Equalization with FSK

Question

What are the downsides of using an LMS (or least squares) equalizer with FSK signals? What are the tradeoffs on doing equalization pre-demoduation vs post-demodulation?

Most literature I can find discusses equalization on linear modulations. I have found very little that covers equalization on non-linear modulation techniques like FSK.

Assumptions:

1. Assume an FSK signal that is framed at M symbols
2. The FSK signal uses a known training sequence of length L symbols, where L << M
3. A matched filter detector is used to determine frame start (i.e., sample timing), which is used by the equalizer
4. The weight estimate produced by the equalizer will be applied across M symbols for ISI and channel correction
5. The equalizer will use an FSK modulated version of the training sequence if used pre-demodulation
6. The equalizer will use frequency deviation values for the training sequence if used post-demodulation
7. The input to the equalizer will be complex baseband integer oversampled symbols

Answer 1

The LMS equalizer would perform equally well for "non-linear" modulations such as FSK. This is because the modulation itself does not come into play. We are using a linear equalizer to compensate for linear (multi-path) channel distortions. What is important is that the sounding waveform occupy the channel of interest as equally as possible (for optimum performance since the result will be weighted by the SNR at any given frequency over the observation time). Within that constraint of spectral occupancy, we can use any sounding pattern or waveform that is known, and use the complex received waveform (prior to demodulation) for that given waveform and with the two determine the channel compensation using least squares approaches. With that we can equalize the channel to bring it as close as possible to a linear phase channel for any modulation of interest.