Keystone transformation of the Wigner–Ville distribution for analysis of multicomponent LFM signals

Signal detection and parameter estimation for mono- and multicomponent linear frequency modulation (LFM) signals are studied by using the keystone transform of the Wigner–Ville distribution (WVD). The keystone-Wigner transform (KWT) introduces a weight factor containing a range of chirp rate into the time-lag instantaneous autocorrelation function and uses a one-dimensional (1-D) interpolation of the phase which we call keystone formatting. The proposed processing eliminates the effects of linear frequency migration (i.e., the frequency linearly varies along the time axis) to all the signal components even if their chirp rates are unknown. The Fourier transform (FFT) over the time variable to results of the KWT make the power of multicomponent LFM signal concentrated as the locations corresponding to their parameters. Furthermore, the KWT can be efficiently implemented using only complex multiplications and FFT based on the scaling principle instead of interpolating. The computational complexity of KWT is O(4N2log2N). Performance analysis is presented by using the perturbation method and verified by simulation results. Finally, the effectiveness of the KWT is validated by a real application example.