you need to transform from the time
domain to the frequency spectrum domain. I think
I am right in saying that the data length L in the
time domain is not relevant.
What is relevant
is the date rate and the modulation method. Thus
a data rate of 8 megabits per second passed through
a 64QAM modulator has a certain symbol rate and
this relates to the spectrum width around the carrier
frequency center. Armed with that knowledge and
the level of the carrier, you can estimate the noise.
Draw a spectrum distribution curve from the data
you have of offset frequency and noise, and superimpose
a Gaussian curve for the signal spectrum. That will
show the relative noise and carrier levels.
At bottom, life is all
Sucking in and blowing out.