Outage probability scaling laws for SISO and MIMO ad‐hoc networks

Abstract

ABSTRACTIn this paper, the outage probability scaling laws for ad‐hoc networks with an arbitrary topology is studied. In single‐input single‐output ad‐hoc networks, the outage probability is tightly bounded as the number of users goes to infinity in case that channel gains are independent and identically distributed (i.i.d.). If channel gains are not i.i.d. or calculating the distribution function is complicated because path loss, it is still possible to bound the outage probability if the distances between transmitter–receiver pairs are bounded. However, there is a gap between the upper and lower bounds. Unlike previous results, our analysis is completely general and is not limited to specific node and fading distributions. In multiple‐input multiple‐output ad‐hoc networks, the calculations are much more complicated, and it is hard to tightly bound the outage probability. For a special case of i.i.d. Gaussian channel matrices, the outage probability is asymptotically bounded in terms of Chi‐square distribution functions. Finally, as an application, the outage probability analysis is utilized to study delay scaling laws in random ad‐hoc networks. Simulation results show accuracy of this estimation for different scenarios. Copyright © 2012 John Wiley & Sons, Ltd.