Parameter Estimation of Polynomial-Phase Signals

Abstract

Introduction . Polynomial phase signals frequently appear in radar, sonar, communication and technical applications. Therefore, estimation of polynomial phase coefficients of such signals is an urgent problem in signal theory. Currently, a large number of estimation algorithms have been proposed. The best way is the maximum likelihood (ML) method. However, its implementation is associated with a multidimensional retrieval, which makes the method unsuitable for practical implementation. A number of alternative strategies have been developed to circumvent the ML difficulties. These strategies are very close to optimal. Among them one can single out the HAF-algorithm based on the computation of the High order Ambiguity Function and the CPF algorithm, which uses the computation of the Cubic Phase Function and produces very accurate estimates for signals with the quadratic frequency modulation. However, both algorithms have obvious drawbacks. The HAF algorithm pro-duces a large number of combinatorial noise components. The CPF algorithm is limited in its implementation to the third order polynomial signals and does not use fast algorithms, such as the Fast Fourier Transform. Aim. Synthesis of an estimation algorithm that produces a small number of noise combinatorial components and uses the Fast Fourier Transform computation algorithms to find coefficient estimates of an arbitrary order phase polynomial. Materials and methods. In the paper a concept of a decisive function was introduced. It was calculated so that its phase contained only a first-order monomial with a coefficient equal to the highest coefficient of the signal phase polynomial. Results. A new estimation algorithm was proposed able to use Fast Fourier Transform computation algorithms to find estimates. Each polynomial coefficient was estimated on the basis of a unified procedure, which reduced the number of combinatorial noise components in an estimate search. Conclusions. The synthesized algorithm gives asymptotically efficient estimates for lower signal-to-noise ratios in comparison with the HAF-algorithm.