How to do base-band simulation of coherent detection of M-ary orthogonal signals? I currently have a complex base-band simulator for non-coherent detection of M-ary orthogonal waveforms (such as M-FSK).  I run the noisy signal through M correlators at lag=0, compute the magnitude squared of the results and pick the largest.  Everything is perfectly synchronized.  

It is just: modulate -> add AWGN -> demod.  

Currently, my non-coherent simulation BER performance matches the theoretical equations derived in Proakis.

What do I have to tweak in order to simulate coherent detection given that my received signal is perfectly synchronized?
Since the answer was given by vaz in the comments I figured I would just post it as an actual answer...

To perform coherent detection for M-ary orthogonal signals in a complex base-band simulation simply take the real part of each matched filter (correlator) output and select the symbol with the largest value.

Also, don't make my mistake and use the absolute value of the real part.  I made those changes and verified against the theoretical coherent equations MATLAB uses.