A Statistical Property of Wireless Channel Capacity: Theory and Application

Abstract

This paper presents a set of new results on wireless channel capacity by exploring its special characteristics. An appealing discovery is that the instantaneous and cumulative capacity distributions of typical fading channels are lighttailed. An implication of this property is that these distributions and subsequently the distributions of delay and backlog for constant arrivals can be upper-bounded by some exponential functions, which is often assumed but not justified in the literature of wireless network performance analysis. In addition, three representative dependence structures of the capacity process are studied, namely comonotonicity, independence, and Markovian, and bounds are derived for the cumulative capacity distribution and delay-constrained capacity. To help gain insights in the performance of a wireless channel whose capacity process may be too complex or detailed dependence information is lacking, stochastic orders are introduced to the capacity process, based on which, comparison results of delay and delay-constrained capacity are obtained. Moreover, the impact of self-interference in communication, which is an open problem in stochastic network calculus (SNC), is investigated and original results are derived. These results complement the SNC literature, easing its application to wireless networks and its extension towards a calculus for wireless networks.