Single-tier Network Research Articles

A Novel ASAPPP Approach to Characterize the SIR Distribution in General Cellular Networks

The non-Poisson point processes have the characteristics of spatial repulsion or aggregation, which well matches the realistic cellular network deployment, but challenges the fundamental analysis of the signal-to-interference ratio (SIR) distribution. In this letter, we propose a novel approximation method via decomposing the ASAPPP method (approximate SIR analysis based on the Poisson point process) to formulate two key intermediate approximate results, namely, the contact distance distribution and the spatial distribution of the interfering nodes. With the aid of these results, the novel ASAPPP is proved to be equivalent with the original one in a single-tier network and obtains the simple yet effective approximate results of association probability and coverage probability in a multi-tier network. Simulation results demonstrate that the proposed method provides a better approximation compared with the original ASAPPP, especially in multi-tier network scenarios.

Optimization of base station density and user transmission power in multi-tier heterogeneous cellular systems

In this paper, a loss minimization issue is proposed, which includes both cost of user power consumption and base station (BS) deployment. A multi-tier heterogeneous network (HetNet) is considered and modeled with random geometry of Poisson point process (PPP). BSs and users are distributed randomly following PPP with the specific densities. Cutoff threshold (ρk) as the average received power at the kth tier BS is proposed to model uplink channels. The kth tier user transmission power is formulated through a channel inversion power control. Tier Selection Probability indicating the possibility of a user accessing a certain tier is derived. Bias (Bk) is proposed to change the kth tier Tier Selection Probability. Thus, an operator is able to change bias based on nearby environment and communication status. Also, Truncated Outage Probability and signal-to-interference ratio (SINR) Outage Probability are derived, which represents a connection failure status. Truncated outage results from insufficient power supply at users and SINR outage results from poor communication environment. Genetic algorithm (GA) is introduced to determine the trade off between outage constraints and the loss minimization issue. Simulation shows that, when equipped with equal bias, multi-tier network has smaller Truncated Outage Probability but larger SINR Outage Probability than single-tier network. On the contrary, with different bias, Truncated Outage Probability in multi-tier is larger than the single-tier case and SINR Outage Probability in multi-tier is less than that in single-tier. A considerable loss reduction can be witnessed in both cases.

On Exact Distribution of Poisson-Voronoi Area in K-Tier HetNets With Generalized Association Rule

This letter characterizes the exact distribution function of a typical Voronoi area in a $K$-tier Poisson network. The users obey a generalized association (GA) rule, which is a superset of nearest base station association and maximum received power based association (with arbitrary fading) rules that are commonly adopted in the literature. Combining the Robbins' theorem and the probability generating functional of a Poisson point process, we obtain the exact moments of a typical $k$-th tier Voronoi area, $k \in \{1,...,K\}$ under the GA rule. We apply this result in several special cases. For example, we prove that in multi-tier networks with the GA rule, the mean of $k$-th tier Voronoi area can exactly be expressed in a closed-form. We also obtain simplified expressions of its higher-order moments for both average and instantaneous received power based user association. In single-tier networks with exponential fading, the later association rule provides closed-form expression of the second-order moment of a typical Voronoi area. We numerically evaluate this exact expression and compare it with an approximated result.

Outage Probability in the Uplink of Multitier Millimeter Wave Cellular Networks

In this article, using the stochastic geometry, we develop a tractable uplink modeling framework for the outage probability of the multitier millimeter wave (mmWave) cellular networks. Each tier’s mmWave base stations (BSs) are randomly located and they have particular spatial density, antenna gain, receiver sensitivity, blockage parameter, and pathloss exponents. Our model takes account of the maximum power limitation and the per-user power control. More specifically, each user, which could be in line-of-sight (LOS) or non-LOS to its serving mmWave BS, controls its transmit power such that the received signal power at its serving BS is equal to a predefined threshold. Hence, a truncated channel inversion power control scheme is implemented for the uplink of mmWave cellular networks. We derive closed-form expressions for the signal-to-interference-plus-noise-ratio (SINR) outage probability for the uplink of the multitier mmWave cellular networks, which we later degrade to the single-tier network. Furthermore, we analyze the case with a dense network by utilizing the simplified model, where the LOS region is approximated as a fixed LOS disk. The results show that imposing a maximum power constraint on the user significantly affects the SINR outage probability in the uplink of mmWave cellular networks.

