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 nonshared (by any other user) multipath cluster. This probability, referred to as PSuccess, 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. In order to find PSuccess, 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 PSuccess 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 PSuccess with a very good agreement, where the maximum error was 0:04.