Downlink Heterogeneous Cellular Networks Research Articles

Multitier heterogeneous network using stochastic geometry and factorial moment approaches

SummaryThe rapid growth of small cells is driving cellular network toward randomness and heterogeneity. Usually, cellular networks are modeled by placing each tier (eg, macro, pico, and relay nodes) deterministically on a grid. In such a heterogeneous cellular network, the rational approach to characterize the base stations (BSs), user, and relay locations is by using random spatial models. When calculating the metric performances such as coverage probability, these networks are idealized without consideration of interference. Therefore, interference modeling remains the key issue for the deployment of small cells. This paper developed a single and multitier cellular network model that captures the downlink heterogeneous cellular network with variable parameters such as the target signal‐to‐interference ratio (SIR), transmitted power, and deployment density. In particular, we model ‐tier transmission and compare it with a single‐tier and traditional grid model to obtain tractable coverage probability using stochastic geometry and factorial moment. The obtained results demonstrate the effectiveness and analytical tractability to study the heterogeneous performance.

Stochastic Analysis of Downlink Heterogeneous Cellular Networks: Based on Spatial Hybrid Model

In this paper, a hybrid model for heterogeneous cellular networks (HCNs) is proposed based on the differences in the distribution characteristics, path loss models and transmit power of macro and micro base stations (BSs). The macro base stations in HCNs are modelled as 2-D PPP which obeys certain parameters, and the small base stations are modelled as 3-D PPP. According to the stochastic geometry theory and the relevant knowledge of probability theory, the interference characteristics in HCNs are analysed, and the downlink coverage probability of the target users in the network are derived. Compared the hybrid interference model proposed in this paper with the traditional model, simulation shows that the hybrid interference model can illustrate the distribution characteristics of each kind of base station in HCNs more accurately, and the network performance based on model proposed in this paper is more accurate.

Coverage in Downlink Heterogeneous mmWave Cellular Networks With User-Centric Small Cell Deployment

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 distributed according to a Poisson cluster process (PCP). Distinguishing features of mmWave communications including directional beamforming and a sophisticated path loss model incorporating both line-of-sight and non-line-of-sight transmissions, are taken into account. Initially, we determine general expressions for the association probabilities of different tier BSs. Using tools from stochastic geometry, we then characterize the Laplace transform of the interference and derive a general expression for the signal-to-interference-plus-noise ratio coverage probability. While these expressions are applicable to any PCP, we later specialize the results to two popular PCPs, namely, first, Thomas cluster process, where the UEs are clustered around the base stations (BSs) according to a Gaussian distribution, and second, Matern cluster process, where the UEs are scattered according to a uniform distribution. Subsequently, upper and lower bounds for the coverage probability are provided. Special cases are also addressed, providing the insight that when the cluster size grows without bound, our PCP-based model specializes to a Poisson point process-based model. Area spectral efficiency is investigated as well. Moreover, we have discussed extensions to cases in which more practical antenna gain patterns are taken into account and also the shadowing is considered. Via numerical and simulation results, we explore the effects of the beamwidth of the main lobe, the main lobe directivity gain, the biasing factor and the transmit power of the small-cell BSs to get insight on the performance in practical scenarios. Performance in dense networks is also analyzed numerically.

SIR Meta Distribution of $K$ -Tier Downlink Heterogeneous Cellular Networks With Cell Range Expansion

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 the beta approximations are evaluated and compared. Key performance metrics including the mean success probability, the variance of the conditional success probability, the mean local delay and the asymptotic SIR gains of each tier are obtained. The results show that the biases are detrimental to the overall mean success probability of the whole network and that the b-th moment curve (versus the SIR threshold) of the conditional success probability of each tier can be excellently approximated by the horizontal shifted versions of the first moment curve of the single-tier PPP network. We also provide lower bounds for the region of the active probabilities of the base stations to keep the mean local delay of each tier finite.

