基于k分辨FB级数展开的多分量LFM信号分离

Multi-component LFM Signal Separation Based on k-FB Series Expansion

针对傅里叶-贝塞尔变换(FBT)难以估计和有效分离多分量LFM信号的问题,提出了一种k分辨-FB(k-FB)级数展开结合dechirp的信号分离与估计算法。在FB级数的基础上引入k分辨参数,通过理论推导,得出了信号频率与级数的关系,证明了参数估计精度与k取值正相关。通过解线频调和k-FB级数计算,实现了信号分离重构和参数估计。在不同信噪比、信号功率比和k分辨条件下对信号的分离精度进行了仿真研究,并与基于分数阶傅里叶变换(FrFT)的方法进行了对比。仿真结果验证了算法的有效性。

Aimed at the problems that parameters are very difficult to be estimated and multi-component LFM signals are difficult to be separated by using the Fourier-Bessel transform（FBT）algorithm,a new method based on k-resolution FB（k-FB）series in conjunction with the Dechirp technique is proposed.The k-resolution is introduced into the FB series,and the relationship between the frequency content and the order of k-FB series is derived.Meanwhile,the positive correlation between the k-resolution and the estimation precision is proved.With the Dechirp technique and the k-FB series expansion,multi-component signal separation and parameter estimation are both realized.The performance of the signal separation precision under various SNR conditions with different k-resolution and signal power ratios is simulated.Moreover,aperformance comparison between the proposed method and the traditional fractional Fourier transform（FrFT）based method is also provided.The simulation results show that the method is valid.