On the Number of Active Transmitters in a Random Multiple-access Channel with a Uniform Spatial Distribution

Paper ID : 1559-IST

Authors:

^{1}jalil etminan *, ^{2}Hengameh Keshavarz

^{1}Department of Communications Engineering , University of Sistan and Baluchestan

^{2}Department of Communications Engineering, University of Sistan and Baluchestan

Abstract:

In this paper, a Multiple-access channel is considered in which transmitters randomly located in the squaredshaped area of width D1. It is assumed the x and y coordinates of each transmitter’s position are Uniform random variables and also the receiver is locatedat the origin. Hence, the distance between any transmitter-receiver pair and consequently, the pathloss term are random variables. It is asymptotically shown as the total number of transmitters goes to infinity, the maximum number of simultaneously active transmitters (i.e. user capacity) is of the order v(n)=b1 ln(b2 n (Pv(n))^(3/2a)), where n is the total number of transmitters and b1 and b2 are constants depending on the minimum-rate, the path-loss exponent and the square width. Simulation results shown as the total number of transmitters is large enough, the numerical results converge the theoretical bounds.

Keywords:

User capacity, Path loss , Multiple access-channels, Power allocation, Minimum rate-constraint