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Although the use of CMA filters to equalize multipath channels for FSK signals is well understood, empirical tests have suggested that in some environments an LMS filter positioned after the demodulator could provide similar performance improvement with lower computational cost. Theoretical analysis of this nonlinear configuration has been hindered by the complex interaction of the system and signal parameters, and reported results have been limited to a narrow and unrealistic operating range. Our previous work explored a much wider operating range and demonstrated that minimizing the MSE did not reliably minimize the BER, so previously reported results needed reexamination. In this work we extend the theoretical analysis to show the relationship of system parameters to the nonlinear system behavior which explains a number of nonintuitive observations. A modification of the LMS filter is demonstrated with improved BER performance.