Optimal Base Station Density Research Articles

Performance of Indoor Small-Cell Networks Under Interior Wall Penetration Losses

The performance of indoor small-cell networks (SCNs) is affected by the indoor environment, such as walls, blockages, etc. In this paper, we investigate the effect of interior wall attenuation on the performance of an indoor SCN. Specifically, the spatial distribution of interior walls is modelled based on the random shape theory and the indoor base stations (BSs) are distributed following a homogeneous Poisson point process. The channel model includes the path loss, Rayleigh fading, and wall attenuation. We analytically derive the downlink coverage probability under the strongest received signal user association strategy, which is validated by Monte Carlo simulations for three typical interior wall layouts (i.e., random layout, binary orientation layout, and Manhattan grid). The analytical results show that for a given density of interior walls and signal strength attenuation per wall, there is an optimal BS density that maximises the coverage probability, and the optimal BS density increases as the wall attenuation increases.

Optimization of Speed and Network Deployment for Reliable V2I Communication in the Presence of Handoffs and Interference

Vehicle-to-infrastructure (V2I) communication is becoming indispensable for successful roll-out of connected and autonomous vehicles (CAVs). While increasing the CAVs’ speed improves the average CAV traffic flow, it increases communication handoffs (HOs) thus reducing wireless data rates. Furthermore, unplanned density of active base-stations (BSs) may result in severe interference which negatively impacts CAV data rate. In this letter, we first characterize macroscopic traffic flow by considering log-normal distribution of the spacing between CAVs. We then derive novel closed-form expressions for the exact HO-aware rate outage probability and ergodic capacity in a large-scale network with interference. Then, we formulate a traffic flow maximization problem to optimize the speed of CAVs and deployment density of BSs with HO-aware rate constraints and collision avoidance constraints. Our numerical results validate the closed-form analytical expressions, extract useful insights about the optimal speed and BS density, and highlight the key trade-offs between the HO-aware data rates and CAV traffic flow.

Tractable performance analysis of small‐cell networks with a novel bounded path loss model

The analysis of dense small-cell networks has largely relied on the use of either unbounded path loss models that may violate the conservation of energy at very short distances, or bounded path loss models that are not tractable. In this Letter, the authors derive the coverage probability and area spectral efficiency (ASE) in closed-forms for dense small-cell networks by using a novel bounded path loss model. Their analytical results demonstrate that the coverage probability will monotonically decrease with the increase of base station (BS) density, and the ASE will first increase with the BS density and then reduce to zero when the network becomes ultra dense. They also give the closed-form expression of the optimal BS density that maximises the ASE.

Optimal picocell base station density for energy-efficient heterogeneous cellular network under received power constraint

Heterogeneous cellular networks (HCNs) have emerged as the primary solution for overwhelming traffic demands. However, the dense deployment of small cell base stations (BSs) inevitably triggers a tremendous escalation of energy consumption. In this paper, we apply tools from stochastic geometry to investigate and optimise the energy efficiency (EE) for a two-tier HCN. The average successful transmission rate per unit area of a two-tier HCN is derived, and then the total power consumption of all the BSs in per unit area of a two-tier HCN is derived. Based on that, the EE expression of the whole HCN is formulated. We analysis the received signal power constraint for a typical user and convert the power constraint to density constraint. Finally, we use a one-dimensional optimisation algorithm to maximise the EE by optimising picocell BS density. Simulation results validate the accuracy of the theoretical analysis and demonstrate the proposed optimal picocell BS density can obviously improve EE.

Optimal Picocell Base Station Density for Energy-efficient Heterogeneous Cellular Network Under Received Power Constraint

Heterogeneous cellular networks (HCNs) have emerged as the primary solution for overwhelming traffic demands. However, the dense deployment of small cell base stations (BSs) inevitably triggers a tremendous escalation of energy consumption. In this paper, we apply tools from stochastic geometry to investigate and optimise the energy efficiency (EE) for a two-tier HCN. The average successful transmission rate per unit area of a two-tier HCN is derived, and then the total power consumption of all the BSs in per unit area of a two-tier HCN is derived. Based on that, the EE expression of the whole HCN is formulated. We analysis the received signal power constraint for a typical user and convert the power constraint to density constraint. Finally, we use a one-dimensional optimisation algorithm to maximise the EE by optimising picocell BS density. Simulation results validate the accuracy of the theoretical analysis and demonstrate the proposed optimal picocell BS density can obviously improve EE.

