Dear Aneek,

I would propose that you verify the calculations of the of the formula using Excel.

And then you can verify the simulations referring to the Formula.

The best way is to make this experience yourself.

Best wishres

Hi I writ from paper this code for point to point Selective DF over flat fading channel.

Read the code and try to do for muti hop

Thank you very much sir Abdelhalim Zekry and Bouteggui Mokhtar .

I have another question .. some researchers used constant noise variance (No=1) and used formula --> y= sqrt(Pr)*h_rd*X+sqrt(N0/2).*(randn(1,1)+1j*randn(1,1)); for transmitted signal...

some other researchers used-->(even I am using)

for ii = 1:length(Eb_N0_dB)

SNR_lin=10.^(Eb_N0_dB(ii)/10);

noise_p1=p./SNR_lin

y1=sqrt(p1).*h_sr.*s1+sqrt(noise_p1).*n_sr ; %tx from source

-------------- are those same? what is the main difference? the best I understand, sqrt(noise variance) gives us the amplitude of noise signal. multiplying it with normalised random signal gives us the actual noise.

( when I use N0=1 and then sqrt(No/2) in my equations, i got BER curve a straight line for all transmit SNR.) so where to use which formula??

Hi Aneek Ghosh ,

Both the formulas are correct. Note that

• received signal = transmitted signal * fading coefficient + noise
• SNR = (transmitted signal power * channel gain)/noise power

So when you write

y = sqrt(P) * h * X + sqrt(N0/2).* (randn(1,1) + 1i * randn(1,1 )),

this means that

• "sqrt(P)" is the energy of the transmitted signal, "h" is the channel coefficient, "X" is the transmitted symbol with "E(|X|^2) = 1", i.e., mean power of the transmitted symbol is unity.
• randn(1,1) gives you a zero-mean Gaussian random variable with unit variance (power). Now for non-binary modulations, since your transmitted symbol may be a complex number, both your channel coefficient and noise should be samples from a complex process. Therefore "(randn(1,1) + 1i * randn(1,1 ))" returns a sample from complex white-Gaussian process. Note that the mean of each "randn(1,1)" is zero and the variance is 1. Therefore the overall variance of "(randn(1,1) + 1i * randn(1,1 ))" is 2 and in order to normalize it, we multiply this with "sqrt(1/2)". In this manner the power of "sqrt(1/2) * (randn(1,1) + 1i * randn(1,1 ))" becomes 1. Now in order to scale it properly according to the required SNR, you further multiply this with "sqrt(N0)".

Hence if you calculate the SNR for

y = sqrt(P) * h * X + sqrt(N0/2).* (randn(1,1) + 1i * randn(1,1 ))

you have

SNR = signal power / noise power

= power of (sqrt(P) * h * X) / power of (sqrt(N0/2).* (randn(1,1) + 1i * randn(1,1 )))

= P / N0,

because "h" is simulated in such a manner that E(|h|^2) = 1, and E(|X|^2) = 1. Note that this is the average SNR (the instantaneous SNR will be different because |h|^2 is not equal to 1).

Now in your equation

y1=sqrt(p1).*h_sr.*s1+sqrt(noise_p1).*n_sr,

I presume that "n_sr" is a zero-mean, unit-variance complex Gaussian process. So

noise_p1=p./SNR_lin = p./(p./N0) = N0

is the same as the other equation.

In your code

for ii = 1:length(Eb_N0_dB)

SNR_lin=10.^(Eb_N0_dB(ii)/10);

noise_p1=p./SNR_lin

y1=sqrt(p1).*h_sr.*s1+sqrt(noise_p1).*n_sr

You don't need to use N0 = 1 (in fact there is no N0 in your code). You can simply define any (non-negative) value of p (say 1) and depending on the value of Eb_NO_dB, the code calculates the appropriate value of "noise_p1".

Hope this answers your query.