Estimation refinement techniques for the cubic phase function

We consider fine parameter estimation of polynomial-phase signals (PPSs) using the cubic phase function (CPF). The CPF outperforms the high-order ambiguity function (HAF) both in the estimation accuracy and performance threshold. However, since the CPF cannot be calculated using the FFT, it is characterized by higher complexity than the HAF. The fine estimation is usually done through the time-consuming oversampling. In this paper, we propose three methods for the fine estimation of the PSS parameters from the CPF. The methods are based on the dichotomous search, Newton-Raphson (NR) method and secant method, iterative maximization methods. All the three methods significantly reduce the calculation complexity with respect to the oversampling or maximum-likelihood (ML) approach.