jointly model spatial and temporal randomness in cellular networks. However, realistic modeling and analysis of dynamic queuing interactions in heterogeneous networks (HetNets) still need to be investigated. In this letter, we establish a realistic spatiotemporal model for a ${K}$ -tier HetNet. Particularly, we model the locations of base stations (BSs) from each tier as an independent Poisson point process (PPP). Packet arrivals are modeled as independent Bernoulli processes. To reveal actual scenario, the effect of bias association is considered. We also allow users to have various packet arrival rates to account for different traffic loads. We capture the coupling relations between transmission success probability and cell active probability. Accurate expression for the mean packet throughput of the network is derived. Our analytical results provide the way to design optimal bias association factors to maximize the mean packet throughput of the HetNet, and also help design BS densities for certain user density in order to achieve a given mean packet throughput level.

Coverage and Rate Analysis in Downlink ${L}$ -Tier HetNets With Fluctuating Beckmann Fading

The fluctuating Beckmann (FB) fading is a general fading model, and it extends the $\kappa $ - $\mu $ shadowed fading to a power imbalance scenario. However, the FB fading contains a generalized Lauricella confluent hypergeometric function, which makes the performance analysis in downlink stochastic geometry-based heterogeneous cellular networks (HetNets) face a big challenge. In this letter, we first approximate the general and complex FB fading as a Gamma distribution based on the second-order moment matching method. For the application of Laplace trick, we then propose a simple and novel Erlang distribution to approximate the Gamma distribution with non-integer parameters. Using the proposed distribution as well as the Rician approximation for a small parameter, we successfully obtain approximate expressions for the coverage probability and average rate in a downlink ${L}$ -tier HetNet with FB fading and validate through simulations.

Unified Analysis of HetNets Using Poisson Cluster Processes Under Max-Power Association

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.

3GPP-Inspired HetNet Model Using Poisson Cluster Process: Sum-Product Functionals and Downlink Coverage

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 Matern cluster processes. Special instances of the proposed model closely resemble the different configurations for BS and user locations considered in 3GPP simulations.

The Connectivity of Millimeter Wave Networks in Urban Environments Modeled Using Random Lattices

Millimeter-wave (mm-wave) communication opens up tens of giga-hertz spectrum in the mm-wave band for use by next-generation wireless systems, thereby solving the problem of spectrum scarcity. Maintaining connectivity stands out as a key design challenge for mm-wave networks deployed in urban regions due to the blockage effect characterizing mm-wave propagation. In this paper, we set out to investigate the blockage effect on the connectivity of mm-wave networks in a Manhattan-type urban region modeled using a random regular lattice, while base stations (BSs) are Poisson distributed in the plane. In particular, we analyze the connectivity probability that a typical user is within the transmission range of a BS and connected by a line-of-sight. First, we consider a single-tier network. By jointly applying the random lattice and stochastic geometry theories, a lower bound on the connectivity probability is derived as a function of building parameters (e.g., size and site occupancy probability) and BS parameters (e.g., transmission range and BS density). For the case of dense buildings, the bound is derived in a simpler form. Next, the preceding lower bounds are tightened based on the geometric technique of partitioning the irregular blockage-free region around the typical user. Moreover, the analysis is generalized to mm-wave channels with both LoS and NLoS paths. Finally, the results are extended to a $K$ -tier heterogeneous network (HetNet), where building heights are random, and depending on its height, a building can block the signals transmitted by a subset of BS tiers but not all. The analysis shows that the connectivity probability of the $K$ -tier HetNet increases linearly with the number of tiers. In general, our work quantifies the relation between the coverage of an mm-wave network and the parameters of building and BS processes, providing useful guidelines for deploying practical networks in a Manhattan-type region.

