Gray code and M-FSK

Question

Does using a gray code mapping with M-FSK improve the BER performance vs no mapping? I know it helps QAM, and it makes intuitive sense. Doesn't seem as clear cut for M-FSK.

Answer 1

No, Gray code mapping does not help M-FSK at all. In M-FSK, a transmitted signal is equally likely to be mistaken for any of the other signals: the signals are equi-distant in signal space, whereas with QAM (including as a special case QPSK or 4PSK), some signals are closer than others and a transmitted signal is more likely to be confused with one of its nearest neighbors than with one of its more distant neighbors. The Gray coding ensures that nearest neighbors differ in only one bit and so the most likely symbol errors contribute only one bit error to the BER calculation. Gray coding also help with M-PSK signals where there are nearest neighbors. But, with equi-distant signals as in MFSK, no advantage results with Gray coding.