Nonlinear Frequency Modulated Signal Detection Based On FRFT

Nonlinear frequency modulated signals are widely applied in many areas, such as communication, radar, sonar, and earthquake signal processing. In these areas, it is always an important problem to detect unknown nonlinear frequency modulated signals in noise or clutter and to estimate their instantaneous frequency curves. The fractional Fourier transformation (FRFT) is a generalization of the traditional Fourier transformation and it can extract synchronously the information of signals in both the time domain and the frequency domain, suitable to deal with nonlinear and nonstationary signals. For recent three decades, many time-frequency tools like STFT, WVD, wavelet transform and FRFT are developed for detection and parameter estimation of nonlinear and nonstationary signals.In this thesis, we review various time-frequency analysis tools and their relationship with FRFT, and summarize the development and applications of FRFT, including definitions, properties, its applications in detection and parameter estimation. The FRFT transfers a signal in the frequency-chirp rate plane and an unknown nonlinear FM signal demonstrates a curve in the frequency-chirp rate plane. Based upon the feature of signals in the FRFT domain, we propose a new scheme to detect unknown nonlinear FM signals in noise, where the window-based WVD and window-based FRFT are jointly exploited to extract the energy ridge of each signal segment in the WVD and the energy onto all the segments is integrated for signal detection. The experimental results show that the proposed method achieves satisfactory detection performance.Besides, we also discuss the instantaneous frequency curve estimation via the Dechirp transform and the cubic spline interpolation. In the proposed method, signal is first separated into multiple disjoint segments and each segment is regarded as an approximate linear frequency modulated (LFM) segment. Second, the Dechirp transform is used to estimate the center frequency of each segment. Third, through these center frequency points, the cubic spline interpolation is used to obtain the instantaneous frequency curve of the signal. The simulated experiments show that our method can efficiently estimate the IF curve of unknown nonlinear FM signals in not too low signal-to-noise ratios.