Relation between Eb/N0 and SNR
I have seen a lot of questions being posted in several forums on the relationship between Eb/N0 and SNR. Like, whether SNR and Eb/No are same or not. In fact , the relationship is very easier to understand.
Lets start with the basic equation and try to verify its authenticity.
Rb = bit rate in bits/second
Eb = Energy per bit in Joules/bit
S = Total Signal power in Watts
We all know from fundamental physics that Power = Energy/Time. Using SI units, lets verify the above equation.
This verifies the power, energy relationship between S and Eb. Now, introducing the noise power in equation (1)
This equation implies that the SNR will be more than by a factor of (if Rb > 1 bit/second)
Increasing the data rate will increase the SNR, however , increasing Rb will also cause more noise and noise term also increases ( due to ISI – intersymbol interference , since more bits are packed closer and sent through the channel).
So we cannot increase SNR by simply increasing Rb. We must strike a compromise between the data rate and the amount of noise our receiver can handle.
Always engineering is about where and when we want to compromise …
where B is the noise bandwidth. Here, I have taken an unity noise bandwidth (ie. B=1) for simplification.
See also: Colored Noise Generation in Matlab
 Sampling Theorem – Baseband Sampling
 Sampling Theorem – Bandpass or Intermediate or Under Sampling
 Window Functions – An Analysis
 FFT and Spectral Leakage
 Raised Cosine Filter
 Moving Average Filter ( MA filter )