Parameter Estimation Of LFM Signal In The Fractional Fourier Domain Via Curve-Fitting Optimization Technique

Linear FM signals (LFM signal), as a special kind of non-stationary signal, has been widely used in many applications, such as communication, radar, sonar and seismic survey systems. The detection and parameter estimation problem has become a hot research spot in recent years.Fractional Fourier transform(FrFT), as a generalization of the Fourier transform, can be regarded as a counterclockwise rotation of the signal coordinates around the origin in the time-frequency plane. The FrFT is a 1-D linear transform. Therefore, the cross-terms interference can be avoided when multiple signals exist. The conventional parameter estimation of LFM signal based on Fractional Fourier Transform is not capable of real-time detection due to a considerable computation burden in the two-dimensional peak searching. The algorithm applicated with curve fitting method can retain the high estimation accuracy and also greatly reduce the computational complexity at the same time. The specific content is as follows:1,The paper introduces the definition and properties of Fractional Fourier transform, and mainly introduces some discrete Fourier algorithm with high practical value and commonly used in many fields. The theories of parameter estimation based on two kinds of discrete FrFT algorithm are deduced. Then this paper analysis the advantages and disadvantages which exists in the problem of parameter estimation of LFM signal in Fractional Fourier domain.2,To solve the problem of peak deviation estimate in the parameter estimation of Linear Frequency Modulated signal based on the Fractional Fourier Transform with the method of two-dimensional research, an algorithm is proposed to approximate the projection of discrete FrFT modular detector with various orders by using moving least-squares curve fitting method and precisely estimate the value of curve peak. Theoretical analysis and simulation results show that it can retain the high estimation accuracy and also greatly reduce the computational complexity at the same time.3,For multi-component parameter estimation problem, separate the multi component signal by establish the high order statistics function of FrFT modulus detector firstly. It can strengthen the signal components in low SNR environments. Secondly, according to the nonlinear least squares theory, the paper further introduces a Gaussian mixture model (GMM) to approximate the distribution of FrFT modular detector. Theoretical analysis and simulation results show that the method can separate the signals and estimate the LFM signals accurately. Moreover, it is verified that it is possible to make real-time detection for the LFM signal based on FrFT and put it into wide application fields.