I am trying to compare the BER performance of fractional and symbol spaced equalizers for channel equalization in colored noise scenario. I have found from simulation that for positively correlated noise, fractional equalizers perform better than symbol spaced equalizers. It is probably due to fact that with more samples we have more information in case of fractional equalizers. Is there any way of theoretically prove that fractional equalizers are better than symbol spaced equalizers for colored noise? Thanks
Yes of course, that's true.
FS equalizer sample the signal in rate faster than Nyquist rate which provide more information about the signal. It's similar when you increase the sampling frequency, you get better results.
If you need to understand that idea, you can read about oversampling, fractional sampling, and if you are working on sparse channel read you compressive sending working method.