Time-Frequency-Based Signal Detection Methods And Their Application In Spectrum Monitoring

Since 1807 Fourier invented Fourier transform, spectrum analysis has become one of the most important tools in signal processing. However, the traditional spectrum analysis has some shortcomings in analyzing a time-varying signal whose spectral contents are changing in time. It can not tell us when the individual frequency components of a signal occur. Therefore, one started with the study of the representations of a time-varying signal by joint time-frequency analysis (TFA). In last several decades, the study of TFA has a large development. Various methods of TFA are presented, and the theories become perfact day and day. TFA which can characterize signals in joint time-frequency (TF) domain has become one of the powerful tools of time-varying signal analysis. Two important methods of TFA are Cohen's class and Gabor spectrogram (GS). Chirp is one of typical time-varying signals. As chirp is widely used in radiodetermination service, such as radar, chirp detection becomes the focus of study. Many methods of chirp detection are presented. One of the methods is discrete chirp-Fourier transform (DCFT) that analyzes chirp signal in chirp rate-frequency (CF) domain. This dissertation mainly studies the detection and analysis methods of time-varying signals based on TFA and applications in radio spectrum monitoring. The main contents are as follows.(1) Study of the Basic Problems in TFA. The basic problems and theories in TFA are discussed. It mainly include the design methods, basic properties and limitations in Cohen's class, the effect of cross term and TF concentration on signal analysis, and the method and its merits of the adaptive optimal-kernel (AOK). Moreover, the fast algorithm, period property, anti-aliasing method and computational complexity of the discrete time-frequency distribution (DTFD) are studied.(2) Removing Cross-terms from Wigner Distribution via Thresholding Multiple Spectrograms. It is well known that Wigner distributions (WDs) of multicomponent signals suffer from serious cross-terms, although they achieve the best TF concentration and have many good mathematical properties. The traditional methods for cross-term suppression in WDs rely on two-dimensional lowpass filtering in the ambiguity function domain. According to the special cross-term mechanism of spectrograms that their cross-terms always appear the intersection regions of two auto-term's supports in the TF domain, a new method is proposed to remove the cross-terms in WDs and to preserve the TF concentration of the auto-terms of individual signal components. This method is based upon the efficient estimation of the auto-term supports in the WDs. First, a set of signal's spectrograms with Gaussian linear chirp windows (GLCWs) along different TF directions are calculated and the support set in each spectrogram is estimated by thresholding and morphological filtering. And then the intersection set of all the estimated support sets is used as the auto-term support set of the WD. By restricting the WD on this set, a new TFD is obtained in that most the cross-terms in the WD are removed while the auto-terms are almost unchanged. Moreover, the joint resolution power of a set of spectrograms with GLCWs is discussed in detail.(3) Modified Gabor Spectrogram Method. GS is one of TFDs different from Cohen's class. A signal can be decomposed into Gabor elementary functions on the TF sampling lattice, i.e., Gabor elementary functions are the time-shifted and harmonically modulated versions of an elementary signal. GS is the sum of the WDs of individual Gabor elementary functions. As the order of GS increases, GS has a better TF concentration and more serious cross-terms. Considering the special mechanism of the spectrograms in that the cross-terms always appear in the intersection regions of two auto-term supports, we restrict GS on the supports of Gabor coefficients which are the sampling form of spectrogram. As a result, a new modified Gabor spectrogram (MGS) is obtained. MGS has a better concentration and suppress cross-terms. Compared with GS, the MGS have three merits. First, the computational cost is reduced greatly. Second, MGS is effective in suppressing cross-terms while retaining the good TF concentration of auto-terms. Third, the TF resolution capability and concentration are improved by high order operation while no serious cross-terms are introduced.(4) Multi-component Chirp Detection Method via Circularly Shifting DCFT. The Discrete Fourier Transform (DFT) has circular shift properties. Similarly, the DCFT motivated by DFT also has circular shift properties. According to the definition of DCFT, the theorems of the circular shift of DCFT are proposed. Based on the theorems, a new method to detect chirp and estimate chirp rate is proposed which utilities not only the chirp characteristic but also the noise characteristic, i.e., chirp rates and initial frequencies of chirp are invariant in time whereas chirp rates and initial frequencies of noise are random in time. The method has a better performance of chirp detection in low signal-to-noise ratio (SNR) environments. Moreover, the relationship of signal energy in time domain and CF domain is proposed. That is, the energy is not preserved in the two domains but only held both in time domain and DCFT domain along linear frequency direction. According to the energy relationship, the characteristics of noise in CF domain are discussed.(5) Applications of TFA in Spectrum Monitoring. The development of spectrum monitoring in the future and applications of TFA in spectrum monitoring are discussed. The applications of TFA in spectrum monitoring mainly include two aspects: digital modulation classification and spectrum monitoring. On the digital modulation classification, the linear component of instantaneous phase and phase upwrapping of communication signals are studied. According to the sense of the least mean square error (LMSE), the method of removing linear component of phase is proposed. A new feature separate phase modulation from unphase modulation is suggested and a simple decision tree classifier based on feature is built up. The method suitable to various pulse shaping filters, roll-off factors and symbol rates. On the spectrum monitoring, spectrum occupy based on spectrogram is studied, and spectrum monitoring is discussed. Some application in real world and experiments result are given out.