OUTAGE PROBABILITY IN A CIRCLE WITH UNIFORMLY DISTRIBUTED USERS Sami Baroudi and Yousef R. Shayan Department of Electrical and Computer Engineering Concordia University Montreal, Quebec, Canada Email: {s_baro, yshayan}@ece.concordia.ca ABSTRACT Outage probability is one of the most important metrics that can be used to study the performance of wireless networks. In this paper, we evaluate outage probability of users which are uniformly distributed in a circular cell. The outage probability is determined in terms of generic parameters and is compared with well-known formula of the percentage of cell coverage area. Simulation is performed in order to confirm the analytical results. Index Terms— Outage probability, Path Loss, Uniform node Distribution, Coverage Area 1. INTRODUCTION Nowadays, wireless communication among users is accessible throughout the world and it is still growing in terms of number of users. During the last decade, in order to increase the number of users, engineers put extra effort trying to understand factors that affect the performance of wireless networks, such as the tradeoff between network capacity, interference, quality of service, and etc. Outage probability is the probability of failing to reach satisfactory reception of a wanted signal. Outage probability is considered as a statistical parameter that is used by designers in order to evaluate the quality of service in a mobile radio system. In this paper we are evaluating the outage probability of the users located uniformly in a circular cell communicating with a base station at the center of the cell. Outage probability can be evaluated based on path loss equations as given in [1] and [2]. Up to now, some work has been done to evaluate the outage probability in a communication system. In [3], outage probability has been evaluated by finding the probability that the received power falls below a predefined minimum power min P . In [4], outage probability has been calculated as the probability of failing to achieve sufficient signal to interference plus noise (SINR). Moreover, outage probability was evaluated based on co-channel interference as in [5]. In this paper we are deriving outage probability based on path loss. The outage probability is simply modeled as the complementary cumulative distribution function CCDF of the pass loss, at a predefined threshold. As a result, in order to find the outage probability, we integrate the probability density function PDF of the path loss of uniformly distributed nodes in a circle based on which has been derived in [1] and then we found its complementary value. This paper is organized as follows. In section 2, it is shown how the PDF of path loss is found in [1]. Derivation of outage probability is given in section 3. The simulation and results are presented in section 4. Section 5 concludes the paper. 2. BACKGROUND In this paper, it is considered that the system is as a circular cell of radius R . Users are uniformly distributed in the cell where the distance of any point from the center is x . Also, users are communicating with a base station (BS) at the center of the circular cell. Therefore, the probability density function PDF of the distance of any point from the center is , 2 ) ( 2 R x x f X = ]. , 0 [ R x ∈ ) 1 ( Now, a quick background of path loss is presented based on [1]. First of all, the path loss (in dB) can be written as ξ + + = ) ( log 10 X b a L ) 2 ( where a is the free space path loss at the close in distance 0 d , n b 10 = and n is the path loss exponent which depends on the propagation environment, 0 / d d X = and d is the distance between a node and base station. The parameter ξ is the shadow fading which is a zero-mean log normally distributed random variable with standard deviation σ . Finally, as shown in [1], the probability density function PDF of path loss distribution in a circular scenario of radius R as seen from the center of the circle is given as, 2012 25th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) 978-1-4673-1433-6/12/$31.00 ©2012 IEEE