Secure Transmission for Heterogeneous Cellular Networks With Wireless Information and Power Transfer

In this paper, we investigate an artificial-noise-aided secure beamforming design for simultaneous wireless information and power transfer in a two-tier downlink heterogeneous cellular network, in which each energy receiver in a femtocell is seen as a potential eavesdropper to wiretap the confidential message intended for the information receiver. Our design objective is to maximize the secrecy rate at the information receiver, while satisfying the signal-to-interference-plus-noise ratio requirement of each macrouser and the energy harvesting and transmit power constraints. Both the scenarios of perfect and imperfect channel state information (CSI) are considered. With perfect CSI, the formulated optimization problem constitutes a difference of a convex function programming problem, which is hard to directly solve. To tackle this challenge, we transform it into a series of semidefinite programs by using successive convex approximation, and an iterative algorithm is proposed to arrive at a provably convergent solution. With imperfect CSI, we address robust secure beamforming relying on the worst-case design philosophy. To circumvent this predicament, we resort to the S-procedure to reformulate the robust quadratic matrix inequality (QMI) constraints and then obtain the linear matrix inequality representations for these QMIs. Numerical results are finally presented to demonstrate the performance of our proposed schemes in improving the secrecy rate of heterogeneous cellular networks.

Deep Reinforcement Learning for Mobile Video Offloading in Heterogeneous Cellular Networks

Heterogeneous cellular networks can balance mobile video loads and reduce cell arrangement costs, which is an important technology of future mobile video communication networks. Because of the characteristics of non-convexity of the mobile offloading problem, the design of the optimal strategy is an essential issue. For the sake of ensuring users' quality of service and the long-term overall network utility, this article proposes the distributive optimal method by means of multiple agent reinforcement learning in the downlink heterogeneous cellular networks. In addition, to solve the computational load issue generated by the large action space, deep reinforcement learning is introduced to gain the optimal policy. The learning policy can provide a near-optimal solution efficiently with a fast convergence speed. Simulation results show that the proposed approach is more efficient at improving the performance than the Q-learning method.

Coherent Joint Transmission in Downlink Heterogeneous Cellular Networks

The analysis of the success probability or signal-to-interference ratio (SIR) distribution for coherent joint transmission (JT) based on stochastic geometry is an open issue. In this letter, we study coherent JT in downlink heterogeneous cellular networks and provide an upper bound of the success probability for the general user and the worst-case user (cell-corner user), and an approximation for the general user. Simulation results show that the derived upper bound and approximation are quite accurate and thus provide an analytical approach to quantify the SIR performance of coherent JT.

Joint User Association and Power Control for Load Balancing in Downlink Heterogeneous Cellular Networks

Instead of achievable rate in the conventional association, we utilize the effective rate to design two association schemes for load balancing in heterogeneous cellular networks (HCNs), which are both formulated as such problems with maximizing the sum of effective rates. In these two schemes, the one just considers user association, but the other introduces power control to mitigate interference and reduce energy consumption while performing user association. Since the effective rate is closely related to the load of some BS and the achievable rate of some user, it can be used as a key factor of association schemes for load balancing in HCNs. To solve the association problem without power control, we design a one-layer iterative algorithm, which converts the sum-of-ratio form of original optimization problem into a parameterized polynomial form. By combining this algorithm with power control algorithm, we propose a two-layer iterative algorithm for the association problem with power control. Specially, the outer layer performs user association using the algorithm of problem without power control, and the inner layer updates the transmit power of each BS using a power update function (PUF). At last, we give some convergence and complexity analyses for the proposed algorithms. As shown in simulation results, the proposed schemes have superior performance than the conventional association, and the scheme with joint user association and power control achieves a higher load balancing gain and energy efficiency than conventional scheme and other offloading scheme.

Modeling and Analysis of Downlink Heterogeneous Cellular Networks

Owing to the irregular deployment of different types of base stations (BSs), cellular networks are now becoming more and more complex. In this study, a tractable and accurate framework based on hybrid model is proposed for heterogeneous cellular networks (HCNs). According to the distribution characteristics of different types of BSs in HCNs, the plane distributed macro BSs are termed as tier-1 cells, whereas the small cells, which are spatial distributed, are modeled as tier-2. First, we derive the probability of a target user communicate with macro BS or small cell. Second, we calculate the coverage probability that the target user communicate with macro or small cell respectively. Finally, we obtain the general closed expressions of whole coverage probability. In some special cases, the expressions present simple closed forms and can be calculated easily. Compared with the presented model, the simulation results show that our model is accurate within 1-2dB.

