SINR-based k-coverage probability in cellular networks

Calculating the k-coverage probability with Poisson process-based cellular network models.


Updated Wed, 29 Jan 2014 23:50:30 +0000

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The scripts calculate the k-coverage probability (based on SINR* values) in a single-tier cellular network using a method based on a homogeneous Poisson process model. More details are found in the (submitted) work [1], which presents the model that these scripts are based on.

The script funProbCov.m uses a inclusion-exclusion-like formula and two types of integral to calculate the k-coverage probability in a network with log-normal shadowing (though the shadowing distribution can be somewhat arbitrary [1]) and without fading.

The simpler integral I_n uses a quadrature method or a simple analytic formula (for the zero-noise or “interference limited” case). The more complex high-dimensional integral J_n uses quadrature methods for low dimensions and quasi-random (Sobol) integration for higher (n>2) dimensions.

The script funProbCovFade.m calculates 1-coverage probability for a network with Rayleigh fading (exponentially distributed with unit mean) and log-normal shadowing. Numerical integration of hypergeometric function 2F1 is used when the model has noise. A close-form solution with 2F1 is used in the no noise case.

Simulation scripts are also included for comparison purposes. All network base stations are sampled on a disk region. The disk region needs to be large enough to reduce "edge effects", which become more prominent when fading is included.

Running the file TestSimVsInt.m is a good place to start. The fading-incorporated model is demonstrated in TestSimVsIntFade.m. Default parameters are based on a Walfisch-Ikegami model for a urban environment. The (submitted) associated work [1] has more details on the equations and the model.

*SINR = signal-to-interference-and-noise-ratio

[1] H.P Keeler, B. Błaszczyszyn and M. Karray, 'SINR-based k-coverage probability in cellular networks with arbitrary shadowing', 2013. Online at

Cite As

H. Paul Keeler (2023). SINR-based k-coverage probability in cellular networks (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
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Version Published Release Notes

The funJn.m has been updated. It uses a fact, discovered in later work*, that eta values sum to one.

*Blaszczyszyn and Keeler, Studying the SINR process of the typical user in Poisson networks by using its factorial moment measures, submitted 2014

Fixed up some typos and improved some of the code slightly.

Uses a different (slightly better) numerical integration method for funIn.m.