weibull fading

8/3/2019 Weibull Fading

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Problem:

Simulate a short term fading channel by considering the transmission of a 900 MhZ signal.

Solution:

The fading channel was generated using following parameters:

Mhz f c 900 , c s f f 4 , cc f 2

The fading channel was generated for different number of paths N, which was allowed to vary. The

amplitude ai was drawn from a weibul distribution with parameters a=1 and b=3.

The RF signal and Signal Envelope for N=2, 5, and 10 is shown below:

a) Chi-square test to determine when Weibull conditions are met

A chi-square test was generated to test when the Weibull conditions are met for the generated faded

signal. Ideally, when larger number of paths are used, the hypothesis test should fail. But we observed

through the chi-square test that the hypothesis was not always rejected. The hypothesis test was done

for 1000 times separately for N=2, 5 and 10 paths and pass and fail rate was noted as shown in Table 1

below.

N=2 N=5 N=10

PASS 550 856 650

FAIL 450 144 350

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It was inconclusive from the above results if the chi-square test was functioning as it should. It should be

also noted that the chi-square rejected the hypothesis for exponential and normal distribution, but

passed for Rayleigh distribution

To further validate if the faded signal envelope meets Weibull condition, Weibull probability plot was

used to see if the envelope data could come from a Weibull Distribution.

The purpose of a Weibull probability plot is to graphically assess whether the data in a given vector

could come from a Weibull distribution. If the data are Weibull the plot will be linear. Other distribution

types might introduce curvature in the plot.

The results for the Weibull plot using the signal envelope data is shown below for N=2, N=5, N=10:


weibull fading

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