On the Probability of Non-Shared Multipath Clusters in Cellular Networks

In Space Division Multiple Access (SDMA) systems, users are separated based on their positions. The base-station (BS) signals typically reach the users through multipath clusters. The goal of this work is to find the probability that a randomly selected user will receive the signal from the BS via at least one non-shared (by any other user) multipath cluster. This probability, referred to as P_Success, provides (under some conditions) the limit of the probability that the BS is able to communicate successfully with a randomly selected user using SDMA without causing significant interference to other users. To find P_Success, we first derive a model describing the probability distribution function (pdf) of the non-overlapping area of a set of circles, that have the same radius and are spatially distributed according to a Poisson distribution. Then, the proposed model for this pdf is used to express P_Success as a function of the user´s intensity and the clusters´ intensity. Simulations, using the COST 2100 model, for outdoor and indoor scenarios, are used to validate the derived expression for P_Success with a very good agreement, where the maximum error was 0.04.