Statistical analysis of SMF algorithm for polynomial phase signals analysis

The stationary moments fitting (SMF) algorithm is designed for the estimation of the coefficients of a constant amplitude polynomial phase signal. It relies on shift invariant signal moments with lower orders than the generalized ambiguity function (GAF) and it does not require maximization. The major contribution of this communication is the derivation of an analytic expression of the SMF error variance for high signal to noise ratios. This result proves the asymptotic efficiency of SMF when a dependency between the number of moments and the number of samples is introduced. Moreover, it underscores the superiority of SMF on GAF with an appropriate choice of the number of moments. Finally, the optimal parameters for order 3 and 4 polynomial phase signal estimation as a function of the signal length are provided