Parameter estimation of polynomial-phase signal using the hybrid LvHAF

Estimating the coefficients of a noisy polynomial phase signal is important in fields including radar, biology and radio communications. In this paper, we consider a novel algorithm for estimating the high-order polynomial-phase signal (PPS). The proposed method, which is called hybrid LvHAF, combines the frequency domain method which is called Lv's Distribution (LVD) and the time domain method which is called high order ambiguity function (HAF) to improve the estimation performance. The HAF-based approach provides a simple order-recursive algorithm for estimating the polynomial-phase coefficients. Due to low complexity, the HAF algorithm is widely used in the field of radar. The LVD is a novel algorithm for estimating the LFM signal, which is simple and only requires a two-dimensional Fourier transform of a parametric scaled symmetric instantaneous autocorrelation function (PSIAF). It can be easily implemented by using the complex multiplications and fast Fourier transforms (FFT) based on the scaling principle. The LVD is searching free and without introducing any nonphysical attributes such as order or rotation angle. It only introduces a time delay into the time-lag instantaneous autocorrelation function and rescales the time axis to eliminate the effects of linear frequency migration for the LFM components on the time-frequency plane. The hybrid LvHAF is following two stage approaches. First, the phase differentiation is applied on the PPSs to produce a linear frequency signal (LFM). Second, the parameters of LFM are estimated by the LVD. The main significance of the LVD is to convert a 1-D LFM into a 2-D single-frequency signal. Through simulations and analyses, we verify the effectiveness of the Hybrid LvHAF algorithm.