Parameter Estimation of LFM Signal by Direct and Spline Interpolation Based on FrFT
An important cause of performance loss in parameter estimation of linear frequency modulation (LFM) signal based on Fractional Fourier Transform (FrFT) is the “picket fence effect” because of the discretization of FrFT. In this work, a direct and spline i
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Parameter Estimation of LFM Signal by Direct and Spline Interpolation Based on FrFT Jun Song and Yunfei Liu
Abstract An important cause of performance loss in parameter estimation of linear frequency modulation (LFM) signal based on Fractional Fourier Transform (FrFT) is the ‘‘picket fence effect’’ because of the discretization of FrFT. In this work, a direct and spline interpolation method, along with a coarse search, is investigated and is used for parameter estimation of LFM signal based on FrFT. In FrFT domain, the parameter estimation of a LFM signal is equivalent to search the peak of the FrFT coefficients. The direct and spline interpolation method, instead of a conventional fine search algorithm, can not only improve the estimation accuracy of the peak coordinate, which leads to a better performance of the LFM parameter estimation, but also save computation load. Performance of the proposed method is analyzed by digital simulations at different signal to noise ratio (SNR) levels, and good performance is achieved. Keywords LFM signal
Parameter estimation FrFT Spline interpolation
5.1 Introduction In this work, we consider the parameter estimation of Linear frequency modulation (LFM) signal. In the recent decades, the fractional Fourier transform (FrFT) is widely used in the parameter estimation for LFM signal because the FrFT can be interpreted as a decomposition to a basis formed by the orthogonal LFM functions.
J. Song (&) Y. Liu Department of Information Science and Technology, Nanjing Forestry University, No.159 Longpan Road, Nanjing, China e-mail: [email protected]
W. Lu et al. (eds.), Proceedings of the 2012 International Conference on Information Technology and Software Engineering, Lecture Notes in Electrical Engineering 210, DOI: 10.1007/978-3-642-34528-9_5, Ó Springer-Verlag Berlin Heidelberg 2013
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J. Song and Y. Liu
Digital FrFT (DFrFT) and Radon-ambiguity transform are employed in [1–3] to estimate the parameters of LFM signal,but the precision of estimation is limited because of the discretization of FrFT. A direct interpolation method based on FrFT is used in [4], and the estimation precision of part parameters of LFM signal is improved at proper signal to noise ratio (SNR) levels, but that of chirp rate can not be improved. DFrFT and quasi-Newton method is introduced in [5], and the precision is perfect. In substance, the method of [5] is based on a coarse search and a nonlinear optimization fine search, so it needs many extra calculations. This paper introduces a direct and spline interpolation method, along with a coarse search, for parameter estimation of LFM signal based on FrFT. The coarse search returns a coarse estimate of the parameters by searching for the maximum DFrFT coefficient of the LFM signal. This coarse estimate can be improved by a fine search algorithm, i.e. that of [5], and some interpolation method. Compare with the fine search algorithm, interpolation method is usually more efficient since they use prior knowledge about the signal. According to th
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