Fast Parameter Estimation Algorithm for Cubic Phase Signal Based on Quantifying Effects of Doppler Frequency Shift

Abstract

Abstract-For the chirp rate and its change rate estimation of cubic phase signal (CPS), conventional algorithms cannot achieve a trade-off between low computational cost and high performance. In this paper, by utilizing the numerical computational method (NCM), effects of Doppler frequency shift are quantified, and the relationships of the optimal signal length with the chirp rate and change rate of chirp rate are obtained. Then a fast parameter estimation algorithm (DMNUFFT), based on dechirp method (DM) and nonuniform fast Fourier transform (NUFFT), is proposed. Compared with existing algorithms, DMNUFFT can achieve high performance with relatively low computational cost. The performance analyses and an application to inverse synthetic aperture radar (ISAR) imaging are shown to validate the effectiveness of DMNUFFT.

ISAR Imaging of Ship Targets Based on an Integrated Cubic Phase Bilinear Autocorrelation Function

“…In this section, combing with a numerical example, we will demonstrate the high anti-noise performance of the ICPBAF. The input-output signal-to-noise ratio (SNR) ($SN{R}_{out}$ is listed in (19)) [31] and mean square error (MSE) [32,33] are utilized as measures of the noise resistance: ${\mathrm{SNR}}_{out}=10{\log }_{10}\frac{{\sigma }_p^2}{N_{t_m}{\sigma }^2}{\left\{{\left|true\sum _{m=-\frac{N_{t_m}}{2}}^{\frac{N_{t_m}}{2}-1}{s}_i\left(m\right)\exp \left[-j\pi a_{2.p}^{\prime }{\left(\frac{m}{F_{t_m}}\right)}^2-j\pi \frac{a_{3,p}^{\prime }}{3}{\left(\frac{m}{F_{t_m}}\right)}^3\right]\right|}_{\max }\right\}}^2$ where ${\sigma }^2$ is the power of the complex white Gaussian noise. $a_{2.p}^{\prime }$ and $a_{3,p}^{\prime }$ are estimations.…”

Inverse synthetic aperture radar imaging of targets with nonsevere maneuverability based on the centroid frequency chirp rate distribution

“…27,28,[35][36][37] The modified Wigner-Ville distribution algorithm and the Lv's distribution algorithm are chosen as references.…”

“…In this section, the input-output signal-to-noise ratio (SNR) [35][36][37] and the mean square error 26,[37][38][39] are utilized to evaluate the antinoise performance of CFCRD. Example 2: A monocomponent LFM signal Bu, which is contaminated with the zero-mean complex white Gaussian noise, is taken into account in this example.…”

ISAR Imaging of Targets With Complex Motion Based on the Chirp Rate–Quadratic Chirp Rate Distribution

“…Therefore, many algorithms have been proposed, such as the Radon-Wigner transform [4], the stretch keystone-Wigner transform [5], the LPP-Hough transform [6], the cyclostationarity method [7], the modified discrete chirp Fourier transform [8], the fractional Fourier transform [9], and the Lv's distribution (LVD) [10]. However, for the targets with complex motion such as fluctuating ships with oceanic waves and high maneuvering airplanes, the azimuth echo has to be modeled as the cubic phase signal (CPS) [11]- [21], and algorithms for the aforementioned slow maneuvering targets are no longer applicable under this situation.…”

“…To resolve the problems of the cross-term, the product HAF [15], the product high-order matched-phase transform (PHMT) [16], the product generalized CPF [17], the time-chirp distribution DechirpClean algorithm [18], and the HAF-integrated CPF (HAF-ICPF) [19] are proposed. The noncorrelation algorithms include the maximum likelihood algorithm [20], the quantifying-based method [21], and the discrete chirp Fourier transform [22] for the CPS. Although noncorrelation algorithms can get high antinoise performance in the lower signal-to-noise ratio (SNR), they are not suitable for the high-resolution ISAR imaging of targets with complex motion due to the high computational cost (O(M 2 N log 2 N ) [20]- [22], where M is the number of searching points and always greater than the effective length of the slow time N in ISAR [10]).…”