LFM信号参数估计的插值FRFT算法

提出了一种基于分数阶傅里叶变换（fractional Fourier transform, FRFT）的线性调频（linear frequency modulation, LFM）信号参数估计的插值算法。首先针对FRFT的旋转角度α搜索步长问题,提出了在较大搜索步长下进行插值以得到α精估计的方法;然后针对离散分数阶傅里叶变换(digital fractional Fourier transform, DFRFT)因参数u离散化而造成的栏栅效应问题,采用相邻谱线进行插值以得到u的精估计;最后用α和u插值精估计结果对单分量LFM信号的参数进行估计。这一方法在不影响估计精度的前提下,降低了计算量和复杂度。仿真结果表明,在较低的信噪比下,LFM信号参数估计的精度仍十分逼近克拉美罗界(Cramer-Rao bound, CRB)。

Parameters estimation of LFM signals by interpolation based on FRFT

An approach for parameters estimation of linear frequency modulation (LFM) signals by interpolation based on fractional Fourier transform (FRFT) is investigated. Firstly, in order to obtain the accurate estimate of α,an interpolation method using coefficients of DFRFT under the condition of a bigger search step is proposed. Then, according to the gate effect problem because of discretization of u,the interpolation on digitalFRFT spectrum lines is also used to improve the estimate accuracy of u. Finally, the results of estimation of αand uare used to estimate the parameters of single component LFM signal. The new interpolation based on FRFTcan reduce the computational complexity, and at the same time, the accuracy of estimation is improved. Simulation resultindicates that the root-mean-square error of parameter estimation is still approaching the Cramer-Rao bound (CRB) under the condition of low signal-to-noise ratio (SNR).