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

Sajjad Ahmed Qasmi, Kainam Thomas Wong

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

5 Citations (Scopus)


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 leastsquares 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 pathloss. All pdf's can sufficiently fit the data when k=4 Nakagami is the best bivariate pdf with LMSE ≤ 1, except the case without micro-fading and low-pathloss (with distance-dependent powerloss 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 ≤ 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.
Original languageEnglish
Title of host publicationMILCOM 2005
Subtitle of host publicationMilitary Communications Conference 2005
Publication statusPublished - 1 Dec 2005
Externally publishedYes
EventMILCOM 2005: Military Communications Conference 2005 - Atlatnic City, NJ, United States
Duration: 17 Oct 200520 Oct 2005


ConferenceMILCOM 2005: Military Communications Conference 2005
Country/TerritoryUnited States
CityAtlatnic City, NJ

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Electrical and Electronic Engineering

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