The probability distribution of the carrier-to-interference ratio (CIR) of a CSMA/CA ad hoc wireless network

This work is first in the open literature to characterize the probability distribution (not merely the mean and variance) of the carrier-to-interference ratio (CIR) of an ad hoc CSMA/CA wireless communication network, via Monte Carlo simulations. This paper is also first in the open literature to model an ad hoc network accounting for all following factors: (1) more realistically modeling of the network nodes´ spatial distribution via a two-dimensional Poisson process whereby network nodes are randomly placed at arbitrary two-dimensional plane (instead of nodes locating deterministically at only regular grid points), (2) suppression of nodes within the carrier sensing range of a transmitting node to micmac the CSMA/CA medium access control (MAC) protocol (i.e. nodes self-restrain from transmission when neighboring a transmitting node), (3) microscopic Rayleigh fading, (4) propagation-distance-dependent path-loss and (5) more than one service class. Monte Carlo simulations of a CSMA/CA ad hoc network generate CIR data, whose probability distribution function and parameters are identified via least-squares curve-fitting. The inverse normal distribution is the most well-rounded distribution, in the sense of providing a good fit (if not the best fit) to all nine Monte-Carlo simulation scenarios. The Rayleigh is the best univariate pdf. It can fit all scenarios very well, except the case without micro-fading and low pathless. All pdf´s can sufficiently fit the data when k=4 Nakagami is the best bivariate pdf with LMSE les1, except the case without micro-fading and low-pathloss (with distance-dependent power-loss exponent k=2). The bivariate Nakagami improves over the best univariate fit (namely, Rayleigh). The trivariate Fisk & quadravariate Burr can fit all scenarios with LMSE les 1. The quadravariate Burr often cuts the trivariate Fisks LMSE by half. The trivariate Fisk cuts the bivariate inverted-normals LMSE often by 2/3