Stationary moments of a polynomial phase signal, application to parameter estimation

This communication addresses the problem of estimating the parameters of a polynomial phase signal using an original approach: although this signal is clearly non stationary, some of its high order moments are shift invariant. The condition verified by the delays of these "stationary" moments is derived in the noiseless and noisy case. It is demonstrate that the only identifiable phase parameter is the highest order coefficient, the estimation requiring moments of order at least the double of the phase degree. An algorithm relying on these high order moments is derived and its performances are presented and compared to a recent algorithm.