Why we scale noise for required Eb/N0 but do not scale transmitted signal as well?

[mazdaspring]

I am working on simulation of bpsk in Rayleigh channel. From the code below, I do not understand why you only scale the noise ( n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)] ) with 10^(-Eb_N0_dB(ii)/20) for the required Eb/No. But why don't you scale transmitted signal as well.

As I understand based on the code below,
s is in voltage scale, n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)] is also in voltage scale...
but why "s" is not scaled to be in dB like we did to "n"

can you please explain. Thank you.

...............................................................................
Matlab:

N=10^5;

ip = rand(1,N)>0.5;

s = 2*ip-1;

n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)];

Eb_N0_dB = [-3:10];

for ii = 1:length(Eb_N0_dB)

.........................................................



y = s + 10^(-Eb_N0_dB(ii)/20)*n;

 

[D.A.(Tony)Stewart]

As I understand it, Rican fading is the occurrence of signal reflections and when out zone of phase and equal amplitude you get a complete dropout of the signal. Rayleigh Fading is different in that the noise in random.

I think they Rayleigh model assumes that random noise will change much quicker than signal energy, but I could be wrong if this applied to Doppler loss or any mobile person who is moving.. Maybe it only applies to a static receiver/transmitter??

THe signal however is fairly constant fo minor variations in antenna orientation, but the reflected signals which becomes noise is amplified by the directionality of the signal and the distance of reflection and angle.. TO test this theory I have many times operated WiFi on a fringe, and vary the direction of the laptop by 1mm in direction or position and found SNR measured form RSSI Signal - RSSI noise to vary as much as 20dB from the noise alone. Some Laptop drivers will not measure Noise or SNR and simply measure Signal such as in certain great WIndows WiFI applications which can graph the signal.. Doing a slow scan can see the variation in SNR and 1mm can make the difference in getting communication at -75 dB and nothing at -85 dB . In this case the Modem autobuad switches down to a sub-optimal speed to improve the SNR of the recovered signal by filtering.

But in cases where the signal is not direct and is also reflected as well as the same source interfering reflections, then you may be correct and the Eb or energy in the signal could be varied as well but to a smaller extend.

I hope my explanation of Rician fading is useful for your question on Rayleigh Channel.

 

[mazdaspring]

I am really sorry but I do not understand (I am new to this area). Would you mind explain it simpler to me again please?

 

[David83]

Because the signal power is 1, so SNR=1/(1/SNR)