A refined PCPF algorithm for estimating the parameters of multicomponent polynomial-phase signals
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A refined PCPF algorithm for estimating the parameters of multicomponent polynomial-phase signals Guojian Ou1 · Yunbing Hu1 · Chunling Wu1 Received: 15 October 2019 / Revised: 25 January 2020 / Accepted: 5 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper considers the parameter estimation of multicomponent polynomial-phase signals (mc-PPSs) with orders greater than two. The proposed method combines the product cubic phase function (PCPF) and high-order ambiguity function (HAF) when the mc-PPS orders exceed three. In the proposed method, the HAF is first applied to the observed mc-PPS to produce a cubic phase signal. Second, the algorithm is modified to estimate the parameters of mc-PPS using the CPF. To obtain accurate estimates of the two highest-order parameters (i.e., a P and a P−1 of each component), all possible a P and a P−1 must be obtained in this step in all combinations of the instantaneous frequencies; then, the maximum absolute value of all sum values must be identified by dechirping with all possible a P and a P−1 . In addition, non-uniformly-spaced signal sample methods are used to employ fast Fourier transformation in the CPF. The proposed method is different from the PCPF–HAF method proposed by other researchers; it is referred to as the improved PCPF–HAF method and can remedy the shortcomings of the traditional method when estimating mc-PPS parameters. Additionally, the PCPF–HAF method cannot be used to treat multicomponent third-order polynomialphase signals, but the proposed method can treat them using non-uniformly-spaced signal sample methods. The cross-terms can also be restrained more effectively than with the CPF, resulting in higher accuracy of the estimated parameters and a lower signal-to noise ratio threshold. Theoretical analysis and simulations are presented to support these claims. Keywords Multicomponent polynomial phase signals (mc-PPSs) · Parameter estimation · High-order ambiguity function (HAF) · Product cubic phase function (PCPF) · Non-uniformly spaced signal sample
1 Introduction Polynomial-phase signals (PPSs) are applied in various fields including radar, sonar, biomedicine, and radio communications (Simeunovi´c and Djurovi´c 2016; Deng et al. 2016; Rakovi´c et al. 2017; Jing et al. 2018; Peleg and Friedlander 1995; Xin and Liao 2017). Numer-
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Guojian Ou [email protected] Chongqing College of Electronic Engineering, Chongqing 401331, China
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Multidimensional Systems and Signal Processing
ous theories and methods involving the parameter estimation of mono-component PPSs have been proposed throughout the last two decades (Djurovi´c and Stankovi´c 2012, 2014, 2015; O’Shea 2002; Simeunovi´c and Djurovi´c 2011; Ou et al. 2019; Djurovi´c et al. 2018; Cao et al. 2018; Djurovi´c 2017; McKilliam et al. 2014; O’Shea 2012; Deng et al. 2016; Wang et al. 2015). Among them, the most popular is the high-order ambiguity function (HAF) method, a phase differentiation (PD) technique that decrements the order of the polynomial
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