A Generalized geometry-inclusive fading model for ad hoc wireless networks

A new generic statistical fading model for wireless ad hoc networks is proposed. Besides small scale fading, our proposed model incorporates the variations due to geometry, i.e. the statistical distribution of transmission and reception distances. The geometry-inclusive fading model presented here can also be considered as a generalization of several prior studies. Consequently, it is valid for any arbitrary but realistic numeric value of parameters. We assume that nodes are distributed according to a Poisson point process, while small scale fading is modeled using a Rayleigh distribution. Under these assumptions, we formulate a statistical framework to determine the probability density function (PDF) and the cumulative density function (CDF) of fading coefficients. Several applications of this fading model are highlighted. Lastly, we employ the developed analytical machinery to show that the fading in ad hoc networks can not be characterized alone by the statistical distribution of the multipath impairment process. Rather, the distribution of the link distances is also required to accurately model the overall random wireless impairment process. Besides link distances, the intensity/density of nodes in a region and path loss exponent determined by the enviornment, also plays a vital role in accurate characterization.