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To accommodate the ever-expanding wireless data traffic volumes, mobile network operators are complementing their macrocellular networks by deploying low-power base stations (or small cells) to offload traffic from congested macrocells and to reuse spectrum. To that end, Ultra Dense Network (UDN) deployments provide means to aggressively reuse spectrum, thus providing significant enhancements in terms of system capacity. However, these deployments entail several challenges, including the increased complexity in network planning and optimization. In this paper, we propose a versatile optimization framework for planning UDN deployments. The planning and optimization framework is underpinned by metrics that consider scalability in terms of number of users, cost of densification, and fairness. The proposed methodology is evaluated using a real-world UDN planning case. The numerical results expose a number of interesting insights, including the impact of different bandwidth allocation strategies and spatial service demand distribution on the performance of various network topologies. Specifically, we provide a performance comparison of the optimized UDN topologies versus random (unplanned), regular grid, and heuristically derived UDN topologies. This comparison further underlines the need for flexible network planning and optimization frameworks as different operator performance metrics of interest may require different radio access networks configurations.

Mobile network operators face the continuous challenge of upgrading their networks which are rapidly expanding traffic volumes. This trend is mostly attributed to the increased adoption of smart devices (e.g., smartphones). Recent projections for global mobile traffic growth anticipate a tenfold increase in average monthly data consumption from the current 2–5 GB/month to 20–50 GB/month by 2020 [

To accommodate those projected traffic growths and meet user needs, mobile network operators are densifying their networks through heterogeneous deployment of low-power base stations (BSs) or^{2} in dense urban scenarios. This is in contrast to legacy 4th generation (4G) heterogeneous network deployments with typical site densities of less than 10 sites/km^{2} and ISD of a few hundred meters [

However, UDNs are creating new and significant challenges for mobile network operators, with network planning and optimization notably becoming increasingly complex with denser network deployments [

This paper addresses the aforementioned challenges by proposing an optimization framework for planning of UDN, which is suitable for real-world deployments. The corresponding research problem can be stated as follows.

Thus, the contribution of this paper, associated with the previous research problem, can be summarized as follows.

The comparative analysis of several bandwidth allocation policies in the context of network planning.

A simple heuristic for planning of UDNs.

The numerical results from a real-world planning case (evaluated under a variety of conditions) reveal a number of interesting insights:

Bandwidth allocation strategies can facilitate the identification of optimized UDN topologies that may enable an operator to flexibly prioritize either system capacity or cell-edge performance.

The results from the benchmarking clearly indicate that, in case of nonuniform STD, optimization is mandatory as the performance of regular and user-deployed (random) topologies is poor, while quasi-optimal performances accompanied with significant gains can be attained through the use of heuristic planning and optimization.

The rest of the paper is organized as follows: the next section presents the system model. The performance metrics and proposed optimization formulations are introduced in Section

As indicated previously, the goal is to plan an ultra dense cellular network composed of low-power BSs for a target service area

In this study, the downlink of an Orthogonal Frequency Division Multiple Access- (OFDMA-) based cellular network with system bandwidth

The radio propagation, that is, the network geometry, is captured by the matrix

Cell selection, the association of each pixel to a serving BS, is based on the average RS received power. Therefore, the

The RS received power is larger than a minimum value:

The Signal to Interference plus Noise Ratio (SINR) is larger than a threshold:

The average channel gain

The

A certain knowledge of the spatial distribution of the service demand is assumed. In practice, this is known by operators in statistical terms [

In this work, full load is assumed to model the intercell interference, which is a reasonable assumption for planning purposes. Other models, such as load-coupling [

The list of symbols is provided in

Generally speaking, planning is about determining the number and location of BSs in the service area. Evidently, the network deployment should be done such that the maximum benefit is obtained; that is, network capacity is maximized (more users) with minimal cost (less infrastructure deployment), while guaranteeing a certain level of coverage, QoS, and fairness. In order to address this problem by means of optimization, several metrics (and constraints) are required. In this work, the following objectives are considered.

