The Estimation And Application Of Spectral Correlation For Almost Cyclostationary Signal

WSCS(Wide Sense Cyclostationary)processes have been the subject of an increasing number of research papers since the late 1950's, and they have been shown to be appropriate models for a wide variety of physical phenomena. Because of their similarity to stationary processes, cyclostationary processes are more amenable to analysis than nonstationary processes in general.Cyclostatioary signals are time-series whose statistical (average) behavior varies periodically with time. Closely related are almost cyclostationary (ACS) signals with statistical behavior characterized by almost periodic function of time.In many signal processing involving modulated communication signals, the waveforms encountered are appropriately modeled as ACS, and the concept of cyclostationarity has draw more attention in diverse signal processing. Taking the advantage of cyclostationarity, we can select the desired signals at the known cycle frequency and eliminate the interferences and background noise which do not exhibit cyclostationarity or have different cycle frequencies. And this does not require a priori knowledge about the ambient noise environment.Motivated by the growing importance of cyclostationary in signal processing, this dissertation mainly discusses the cyclostationary signal.First,this dissertation presents a new method of cyclic spectra estimation which uses time aliasing method and sidelobe eliminated ssinc(Smooth sinc) window which were presented by Smith in 1994 in it. The relationship between the TA (Time Aliasing) cyclospectrum estimation and the general scheme of cyclic spectrum estimation is also discussed mathematically.This new method makes two great progresses in the estimation of cyclic spectra as follows: One is, the quality of the cyclic spectra is raised excellently by the improvement of effective frequency resolution and the reduction of bias error, and the spectrum peaks can be identified clearly both in cyclic frequency direction and in the spectrum frequency direction. The other is, the burden of calculation is lessened greatly by the time aliasing process. It reduces the quantity of data in DFT, and increases the capability for the real time processing in cyclic spectra estimation.Second, this dissertation analysises the performance of TA cyclospectrum estimation, and derives the averaged cyclic periodogram which can make the variance to be reduced.The bias of cyclic periodogram with ssinc window is analyzed in both spectrum frequency direction and cycle frequency direction, and that the TA cyclic spectrum estimation is unbiased is analyzed. The average method of cyclic periodogram is also derived in terms of STFT. Meanwhile, this dissertation indicates that the variance can be optimistically reduced through the cyclic spectrum estimation with ssinc window. The estimations of cyclic spectrum of the signal which is the sum of two cyclostationary signals are then done by the way of averaged TA cyclic spectrum estimation, and the results show us the spectrum in the spectrum frequency direction is exactly presented at each cycle frequency.Third, this dissertation makes a modification to the periodic-component extraction method presented by Gardner in 1991, and presents a new periodic-component extraction method for cyclostationary signal, which makes use of the cyclic spectrum of FOT (Fraction Of Time) probability.In this dissertation, the FOT probability is analyzed in detail with the knowledge of the probability and the knowledge of the isometric isomorphism of metric space. And this dissertation improves the periodic-component extraction method by the way of cyclic spectrum estimating of the FOT probability instead of the Fourier transformation of the FOT probability which was presented by Gardner in 1991.At last, this dissertation introduces the spectral correlation method into software antenna to identify the number and the direction of multi-path in the environment of frequency-selective fading channel, and to identify the Doppler frequency in the environment of time-selective fading channel.