Network Deployment for Maximal Energy Efficiency in Uplink With Multislope Path Loss

This work aims to design the uplink (UL) of a cellular network for maximal energy efficiency (EE). Each base station (BS) is randomly deployed within a given area and is equipped with $M$ antennas to serve $K$ user equipments (UEs). A multislope (distance-dependent) path loss model is considered and linear processing is used, under the assumption that channel state information is acquired by using pilot sequences (reused across the network). Within this setting, a lower bound on the UL spectral efficiency and a realistic circuit power consumption model are used to evaluate the network EE. Numerical results are first used to compute the optimal BS density and pilot reuse factor for a Massive MIMO network with three different detection schemes, namely, maximum ratio combining, zero-forcing (ZF) and multicell minimum mean-squared error. The numerical analysis shows that the EE is a unimodal function of BS density and achieves its maximum for a relatively small density of BS, irrespective of the employed detection scheme. This is in contrast to the single-slope (distance-independent) path loss model, for which the EE is a monotonic non-decreasing function of BS density. Then, we concentrate on ZF and use stochastic geometry to compute a new lower bound on the spectral efficiency, which is then used to optimize, for a given BS density, the pilot reuse factor, number of BS antennas and UEs. Closed- form expressions are computed from which valuable insights into the interplay between optimization variables, hardware characteristics, and propagation environment are obtained.

Energy Efficiency Analysis of Cache‐Enabled Cellular Networks with Limited Backhaul

Caching in the cellular networks has been proposed as a promising technology for reducing the content delivery latency and backhaul cost. Since the backhaul capacity is limited in the practical scenario, the network performance analysis of base station (BS) caching should address the effects of the limited backhaul. This paper investigates the energy efficiency of the cache‐enabled cellular networks with the limited backhaul based on the stochastic geometry method. First, the successful content delivery probability (SCDP), which depends on the successful access delivery probability, successful backhaul delivery probability, and cache hit ratio, is analyzed under the limited backhaul. Based on the obtained SCDP results, we derive the analytical expressions of throughput, power consumption, and energy efficiency for various scenes including the general case, the interference‐limited case, and the mean load approximation case. The accuracy of theoretical analysis is verified by the Monte Carlo simulation. The simulation results show that BS caching can dramatically improve energy efficiency when the content popularity is skewed, the content library size is small, and the backhaul capacity is relatively small. Furthermore, it is confirmed that there exists an optimal BS density which maximizes the energy efficiency of the cache‐enabled cellular networks.

Capacity- and Trust-Aware BS Cooperation in Nonuniform HetNets: Spectral Efficiency and Optimal BS Density

This paper studies base station (BS) cooperation in nonuniform heterogeneous networks. Considering the limited capacity at BS and existence of untrusted small cell BSs (SBSs) in practical scenarios, a novel capacity- and trust-aware BS cooperation strategy is proposed. The BS cooperation is performed in a user centric manner, based on the average received signal strength at users, the capacity of BSs, and the trustworthiness of SBSs. Furthermore, with the proposed BS cooperation, the statistics of aggregate information-signal strength and interference strength are theoretically analyzed, based on stochastic geometry. Then, expressions for spectral efficiency (SE) and area SE (ASE) are analytically derived. In addition, to study the impact of the SBS density on the SE and ASE, the optimal densities of normal SBSs to maximize the SE and ASE are proved to exist and obtained. Finally, simulations and numerical evaluations validate the theoretical analysis and reveal that with the awareness of BS capacity and trustworthiness, optimal cooperative thresholds achieving the maximum SE and ASE exist, which decrease with high path-loss exponent; and in high path-loss fading environment with high existence probability of untrusted SBSs, more normal SBSs are required to be deployed to achieve the maximum SE and ASE performance.

