Effects of spatial receiver distributions on the user capacity of broadcast channels

In this paper, a broadcast channel is considered in which receivers are randomly distributed on the plane. It is assumed that the x and y coordinates of receivers positions are Gaussian-distributed random variables with the same variance. Hence, the distance between each transmitter–receiver pair and consequently, the path loss term is random. It is shown that as the total number of receivers, n  , in the broadcast channel goes to infinity, the maximum number of active receivers (i.e. user capacity) scales with (α/Rmin)lnbn where b = (Rmin P1/α)/(α σ2). Convergence of numerical results to the theoretical bounds in practical situations and the user capacity dependency on system parameters are shown in simulations results.