If X = x +iy; where x, y are Independent and Normally distributed variables.
Then X is the rayleigh distributed signal.
For a Rayleigh distributed channel, does abs(X)^2 represent the power of channel gain from Rayleigh fading?
Hello,
what do you mean by X is the Rayleigh distributed signal ?
From my point of view, X is a complex Gaussian (Normally) variable, and then |X| is Rayleigh distributed. However, is X a signal or a channel ?
If X is a signal, and if X is an ergodic process, then E{|X|^2} is indeed the power of X.
If X is a channel, then it is preferable not to use the term "power", but gain instead (a power has a unit of measurement, not the gain). Or, in order to avoid any misunderstanding, if X is zero-mean, then E{|X|^2} is the variance of the channel.
Vincent
Thanks for your answer,
So if Pr (dB) = (Multipath channel effect + Shadowing + Path loss) Pt
Where Multipath channel effect is denoted by Raleigh distributed. Is the following equation all right then...
Pr (dB) = [10log10(E{|X|^2}) + N(0, sigma) + 10log10(lambda/4*pi*d)^2 ] + 10log10(Pt)
10log10(E{|X|^2}) = Multipath channel effect denoted as Rayleigh distribution
N(0, sigma) = log normal Shadowing with variance sigma and mean 0
10log10(lambda/4*pi*d)^2 = Free Space model Channel Gain
Please see the image for understanding of formula
Thanks again
Shan
Ok, it seems good, I just have a comment on the path-loss model and the notation of the log-normal distribution:
for the path-loss, you can see the wikipedia page:
https://en.wikipedia.org/wiki/Log-distance_path_loss_model
also, I think Log-N(0,sigma) is a better notation than N(0,sigma), which is usually used for normal (Gaussian) distribution.
However, the model seems OK, in my opinion, even though it should be confirmed by other experts.
Vincent
I agree with Vincent Savaux. His explanation was very good. |X| is the Rayleigh distributed variable. If you execute
sum(abs(X)^2)
in MATLAB you’ll get the average power or gain (for a system).
You should verify that X is ergodic for applying this procedure.
An ergodic signal is one where the statistical average is equal to the time average.
Good Luck!
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