Adaptive cross wigner-ville distribution for parameter estimation of digitally modulated signals

Abstract

Spectrum monitoring is important, not only to regulatory bodies for spectrum management, but also to the military for intelligence gathering. In recent years, it has become part of spectrum sensing process which is the key in cognitive radio system. Among the features of a spectrum monitoring system is to obtain spectrum usage characteristics and determining signal modulation parameters. All these required a powerful signal analysis technique suitable for use with classifier network. The loss of phase information in the Quadratic Time–Frequency Distributions (QTFDs) makes it an incomplete solution as Phase Shift Keying (PSK) modulation is widely employed in many wireless communication applications nowadays. Therefore, Cross Time–Frequency Distribution (XTFD) which can provide localised phase information is proposed in this research. The Adaptive Windowed Cross Wigner– Ville Distribution (AW–XWVD) and Adaptive Smoothed Windowed Cross Wigner– Ville Distribution (ASW–XWVD) are developed to analyse a broader class of signals such as PSK, Quadrature Amplitude Modulation (QAM), Amplitude Shift Keying (ASK) and Frequency Shift Keying (FSK) signals without any prior knowledge. In non–cooperative environment, two kernel adaptation methods are proposed: local and global adaptive. The developed XTFD is proven to be an efficient estimator as it meets the Cramer–Rao Lower Bound (CRLB) for phase estimation at Signal-to- Noise Ratio (SNR) =4 dB and Instantaneous Frequency (IF) estimation at SNR =–3 dB. Other TFDs such as the S–transform never meet the CRLB in both phase and frequency estimation. A complete signal analysis and classification system is implemented by combining the AW–XWVD and ASW–XWVD for signal analysis. In the presence of Additive White Gaussian Noise, the classifier gives 90% correct classification for all the signals at SNR of about 6 dB. Thus, it has been demonstrated that the XTFD is a complete solution for the analysis and classification of digitally modulated signals.