Downlink coverage analysis of n-tier heterogeneous cellular networks based on clustered stochastic geometry

How many small cell (SC) access points (APs) are required to guarantee a chosen quality of service in a heterogeneous network? In this chapter, we answer this question considering two different network models. The first is the downlink of a finite-area SC network where the locations of APs within the chosen area are uniformly distributed. A key step in obtaining the closed-form expressions is to generalize the well-accepted moment matching approximation for the linear combination of lognormal random variables. For the second model, we focus on a two-layer downlink heterogeneous network with frequency reuse-1 hexagonal macro cells (MCs), and SC APs that are placed at locations that do not meet a chosen quality of service from macro base stations (BSs). An important property of this model is that the SC AP locations are coupled with the MC coverage. Here, simple bounds for the average total interference within an MC makes the formulation possible for the percentage of MC area in outage, as well as the required average number of SCs (per MC) to overcome outage, assuming isolated SCs. Introduction Heterogeneous cellular networks (HCNs) are being considered as an efficient way to improve system capacity as well as effectively enhance network coverage [1, 2]. Comprising multiple layers of access points (APs), HCNs encompass a conventional macro cellular network (first layer) overlaid with a diverse set of small cells (SCs) (higher layers). Cell deployment is an important problem in heterogeneous networks, both in terms of the number and positioning of the SCs. Traditional network models are either impractically simple (such as the Wyner model [3]) or excessively complex (e.g., the general case of random user locations in a hexagonal lattice network [4]) to accurately model SC networks. A useful mathematical model that accounts for the randomness in SC locations and irregularity in the cells uses spatial point processes, such as Poisson point process (PPP), to model the location of SCs in the network [5–10]. The independent placement of SCs from the MC layer, has the advantage of analytical tractability and leads to many useful SINR and/or rate expressions. However, even assuming that wireless providers would deploy SCs to support mobile broadband services, the dominant assumption remains that SCs are deployed randomly and independent of the MC layer [11].

To satisfy the requirement of increasing mobile traffic, heterogeneous networks (HetNets) will be deployed for the fifth generation (5G) mobile communications systems. Since the deployment of base stations (BSs) in HetNets is generally dense and random, stochastic geometry has increasingly been used to analyze the performance of HetNets. Most of the existing work is based on Poisson point processes (PPPs), which lead to some closed-form expressions for local delay and energy efficiency. Considering the geographical distribution of BSs, PPP may not be accurate enough. In contrast, a Poisson cluster process (PCP) proves more realistic for the deployment of BSs. In this paper, by using the discontinuous transmission (DTX) mode, the local delay and energy efficiency based on PCP have been analyzed. It is found that the local delay is larger and the energy efficiency is lower under PCP because of the strong intra-cluster interference. However, the local delay under PCP becomes similar to that under PPP if the radii of clusters are sufficiently large.

Cellular networks have a great transformation during the last decade. The traditional cellular network system is often overlaid with well-deployed BSs of proper power. However, more and more complex elements such as picocells, femtocells and relays have been introduced to cellular network system. BSs in these elements are unplanned, user-installed and randomly deployed. All of these things compose heterogeneous cellular networks (HCNs). In order to evaluate the performance of HCNs, people usually model the distribution of BSs in HCNs as spatial stochastic point process model. One of the most popular spatial models for these HCNs is Poisson Point Process (PPP) model. However the PPP model is not exact for some cases where BSs in PPP model may be too close to each other. In this paper, we propose a more reasonable and practical model called Matern-like point process (MLPP) model which imposes a certain minimal distance between any two BSs to overcome this problem. Simulations show that the coverage probability of the proposed model noticeably outperforms the PPP model. This improvement depends on the value of minimal distance. We also evaluate the system efficiency defined by the ratio of coverage probability and total power. The results show that the MLPP model has a significant improvement compared to PPP model.

