Adaptive Optimal Kernel Smooth-Windowed Wigner-Ville Distribution for Digital Communication Signal

Time-frequency distributions (TFDs) are powerful tools to represent the energy content of time-varying signal in both time and frequency domains simultaneously but they suffer from interference due to cross-terms. Various methods have been described to remove these cross-terms and they are typically signal-dependent. Thus, there is no single TFD with a fixed window or kernel that can produce accurate time-frequency representation (TFR) for all types of signals. In this paper, a globally adaptive optimal kernel smooth-windowed Wigner-Ville distribution (AOK-SWWVD) is designed for digital modulation signals such as ASK, FSK, and M-ary FSK, where its separable kernel is determined automatically from the input signal, without prior knowledge of the signal. This optimum kernel is capable of removing the cross-terms and maintaining accurate time-frequency representation at SNR as low as 0 dB. It is shown that this system is comparable to the system with prior knowledge of the signal.