Multi-Objective Planning and Optimization for Base Station Placement in WiMAX Network Chitapong Wechtaisong, Teeraphant Sutthitep Major of Electronics and Telecommunication Technology Faculty of Industrial Technology Nakhon Ratchasima Rajabhat University Nakhon Ratchasima, Thailand
[email protected],
[email protected] Abstract—This paper presents the novel access network planning model for Wireless Interoperability for Microwave Access. The proposed model aims to assign optimize amount and location of Base Stations in study area. Integer Linear Programming is used for formulating optimization problem which objectives are minimize installation cost and maximize service coverage simultaneously. Numerical network planning result demonstrate that proposed model can achieve overall service area and can efficient serve almost service area in case of budget limitation. Index Terms—WiMAX, multi-objective optimization, siteselection, access network planning.
I. INTRODUCTION Wireless Interoperability for Microwave Access (WiMAX) is wireless access technology that serves broadband networks for distance areas. Both a high data rate and large coverage are attractive advantages of WiMAX. In countryside area that wired broadband infrastructure cannot provide, WiMAX is a good choice for offer broadband connection. Moreover, it can be used for expanding wireless broadband service in existing wireless networks. The optimized network planning is necessary for network operators. This is a basic thing in business to expect high profit after investment. Therefore, a network operator has to plan his new networks carefully. In addition, many issues need to be considered such as investment values, revenue, the quality of services and future expandability. In WiMAX network planning, base station (BS) placement is an important process to optimize investment cost and quality of services. If the objective of the planning is to increase network coverage and signal strength, many BSs are placed close to each other. This can improve the quality of services. However, it is not good in terms of investment cost. In contrast, economical objective can be attained by defining far distance between each BS, but signal problem can occur. Hence, there is a tradeoff between investment cost and the quality of services which many research groups are interested in. In this study, we examined the novel planning of WiMAX BS placement. Integer linear programming (ILP) was our tools to define problem. This is the popular scheme for researchers to solve the optimization problems and get exact result.
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Chutima Prommak School of Telecommunication Engineering Institute of Engineering Suranaree University of Technology Nakhon Ratchasima, Thailand
[email protected] Moreover the weighted sum method (WSM) was used to solve multi-objective optimization problem by combining two objectives problem and transforming to one function for the convenient calculation. The rest of paper is organized as follows. First, we discuss the related work in Section II to prepare background information for our study. Section III presents an evaluation methodology. We present the findings of our experiment in Section IV and conclude the paper in Section V. II. RELATED WORKS There are many existing studies on the network planning and performance improvement for wireless networks. In [1], focus on adaptive cross-layer bandwidth scheduling strategy for hierarchical cellular networks. In addition, WiMAX baseband transceiver was implemented on multi-core softwaredefine radio platform [2]. Furthermore, there are several research works paid attention on wireless network planning schemes. For example, the studies on the wireless network planning for mobile cellular networks are presented in [3] and [4]. The practical network planning and implementation of WiMAX along with performance evaluation and analysis are presented in [5-7]. However, these research studies interested in realistic network performances. The network planning was done manually and lack of mathematical formulation to optimize the network configuration. Recent research works formulated mathematical equation for optimizing WiMAX access network planning. In [8] and [9]_presented network design and optimization model for WiMAX access networks which effectively minimize investment cost by reducing number of BS and relay station (RS) while guarantied quality of receive signal strength for user equipments. Moreover, [10] presented planning and optimization in WiMAX access network that can enhance network service coverage under budget limitation. Although, each of these literatures considered one side of network optimization problem and cannot support whole network planning problem. Therefore, multi-objective planning and optimization problem is needed.
MULTI-OBJECTIVE PLANNING AND OPTIMIZATION A. Multi-Objective problem Definition In this research presents the method for consider location for placement BSs from candidate sites along with effect of weighted value with optimization result from two opposite objectives. The first objective was minimize investment cost that considers from [8, 9] and another one was enhance network service coverage from [10]. ILP was applied to formulate network planning problem. We used WSM to combine two opposite ILP objective functions for easier calculation. Table 1 shows definition of notations used in proposed models. In the network design model, we considered that every BSs have same infrastructure and transmitting power. Signal test points (STPs) were represented demand of users in study area. We guarantee quality of service in terms of receive signal strength by threshold (Pt). B. Multi-Objective problem formulation The WiMAX network planning problem in this research was formulated as an ILP model which consisted of three necessary parts. There were decision variables, objective functions and constraints. This model is popular to use as optimization tools for many research works. Table 1 describes the notation used in the proposed model. There were two binary decision variables in our study. Installation of BS sites was represented by βj which equal 1 if BS was installed at candidate site j and equal 0 if candidate site j was not chosen to install BS. In addition, Connection of STPs to network was represented by uhj which equal 1 if STP h connected with BS j and equal 0 if there were no connection. TABLE 1. DEFINITION OF NOTATION USED IN PROPOSED MODEL Notations Sets: B