Optimal Base Station Density of Dense Network: From the Viewpoint of Interference and Load.

Network densification is attracting increasing attention recently due to its ability to improve network capacity by spatial reuse and relieve congestion by offloading. However, excessive densification and aggressive offloading can also cause the degradation of network performance due to problems of interference and load. In this paper, with consideration of load issues, we study the optimal base station density that maximizes the throughput of the network. The expected link rate and the utilization ratio of the contention-based channel are derived as the functions of base station density using the Poisson Point Process (PPP) and Markov Chain. They reveal the rules of deployment. Based on these results, we obtain the throughput of the network and indicate the optimal deployment density under different network conditions. Extensive simulations are conducted to validate our analysis and show the substantial performance gain obtained by the proposed deployment scheme. These results can provide guidance for the network densification.

User Association in Energy-Aware Dense Heterogeneous Cellular Networks

Mobile traffic demand has been increasing exponentially over the last few years and forecasts show that this trend will continue in the foreseeable future. As a result, operators are forced to densify and upgrade their networks to meet this demand. This has created concerns, such as increasing greenhouse gas emissions, high capital expenditures, and associated energy costs. This paper uses tools from stochastic geometry to analyze and formulate energy-efficient deployment strategies for multi-tier heterogeneous networks (HetNets) using various user association schemes. We use simple approximations to combine the required base station (BS) density and associated transmit power per tier subject to both coverage probability and average user rate constraints. In this paper, this combination is called the deployment factor and it can be expressed in closed form for unbiased HetNets. We then formulate area power consumption (APC) minimization framework, which optimizes the deployment factor to derive specific optimal BS density and transmit power values. Furthermore, we perform a comprehensive study of the effect of biasing on the APC performance of biased HetNets. Our results show that for HetNets using the maximum average-biased-received-power association scheme, significant energy savings are possible with appropriate biasing.

Energy Efficiency Analysis of Cache-Enabled Two-Tier HetNets Under Different Spectrum Deployment Strategies

Heterogeneous networks (HetNets) consisting of macrocells overlaid with small cells (e.g. femtocell, picocell, microcell, and relay) are conceived as an appealing technology to cope with the explosive growth of service traffic in future cellular networks. However, the backhaul limitation has become a bottleneck in HetNets, which affects the network performance and users’ quality of experience. Wireless edge caching that caches popular contents at the network edge (e.g., base stations (BSs)) can effectively unblock the bottleneck and further unleash the potential of HetNets. In this paper, considering a cache-enabled two-tier HetNet, we resort to the stochastic geometry theory to model and analyze the energy efficiency performance of the HetNet with closed-access policy under cochannel and orthogonal channel deployment scenarios. Specifically, the exact closed-form expressions of outage probability, throughput and energy efficiency are derived, respectively. Numerical results show that the larger small-cell local cache capability may not always lead to higher network energy efficiency due to the caching power cost. The results also show that with a given cache capacity for small cells, there exists an optimal small BS density that maximizes the network energy efficiency.

Energy-aware deployment of dense heterogeneous cellular networks with QoS constraints

The base station (BS) configuration is a key factor to improve energy efficiency (EE). In this paper, we focus on designing the network deployment parameters (i.e., BS densities) for biased $K$-tier heterogeneous cellular network (HCN) with quality of service (QoS) provisioning. Using appropriate approximations, we derive the closed-form expressions of optimal BS density across all tiers to minimize the area power consumption (APC) by applying the stochastic geometry theory, while satisfying the users QoS requirements. These results are used to obtain some new insights into the EE performance of biased HCN deployment. With the aid of this approach, the best type of BSs to be deployed or switched off for energy saving purposes can be identified from the perspectives of BS transmission power. More precisely, if the BS transmission power ratio between an arbitrary pair of tiers of $K$-tier HCN, e.g., the small cell BS and macro BS tiers, is higher than a threshold which is a function of path loss exponent, bias factor and power consumption, the small cell BSs are preferred. The opposite situation takes place otherwise. Furthermore, it is also shown that, compared to the unbiased HCN scenario, significant energy savings are possible by appropriately biasing the HCN and optimizing the BS density, subject to the QoS constraints among all tiers.