Heterogeneous Networks (HetNets) have gained the attraction of the communication industry recently, due to their promising ability to enhance the performance of future broadband Fifth Generation (5G) networks and are integral parts of 5G systems. They can be viewed in multi-dimensional space where, each slice represents a unique tier that has its own Base Station (BS)s and User Equipment (UE)s. Different tiers cooperate with each other for their mutual benefit. Data can be interactively exchanged among the tiers, and UEs have the flexibility to switch between the tiers. The cells in such a heterogeneous cellular networks have variable sizes, shapes, and coverage regions. However, in HetNets with ultra dense BSs, the distance between them gets very small and, they suffer from very high levels of mutual interference. To improve the performance of HetNets, we have done multiple contributions in this dissertation. First, we have developed analytical derivations for optimizing pilot sequence length which is a very crucial factor in acquiring the Channel State Information (CSI) and the channel estimation process in general. Poisson Point Process (PPP) has been widely used to allocate BSs among various tiers so far. However, BS locations obtained using PPP approach may not be optimum to reduce interference. Therefore, in this dissertation, BSs locations are optimized to reduce the interference and improve the coverage and received signal power. Also, we have derived expressions for static UEs coverage probability and network energy efficiency in HetNets. A proper UE association algorithm for HetNets is a great challenge. The classic max-Signal to Interference and Noise Ratio (SINR) or max-received signal strength (RSS) user association algorithms are inappropriate solutions for HetNets as UEs in this context will tend to connect to the Macro BS, which is the one with the highest signal power. A severe load imbalance and significant inefficiency arises and impacts the performance. The aforementioned algorithms tend to associate UEs to BSs with the best received signal power or signal quality. In HetNets, usually Macro BSs are the ones transmitting the strongest signals; hence most UEs tend to associate with the Macro BS leaving Micro BSs with less load. Also, the conventional max-SINR and max-RSS algorithms do not provide adequate results in multi-tier systems. We suggest two centralized algorithms, LSTD and RTLB, for an even UE association to provide fair load distribution. However RTLB outperforms LSTD in real time scenarios as it easily and quickly adapts to rapid network changes. Furthermore, we consider the mobility of nodes. We derive coverage probability for moving UEs considering both handover and no handover scenarios. Proposed algorithms are fast enough to associate the moving users to different Micro and Macro BSs appropriately in real time. Our algorithms are proved to be feasible and provide a path towards attainable future communication systems.

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated the need to consider variety of user and base station (BS) configurations for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models considered by standardization bodies, such as the third generation partnership project (3GPP). Complementary to these simulation models, stochastic geometry-based approach modeling the user and BS locations 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 model is not rich enough to capture all the spatial configurations that appear in real-world HetNet deployments (on which 3GPP simulation models are based). In this paper, we bridge the gap between the 3GPP simulation models and the popular PPP-based analytical model by developing a new unified HetNet model in which a fraction of users and some BS tiers are modeled as Poisson cluster processes (PCPs). This model captures both non-uniformity and coupling in the BS and user locations. For this setup, we derive exact expression for downlink coverage probability under maximum signal-to-interference ratio (SIR) cell association model. As intermediate results, we define and evaluate sum-product functionals for PPP and PCP. Special instances of the proposed model are shown to closely resemble different configurations considered in 3GPP HetNet models. Our results concretely demonstrate that the performance trends are highly sensitive to the assumptions made on the user and SBS configurations.

In cellular network models, the base stations are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. Accordingly, in this paper, we consider the very general class of motion-invariant models and analyze the behavior of the coverage probability (the probability that the signal-to-interference-plus-noise-ratio (SINR) exceeds a threshold) as the threshold goes to zero. We show that, surprisingly, the slope of the outage probability (complementary to the coverage probability, in dB) as a function of the threshold (also in dB) is the same for essentially all motion-invariant point processes. The slope merely depends on the fading statistics. Using this result, we introduce the notion of the asymptotic deployment gain (ADG), which characterizes the horizontal gap between the coverage probability of the PPP and another point process in the high-reliability regime (where the coverage probability is near 1). To demonstrate the usefulness of the ADG for the characterization of coverage probabilities, we investigate the coverage properties and the ADGs for different point processes and fading statistics by simulations.

Coverage probability of uplink millimeter wave cellular network with non-homogeneous interferers’ point process

Indoor coverage and capacity are the major limitations of the current cellular systems. In such perspective, femtocells deployment has attracted considerable interest. However, the random and co-channel deployment of femtocells poses severe interference management challenges, especially at the cell edges. Recently, Fractional Frequency Reuse (FFR) has emerged an attractive technique for co-tier and cross-tier interference in multi-tier cellular deployment. However, most of the previous work analyzes the performance of FFR for perfect cell geometry models. Applying regular resource of the standard FFR scheme to the realistic cellular networks with high irregularity in the cell geometry and channel conditions leads to sub-optimal performance. In this paper we investigate the performance of FFR for two-tier cellular network based on irregular cell geometry. To capture the realistic network scenario the position of Macro Base Stations (MBSs) and Femto Base Station (FBSs) are modeled with Hard Core Point Process (HCPP) and Poisson Point Process (PPP) respectively. Furthermore, Sectored-FFR scheme with optimal sub-band allocation is proposed in this paper and the capacity of the system is evaluated. Simulation results show that the proposed Sectored-FFR scheme outperforms the conventional FFR schemes in terms of throughput and capacity.

Low-power base stations (BSs), such as pico BSs, femto BSs, and relay nodes, are introduced to the heterogeneous cellular networks to enhance coverage and improve system capacity. Compare with macro BS, low-power BS has much lower transmission power, smaller physical size and lower cost. Deploying low-power BSs within the coverage of macro BSs is considered as a cost-efficient way to meet the sharp increase of wireless applications, leading to a new radio network planning paradigm for the next generation cellular networks. In this paper, we study the minimum cost cell planning problem in such heterogeneous networks, where planning task is how to select a subset of possible BS sites, including macro BSs, pico BSs and relay nodes, to minimize the total deployment cost while satisfying all rate requirements of demand nodes. We develop an approximation algorithm to tackle the formulated NP-hard problem, which guarantees an approximation ratio of O(log R) to the optimal solution, where R is the maximal achievable capacity of BSs.

