Order determination and parameter estimation of multicomponent polynomial phase signals

AM-FM signals whose phases are polynomial functions of time are encountered in many communication and signal processing applications such as synthetic aperture radar (SAR) imaging, speech processing and mobile communications. This paper addresses the issue of parameter estimation of multicomponent polynomial phase signals (MC-PPS) embedded in noise. We focus on analyzing a general class of MC-PPS in the sense that we allow the components to have drastically different amplitudes and unknown phase orders and that we do not assume knowledge of the number of components. We show how existing techniques are inadequate in providing reliable estimates for such a broad class of MC-PPS, unless the components have similar amplitudes and the number of components and their phase orders are known. We then present a simple yet effective algorithm that obviates these stringent assumptions and uses a product high-order ambiguity function to estimate all the parameters in the MC-PPS. Numerical simulations are carried out that clearly illustrate the advantage of the proposed algorithm over existing techniques