Simultaneous wireless information and power transfer in heterogeneous cellular networks with underlay D2D communication

Device to device (D2D) communication that provides high data rate proximity based direct communication between users, along with simultaneous wireless information and power transfer (SWIPT) that extracts energy from the received RF power, can achieve high energy and spectral efficiencies together with low latency communication. Heterogeneous networks, that employ efficient frequency reuse, provide high gains in the coverage and capacity of the cellular networks. SWIPT helps in converting the harmful interference, incurred by the frequency reuse of D2D tier underlaying the Hetnet, into energy that can be stored for the future. This work presents a resource allocation and power control scheme for SWIPT enabled underlay D2D networks, designed to improve the energy efficiency and the amount of energy harvested while ensuring the minimum required data rates for the users. Resource allocation is performed using a stable many-to-one matching game model inspired from Gale-Shapley algorithm. Two techniques of SWIPT, namely power splitting SWIPT and time splitting SWIPT, are considered and the resource allocation schemes are designed for both. Simulation results demonstrate the superior performance of the proposed algorithm compared to an existing work in single tier network with power splitting SWIPT. The work is extended to a typical 5G HetNet scenario, and extensive simulations are done to compare the performance of the two SWIPT architectures in the HetNet scenario.

Fractional Frequency Reuse in Multi-tier Networks: Performance Analysis and Optimization

Frequency Reuse (FR) is an efficient approach to improve the network performance in a multi-cell cellular network. In this paper, we investigate the performance of heterogeneous networks utilising two well-known frequency reuse algorithms, called Strict FR and Soft FR, with a reuse factor of $$\varDelta$$ ($$\varDelta > 1$$). Based on a two-phase operation of the FR algorithm, we develop a new approach to analyse cellular networks based on the Poisson Point Process (PPP) model which successfully demonstrates the impact of the network parameters (such as the number of allocated Resource Blocks (RBs) and bias factor) and FR parameters (such as Base Station (BS) transmit power) on the performance of a user and overall network. Compared to related works, we propose the following novel approaches: (i) we investigate flexible FR networks in which users have connections with the BSs which deliver the highest performance; (ii) the BS observes SINR on the data channel to classify each user into either a Cell-Edge User (CEU) or Cell-Center User (CCU); (iii) the initial state of the network is considered to establish the initial network interference when new users arrive and request connections to the BSs. In the case of a single-tier network, it is proved that our analytical approach is more accurate than previous works. In the case of a two-tier network, the analytical results indicate that compared to the 3GPP model, our proposed model not only reduces up to 40.79% and 3.8% power consumption of a BS on the data channel but also achieves 16.08% and 18.63% higher data rates in the case of Strict FR and Soft FR respectively. Furthermore, the paper presents an approach to find an optimal value of SINR thresholds and bias factor to achieve the maximum network performance.

SIR Meta Distribution for Spatiotemporal Cooperation in Poisson Cellular Networks

The meta-distribution provides more fine-grained information on the signal-to-interference ratio (SIR) compared to the SIR distribution at the typical user. This paper studies the SIR meta-distribution in heterogeneous cellular networks (HCNs) for JT-DPB with two types of hybrid automatic repeat request (HARQ) techniques, where JT-DPB is a general scheme for base station cooperation that combines joint transmission (JT) and dynamic point blanking (DPB). This paper also considers two types of typical users—the general user and the worst-case user (the typical user located at the Voronoi vertex in a single-tier network). For the Type-II HARQ, a simplified network model is proposed, which leads to a tractable and accurate approach for the SIR meta-distribution analysis. The analytical results for the Type-I HARQ and Type-II HARQ are presented.

