The problem with using a directly modulated laser source for QAM, especially 64 QAM, is that they inherently introduce a lot of phase noise and also a chirp across each pulse. For QAM, where phase coherence is very important to the signal integrity, I don’t see a very simple solution to this problem. Now there might be a way to compensate for the chirp over each pulse, but this is not my area of expertise.
I did read an article recently on mitigating chirp in directly modulated lasers:
A. Karar, M. Yañez, Y. Jiang, J. Cartledge, J. Harley, and K. Roberts, “Electronic dispersion pre-compensation for 10.709-Gb/s using a look-up table and a directly modulated laser,” Opt. Express 19, B81-B89 (2011).
But again even this paper was for NRZ, where phase information plays a lesser role. However, if you figure out a way for reliably transmitting QAM with a directly modulated laser source, I’m sure you will have a bright future in academia!
Good luck!