Fast Algorithm Research Of Parameters Estimation Of The LFM Signal Based On The Fractional Fourier Transform

The LFM (linear frequency modulated signal) which is widely used in radar communications, and seismic survey system is a typical non-stationary signal, and its parameter estimation problem is more complex than the general stationary signal.For its processing, the time-frequency tools is the most direct and effective mean. The fractional Fourier transform which can be understood as the decomposition of the linear frequency modulation is a special case of Frequency transforms, and it will not produce cross terms when dealing with multi-component, so it has been widely applied in the estimation of the parameters of the LFM signal. The parameters estimation of LFM signal based on the traditional fractional Fourier transform needs two-dimensional searching throughout the whole time-frequency plane, in which the large amount of computation is not suitable for real-time processing, so it’s of great significance and practical value to look for a rapid and easy algorithm of the good performance.In this paper, we use the fractional Fourier transform and other optimization algorithms to explore and research LFM Parameter Estimation Fast Algorithm. The paper is as follows:1. First, the basic definitions and properties of fractional Fourier transform are expounded, and then the sampling algorithm of the discrete fractional Fourier transform algorithm is emphatically introduced, namely Ozaktas sampling algorithm and Pei sampling algorithm. Based on the both models, the LFM signal parameter estimation theory model is obtained.We also introduce a special kind of discrete fractional Fourier transform, which is single point fast calculation method of FRFT (SP-FRFT), and verify its performance by simulation.2. The factors which influence the estimation accuracy when using the fractional Fourier transform to estimate the parameters of the LFM signal are analyzed. Under the premise of getting the initial tone frequency by delay-phase multiplication, this paper combine optimum seeking method and the fractional Fourier transform to improve the precision of parameter estimation and reduce the amount of search operation. The simulation results show the feasibility of this method.3. For the cross terms in Parameter Estimation of Multicomponent LFM Signals, the Product High-order Ambiguity Function method (PHAF method) and the Fractional Fourier Domain filtering technology are employed to separate the multi-component signals. Based on this, we use the simplex method to search on the time-frequency plane around peak value in order to achieve the purpose to improve parameter estimation accuracy. Theoretical analysis and simulation results show that this method can effectively detect various signal components and is of a certain practical value.