An Approach for Solving the Base Station Placement Problem using Particle Swarm Intelligence

A large amount of studies deals with the base station placement problem (BSP), but few studies involve the selection of base stations to meet a set of users. This paper presents an approach for solving BSP problems in an indoor environment, aiming at meeting a set of users, with a minimum number of base stations, using a binary particle swarm optimization (PSO). A benchmark of four maps of increasing complexity was created for testing the system. Results of the binary PSO were compared with optimal solutions found by an exhaustive search algorithm. The computational results sugges t that the PSO algorithm provides a quite efficient approach to obtain (near) optimal solutions with small computational effort. Keywords— Binary PSO; BSP; CDMA. I. I NTRODUCTION With the growing use of wireless base stations in the indoor environment, to seek meeting the total number of users effectively, it becomes necessary to adopt some computational optimization method in order to provide a servic e of satisfactory quality with the minimal number of base stations. The base station placement problem (henceforth, BSP) is characterized as the most important issue to solve in planning a wireless network [1]. This problem was considered NP-hard by many authors [1]–[4]. This fact suggests the use of metaheuristics for solving large instances of the BSP. Only few works about the BSP considered the placement of base stations committed to meet the demands of users in a code division multiple access (CDMA) indoor environment [5] [6]. In these works, only one problem instance (map) was considered, the same for both. This paper presents a model for solving BSP problems in a CDMA indoor environment, concerned with quality of service for a set of users. We propose a model and a benchmark of four instances (maps) with increasing complexity. The instances of BSP were solved using the binary particle swarm optimization (PSO), from evolutionary computation. Solutions were validated with the application of the formulation proposed by [5]. The optimal solutions for this benchmark were found by means of an exhaustive search algorithm. The optimal results were compared with those of the PSO. This paper is organized as follows. In Section II some related works are presented. Section III describes the vari ables and the formulation of the problem. In Section IV we present the model for solving the problem using PSO. Section V shows the benchmarks and the results obtained. Finally, Section VI concludes the paper and points to future directions of research. II. RELATED WORK Research in [5] proposed a binary integer programming (BIP) formulation for solving the BSP problem. It aimed at finding an optimal configuration, in a CDMA system, using the branch-and-bound (B&B) method. The results were compared with a customized version of a genetic algorithm. In [6] an algorithm to find the optimal configuration of base stations of a CDMA network in an indoor environment was proposed. The algorithm combines a heuristic technique with a brute force search. The heuristic search was used to find the minimum number of base stations, and the brute force searched for places for the base stations in predefined positions. The algorithm managed to reach the optimal solution in 10 runs, consuming an average time of one second of runtime, in a scenario with 12 base stations, 54 users (25 randomly selected) and with an area of 18.5m x 18.5m. We will show in Section V that the benchmarks proposed here are much more complex than the test scenario proposed by [6]. Several studies that used evolutionary computation techniques for the BSP were based on genetic algorithms, such as [1], [5], [7]. In these studies the genetic algorithm was found to be effective in solving the problem. The PSO was used for this problem in [4]. Authors adapted the PSO specifically for BSP problems. Solutions considered both coverage and economy for the Pareto curve using the divided range multiobjective particle swarm opti mization (DRMPSO). The results showed the efficiency of the method to find the optimum. The work of [4] deals only with the problem of locating the best position ( x,y) for the installation of the base stations. In the present paper, instead, the base stations are install ed at fixed locations. Most of the works cited consider only the placement of antennas [1], [4], [7]. In [5] [6] it was considered not only the base station placement, but also the location of the The 7th International Telecommunications Symposium (ITS 2010) users. However, only one scenario (with twelve antennas and measured twenty-five users) was used for tests, running for ten times the branch-and-bound and genetic algorithm methods. III. PROBLEM FORMULATION This section describes the base station placement problem as presented in [5]. Considering a CDMA indoor wireless network environment, we assume that there exists a finite number of potential base station sites ( B) and a finite number of user locations requiring service ( U). All users are identical and have a fixed known location. Each potential base station site has its own installation cost (in order to reflect the ease of installation and maintenance at the different sites, for instance). The loading of a base statio n corresponds to the number of users that are connected to that particular base station (with maximum capacity of L users). The problem is defined as selecting the least cost set of base station sites fromB potential sites, so as to provide service toU users, while ensuring that the signal-tointerference ratios on both the forward and reverse links exceed a predefined threshold. The complexity of a problem of an environment is defined by the number of B base stations plus the number of U users. The following notation is necessary for developing a mathematical formulation for the BSP problem: b – the index for potential base station sites. u – the index for user locations. l – the index for base station loading. Abu – the attenuation (pathloss) between b andu. Pt1 – the transmission signal strength at a base station when one user is being served. Ptar – the signal strength received at the base station from one of its users under ideal conditions. Pmin – the minimum signal strength required to maintain adequate communications as received by a user. Pmax – the maximum transmission power output on a handset. Gp – the processing gain of the system. Lb – the loading level (number of users) at base station b. Fb – the cost of installing a base station at potential site b. The BSP problem is formulated using BIP, as in [5]. Assuming a base station can host up to L users, the decision variable Ybl determines whether a base station is to be deployed at a siteb with a loading of l users, andXbul determines whether a link is to be established from potentia l base station siteb to a user locationu. Thus, the decision variables areXbul = 1 (0) if a link is (is not) established between base station b and user locationu, and there are a total of l users communicating with this base station; and Ybl= 1 (0) if a base station is (is not) deployed at potential site b with a loading ofl users. The objective function, to be minimized, evaluates the total cost of a solution and it is given by Equation (1): Z = B ∑ b=1 L ∑ l=1 FbYbl (1) Accordingly, a feasible solution must satisfy the followin g constraints: 1) The signal received by each user is required to be QF times stronger than the sum of the interference on the forward link. Thus, for each mobile receiver location u: B ∑ b=1 L ∑ l=1 GpPt1AbuXbul ≥ QF×