A K-tier heterogeneous downlink millimeter wave (mmWave) cellular network with user-centric small cell deployments is studied in this paper. In particular, we consider a heterogeneous network model with user equipments (UEs) being deployed according to a Poisson Cluster Process (PCP), i.e., Thomas cluster process, where the UEs are clustered around the base stations (BSs) and the distances between UEs and the BS are modeled as Gaussian distributed. In addition, distinguishing features of mmWave communications including directional beamforming and a sophisticated path loss model incorporating both line-of-sight (LOS) and non-line-of-sight (NLOS) transmissions, are taken into account. In this paper, the complementary cumulative distribution function (CCDF) and probability density function (PDF) of the path loss are provided. Also, using tools from stochastic geometry, we derive a general expression of the signal-to-interference-plus-noise ratio (SINR) coverage probability. Our results demonstrate that coverage probability can be improved by decreasing the size of UE clusters around BSs, and interference has noticeable influence on the coverage performance of our model.

As current cellular networks are becoming increasingly heterogeneous, traditional cell association rule based on the downlink reference signal receiving power (RSRP) no longer serves well. Under this circumstance, the concept of downlink (DL) and uplink (UL) decoupling (DUDe), in which user equipments choose the serving Base Station (BS) in DL and UL separately, has drawn great attention during the design of next generation cellular networks. In this paper, using the framework of stochastic geometry, we at first derive the theoretical energy efficiency (EE) distribution of a two-tier heterogeneous network both in DL and UL with DUDe. Then through numerical simulation, we verify that the DUDe rule can improve EE of a heterogeneous network comparing with the traditional RSRP rule. The improvement is shown to be significant through a further comparison with bias-based Cell Range Extension (CRE).

Considering the ever‐growing demand for network traffic, increasing the capacity of cellular networks has always been a necessity. Heterogeneous cellular networks using small‐scale base stations in addition to macro base stations (BSs) are a low cost and effective solution to this problem. The diversity of the BSs in heterogeneous networks, however, has raised new issues in terms of cell association and interference management compared with the traditional single‐tier networks. Devising novel and effective methods for cell association and resource allocation in these networks is currently an open and developing problem. This paper addresses cell and subband association in the downlink of orthogonal frequency‐division multiple‐access heterogeneous networks. Unlike the existing works in this field, our scheme maximizes network utility while preventing harmful interference for all connections in the network. Using the protocol interference model, necessary and sufficient constraints for preventing interference in cellular networks are presented. By choosing the appropriate interference constraint, the joint problem of cell and subband association is formulated as an integer optimization problem. After simplifying the optimization problem, an equivalent linear problem is obtained. Using one‐level dual decomposition, an iterative algorithm with a near‐optimal solution has been devised. A distributed protocol is then presented, in which each user and each BS requires only its own local data to determine its connection for service. The simulation results demonstrate the algorithm behavior and confirm the efficiency and near‐optimality of the proposed solution.

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 Soft FR with a reuse factor of $\Delta=1$ in a Rayleigh fading channel. It has been assumed that all Base Stations (BSs) transmit continuously which leads to a reduction on the impact of number of users and RBs on network performance. In this paper, the performance of Soft FR with a reuse factor of $\Delta>1$ in Rayleigh-Lognormal fading channel is evaluated. The impact of the number of users and Resource Blocks (RBs) on Intercell Interference (ICI) are presented for Round Robin scheduling and indicator functions. The results show that there are opposite trends between coverage probability of Cell-Center User (CCU) and Cell-Edge User (CEU).

In heterogeneous networks, interference is one of the critical issues. In this letter, we consider a two-tier downlink network composed of macrocell base stations (MBSs) and femtocell base stations (FBSs), where the locations of MBSs and FBSs are modeled by two independent Poisson point processes (PPPs). FBSs are assumed to be cognitive and become inactive when within a certain range of active MBSs. Due to the inactivation regions, the location distribution of active FBSs no longer follows PPP, complicating the calculation of coverage probability. To circumvent this, we propose an approximation to the coverage probability for both the open access and closed access policies.

Due to its mathematical tractability, the homogeneous Poisson point process (PPP) has been employed to model wireless networks and analyze their performance widely. PPP falls short in modeling the effect of interference management techniques, which typically introduces some form of spatial mutual exclusion among base stations (BSs). Considering the spatial mutual exclusion between macro BSs s (BSs), in this paper, we studies the coverage performance of a two-tier heterogeneous cellular network (HCN) modeled by Poisson hard-core process (PHCP) and PPP. We first provide the approximate expression of coverage probability of the two-tier PHCP-PPP HCN with the use of PT-ASAPPP method, which stands for “per tier approximate signal to interference ratio (SIR) analysis based on PPP. In this method, each tier is approximated to PPP by using SIR gain. The concrete expression of the SIR gain G PHCP for PHCP model is derived through simulation and data fitting. Simulation results verify the correctness of theoretical analysis and the effectiveness of PT-ASAPPP method.