Heterogeneous Cellular Networks With LoS and NLoS Transmissions—The Role of Massive MIMO and Small Cells

We develop a framework for downlink heterogeneous cellular networks with line-of-sight (LoS) and non-LoS transmissions. Using stochastic geometry, we derive tight approximation of average downlink rate that enables us to compare the performance between densifying small cells and expanding base station (BS) antenna arrays. Interestingly, we find that adding small cells into the network improves the downlink rate much faster than expanding antenna arrays at the macro BS. However, when the small cell density exceeds a critical threshold, the spatial densification will lose its benefits and further impair the network capacity. To this end, we provide the optimal small cell density that maximizes the rate via numerical results for practical deployment guidance. In contrast, expanding macro BS antenna array can always benefit the capacity until an upper bound caused by pilot contamination, and this bound also surpasses the peak rate obtained from the deployment of small cells. Furthermore, we find that allocating part of antennas to distributed small cell BSs works better than centralizing all antennas at the macro BS, and the optimal allocation proportion is also given numerically for practical configuration reference. In summary, this paper provides a further understanding on how to leverage small cells and massive MIMO in future heterogeneous cellular networks deployment.

Modeling and SINR Analysis of Dual Connectivity in Downlink Heterogeneous Cellular Networks

Modeling and SINR Analysis of Dual Connectivity in Downlink Heterogeneous Cellular Networks

Flexible Multiple Base Station Association and Activation for Downlink Heterogeneous Networks

This letter shows that the flexible association of possibly multiple base stations (BSs) to each user over multiple frequency bands, along with the joint optimization of BS transmit power that encourages the turning-off of the BSs at off-peak time, can significantly improve the performance of a downlink heterogeneous wireless cellular network. We propose a gradient projection algorithm for optimizing BS association and an iteratively reweighting scheme together with a novel proximal gradient method for optimizing power in order to find the optimal tradeoff between network utility and power consumption. Simulation results reveal significant performance improvement as compared to the conventional single-BS association.

A Novel Power-Efficient BS Operation Scheme for Green Heterogeneous Cellular Networks

Power-efficient base station (BS) operation is one of the important issues in future green cellular networks. Previously well-known BS operation schemes, the cell zooming scheme and the cell wilting and blossoming scheme, require tight cooperation between cells in cellular networks. With the previous schemes, the non-cooperative BSs of a serving cell and neighboring cells could cause coverage holes between the cells, thereby seriously degrading the quality of service as well as the power saving efficiency of the cellular networks. In this paper, we propose a novel power-efficient BS operation scheme for green downlink heterogeneous cellular networks, in which the networks virtually adjust the coverage of a serving macrocell (SM) and neighboring macrocells (NMs) without adjusting the transmission power of the BSs when the SM is lightly loaded, and the networks turn off the BS of the SM when none of active users are associated with the SM. Simulation results show that our proposed scheme significantly improves the power saving efficiency without degrading the quality of service (e.g., system throughput) of a downlink heterogeneous LTE network and outperforms the previous schemes in terms of system throughput and power saving efficiency. In particular, with the proposed scheme, macrocells are able to operate independently without the cooperation of a SM and NMs for green heterogeneous cellular networks.

Energy‐efficient user association in downlink heterogeneous cellular networks

In this study, the authors propose an energy-efficient user association scheme to maximise the overall energy efficiency for downlink heterogeneous cellular networks, and formulate it as a non-linear and mixed-integer optimisation problem. Such a problem includes user association problem and power control problem. Since the formulated problem is in a fractional and mixed-integer form, it is challenging for designers to achieve the optimal solutions of this problem. To this end, they design an effective three-layer iterative algorithm. In the first layer, the energy efficiency parameter is found via bisection method. In the second layer, association index and transmit power are optimised alternately. In the third layer, the user association problem is solved via dual decomposition method and the transmit power is updated by employing a power update function. In addition, they further give some convergence analyses for some parts (user association algorithm and power control algorithm) of the proposed algorithm, and also give some complexity analyses for the whole algorithm. Numerical results show that, compared with non-energy-efficient association, the energy-efficient association has significant superiorities on load balancing level, system throughput and energy efficiency.

Moving Relays in Heterogeneous Cellular Networks—A Coverage Performance Analysis

A large number of today's cellular users are vehicular, i.e., traveling in public transports. To improve the weak received signal of vehicular users and to mitigate vehicle penetration loss, researchers have recently proposed the use of moving relays (MRs). People in vehicles can use these MRs that are mounted on top of public transports for better communication. Recent research on MRs, however, is mainly limited to providing performance analysis of vehicular users. The effect of these relays on current heterogeneous cellular networks has yet to be studied. In this paper, we develop a system model for a downlink heterogeneous cellular network, which includes MRs. We derive the coverage probability of macro users, vehicular users, and the overall network. We also show that, in addition to providing better coverage to vehicular users, MRs can also enhance coverage of nonvehicular boundary users with the help of cooperative communication.

