Optimal Placement of Access Point in WLAN Based on a New Algorithm S. Kouhbor, Julien Ugon, Alex Kruger, Alex Rubinov School of Information Technology and Mathematical Sciences University of Ballarat, Ballarat, Vic 3353 skouhbor@students.ballarat.edu.au Abstract When designing wireless communication systems, it is very important to know the optimum numbers and locations for the access points (APs). The impact of incorrect placement of APs is significant. If they are placed too far apart, they will generate a coverage gap, but if they are too close to each other, this will lead to excessive co-channel interferences. In this paper we describe a mathematical model developed to find the optimal number and location of APs. To solve the problem, we use the Discrete Gradient optimization algorithm developed at the University of Ballarat. Results indicate that our model is able to solve optimal coverage problems for different numbers of users. 1. Introduction The primary goal of Wireless Local Area Network (WLAN) deployment is to provide total coverage for all users in the design area. In other words, how and where to locate the APs, so that the primary goal of deployment is satisfied. The location of the APs determines the standard of coverage of the design area. Coverage is determined by the number of APs that are placed in the design area. Placing too many APs increases the cost of deployment and placing a few will lead to coverage gaps which prevents users from having access to their data through APs. The method used by network operators to find the placement of AP is based on the RF (radio frequency) site survey. This involves network designer going around the facility and measuring the RF signal strengths at various locations using software running on a laptop or PDA (Personal Digital Assistant). This software detects places that are suitable for APs to be installed based on signal strength, noise levels, and signal quality. These measurements have to be repeated many times to ensure reliable results. However, this method is expensive and its results are not very reliable due to characteristics of the building and location of the users that can change with time [1]. Another approach that is used by researchers [1-13] to find the optimal placement of APs is through the use of optimization techniques. Most of the authors [1-8] use discrete mathematical models to find the position of APs. In this case, the design area is divided into rectangles (grids). APs are only allowed to be placed in the centers of the rectangles. To obtain satisfactory results, the size of the grid must be sufficiently small. However, in this case, the dimension of the problem can be very high. For this reason some authors [9-11] prefer continuous mathematical models. Others [12,13] have tried to compare their results using both methods. The model investigated in the current paper is also based on applying continuous optimization techniques with no restrictions on the position of APs. It should be noted that there are different approaches to solve optimization problem in hand. In all these approaches there are two types of variables in the model: integer variables and continuous ones. Continuous variables describe the location of APs whereas integer variables describe the membership degree of receivers to clusters (group of users/receivers congregating in one area and using the same AP). Since each receiver can belong only to one cluster, integer variables can attain values of 0 and 1 only. As a result we get a mixed integer nonlinear programming problem. It is well known that such problems are difficult to solve in many situations. A nonsmooth optimization approach described in this paper allows one to exclude integer variables, to reduce significantly the number of variables in the optimization problem and to replace the mixed integer nonlinear programming problem with a continuous nonlinear programming problem. This paper is organized as follow: Section 2 shows the model notation. Section 3 presents the mathematical model. Method for the solution of the problems is described in Section 4. The testing method is described in Section 5. Results and the effect of AP parameters on coverage are discussed in Section 6. The Proceedings of the International Conference on Mobile Business (ICMB’05) 0-7695-2367-6/05 $20.00 © 2005 IEEE