The concise fractional Fourier transform and its application in detection and parameter estimation of the linear frequency-modulated signal

A concise fractional Fourier transform （CFRFT） is proposed to detect the linear frequency-modulated （LFM） signal with low signal to noise ratio （SNR）. The frequency axis in time-frequency plane of the CFRFT is rotated to get the spectrum of the signal in different an- gles using chirp multiplication and Fourier transform （FT）. For LFM signal which distributes as a straight line in time-frequency plane, the CFRFT can gather the energy in the corresponding angle as a peak and improve the detection SNR, thus the LFM signal of low SNR can be de- tected. Meanwhile, the location of the peak value relates to the parameters of the LFM signal. Numerical simulations and experimental results show that, the proposed method can be used to efficiently detect the LFM signal masked by noise and to estimate the signal＇s parameters accurately. Compared with the conventional fractional Fourier transform （FRFT）, the CFRFT reduces the transform complexity and improves the real-time detection performance of LFM signal.

脉冲噪声下基于Sigmoid的LFM信号参数估计

由于脉冲噪声具有的短时大幅值特性,使得基于高斯假设的信号参数估计方法无法在脉冲噪声环境下有效估计参数。针对此问题,利用α稳定分布模拟随机脉冲噪声,提出了一种基于Sigmoid-CFRFT的LFM信号参数估计方法。首先,建立了一种自适应Sigmoid函数,证明了信号经过此非线性变换后,信号的2阶矩由无界变为有界,且信号的相位信息保持不变。其次,将变换后的信号进行离散时间CFRFT,建立了数学优化模型,并使用水循环算法搜索最优值点。最后,利用了非标准SαS分布噪声的修正方法,分析了标准和非标准分布下参数估计的性能。仿真结果说明,所提方法不仅可以有效抑制脉冲噪声对LFM信号分数谱特征的影响,而且能够实现低信噪比信号参数的高精度估计。相比于现有的基于非线性变换的参数估计方法,本文方法具有更好的精度,稳定性和噪声鲁棒性。

海面小目标分数域检测快速算法

针对海杂波背景下小目标检测困难的问题,为解决传统分数阶傅里叶变换(FRFT)算法检测性能不稳定、运算量大、检测效率低等问题,提出新的海杂波中小目标检测快速新算法。利用CEMD-RobustICA去噪算法抑制海杂波,减小海杂波对双正交傅里叶变换(BFT)与简明分数阶傅里叶变换(CFRFT)性能的影响,通过BFT-CFRFT算法进行小目标检测,将传统算法的二维搜索转换为两次一维搜索,大幅减小了运算量。利用IPIX实测数据验证新算法,实验结果表明:新算法有效抑制了海杂波,且大大减小了检测运算量,提高了目标检测准确性与时效性,并且在HH极化条件下检测性能最好。新算法检测效率高,性能稳定,有利于在实际工程中广泛应用。