Cost-Efficient Optimization of Base Station Densities for Multitier Heterogeneous Cellular Networks

Heterogeneous cellular networks have emerged as the primary solution for overwhelming traffic demands. This study addresses the architecture optimization of multitier open-access downlink heterogeneous cellular networks. A distinguishing feature of this work is that the transmission requirements of mobile users and the profit requirements of operators are all considered. Spatial throughput is maximized under practical constrains on the network deployment cost and traffic loads of individual tiers. By using stochastic geometry, the problems of optimizing the densities of base stations (BSs) in different tiers are shown to be linear-fractional programming that can be further transformed into linear programming by employing Charnes–Cooper transformation. The linear-fractional programming can then be solved efficiently. For a two-tier network, the optimal BS densities are derived in closed form by using the graphical method. Our results indicate that enlarging the densities of BSs may not always improve network throughput and that the optimal densities of each tier exist to satisfy the communication demands of mobile users and the profit requirements of operators. Numerical results demonstrate the significant throughput gain from the optimal deployment of multitier heterogeneous cellular networks.

Analytical Coverage Probability of a Typical User In Heterogeneous Cellular Networks

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).

Traffic Offloading in Heterogeneous Networks With Energy Harvesting Personal Cells-Network Throughput and Energy Efficiency

This work develops a tractable model to analyze the performance of downlink heterogeneous cellular networks (HCNs) with both power-grid-connected base stations (PG-BSs) and energy harvesting small cell access points (EH-SAPs). Each EH-SAP forms a personal cell that is active (and is available to serve others) only when its own priority user requests service and its battery contains sufficient energy to transmit. By modeling the battery dynamics of an EH-SAP as a discrete-time Markov chain and by considering a practical power consumption model, the rate coverage, network throughput, and energy efficiency are derived as functions of the PG-BS and EH-SAP densities, transmission powers, cell association biases, and energy harvesting capabilities. Cell association biases control the traffic load among different tiers and transmission powers affect EH-SAPs’ probability of being active. Exact expressions of the performance metrics are first derived for the general multitier scenario and are then used to obtain approximate closed-form expressions for two-tier networks using the mean load approximation. The analytic results of the two-tier network provide valuable insights on the achievable performance and the choice of system parameters, and are further validated with numerical results.

Multi-Antenna Transmission in Downlink Heterogeneous Cellular Networks Under A Threshold-based Mobile Association Policy

With the recent emergence of 5G era, heterogeneous cellular networks (HCNs) have invoked a popular research interest. In this paper, we provide a comprehensive analysis for multiantenna transmissions in a multi-tier downlink HCN. We first propose a reliability-oriented threshold-based mobile association policy, where each user connects to the strongest base station from which this user can obtain the largest truncated long-term received power. Under our mobile association policy, we derive analytical expressions for the exact outage probability of an arbitrary randomly located user, along with computationally convenient lower and upper bounds. Asymptotic analysis on the outage probability shows that introducing a large access threshold into mobile association significantly decreases the outage probability. We further investigate the spectrum efficiency and the energy efficiency of the HCN. Our theoretic analysis and numerical validations show that both the spectrum and energy efficiencies can be improved by properly choosing the access threshold.

Analysis of Joint Transmit–Receive Diversity in Downlink MIMO Heterogeneous Cellular Networks

We study multiple-input–multiple-output (MIMO)-based downlink heterogeneous cellular networks (HetNets) with joint transmit–receive diversity using orthogonal space–time block coding at the base stations (BSs) and maximal-ratio combining (MRC) at the users. MIMO diversity with MRC receivers is particularly appealing in cellular networks due to the relatively low hardware complexity at both the BS and the user device. Using stochastic geometry, we develop a tractable stochastic model for analyzing such HetNets taking into account the irregular and multitier BS deployment. We derive the coverage probability for both interference-blind (IB) and interference-aware (IA) MRC as a function of the relevant tier-specific system parameters such as BS density and transmit (Tx) power, number of Tx antennas, and path-loss law. Important insights arising from our analysis for typical HetNets are as follows: 1) IA-MRC becomes less favorable than IB-MRC with Tx diversity due to the smaller interference variance and increased interference correlation across receive (Rx) antennas; 2) ignoring spatial interference correlation significantly overestimates the performance of IA-MRC; and 3) for a small number of Rx antennas, selection combining may offer a better performance–complexity tradeoff than MRC.