基于改进精估计与FrFT的Chirp信号参数估计

Chirp Signal Parameter Estimation Based on Improved Accurate Estimation and FrFT

为了解决Chirp信号参数估计在低信噪比下保持高精度等问题,提出了一种基于粗精二次估计的Chirp参数算法。粗估计采用分数阶傅里叶变换(Fractional Fourier Transform,FrFT),能够在低信噪比下检测到Chirp信号并估计出调频率的范围。同时,提出了一种FrFT插值算法提高FrFT估计中心频率的精度。精估计根据信号能量和周期长度一定时Chirp信号频谱幅度的平方与调频率成反比的特性,不断地用已知Chirp信号的共轭与未知Chirp信号相乘,寻找使相乘后频谱幅度平方最大的已知Chirp信号的调频率。为了提高精估计算法性能,用提出的H-Rife算法估计中心频率和相乘后信号的频谱中最大的幅值。用二分法代替等步长使精估计在粗估计出的调频率范围内搜索,极大降低了复杂度。在信噪比不小于-10 dB时,该算法估计调频率归一化均方误差(Normalized Mean Square Error,NMSE)较FrFT线性提升,估计中心频率NMSE较FrFT线性提升,接近克拉美罗界。

In order to solve the problem that the Chirp signal parameter estimation maintains high precision under low signal-to-noise ratio(SNR),a rough and accurate Chirp parameter estimation algorithm is proposed.The rough estimation uses fractional Fourier transform(FrFT)to detect the Chirp signal and estimate the range of the modulation frequency at a low SNR.An FrFT interpolation algorithm is proposed to improve the accuracy of center frequency than FrFT.Accurate estimation is based on the fact that the square of the spectral amplitude of the Chirp signal is inversely proportional to the modulation frequency when the signal energy and the period length are not varying.The conjugate of the known Chirp signal is multiplied by the unknown Chirp signal to find the largest square of the spectral amplitude after multiplication.In order to improve the performance of the accurate estimation algorithm,the proposed H-Rife algorithm is used to estimate the center frequency and the amplitude of the multiplied signal spectrum.The dichotomy instead of the equal step size is used to make the accurate estimation to be searched within the coarsely estimated frequency range,thus greatly reducing the complexity.When the SNR is not less than-10 dB,the modulation frequency normalized mean square error(NMSE)and center frequency NMSE estimated by the proposed algorithm are linearly improved compared with FrFT.The latter is close to Cramér-Rao lower bound(CRLB).