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# Are gaussian distributed noise always white noises in awgn channel?

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#### lordsathish

##### Full Member level 5
In the awgn channel the noise added is gaussian as well as white noise...
my question is whether gaussian distributed noises are always white noise....?
is the vice versa is also correct...?

uncorrelated awgn

The answer is "NO". Distribution does not concern anything about time or frequency. Gaussion noise can have any power spectrum shape, and the very special one of it is white.

### lordsathish

Points: 2
awgn channel wiki

Then how come one can make sure that the noise added is gaussian as well as white noise... suppose i do a awgn simulation in matlab without using the function awgn... randn function will generate gaussian noise but to make sure it is white noise...

what is awgn channel

when we say that a process is white we just define its second moment,but by knowing that its gaussian some more information will be known such as mean,etc.

and about randn. it produce a white gaussian noise because its samples are uncorrelated and so its white,to produce a colored noise you should use a proper innovation filter which is applied to your white noise and its output will have your desired spectrum charactristics.

### lordsathish

Points: 2
verilog awgn

actually my problem is to create a verilog model of the awgn channel... for my turbo decoder... so can any one give me idea how to generate this uncorrelated gaussian noise...i think generating this gaussian noise won be a problem... but how to make it uncorrelated so that it is white noise...?

where does awgn come from?

white noise means that when you take samples of the noise at different time, these samples are independent.

to draw white gaussian noise, there are several ways. u can try in google. a popular method is box-muller method.

pls see the following c program, which is implemented by the box-muller method.

float x1, x2, w, y1, y2;

do {
x1 = 2.0 * ranf() - 1.0;
x2 = 2.0 * ranf() - 1.0;
w = x1 * x1 + x2 * x2;
} while ( w >= 1.0 );

w = sqrt( (-2.0 * ln( w ) ) / w );
y1 = x1 * w;
y2 = x2 * w;
(https://www.taygeta.com/random/gaussian.html)

y1 and y2 are independent gaussian r.v.'s.

hope it helps.

### lordsathish

Points: 2
how to make awgn channel

"A random vector w is a white random vector if and only if its mean vector and autocorrelation matrix are the following:

Mean(w)=0;
E(wwH)=sigma^2*I

I. e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix. " ( https://en.wikipedia.org/wiki/White_noise)

As you see the white noise is independent from the distortion of that random variable.
in other wird you could have a white signal with any distribution.

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