Are genetic algorithms useful for the parameter estimation of FM signals?

The estimation of polynomial-phase signals (PPSs) is a multiparameter problem, and the maximum likelihood (ML) optimization functions have numerous local optima, making the application of gradient techniques impossible. The common solution to this problem is based on the phase differentiation (PD) techniques that reduce the number of dimensions but, at the same time, reduce the accuracy and generate additional difficulties such as spurious components and error propagation. Here we show that genetic algorithms (GAS) can serve as a powerful alternative to the PD techniques. We investigate the limits of accuracy of the ML technique, and of some alternatives such as the high-order cubic phase function (HO-CPF) and high-order Wigner distribution (HO-WD). The ML approach combined with the proposed GA setup is limited up to the fifth-order PPS, which is not sufficient in many applications. However, the HO-CPF and HO-WD techniques coupled with the GA are able to accurately estimate phase parameters up to the tenth-order PPS. They significantly improve the accuracy with respect to the high-order ambiguity function (HAF) and product HAF (PHAF) and, for higher-order PPSs, they are much simpler and more efficient than the integrated generalized ambiguity function (IGAF). (C) 2012 Elsevier Inc. All rights reserved.