Rayleigh model. X and Y independent?

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bravoegg

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h is a mutipath channel, as depicted in the following picture.

a_i is the channel gain. tao_i is the channel delay.
a_i and tao_i are i.i.d random variables respectively. It could be reinterpreted in the form of h = X + j*Y.

In the following picture, X is the real part, and Y is the imaginary part.

What I fall to understand is why is X and Y are independent from each other?
It seems to me they both consists of the same two random variables.
My friends suggest they're irrelavant and orthogonal, which I still couldn't know how?

 

When you write h=X+jY then X and Y are orthogonal. And since they are Gaussian random variables then they're independent.
 

Yes, they are statisticaly independent.
 

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