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Plotting Rician Fading Channel

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I'm having trouble plotting rician pdf.
I have already managed to plot what i think is the empircal density funtction in a histogram.
What i need is a trace red line like this image:
so far i have this:
generated using this code:
u = 2;
s = sqrt(0.5);
% Generate in-phase component
X = normrnd( u, s, [1 randSamples]);
% Generate quadrature component
Y = normrnd( u, s, [1 randSamples]);
% Rician RV, S = sqrt( X^2 + Y^2 )
S = sqrt( X .^ 2 + Y .^ 2 );
% empirical probability density
[f,x] = ecdf(S);
ecdfhist(f,x, 20); hold on
How to get the red line?
This is the question for reference:
Thanks.

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Accepted Answer

Swetha Polemoni
Swetha Polemoni on 4 Nov 2020
Edited: Swetha Polemoni on 4 Nov 2020
Hi Saad Khan,
You might want to smoothen the histogram.
Here is the example for understanding smoothening of histogram using "spline" command.
You might consider "ksdensity" for smoothening. Below code snippet is for better understanding.
k=5;
s = [randn(100,1); randn(100,1)+k];
histogram(s,'Normalization','probability')
[f,x] = ksdensity(s);
hold on
plot(x,f)
These might help you.

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Swetha Polemoni
Swetha Polemoni on 4 Nov 2020
Hi
There is no ricepdf command in Matlab. You may find the following code snippet useful in plotting Rician Distribution
pd = makedist('Rician','s',2,'sigma',sqrt(2))
x=1:0.1:6;
k=pdf(pd,x)
plot(x,k)
Saad Khan
Saad Khan on 4 Nov 2020
Thank you!
Can you tell me which value corresponds to the K factor of 4 referred to in the question?
Swetha Polemoni
Swetha Polemoni on 4 Nov 2020
Not sure about K factor.

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