JOURNAL OF SYSTEMICS, CYBERNETICS AND INFORMATICS, VOL. 3, NO. 1, 2006 1 Effects of Interference on Capacity in Multi-Cell CDMA Networks Robert AKL, Asad PARVEZ, and Son NGUYEN Department of Computer Science and Engineering University of North Texas Denton, TX, 76207 ABSTRACT An overwhelming number of models in the literature use average interference for calculation of capacity of a CDMA network. In this paper, we calculate the actual per-user interference and analyze the effect of user-distribution on the capacity of a CDMA network. We show that even though the capacity ob- tained using average interference is a good approximation to the capacity calculated using actual interference for a uniform user distribution, the deviation can be tremendously large for non- uniform user distributions. We also present an analytical model for approximating the user distributions using 2-dimensional Gaussian distributions by determining the means and the stan- dard deviations of the distributions for every cell. This allows us to calculate the inter-cell interference and the reverse-link capacity of the network. We compare our model with simulation results and show that it is fast and accurate enough to be used efficiently in the planning process of large CDMA networks. Keywords: Inter-cell interference, Capacity, CDMA, User dis- tribution, 2-D Gaussian. 1. INTRODUCTION The ability to offer greater capacity and multi-rate transmission with backward compatibility, seamless integration, and easier migration path to 3G cellular systems has fueled the widespread deployment of CDMA systems all over the world. But the principal attraction has always been the increased capacity over TDMA and FDMA systems, which explains multitudes of research devoted to study capacity of CDMA systems. And since CDMA capacity is limited by interference [1], [2], it is inevitable to investigate the factors involved in determining interference. One of such variables is the user’s distance from its base station. It has been shown in [3]–[6] that the capacity of a CDMA network is reverse link limited, and hence our study is confined to reverse link capacity. One of the principal characteristics of a CDMA network is that the capacity of the system is a function of total interference experienced by the network, and is upper bounded by the cell experiencing the most interference. Thus, it is imminent to characterize total inter-cell interference seen by a single cell in terms of the user distribution in every other cell for determining capacity in that single cell. Traditionally, the total interference contributed by a cell has been viewed as an approximation, determined by simply multiplying the number of users in that cell by the average interference offered by that cell [1]. In other words, a user placed anywhere within a cell generated the same amount of interference. Clearly, a more realistic approach will use per-user interference as a function of its actual distance to the point of interest. There is a dearth of literature where actual distance was used in the interference model. In [7], even though interference was calculated using actual distance, the capacity calculations were done using mean value of interference. User positions were varied over time, but the number of users was kept constant. In this paper, we use a model where interference is calculated with actual distance to investigate the effect of user distribution Fig. 1. Inter-cell interference on cell i from users in cell j . over reverse link capacity. Computer simulations of a CDMA network are carried out where interference is calculated in real time as the network is being populated. We assume several user distributions. We investigate the cases of equal capacity in every cell as well as the capacity obtained through optimiza- tion techniques discussed in [8]. We also present an analytical model for the approximation of the user distribution using 2- dimensional Gaussian distributions by determining the means and the standard deviations of the distributions for every cell. We verify the numerical analysis results published in [8], and also show that it is possible to have much higher or lower capacity if actual interference is used for specific user distributions. The remainder of this paper is organized as follows. In section 2, we present the traditional model for calculation of relative average interference. In section 3, we describe our model for calculating capacity using actual relative interference. In section 4, we describe the definition of equal and optimized capacity. In section 5, results from simulation are shown and compared to analytical results. Finally, the conclusions drawn from this paper are summarized in section 6. 2. RELATIVE AVERAGE INTER-CELL INTERFERENCE MODEL Consider two cells i and j . The user is power controlled by the base station of cell j , and is at distance rj (x, y) from the base station. The distance of the same user from the base station in cell i is ri (x, y) as shown in Fig. 1. Let nj be the number of users in cell j , denoted by region Cj and area Aj =Area(Cj ). The user’s transmitter power gain equals the propagation loss in cell j . The propagation loss is generally modeled as the product of the mth power of distance and a log-normal component representing shadowing losses. The large scale path loss and shadow fading are assumed to be circumvented by the power control mechanism. However, it cannot compensate for the fast fluctuations of the signal power associated with Rayleigh fading [1]. Now let χi denote the Rayleigh random variable that