Optimization and Analysis of Probabilistic Caching in $N$ -Tier Heterogeneous Networks

In this paper, we study the probabilistic caching for an $N$ -tier wireless heterogeneous network (HetNet) using stochastic geometry. A general and tractable expression of the successful delivery probability (SDP) is first derived. We then optimize the caching probabilities for maximizing the SDP in the high signal-to-noise ratio regime. The problem is proved to be convex and solved efficiently. We next establish an interesting connection between $N$ -tier HetNets and single-tier networks. Unlike the single-tier network where the optimal performance only depends on the cache size, the optimal performance of $N$ -tier HetNets depends also on the base station (BS) densities. The performance upper bound is, however, determined by an equivalent single-tier network. We further show that with uniform caching probabilities regardless of content popularities, to achieve a target SDP, the BS density of a tier can be reduced by increasing the cache size of the tier when the cache size is larger than a threshold; otherwise, the BS density and BS cache size can be increased simultaneously. It is also found analytically that the BS density of a tier is inverse to the BS cache size of the same tier and is linear to BS cache sizes of other tiers.

A Comprehensive Analysis of 5G Heterogeneous Cellular Systems Operating Over $\kappa$ – $\mu$ Shadowed Fading Channels

Emerging cellular technologies such as those proposed for use in 5G communications will accommodate a wide range of usage scenarios with diverse link requirements. This will include the necessity to operate over a versatile set of wireless channels ranging from indoor to outdoor, from line-of-sight (LOS) to non-LOS, and from circularly symmetric scattering to environments which promote the clustering of scattered multipath waves. Unfortunately, many of the conventional fading models adopted in the literature to develop network models lack the flexibility to account for such disparate signal propagation mechanisms. To bridge the gap between theory and practical channels, we consider $\kappa$-$\mu$ shadowed fading, which contains as special cases, the majority of the linear fading models proposed in the open literature, including Rayleigh, Rician, Nakagami-m, Nakagami-q, One-sided Gaussian, $\kappa$-$\mu$, $\eta$-$\mu$, and Rician shadowed to name but a few. In particular, we apply an orthogonal expansion to represent the $\kappa$-$\mu$ shadowed fading distribution as a simplified series expression. Then using the series expressions with stochastic geometry, we propose an analytic framework to evaluate the average of an arbitrary function of the SINR over $\kappa$-$\mu$ shadowed fading channels. Using the proposed method, we evaluate the spectral efficiency, moments of the SINR, bit error probability and outage probability of a $K$-tier HetNet with $K$ classes of BSs, differing in terms of the transmit power, BS density, shadowing characteristics and small-scale fading. Building upon these results, we provide important new insights into the network performance of these emerging wireless applications while considering a diverse range of fading conditions and link qualities.

Effect of Cell-Selection on the Effective Fading Distribution in a Downlink $K$ -Tier HetNet

This letter characterizes the statistics of effective fading gain in multi-tier cellular networks with strongest base station (BS) cell association policy. First, we derive the probability of association with the ${n}$ -th nearest BS in the ${k}$ -th tier. Next, we use this result to derive the probability density function of the channel fading gain (effective fading) experienced by the user when associating with the strongest BS. Interestingly, our results show that the effective channel gain distribution solely depends upon the original channel fading and the path-loss exponent. Moreover, we show that in the case of Nakagami- ${m}$ fading channels (Gamma distribution), the distribution of the effective fading is also Gamma but with a gain of ${({\alpha }/{2})}$ in the shape parameter, where ${\alpha }$ is the path-loss exponent.

Location‐based coverage and capacity analysis of a two tier HetNet

Stochastic geometry tool is an accurate and tractable approach to analyse the performance characteristics of heterogeneous networks (HetNets) with unplanned deployment of base stations (BSs). In this study, the authors analyse the downlink coverage and capacity by taking into account the separation between the macro BS (MBS) and small BSs (SBSs) in a HetNet. MBSs, SBSs, and users are spatially distributed as independent Poisson point processes. The whole space is divided into inner and outer subspaces around the MBSs and a typical user is assumed to be in outer subspace. Analysis on the typical user in the outer subspace incorporates the effect of distance of SBSs from MBS. They derive the expressions for the coverage probability of an outer subspace typical user from SBS and MBS. They also derive the expressions for rate coverage of an outer subspace typical user from SBS and MBS. These metrics are analysed with varying inner subspace radius to incorporate the effect of BSs separation. Simulation results show that SBSs away from MBS in the coverage region of MBS provide good performance to their associated users in terms of coverage probability and rate coverage.