_{ 1 }

_{ 2 }

_{ 3 }

The definition of the previous metrics is given next. The number of BSs (

From a planning point of view, it is important to consider the spatial distribution of the service demand. In other words, the planning should favor network topologies that provides more capacity to the zones of the service area where the traffic is more likely to appear. Given that this information is contained in the vector

In cellular networks, a very important aspect is the frequency reuse; that is, the system bandwidth can be reutilized at each cell. This is the most distinctive aspect of cellular networks that allows these systems to provide radio access to a large amount of users (and things). The way in which the bandwidth is allocated to the users largely determines the resulting system capacity and/or users’ satisfaction. In this sense, cell-edge performance [

The vectors

Thus, the network capacity metric is defined as follows:

Cell-edge performance is defined, for planning purposes herein, as the aggregate rate of the worst

In this work, two different optimization formulations are considered. They can be used depending on the network planning strategy of the operator. On the one hand, if the network operator’s target is to maximize the network aggregate capacity (

Multiobjective optimization [

In problem (

Problem (

Single-objective optimization is proposed if planning needs to be carried out following a max-min approach, such as the maximization of aggregate rate in the area elements with

Problem (

The network densification as planned by operators is both difficult and highly constrained in certain scenarios. This includes the fast expanding high-density urban and periurban settlements in emerging market areas. Indeed, 90% of the urban population growth by 2050 is expected to be concentrated in Asia and Africa. These settlements already have populations densities typically in the range of 40,000–200,000 people/km^{2} [

One of the interesting approaches is to leverage third-party nonoperator entities, such as individual end users, households, microenterprises, and public venue owners, to deploy shared-access small cells that will provide service as an integral part of the operator’s network. An example is the neighborhood small cell concept by Qualcomm promoting the use of privately deployed residential small cells as shared-access points [

Therefore, to contextualize the proposed UDN planning and optimization framework in a realistic setting, we consider a case study for UDN in a high-density urban settlement. To that end, we use the Hanna Nassif ward in Dar es Salaam, Tanzania, as the planning study case. Hanna Nassif has an estimated population density of 40000 people/km^{2}. The approximately 1 km^{2} Hanna Nassif area includes around 3000 buildings (mostly 3–6 m tall) and is located on a terrain with a topographical difference of 19 m. A three-dimensional (3D) representation of this scenario is shown in Figure

The visualisation of the 3D buildings and topography of the planning case study deployment scenario. The candidate locations for the UDN small cells are depicted with solid blue-white dots.

The radio coverage estimations are based on realistic 3D building vectors and topographical data (see Figure

Evaluation setting and parameters.

General setting | |||||
---|---|---|---|---|---|

Candidate locations ( | 368 | Carrier freq. | 2.6 GHz | Bandwidth ( | 20 MHz |

Building material | Brick, 10 cm | Number of pixels | 350000 | Number of PRBs | 100 |

Max. BS transmit power ( | 30 dBm | Pixels’ resolution | ^{2} | Path loss | WinProp ray tracing [ |

BS’s height | 7 m | Noise power ( | −174 dBm/Hz | Shadowing | |

Cell selection ( | One server/highest Rx. power | Rx. power ( | −126 dBm | Small scale fad. | As in [ |

Link performance ( | Shannon’s formula | Cov. ( | 0.02 (2%) | | |

Max. path loss ( | −163.40 dB | Antenna pattern | Omnidirectional | | 180 |

Spatial user distribution | Uniform | SINR ( | −10.0 dB | — | — |

| |||||

Calibration of NSGA-II | |||||

| |||||

Population size | 100 | Crossover prob. | 1.00 | Type of var. | Discrete |

Mutation prob. | | Termination crit. | Hypervolume |

Two different spatial traffic distributions have been considered for the numerical evaluations presented in the next section: uniform and nonuniform. Uniform STD implies that the service demand is uniformly distributed in the coverage area. Nonuniform STD implies that the traffic is more likely to appear in certain areas (hotspots), which is representative of how traffic is commonly distributed in practice. The system model and optimization framework presented herein are able to consider any arbitrary STD by means of the vector

Nonuniform service demand distribution used in numerical evaluations.

Nonuniform service demand distribution map (

CDF of

In order to clarify the merit of the proposed optimization framework, several benchmarks have been considered.

