SNR in AWGN

Hello,

i am trying to do some simulation of AWGN channel. matlab has a function awgn(x,snr). what kind of snr does it use here? is it Eb/No (average bit energy/power spectral density)? If so, then i know the awgn has a PSD equal to No/2. does that psd in the snr term implies No/2?

-OBLI

Answer 1

[Darel]

The function awgn does not use EbNo. It uses SNR, defined in the same manner as the snr() function from the Signal Processing Toolbox: sum of the squared samples of the signal over sum of the squared samples of the noise, where that ratio is converted to dB. Thus, if you created noisy data according to

y = awgn(x, SNR);

you should be able to check that

mySNR  = snr(x, y-x)

is about the same as SNR in the first call.

Answer 2

[Wayne King]

With the syntax

    y = awgn(x,snr);

You generate a white noise vector with a variance of

   variance = 10^(-snr/10);
   noise = sqrt(variance)*randn(size(x));

If you use 'measured', then awgn actually measures the signal power.

For example:

x = cos(pi/4*(0:99));
y = awgn(x,5,'measured');

In this case the variance of the additive white noise is:

    sigp = 10*log10(norm(x,2)^2/numel(x));
    snr = sigp-5;
    noisep = 10^(snr/10);
    noise = sqrt(noisep)*randn(size(x));

[Gautam Sreekumar]

Is snr in dB or in linear scale?

[shaunaksinha]

Going by the official MATLAB documentation for awgn, I think snr is in dB. [https://www.mathworks.com/help/comm/ref/awgn.html?searchHighlight=awgn&s_tid=doc_srchtitle]

[shaunaksinha]

Why do we have this:

snr = sigp-5;

in the code. Seems like we are subtracting the given snr from the signal power. Not sure why this makes sense. Could somebody kindly explain this please?

[Mustafa qays]

The calculation is correct but the variable names need to be corrected

Signal to noise ratio SNR = sigp/noise_p (in ratio)

or

SNR = sigp - noise_p (in dB)

=>

noise_p(dB) = sigp - SNR , SNR = 5 dB

noise_p(db) = sigp - 5

noise_p = 10^(noise_p(db)/10)

So , (snr) in his equation should be written as noise power in the last section of code

[Mrutyunjaya Hiremath]

Meaningful Explanation

Answer 3

[philip]

x = cos(pi/4*(0:99));

y = awgn(x,5,'measured');