Novel parameter estimation of high-order polynomial phase signals using group delay

A novel parameter estimator of polynomial phase signals (PPSs) is proposed. The proposed approach unwraps a spectrum phase to obtain the group delay (GD) for parameter estimation. For PPSs with monotonic instantaneous frequency (IF) laws, which are referred to as strictly monotonic PPSs (SMPPSs), the GD and IF are inverses of each other. According to this property, we can perform polynomial regression on the GD instead of the IF to estimate parameters. However, the proposed method cannot be applied to general PPSs without monotonic IF laws. We prove that linear frequency modulation signals can be used to transform general PPSs into SMPPSs. In this manner, the proposed strategy is easily extended to general PPSs. Finally, the obtained results are refined by employing the O'Shea refinement strategy to achieve the Cramér–Rao lower bound. Simulation results show that the proposed technique has a lower estimation threshold and is less complex than the existing methods for high-order PPSs.