Enriched $K$ -Tier HetNet Model to Enable the Analysis of User-Centric Small Cell Deployments

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) Matern 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.

Uplink Modeling of $K$ -Tier Heterogeneous Networks: A Queuing Theory Approach

Heterogeneous networks (HetNets) are expected to release enormous capacity beyond what is achievable now. This comes at the price of higher interference that may jeopardize proper network operation if not managed cautiously. In handling this problem, mathematical modeling of HetNets to understand their underlying facts is necessary. As the mathematical theory of waiting lines, queuing theory is exploited in this paper as a powerful tool to model the uplink transmission of a user equipment (UE) in a $K$ -tier HetNet, as an M/G/1 queue with interruption operating at the packet level. By integrating key findings on HetNets (using stochastic geometry) into the queue, a realistic model is obtained. This model enables us to understand what a UE experiences in terms of throughput, an angle that has barely been looked through by others. The modeling framework considers all the essential HetNet parameters, including the transmit power, spatial distribution, service rate, traffic flow intensity, and base station coverage threshold, to obtain the probability generating function and related statistics of the UE queue length.

Joint Effect of User Activity Sensing and Biased Cell Association in Energy Efficient HetNets

In heterogeneous networks, the active/sleep strategy for base stations (BSs) provides an effective way to match capacity to demand and also improve energy efficiency. At the same time, environmental awareness and self-organizing features are expected to play important roles in improving the network performance. In this letter, we propose an active/sleep scheme based on user activity sensing of small cell BSs considering biased cell association. The effect on coverage probability, user throughput, and energy consumption of the proposed scheme in $K$ -tier HetNets is analyzed using stochastic geometry theory. The performance analysis can be effectively used to design an energy-efficient active/sleep scheme for multi-tier HetNets.

Secrecy Outage Probability in Multi-RAT Heterogeneous Networks

Practical difficulty in examining all base stations (BSs) to choose the best one providing secure transmission in heterogeneous networks (HetNets), we impose a BS association constraint in this letter that the BSs providing an average received signal power at the legitimate user greater than a predetermined receiving threshold can be candidate serving BSs. With this constraint, we derive closed-form expressions for secrecy outage probability (SOP) of both homogeneous networks and $K$ -tier HetNets based on stochastic geometry. Our analysis reveals that security performance can be improved by deploying more low-power BSs in high path-loss environments. Besides, the SOP stays unchanged when the receiving threshold is below a critical point and increases rapidly when exceeding that point. These results depict features of SOP with practical constraint, which could provide new insights into the physical layer security in HetNets.

Modeling Heterogeneous Cellular Networks Interference Using Poisson Cluster Processes

Future mobile networks are converging toward heterogeneous multitier networks, where macro-, pico-, and femto-cells are randomly deployed based on user demand. A popular approach for analyzing heterogeneous networks (HetNets) is to use stochastic geometry and treat the location of BSs as points distributed according to a homogeneous Poisson point process (PPP). However, a PPP model does not provide an accurate model for the interference when nodes are clustered around highly populated areas. This motivates us to find better ways to characterize the aggregate interference when transmitting nodes are clustered following a Poisson cluster process (PCP) while taking into consideration the fact that BSs belonging to different tiers may differ in terms of transmit power, node densities, and link reliabilities. To this end, we consider $K$ -tier HetNets and investigate the outage probability, the coverage probability, and the average achievable rate for such networks. We compare the performance of HetNets when nodes are clustered and otherwise. By comparing these two types of networks, we conclude that the fundamental difference between a PPP and a PCP is that, for a PPP, the number of simultaneously covered mobiles and the network capacity linearly increase with $K$ . However, for a PCP, the improvements in the coverage and the capacity diminish as $K$ grows larger, where the curves saturate at some point. Based on these observations, we determine the scenarios that jointly maximize the average achievable rate and minimize the outage probability.