IF estimation of FSK signals using adaptive smoothed windowed cross Wigner–Ville distribution

• We analysed the characteristics of Frequency Shift Keying (FSK) signal in the time–lag domain.
• We designed an appropriate kernel function for FSK signals to generate accurate cross TFR.
• Instantaneous frequency is estimated from the peak of the TFR.
• The cross time–frequency distribution proposed meets the Cramer–Rao lower bound at SNR of −3 dB and outperforms the S-transform.
• The proposed method is tested in real digital communication applications.

Time-varying signals such as frequency shift-keying (FSK) signals can be characterized by the instantaneous frequency (IF). From the estimated IF, it is possible to derive the signal modulation parameters such as the subcarrier frequencies and the symbol duration. If accurate time–frequency representation (TFR) is obtained, the cross time–frequency distribution (XTFD) provides an optimum solution to IF estimation over quadratic time–frequency distribution (QTFD). Thus, an adaptive XTFD is proposed, the adaptive smoothed windowed cross Wigner–Ville distribution (ASW-XWVD), for which the kernel parameters are estimated according to the signal characteristics and the choice of reference signal. The IF is estimated from the peak of the TFR and comparison is performed using the S-transform. The variance in the IF estimation using the proposed ASW-XWVD meets the Cramer–Rao lower bound (CRLB) at minimum signal-to-noise ratio (SNR) of −3 dB, while the S-transform never meets the CRLB, even at SNR of 12 dB. For practical applications, the ASW-XWVD is applied to the FSK signal in the high frequency (HF) band and is able to provide accurate TFR and IF estimates at SNR of 14 dB.