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!
how to calculate Rayleigh channel gain coefficient for single user using matlab
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