Optimization of Base-Station Density for High Energy-Efficient Cellular Networks With Sleeping Strategies

The base station (BS) density configuration is a crucial factor in improving energy efficiency (EE) in cellular networks, particularly when the sleeping strategy is used to reduce energy consumption. In this paper, the optimization of BS density for enhancing EE through traffic-aware sleeping strategies in both one- and two-tier cellular networks is researched, where the BS location is modeled as a Poisson point process. In the one-tier scenario, the EE optimization objective function is proved to be quasi-concave, and the optimal BS density solution is derived, where the maximum achievable EE is demonstrated to be independent of user density. In the two-tier scenario, both the activation probability of BSs and the coverage probability are analyzed, where the EE optimization objective function is proved to be not necessarily quasi-concave. To handle this nonconvex issue, an equivalent optimization problem that jointly optimizes the ratio and weighted sum of BS densities is proposed and solved by a dynamic gradient iterative algorithm. Meanwhile, a data fitting method is utilized to quantitatively analyze EE performances, in which the relationship between the optimal BS density and the user density is approximately linear when the user density is sufficiently high. Simulation results verify the relevant derivations and reflect that the sleeping strategy can not only save energy but improve the quality of radio links as well.

Energy‐optimal base station density considering traffic dynamics

Optimal base station (BS) density, to minimise network energy consumption, is studied. Contrary to previous works, both the spatial randomness of the network topology and the wireless traffic dynamics are taken into consideration. With the technology of cell discontinuous transmission, network energy consumption depends on the average transmission probability of BSs. On the basis of stochastic geometry, it is found that the BS transmission probability and BS density satisfy a nonlinear equation. To reduce overall energy consumption, an iteration algorithm that can converge to the global optimal BS density is proposed.

Energy-Aware Cellular Deployment Strategy Under Coverage Performance Constraints

The last ten years have witnessed explosive growth in mobile data traffic, which leads to rapid increases in energy consumption of cellular networks. One potential solution to this issue is to seek out a green deployment strategy. In this paper, we investigate the energy-efficient deployment strategy under coverage performance constraints for both homogeneous and heterogeneous cellular networks. Unlike just considering the base station (BS) density in previous work, we jointly optimize the BS density and the BS transmission power. First, we derive the relation between the average coverage probability and deployment strategy (i.e., BS density and BS transmission power) with stochastic geometry tools. Then, based on the expression results, we formulate a network energy consumption minimization framework considering coverage performance constraints and jointly determine the optimal macro BS (MaBS) density, MaBS transmission power, and micro BS (MiBS) density. With practical data sets, numerical simulation results show the following: 1) compared with homogeneous network deployment, heterogeneous network deployment has the advantage in energy efficiency performance, and 2) our joint BS density and BS transmission power optimization strategy exceeds the existing strategy, which just considers the BS density optimization in terms of energy efficiency.

Throughput and Energy Efficiency Analysis of Small Cell Networks with Multi-Antenna Base Stations

Small cell networks have recently been proposed as an important evolution path for the next-generation cellular networks. However, with more and more irregularly deployed base stations (BSs), it is becoming increasingly difficult to quantify the achievable network throughput or energy efficiency. In this paper, we develop an analytical framework for downlink performance evaluation of small cell networks, based on a random spatial network model, where BSs and users are modeled as two independent spatial Poisson point processes. A new simple expression of the outage probability is derived, which is analytically tractable and is especially useful with multi-antenna transmissions. This new result is then applied to evaluate the network throughput and energy efficiency. It is analytically shown that deploying more BSs can always increase the network throughput, but the throughput will scale with the BS density first linearly, then logarithmically, and finally converge to a constant. On the other hand, increasing the number of BS antennas can decrease the outage probability exponentially, thus can always increase the network throughput. However, increasing the BS density or the number of transmit antennas will first increase and then decrease the energy efficiency if the non-transmission power or the circuit power consumption is less than certain thresholds, and the optimal BS density and the optimal number of BS antennas can be found. Otherwise, the energy efficiency will always decrease. Simulation results shall demonstrate that our conclusions based on the random network model are general and also hold in a regular grid-based model.