Cross-Layer QoE Optimization for D2D Communication in CR-Enabled Heterogeneous Cellular Networks

Device-to-device (D2D) communication based on cognitive radio (CR) technology can significantly improve the coverage and spectral efficiency. Existing research on D2D communications mainly focus on optimizing the network quality of service in single-tier networks. However, the exponential growth in data traffic has inspired the move from traditional single-tier cellular networks toward heterogeneous cellular networks. Hence, in this paper, we consider a CR-based HetNet coexisting with cognitive D2D pairs and cellular users, where the cellular users are primary users and D2D pairs are secondary users. Considering quality of experience (QoE) is an important metric to quantify and measure quality of experience from the user perspective, we focus on the QoE optimization of the D2D pairs via the BS association, the discrete power control, and the resource block (RB) assignment. To do so, we first formulate the cross-layer optimization problem to maximize the average QoE of the D2D pairs while satisfying the QoE requirements of cellular users. We then propose the centralized resource allocation, namely the genetic algorithm (GA), and semi-distributed resource allocation method, namely Stackelberg game based algorithm, to solve the non-convex optimization problem. The GA is proposed to ensure the maximum achievable QoE with known channel state information (CSI), whereas the Stackelberg game based algorithm is proposed to cope with the strong needs for distributed D2D solutions with only local CSI of each D2D link. Our proposed algorithms can achieve substantial improvement of QoE performance for D2D pairs via increasing the number of RBs.

2-to-<inline-formula> <tex-math notation="LaTeX">$M$ </tex-math> </inline-formula> Coordinated Multipoint-Based Uplink Transmission in Ultra-Dense Cellular Networks

The ongoing densification of small cells, i.e., ultimately evolving toward ultra-dense networks (UDNs), yields an unprecedented paradigm shift in network design by bringing the base stations (BSs) and users to approximate the spatial scale and number magnitude. To address the super-frequent handovers of mobile users in such UDNs, the coordinated multipoint (CoMP) then becomes a feasible solution by effectively improving communication reliability. In this paper, we consider CoMP-based uplink transmission in heterogeneous UDNs. As our first step, a CoMP uplink transmission scheme is proposed for each user to transmit to multiple (2 to $M$ ) cooperating BSs with channel inversion power control in a multi-channel scenario. The performance of the proposed uplink CoMP is analyzed in the context of UDNs using stochastic geometry, in terms of outage probability and ergodic capacity, considering the effects of BS intensity, power control, number of cooperating nodes, and network tiers, first in a single-tier network, and later extended to a $K$ -tier heterogeneous network. Performance evaluation through extensive simulations is conducted and it is shown that the simulation results fit well with the analytical ones. The performance of the proposed scheme is then compared with that of the non-CoMP scheme, and it is found that the proposed scheme can significantly improve outage probability and ergodic capacity of mobile users.

Game theoretic approach for multi-tier 5G heterogeneous network optimization based on joint power control and spectrum trading

Multi-tier heterogeneous network (MHN) has recently emerged as a main technology in 5G network. Dense deployment of heterogeneous nodes in 5G MHN will have more density than single-tier networks. In 5G MHN, by increasing the number of small cells, network capacity, spectral efficiency, and data rate will increase. But reducing the dimension of the cell will cause inter/intra-tier interference in both uplink and downlink channels of MHN. High transmit power of Macro Base Station (MBS) downlink channel causes interference to Small cell User Equipment (SUE). Also, neighbor macrocell and small cell users suffer from interference created in both uplink and downlink channels of small cell. Thus interference management and mitigation is the important challenge for 5G MHN. In this paper, in order to mitigate both types of inter/intra-tier interferences, spectrum trading issue and power control are presented based on non-cooperative Stackelberg game under some sub-games through a pricing-based algorithm and convex optimization method. Finally, simulation results show that the performance of our system model such as average utility function of the small cell, SBS, energy efficiency and so on, will be improved through the proposed algorithm.

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.

The SIR Meta Distribution in Poisson Cellular Networks With Base Station Cooperation

The meta distribution provides fine-grained information on the signal-to-interference ratio (SIR) compared with the SIR distribution at the typical user. This paper first derives the meta distribution of the SIR in heterogeneous cellular networks with downlink coordinated multipoint transmission/reception, including joint transmission (JT), dynamic point blanking (DPB), and dynamic point selection/dynamic point blanking (DPS/DPB), for the general typical user and the worst-case user (the typical user located at the Voronoi vertex in a single-tier network). A more general scheme called JT-DPB, which is the combination of JT and DPB, is studied. The moments of the conditional success probability are derived for the calculation of the meta distribution and the mean local delay. An exact analytical expression, the beta approximation, and simulation results of the meta distribution are provided. From the theoretical results, we gain insights on the benefits of different cooperation schemes and the impact of the number of cooperating base stations and other network parameters.

