Is it a good idea to whiten a colored noise in order to apply formulas for AWGN? I have posted a question before regarding the detection of a signal under colored Gaussian noise:
Energy detection in presence of colored Gaussian noise

Theoretical formulas for setting the detection threshold are widely used for AWGN. 

Is it a good idea to just perform a pre-whitening to the colored noise and then apply the well-know formulas for energy detection under white Gaussian noise? 

Do you have any happy experience using this approach in practice?
The short answer is yes, whitening noise is usually recomended (if you know the spectrum of the noise) but whitening also whitens your signal.  Detecting random signals in colored noise is a well known problem is sonar signal processing.  There are a number of derivation that I like particularly:

Nielsen, Richard O. Sonar signal processing. Artech House, Inc., 1991.

and Burdic

@book{RN17,
   author = {Burdic, William S.},
   title = {Underwater acoustic system analysis},
   publisher = {Prentice Hall},
   ISBN = {0139476075},
   year = {1991},
   type = {Book}
}


Also the updated 

@book{van2004detection,
  title={Detection, estimation, and modulation theory, part I: detection, estimation, and linear modulation theory},
  author={Van Trees, Harry L},
  year={2004},
  publisher={John Wiley \&amp; Sons}
}


in section 4.3

and if you can find it, in the old volume 3

If you look, a copy of Eckart's  classic paper can be found at Scripts.