The Probability Distribution of the Carrier-to-Interference Ratio (CIR) of a CSMA/CA Ad Hoc Wireless Network

Abstract

1 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.

Mean Weight Behavior for the Generalized Subband Decomposition LMS Algorithm

“…is given by (2). With (5) and (24), the capture probability is then calculated. As an example, let us use the quasi-constant traffic density given in [7], expressed as and depicted in Fig.…”

“…With the results obtained in Section III-B, applying the results of (4) and (28) in (5), and the latter in (8), the throughput can be calculated. Fig.…”

“…However, this is not necessarily the case. For instance, in a channel model that takes into account the effects of fading, competing packets arriving at a common radio receiver antenna will not always destroy each other because they may show different and independent fading and attenuation levels [5], [6]. This leads to expect that wireless systems may actually exhibit successful reception rate higher than that of original (wireline) systems.…”

Throughput of CSMA in a Rice-signal with Hoyt-interference environment

“…However, this is not necessarily the case. For instance, in a channel model that takes into account the effects of fading, competing packets arriving at a common radio receiver antenna will not always destroy each other because they may show different and independent fading and attenuation levels [4], [5]. This leads to expect that wireless systems may actually exhibit successful reception rate higher than that of wireline systems.…”

Probability density functions for SNIR in DS-CDMA

“…This includes [22] and [23] for ad hoc and downlink cases, respectively. Another reference [24] describes how to use SNR (averaged over a block) for multiuser diversity.…”