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.

Analysis of Heterogeneous Wireless Networks Using Poisson Hard-Core Hole Process

The Poisson point process (PPP) has been widely employed to model wireless networks and analyze their performance. The PPP has the property that nodes are conditionally independent from each other. As such, it may not be a suitable model for many networks, where there exists repulsion among the nodes. In order to address this limitation, we adopt a Poisson hardcore process (PHCP), in which no two nodes can be closer than a repulsion radius from one another. We consider two-tier heterogeneous networks, where the spatial distributions of transmitters in the first-tier and the second-tier networks follow a PHCP and a PPP, respectively. To alleviate inter-tier interference, we consider a guard zone for the first-tier network and presume that the second-tier transmitters located in the zone are deactivated. Under this setup, the activated second-tier transmitters form a Poisson hard-core hole process. We first derive exact computable expressions of the coverage probability and introduce a method to efficiently evaluate the expressions. Then, we provide approximations of the coverage probability, which have lower computational complexities. In addition, as a special case, we investigate the coverage probability of single-tier networks by modeling the locations of transmitters as a PHCP.

Outage and energy efficiency analysis for cognitive based heterogeneous cellular networks

Cognitive radio and small cells are the promising techniques to minimize energy consumption and satisfy the exponentially increasing data rates for the heterogeneous cellular network (HCN). In this paper, a theoretical framework is developed to calculate the outage probability of the HCN based on the opportunistic utilization of the traditional cellular bandwidth and television white space (TVWS) for the cognitive femto base stations. This work investigates overlay, underlay, mixed overlay-underlay based two tiers cognitive HCN. It also investigates the impact of the TVWS in the overlay-TVWS mixed spectrum sharing technique (SST). Tools from stochastic geometry are used to model cognitive HCN. Furthermore, the tier selection probability, average ergodic rate, area spectral efficiency (ASE), and energy efficiency (EE) of the HCN are also calculated for different SSTs. Numerical results show that mixed SST achieves a significant reduction in tier outage probability and total outage probability as compared to underlay and overlay techniques alone. It is also demonstrated that compared to the traditional single tier network, cognitive based HCN can improve the total ASE and EE of the order of \(10^{2}\) and 10, respectively.

Device-to-Device Communication for Mobile Multimedia in Emerging 5G Networks

Device-to-device (D2D) communication, which utilizes mobile devices located within close proximity for direct connection and data exchange, holds great promise for improving energy and spectrum efficiency of mobile multimedia in 5G networks. It has been observed that most available D2D-based works—considered only the single-cell scenario with a single BS. Such scenario-based schemes, although tractable and able to illustrate the relationship between D2D links and cellular links, failed to take into account the distribution of surrounding base stations and user equipments (UEs), as well as the accumulated interference from ongoing transmissions in other cells. Furthermore, the single-tier network with one BS considered in available works is far from the real 5G scenario in which multi-tier BSs are heterogeneously distributed among the whole network area. In light of such observations, we present in this article a model for network coverage probability and average rate analysis in a D2D communication overlaying a two-tier downlink cellular network, where nineteen macro base stations (MBSs) with pico base stations (PBSs) placed at the end point of macro cell (hexagons) borders are employed according to the 3GPP specifications, and mobile users are spatially distributed according to the homogeneous Poisson Point Process model. Each mobile UE is able to establish a D2D link with adjacent UEs or connect to a nearby macro or pico base station. Stochastic geometric analysis is adopted to characterize the intratier interference distribution within the MBS-tier, PBS-tier, and D2D-tier based on which network coverage probability and per-user average rate are derived with a careful consideration of important issues such as threshold value, SINR value, user density, content hit rate, spectrum allocation, and cell coverage range. Our results show that, even for the overlaying case, D2D communication can significantly improve network coverage probability and per-user average downlink rate. Another finding is that the frequency allocation for D2D communications should be carefully tuned according to network settings, which may result in totally different varying behaviors for the per-user average rate.

