Research On Adaptive Filter For LFM Signal Based On FRFT

Adaptive filtering algorithm was widely used in adaptive signal processing. It wasconcerned by most people, because it had the characteristic of keep trace the change of signalenvironment, so it was suitable for processing non-stationary signals. The LFM signal wasrapidly development in recent years, it was widely used in various engineering, LFM signalsbased on fractional Fourier transform was highly concerned. LFM signal had the advantage ofexcellent frequency focusing in the fractional Fourier domain, so it made LFM signals to getbetter analysis results in fractional Fourier domain. Therefore, the article researched adaptivefiltering based on non-stationary signal in fractional Fourier transform domain. There weresome deep discussion and research of signal filtering and filtering algorithm in the fractionalFourier domain. The content and innovation as follows:1. According to the principles of the traditional LMS algorithm, this paper analyzed thecharacteristic and application of LMS algorithm in various transform domain. The paperfocused on the characteristics of adaptive filtering in fractional Fourier transform domain, andrealized the adaptive LMS filtering, it also showed performance analysis.2. LFM signal had a good focus with time and frequency in the fractional Fourier domain,This article used the feature to achieved adaptive filtering in FRFT domain, it made someimprovement relative to the traditional LMS algorithm. Adaptive step was introduced alimiting factor, so the improved step size FRFT-LMS algorithm was proposed based on FRFT.This algorithm solved the contradiction between convergence rate and steady-state offsetamount. The simulation results show that this algorithm has better filtering effect thantraditional LMS algorithm in the fractional Fourier domains.3. The paper presented the convex combination LMS algorithm (FRFT-CLMS) infractional Fourier domain. Convex combination algorithm is a novel method of combinationfilter, it has emerged in recent years, it had been overcame the deficiencies of the traditionalsingle filter, it solved the contradiction between the convergence speed and steady-state error.The paper utilized this filter characteristic and time-frequency analysis of fractional Fouriertransform, it achieved adaptive LMS convex combination filtering of the LFM signal infractional Fourier domain. For inherent CLMS algorithm, the adaptive step size is fixed in the entire system, so thesemade filter algorithm high accuracy requirements to error and output items. As a result, it hadnot good filtering performance in strong noise environment. Improved FRFT-CLMSalgorithm has been proposed, it combined the improved FRFT-LMS algorithm with a fastfilter, it deal well with the problem between the convergence rate and steady-state error, it wasflexible in the filtering process, the adaptive step adapt the change of system environment atany time, it reduced the dependence of the joint parameter to traditional CLMS algorithm.