Study On Algorithms Of Polynomial Phase Signal And Cyclostationary Signal Processing

The main study objects of modern signal processing are non-linear, non-Gaussian and non-stationary signals. Among them, the development of non-stationary signal processing has attracted increasingly more attention in signal processing society. Around the non-stationary signal analysis and processing, the proposed theory and algorithms are so rich, the development trend is so fierce and the application fields are so wide that those are unprecedented in the history of signal and information processing disciplines. Therefore, the non-stationary signal processing has been a main subject in signal and information processing fields.Two conventional non-stationary signals, polynomial phase signal and cyclostationary signal, are studied in this thesis. The concrete subjects involve the parameter estimation of polynomial phase signal, array signal processing based on the second-order cyclostationarity, the stationary representation of a cyclostationary signal and so on. Specifically, this thesis completes the following tasks.(1) Present a novel algorithm to estimate the parameters of a quadratic frequency modulated (QFM) signal based on the fractional Fourier transform (FRFT). The proposed algorithm transforms the QFM signal into the linear frequency modulated (LFM) signal by means of the instantaneous correlation function, and then the parameter estimation of the QFM signal is performed by the FRFT arid dechirping method. In order to study the effects of delay parameter on the estimated performances, we derive the asymptotic mean square error (MSE) expressions for all the estimated parameters using a first-order perturbation analysis, and give out the criteria for selecting delay parameter. The results of statistical analysis and simulations show that the estimated MSEs can approximate the Cramer-Rao lower bounds (CRLBs) by the reasonable choice of delay parameter at high SNR. Furthermore, due to only second-order nonlinearity involved, the proposed algorithm has lower SNR threshold. Extension to the multicomponent and higher order frequency modulated signals is also discussed.(2) Propose an adaptive method to calculate discrete fractional Fourier transform and estimate the parameters of multi-component LFM signals. Through the discrete sampling of continuous inverse fractional Fourier transform, a discrete form for numerical calculation is obtained, and then an adaptive filter is constructed with the appropriate choices of the input vector and the desired sequence. The weight vector of the adaptive filter is trained according to least mean square (LMS) algorithm, and the stable weight vector is just the result of discrete fractional Fourier transform (DFRFT). And then, the convergence condition of the proposed algorithm is pointed out through theoretical analysis. Subsequently, we apply the proposed algorithm to estimate the parameters of the multi-component LFMs. The simulation results show that the proposed algorithm can be used to calculate DFRFT and to detect and estimate parameters of LFM signals and the delay of calculation is relatively small.(3) Study on the parametric model respresentation of a cyclostationary signal and propose a novel method to obtain the periodically moving average parametric model from the harmonic series representation (HSR) of a cyclostationary signal. Firstly, the joint stationary random process in the HSR is represented by moving average parameter model and then a periodically moving average parametric model is modeled by using the periodicity of harmonic signal. Lastly, the consistency between the two models is illustrated by the simulations. The theoretical analysis and simulation results show that periodically moving average parameter model can be obtained from the HSR of a cyclostationary signal in certain accuracy.(4) Study on the basic algorithms of the array signal processing for narrowband cyclostationary signal inputs. Firstly, propose a novel adaptive beamforming algorithm based on cyclic least mean square (CLMS) algorithm. Since the performances of traditional beamformer based on the LMS algorithm will deteriorate in the case of the cyclostationary signal inputs, this thesis proposes to construct a novel cost function by averaging the mean square error according to the cyclic period of the inputs and optimizes the cost function by the LMS algorithm. And then, the convergence performances of the proposed algorithm are analyzed. The simulation results indicate that the performances of the proposed algorithm are better than those of the traditional algorithms since the cyclostationarity is considered in the proposed algorithm. Meanwhile, in order to improve the estimation precision of cyclic ESPRIT algorithm, this thesis extends the method to choose the frequency for evaluating the steering vector used in improved cyclic MUSIC algorithm to form an improved cyclic ESPRIT algorithm. Sequentially, a simple array configure is used for joint elevation angle and azimuth angle estimations. Simulation results show that, comparing with the classic ESPRIT algorithm, the improved algorithm is able to perform signal selective direction of arrival estimation and improves the estimation performance greatly; comparing with classic cyclic ESPRIT algorithm, the estimation precision is also improved in some manner.