equalizer in matlab

It seems that the training symbols have to use the same modulation as
the data symbols.  Is there any way that I can use different
modulations?  say QPSK for training and 16QAM for data.  I tried
equalizing the two parts separately with a constellation change in
between.  The shape of the equalized constellation seems correct, but
it is compressed. Of course the demodulation result is wrong.
Thanks