Instantaneous Frequency Rate Estimation for High-Order Polynomial-Phase Signals

Instantaneous frequency rate (IFR) estimation for high-order polynomial phase signals (PPSs) is considered. Specifically, an IFR estimator with only a second-order nonlinearity is proposed. The asymptotic mean-squared error (MSE) of the proposed IFR estimator is obtained via a multivariate first-order perturbation analysis. Our results show that the proposed estimator yields a smaller MSE and a lower signal-to-noise ratio (SNR) threshold than a popular IFR estimator involving higher nonlinearity. The proposed IFR estimator is also extended to estimate the phase parameters of a PPS. Numerical studies are presented to illustrate the performance of the proposed estimator.