The max data rate for a given channel and SNR is given as,
rate = available BW * log2(1+SNR)
In the above equation, in using th term log2(1+SNR), is there a fundamental assumption that noise is additive in nature?
Does this equation change in system where is noise is not additive in nature?
The equation doesn't care how the noise over rides the signal. It's just a reference to signal/noise. Nominally noise is Gaussian, but that doesn't matter either. log base 2 is the number of bits. If snr < 1 then you can't even send 1 bit per cycle of bandwidth. But you can send something. Just because it is theoretically possible doesn't mean you can actually get it either. The equation doesn't care how the different noise sources clobber your signal, anything that kills signal will kill data rate.
So, irrespective of what method I use to do source encoding or modulation method, the above equation stands?
Also, a follow-up question.
Since SNR is related to signal power to noise power, so, does it mean that irrespective of what clever method I use for signal encoding or modulation, if noise power is higher than it is likely to reduce the effective data rate?
Thanks a lot ...
I don't know the assumptions that went into the derivation of that formula, but yes - methods don't matter. It is an information theoretical limit.
And yes - higher noise power reduces the effective rate. It just makes sense physically: if your signal is 1 Watt and your noise is 10 Watts you will have a hard time finding the signal no matter what kind of modulation scheme you use. That you can find it at all is actually amazing, but it can be done.
The assumptions are that the noise is additive, the spectrum of the signal and noise are flat over the bandwidth, and that there is no correlation between the signal and noise.
If the noise is additive but the SNR is not flat (as in ADSL or VDSL where the attenuation increases with frequency), you need to do an integral over the frequency dependent SNR. For cases where the noise is not simply added to the signal (such as in optical fiber), there is a nonlinear extension to Shannon theory.