Adaptive windowed cross Wigner-Ville distribution as an optimum phase estimator for PSK signals

Cross time-frequency distribution (XTFD), unlike the quadratic time-frequency distribution (QTFD), can represent phase information for phase shift keying (PSK) signals such as binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK). However, it suffers from interference due to duplicated terms that cause inaccuracy in the phase estimate. Thus, a time-dependent lag window is proposed in this article where the window width is adaptively adjusted according to the localized lag autocorrelation function (LLAC). This adaptive windowed cross Wigner-Ville distribution (AWXWVD) is proven capable to remove most of the duplicated terms. The instantaneous information bearing phase (IIB-phase) is then estimated from the peak of the cross time-frequency representation (XTFR). Simulation results show that the AWXWVD is an optimum phase estimator as it meets the Cramer-Rao lower bound (CRLB) at SNR>=5 dB and SNR>=6 dB for BPSK and QPSK signals respectively. The AWXWVD also outperforms the conventional IQ demodulator as a phase estimator with difference in the IIB-phase variance of about 5 dB.

[1]  Jo Lynn Tan,et al.  Adaptive Optimal Kernel Smooth-Windowed Wigner-Ville Distribution for Digital Communication Signal , 2008, EURASIP J. Adv. Signal Process..

[2]  Boualem Boashash,et al.  A methodology for detection and classification of some underwater acoustic signals using time-frequency analysis techniques , 1990, IEEE Trans. