Plotting Rician Fading Channel

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.

Answer 1

[Swetha Polemoni]

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.

[Saad Khan]

Thank you for your reply. I'm afraid this isn't exatxly what I'm looking for.

I mainly just need to use the ricepdf command to draw the theortical pdf line over the histogram.

i.e. the red trace line following the trend of the histogram.

[Swetha Polemoni]

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]

Thank you!

Can you tell me which value corresponds to the K factor of 4 referred to in the question?

[Swetha Polemoni]

Not sure about K factor.