Fractional Fourier Transform And Its Application In Communication

The traditional fourier transform describe the signal characteristic of time andfrequency domain, instead of the signal’s characteristic of time-frequency, so people haveproposed a series of new time-frequency analysis theories and methods to deal with thenonstationary signal and fractional fourier transform is one of these. With the proposal ofdiscretization method, fractional fourier transform has begun to be applied incommunications system. Based on the discrete algorithm of Fractional Fourier transformand its application in communications system, this paper mainly studies:Firstly, based on the basic principles and the classic discrete algorithm of fractionalfourier transform, this paper designs a new algorithm of discrete fractional fouriertransform: take CDFT’s fourth power as identity matrix, construct a matrix which isexchangeable with DFT, obtain a new algorithm of discrete fractional fourier transformwith the combination of S matrix and T matrix, and focus on simulation analysis of theapproximation effect of the new discrete algorithm and the continuous fractional fouriertransform.Secondly, separate the signal and noise in fractional fourier transform domain. Formixed-signal with multiple chirps, by masking the strong energy chirp in the fractionalFourier domain to reduce the its impact on the weak component signal, and ultimatelycarry out the detection of the weak component signal.Then, studies the OFDM system based on fractional fourier transform and offer thealgorithm of the optimal fractional Fourier transform power and adopts minimum meansquare error to equal the receiving signal in the fractional fourier domain, and focuses onBER of the OFDM system based on fractional fourier transform and that of the traditionalOFDM system under three kinds of time-varying channel environment.Finally, in OFDM system based on fractional fourier transform, introduce a simpletime-varying channel estimation algorithm: in the transmitter take chirp sequence insteadof the traditional PN sequence as the pilot sequence and obtain time-varying channelinformation using in the receiver by harmonicwave recovery.