Efficient Cache Placement Strategy in Two-Tier Wireless Content Delivery Network

Internet content caching for multimedia services has received much attention mainly in the field of large-scale wired networking as a primary solution to save network resources and improve quality of service (QoS). Rapidly increasing consumption of multimedia content in mobile networks brings a challenge of how to efficiently deliver content in local wireless access networks. Cache embedment in wireless mesh environment is an intriguing attempt to enhance the QoS and service capacity, leading to the question of how to design an efficient content delivery network considering the inherent characteristics of the wireless environment. We propose and investigate an efficient cache placement strategy in novel two-tier wireless content delivery networks, which utilize separate channels for content dissemination and content service. Such a two-tier network system model helps to achieve much better content delivery performance with a greatly reduced system design complexity compared to single-tier network system models. Further, we incorporate a delay cost due to contention, which is mainly responsible for performance in shared-medium wireless networks, as a key metric for cache placement under the system model. After formally formulating the cache placement problem, we propose a cross-layer heuristic algorithm and demonstrate its performance compared with an optimal solution by integer linear programming. Simulation results show significant performance improvements by our strategy compared to the performance of existing representative strategies in terms of service delay, packet delivery ratio, and the amount of delivered packets within a given delay deadline.

Asymptotics and Approximation of the SIR Distribution in General Cellular Networks

It has recently been observed that the SIR distributions of a variety of cellular network models and transmission techniques look very similar in shape. As a result, they are well approximated by a simple horizontal shift (or gain) of the distribution of the most tractable model, the Poisson point process (PPP). To study and explain this behavior, this paper focuses on general single-tier network models with nearest-base station association and studies the asymptotic gain both at 0 and at infinity. We show that the gain at 0 is determined by the so-called mean interference-to-signal ratio (MISR) between the PPP and the network model under consideration, while the gain at infinity is determined by the expected fading-to-interference ratio (EFIR). The analysis of the MISR is based on a novel type of point process, the so-called relative distance process, which is a one-dimensional point process on the unit interval [0,1] that fully determines the SIR. A comparison of the gains at 0 and infinity shows that the gain at 0 indeed provides an excellent approximation for the entire SIR distribution. Moreover, the gain is mostly a function of the network geometry and barely depends on the path loss exponent and the fading. The results are illustrated using several examples of repulsive point processes.

Interference Minimization in 5G Heterogeneous Networks

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. Then using TPNM, the signal and interference received at any point in the complex multi-tier environment can be analyzed by considering the same point in the equivalent single-tier cellular network model, thus significantly simplifying the analysis. On this basis, we propose a new user association scheme in heterogeneous cellular networks, where the base station that leads to the smallest interference to other co-channel mobile stations is chosen from a set of candidate base stations that satisfy the quality-of-service (QoS) constraint for an intended mobile station. Numerical results show that the proposed user association scheme is able to significantly reduce the down-link interference compared with existing schemes while maintaining a reasonably good QoS.

Multicell Cooperative Scheduling for Two-Tier Cellular Networks

Cellular wireless network architectures employing a tiered structure, consisting of traditional macro-cells and small-cells, have attracted much attention recently because of their potential to dramatically increase network capacity. These architectures can reduce the distances of transmit-receiver pairs, thus enhancing radio link qualities. However, a tiered cell deployment could incur severe cochannel interference. Prior work for single-tier networks has proposed coordinated multi-point (CoMP) transmission, which includes joint transmission, as a possible solution for overcoming the rate limitations induced by cochannel interference. Because users in each cell experience various interference conditions, each cell needs to support single transmission (in which only one cell transmits to a single user) and joint transmission. In a conventional implementation, a particular combination of transmissions over the entire network is fixed in advance for each time slot and opportunistic scheduling chooses one of the users supported by each transmission. However, when the number of users to be scheduled is small, the throughput improvement from opportunistic scheduling becomes limited. To overcome this problem, we propose a cumulative distribution function-based scheduling scheme which jointly chooses the transmitter set and the corresponding scheduled users in a two-tier network. It is shown that the throughput performance can be improved compared to those of the fixed slot resource allocation scheme because more users "compete" for slot resources.