A refined PCPF algorithm for estimating the parameters of multicomponent polynomial-phase signals

Abstract

This paper considers the parameter estimation of multicomponent polynomial-phase signals (mc-PPSs) with orders greater than two. The proposed method combines the product cubic phase function (PCPF) and high-order ambiguity function (HAF) when the mc-PPS orders exceed three. In the proposed method, the HAF is first applied to the observed mc-PPS to produce a cubic phase signal. Second, the algorithm is modified to estimate the parameters of mc-PPS using the CPF. To obtain accurate estimates of the two highest-order parameters (i.e., $$ a_{P} $$ and $$ a_{P - 1} $$ of each component), all possible $$ a_{P} $$ and $$ a_{P - 1} $$ must be obtained in this step in all combinations of the instantaneous frequencies; then, the maximum absolute value of all sum values must be identified by dechirping with all possible $$ a_{P} $$ and $$ a_{P - 1} $$ . In addition, non-uniformly-spaced signal sample methods are used to employ fast Fourier transformation in the CPF. The proposed method is different from the PCPF–HAF method proposed by other researchers; it is referred to as the improved PCPF–HAF method and can remedy the shortcomings of the traditional method when estimating mc-PPS parameters. Additionally, the PCPF–HAF method cannot be used to treat multicomponent third-order polynomial-phase signals, but the proposed method can treat them using non-uniformly-spaced signal sample methods. The cross-terms can also be restrained more effectively than with the CPF, resulting in higher accuracy of the estimated parameters and a lower signal-to noise ratio threshold. Theoretical analysis and simulations are presented to support these claims.