基于新型DFrFT的LFM信号参数估计算法

Parameter estimation algorithm for LFM signal based on new DFrFT

摘要:

针对传统算法对高调频率线性调频(linear frequency modulation,LFM)信号进行参数估计时误差较大的问题,提出了一种基于新型离散分数阶傅里叶变换(discrete fractional Fourier transform,DFrFT)的LFM信号参数估计算法。新型DFrFT在传统离散算法的基础上引入一种新型尺度变换型量纲归一化方法,其归一化因子可随变换阶次的改变自适应变化。基于该新型DFrFT,本文建立了LFM信号参数估计算法的数学模型。首先,通过新型量纲归一化方法对待估计LFM信号进行预处理,将信号由时频域转换至两个无量纲域,再对信号进行DFrFT；然后,利用新型量纲归一化方法的尺度变换特性提升高调频率段的调频率参数估计分辨率,并理论推导了该参数估计算法相较于传统算法调频率的优势区间；最后,在不同调频率与信噪比条件下,对所提算法的有效性进行了仿真验证,并与传统算法进行对比分析。仿真实验结果表明:当待估计LFM信号的调频率较高时,相较于传统算法,新型尺度变换型量纲归一化方法的引入有效提升了本文算法对调频率的估计精度,且在信噪比较高的环境中,其参数估计性能提升更为明显。

Abstract:

To alleviate the problem of large error in the parameter estimation of linear frequency modulation (LFM) signal with high chirp-rates by traditional algorithms, a parameter estimation algorithm of LFM signal was proposed based on a new discrete fractional Fourier transform (DFrFT). A new dimensional normalization method combined with scale transformation was introduced into the DFrFT on the basis of the traditional discrete algorithm, and its normalization factor could change adaptively with the change in the transformation order. Based on the proposed DFrFT, the mathematical model of the parameter estimation algorithm of LFM signal was established. First, the LFM signal to be estimated was preprocessed by the new dimensional normalization method. The signal was converted from time-frequency domain to two dimensionless domains, and then the signal was processed by DFrFT. Next, the resolution of chirp-rate parameter estimation in high chirp-rate band was improved using the scale transformation characteristics of the new dimensional normalization method, and the chirp-rate optimize-range of the parameter estimation algorithm was theoretically deduced in comparison with the traditional algorithm. Finally, the effectiveness of the proposed algorithm was simulated under different chirp-rates and signal-to-noise ratios, and the results were compared with those of the traditional algorithm. Simulation results show that when the chirp-rate of the signal to be estimated was high, the proposed dimensional normalization method could effectively improve the estimation accuracy of the chirp-rate, and the performance improvement was more obvious in the environment of high signal-to-noise ratio.