Identification of Parameters of High Order Polynomial Phase Signals

Abstract

Estimation of feautres of instantaneous phase of non-stationary signals from discrete-time observations is an important issue in numerous scientific and engineering areas including biological research, speech and music signal processing, radar and wireless communication systems development. The most popular model of an observed non-stationary signal is the polynomial phase signal (PPS). In the paper, low-order time-frequency distributions with a non-uniform sampling are used for estimation of coefficients of the high order phase polynomial (order > 3). The cubic phase function (CPF) with one phase differentiation (PD) operation is used for parameter estimation of the third order PPS, which is known as the cubic phase (CP) signal. The CP signal can be used for decomposition of the high order PPS into PPSs of lower orders, so the combination of CPFs can allow to obtain efficient methods for estimating the parameters of the polynomial phase. In the paper, a high order PPS is examined and a whole set of phase polynomial parameters is estimated with using CPF and distributions defined by the kernel with non-uniform sampling. It has been shown that significant improvement of the performance of algorithms is achived by using non-uniform sampling. The presented approach requires only few one-dimensional optimization processes instead of multidimensional optimization required in direct application of the Maximum Likelihood Estimation (MLE). The presented analysis is supported by simulations, which show the high efficiency of presented methods.