Energy Efficient Network Deployment With Cell DTX

Cell discontinuous transmission (DTX) is a new feature that enables sleep mode operations at base station (BS) side during the transmission time intervals when there is no traffic. In this letter, we analyze the maximum achievable energy saving of the cell DTX. We incorporate the cell DTX with a clean-slate network deployment and obtain optimal BS density for lowest energy consumption satisfying a certain quality of service requirement considering daily traffic variation. The numerical result indicates that the fast traffic adaptation capability of cell DTX favors dense network deployment with lightly loaded cells, which brings about considerable improvement in energy saving.

Optimal Combination of Base Station Densities for Energy-Efficient Two-Tier Heterogeneous Cellular Networks

In this paper, the optimal BS (Base Station) density for both homogeneous and heterogeneous cellular networks to minimize network energy cost is analyzed with stochastic geometry theory. For homogeneous cellular networks, both upper and lower bounds of the optimal BS density are derived. For heterogeneous cellular networks, our analysis reveals the best type of BSs to be deployed for capacity extension, or to be switched off for energy saving. Specifically, if the ratio between the micro BS cost and the macro BS cost is lower than a threshold, which is a function of path loss and their transmit power, then the optimal strategy is to deploy micro BSs for capacity extension or to switch off macro BSs (if possible) for energy saving with higher priority. Otherwise, the optimal strategy is the opposite. The optimal combination of macro and micro BS densities can be calculated numerically through our analysis, or alternatively be conservatively approximated with a closed-form solution. Based on the parameters from EARTH, numerical results show that in the dense urban scenario, compared to the traditional macro-only homogeneous cellular network with no BS sleeping, deploying micro BSs can reduce about 40% of the total energy cost, and further reduce up to 35% with BS sleeping capability.

On the Tradeoff Between Spectral Efficiency and Energy Efficiency of Homogeneous Cellular Networks With Outage Constraint

In this paper, the tradeoff relationship between the spectral efficiency (SE) and energy efficiency (EE) of homogenous cellular networks in which the BSs are arbitrarily distributed is investigated. The network performance metrics of SE and EE are assessed subject to a downlink transmission outage constraint in interference-limited operational environments. The EE is expressed in closed form as a function of SE, based on which the performance bounds of the network are derived. Unlike the traditional inverse relationship between SE and EE, it is found in this paper that there exists an operational regime for which both the SE and EE increase while satisfying the outage requirement, and the density of base stations (BSs) simultaneously sharing the spectrum is optimal. The difference in the performance achieved for the SE when operating in the EE maximizing mode as compared with the SE maximizing mode strongly depends on the received signal-to-interference ratio (SIR) threshold. In the SE-EE tradeoff regime, the analytical tools from microeconomics theory are applied to determine the optimal BS density with respect to the utility achieved by the network operator via balancing the SE and EE objectives. Numerical results show that, by tuning a preference factor toward either the SE or EE metrics, it is feasible to realize Pareto optimal performance.

Coverage and Economy of Cellular Networks with Many Base Stations

The performance of a cellular network can be significantly improved by employing many base stations (BSs), which shortens transmission distances. However, there exist no known results on quantifying the performance gains from deploying many BSs. To address this issue, we adopt a stochastic-geometry model of the downlink cellular network and analyze the mobile outage probability. Specifically, given Poisson distributed BSs, the outage probability is shown to diminish inversely with the increasing ratio between the BS and mobile densities. Furthermore, we analyze the optimal tradeoff between the performance gain from increasing the BS density and the resultant network cost accounting for energy consumption, BS hardware and backhaul cables. The optimal BS density is proved to be proportional to the square root of the mobile density and the inverse of the square root of the cost factors considered.