# Rayleigh Channel Pearson Chi Square Test 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris
Script Licensing : Freeware
Created : Sep 15, 2007
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## CHI2RAYLTEST: Single sample Pearson Chi Square ...

test: Single sample Pearson Chi Square goodness-of-fit statistical test to examine a null hypothesis of Rayleigh Channel.
H=CHI2RAYLTEST(X, ALPHA) performs the particular case of pearson Chi Square
test to determine whether the null hypothesis of a Rayleigh channel realization is a reasonable assumption regarding the population distribution of a complex random sample X with the desired significance level ALPHA.
H indicates the result of the hypothesis test according to the MATLAB rules of conditional statements:
H=1 => Do not reject the null hypothesis at significance level ALPHA.
H=0 => Reject the null hypothesis at significance level ALPHA.
The Chi Square hypotheses and test statistic in this particular case are:
Null Hypothesis: X is a base-band rayleigh_channel realization with unknown mean and variance.
Alternative Hypothesis: X is not a Rayleigh channel realization.
The complex random sample X is shifted by its estimated mean and normalized by its estimated standard deviation giving Rayleigh parameter b=1/sqrt(2).
The test drops K factor of Rician distribution for K > -inf[dB], so that the random sample from a Rician channel realization will pass the test as well. The tested bins XP are chosen to give 10 tested bins with equal expected probability. These bins supply a sufficient statistic for LENGTH(X)>=100.
Let E(x) be the expected frequency X falls within XP according to the Rayleigh distribution and O(x) be the observed frequency. The Pearson statistic, X2=SUM((E(x)-O(x))^2/E(x)) distributes Chi Square with
LENGTH(XP)-2 degrees of freedom.
The decision to reject the null hypothesis is taken when the P value (probability that Chi2 random value with length(XP)-2 degrees of freedom is greater than X2) is less than significance level ALPHA.
X must be a complex row vector representing a random sample corresponding to a base-band channel realization.
ALPHA must be a scalar.
The function doesn't check the formats of X and ALPHA, as well as a number of the input and output parameters.
Demands:
• MATLAB Release: R12. 1

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