Representation of additional benchmarks: two regular deployments (

one access point, thus

metric

The solution of multiobjective optimization problems, such as (

Multiobjective optimization:

Analogously, problem (

The comparison is shown in Figure

Comparison among optimized topologies. Each optimized topology is evaluated with respect to each performance metric and bandwidth allocation policy. Both cases, uniform and nonuniform spatial traffic distribution (STD), are illustrated. Description of the notation is in

A pictorial representation of these optimized topologies is shown in Figure

Representation of the optimized topologies for

It is worth noting that, in the study case considered herein (

In order to justify and explain the previous differences in performance, Figure

Comparison of the optimized topologies with 180 base stations (

Spectral efficiency

Achievable rate

Optimized topologies are compared with random deployments. In order to make the comparison fair, 1000 random deployments with

The comparisons for uniform and nonuniform STD are shown in Figures

Comparison of the optimized and random topologies with 180 base stations (

CDF of

CDF of

CDF of

CDF of

Legend

Comparison of the optimized and random topologies with 180 base stations (

CDF of

CDF of

CDF of

CDF of

Legend

From Figure

Figures

As mentioned, the analysis of Figure

In order to provide another quantitative perspective of the merit of the proposed scheme, a comparative assessment with regular deployments and network topologies obtained through basic heuristic planning, in terms of network capacity (^{2}). Thus, the proposed optimization formulation succeeds in finding near-to-optimal and Pareto efficient network topologies under different bandwidth allocation strategies and spatial traffic distribution conditions. The effectiveness of the optimization comes from the fact that the objective functions take into account

Comparison of the optimized topologies with 180 base stations (

Uniform bandwidth allocation:

Proportional bandwidth allocation:

Uniform bandwidth allocation:

Proportional bandwidth allocation:

Legend

All in all, the previous results show (and confirm) that

To close this section, complexity and calibration aspects are discussed. According to [

Network planning is the process of determining the amount and location of BSs that are required to provide wireless access to a given service area. In this article, a novel planning framework for UDN has been presented to address the general planning problem: that of finding network topologies which are compatible with a certain spatial traffic distribution while maximizing the benefit in terms of a given performance metric. To that end, a flexible multiobjective framework (system model and optimization formulation) has been presented. One interesting feature of the proposed scheme is the use of different bandwidth allocation strategies, which have been shown to have a profound impact on the ability to identify network topologies delivering the best performances in terms of the metrics of interest (network capacity, fairness, or cell-edge performance).

In addition, by benchmarking with regular and random deployments as well as network topologies obtained though simple heuristic planning, the notable benefit that can be achieved by means of the proposed optimization framework was quantified. Based on these results, the need for methodological planning means (such as the one provided in this article) becomes strongly recommended, specially in scenarios where the service demand is not uniformly distributed (the case commonly found in practice).

In the light of the results, it can be concluded that planning is still a quite valid tool for mobile operators, both nowadays and in future 5G systems, where small cells are of utmost importance. The framework studied herein is rich and admits several future research directions. Considering additional objective functions is definitely a study item, as well as other optimization formulations that could be specific for certain use cases, such as Downlink Uplink Decoupling. In addition, upgrading fixed/existing deployments is of great practical interest, as well as adaptation of coverage patterns, and power optimization. Finally, planning studies for UDN operating at higher frequency bands is also on our roadmap.

Multiobjective optimization is the discipline that focuses on the resolution of problems involving simultaneous optimization of several conflicting objectives. The target is to find a subset of

Pictorial representation of a Pareto Front.

In multiobjective optimization, it is unusual to obtain the OPF due to problem complexity; instead, a near-optimal or estimated Pareto Front (PF) is found. Interested readers are referred to [

Multiobjective evolutionary algorithms (MOEAs) [

Heuristic solutions have been considered for solving complex optimization problems in many fields, including engineering. Since planning and topology optimization for UDN are NP-complete problems, heuristics are naturally an option. In this appendix, a simple heuristic for planning of UDN is presented. The idea is adapted to planning from the

The basic idea is to start identifying the best single access point (a network with only one cell) for a given metric (

System bandwidth

Number of candidate locations

Number of area elements

Channel gain matrix

Target received power

Minimum channel gain

Spatial demand distribution

Spectral efficiency vector

Average SINR vector

Inverse of cell’s size

Maximum transmit power per cell

Set of area elements in the target area

Received power matrix

Power vectors: pilots and data channels

Network topology

Coverage of the

Coverage matrices

Minimum SINR

Coverage vector

Coverage threshold

Optimal topology with respect to

Optimal topology with respect to

Optimal topology with respect to

Optimal topology with respect to

The authors declare that there is no conflict of interests regarding the publication of this paper.

Hanna Nassif GIS data was kindly provided by Professor R. Sliuzas of ITC-Faculty of Geo-Information Science & Earth Observation, University of Twente. This work is partially supported by the Academy of Finland under Grants 287249 and 284634. Furthermore, this work received partial support from the National Bureau of Science, Technology and Innovation of Panama (SENACYT) through the project RAPIDO (ITE15-021).