Definitions
A set of candidate sites to install base stations (BSs); (1,2,3,..,b) B T A set of best signal test points (STPs); (1,2,3,..,t) T Decision variables: βj A binary {0, 1} variable that equals 1 if the BS is installed at site j, j∈B; 0 otherwise uhj A binary {0, 1} variable that equals 1 if the STP h is assigned to BS j, h∈T and j∈B; 0 otherwise Constant parameters: Cb Cost to install base station Ct Total investment cost implement network Phj The signal strength that a STP h receives from BS j, h∈T and j∈B Pt The received signal strength threshold for STPs Pn The signal strength of thermal noise SNR The signal to noise ratio threshold
We considered two different objective functions for effectively cover many side of network design problem. The first objective function aimed to minimize the network cost in terms of BS installation cost which can be written as objective function (1). The second objective function aimed to maximize coverage in terms of number of STP as show in objective function (2). These objective functions would be
collaborated with each other by WSM that would be explained in next topic. Objective functions: ,
,
(1)
,
,
(2)
, , ,
, , ,
(3) (4) (5)
1
Subject to: 0
We defined the network design requirement to a set of constraints. There were three mathematical equations that represent purpose of radio network planning. Equation (3) is a constraint that ensures STPs connect with only installed BSs. The guarantee of receive signal strength for each STPs and signal to noise ratio are defined in equation (4) and (5) respectively. C. Collaboration of multi-objective function In this topic, we developed multi-objective optimization mathematical equation for ILP. The tradeoff between two opposite objective function is considered. There were objectives that minimize network implementation cost and increase network coverage. The WSM is necessary tool for study tradeoff between two difference objective functions. In other word, it can obtain set of possible optimization solutions. Table 2 describes the notation used in the WSM. TABLE 2. NOTATION USED IN WEIGHTED SUM METHOD Notations
Definitions Weighted value of objective function 1 ; Weighted value of objective function 2 ; Normalized objective function 1 Normalized objective function 2 Minimize value of objective function 1 Maximize value of objective function 1 Minimize value of objective function 2 Maximize value of objective function 2
0,1 0,1
Two objectives were transformed to one objective format as show in equation (6). Normalization equation is represented by equation (7) and (8). We normalize both objective functions before collaborating each other because of releasing different units [11]. The weighted values was used for compare the tradeoff results. To divisibly combine two different objectives, the maximization objective of equation (2) was reversed to minimization objective in equation (9) which t was amount of total STPs in study area however it stilled be same as original meaning. The final equation of multi objective optimization by WSM is shown in (10).
Weighted sum method functions: (6) Normalize functions: (7)
The computation was run on an Intel Centrino Core2 Duo Processor 2.0 GHz and 2.0 GB of RAM. The network performance was evaluated in term of the physical receive signal strength guarantee and the SNR guarantee at the specified parameters. TABLE 3. PARAMETERS USED IN NUMERICAL EXPERIMENTS
(8) Reverse form of equation (2): ,
,
(9)
Final WSM multi-objective function: ∑ ∑
, ,
∑
(10)
D. Numerical Experiments In numerical experiments, we designed 10km x 10km as study area. The number of candidate site and STPs was 45 and 100 respectively. We used the Stanford University Interim (SUI) model which was recommended by the IEEE 802.16 to obtain the path loss in WiMAX networks [12]. Receive signal threshold and SNR was set at -100 dBm and 6.5 dB respectively [13]. Implement cost of each BS was 120,000$ [8]. Table 3 shows the parameters used in numerical experiments. Positions of candidate sites and STPs were simulated which spread over study area with uniform random as shows in fig. 1. STPs
Candidate Sites
10 9
Distance (km)
8 7
Parameters Height of BSs Height of TPs Transmitted Power Transmitted antenna gain Received antenna gain Frequency Terrain type Bandwidth Cost of each base station
Value 30 m 1.5 m 40 dBm 15dBi 6 dBi 3.5 GHz A 5 MHz 120,000 $
Weighted values were set to change 0.1 for each step, W1 decrease from 1.0 to 0.0 and W2 increase from 0.0 to 1.0, to consider the tradeoff results between conflict objectives. From position of candidate site as decision variable in table 1 with muti-objective function in equation (10) and constraint equations (3)-(5), this numerical information were inserted to calculation method. The numerical results of WiMAX network planning in terms of site placement by ILP and WSM are shown in table 4. TABLE 4.RESULTS OF NETWORK PLANNING EXPERIMENT
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.08 0.65 0.17 0.30 0.37 0.35 0.31 0.25 0.18 0.10 4.17
BSs
STPs
0 0 0 1 4 7 9 10 10 13 45
0 0 0 17 55 84 94 97 97 100 100
Installation cost (Million $) 0.00 0.00 0.00 0.12 0.48 0.84 1.08 1.20 1.20 1.56 5.40
IV. ANALYSIS AND DISCUSSION
6 5 4 3 2 1 0 0
2
4 Distance (km)
6
8
10
Fig. 1. Numerical experiment setup
E. Numerical Results The numerical experiments were implemented with the ILOG-OPL development studio same as in [8-10]. The ILP problems were solved with CPLEX 5.2 optimization solver.
In table 4, W1 and W2 represent weighted values of objective function 1 and objective function 2 respectively. Z represents optimized value of WSM function from equation (6). Number of installed BSs from 45 candidate site is represented by f1(x). In addition, amount of STPs which receive service coverage from network is represented by f2(x). When W1 = 0.1 and W2 = 0.9, the network planning can achieve 100% service coverage of STPs by install 13 BSs with 1,560,000$ of installation cost. In the other hand, when consider W1 and W2 at 0.4 and 0.6 respectively, it obtain 9 BSs which can support 94% of STPs by 1,080,000$. To compare these two cases of weighting, the second case cannot support overall STPs just 6% however it can save 30.8% of installation cost. For this reason, this can be option for network planner who has limitation in terms of capital budget.
Densities
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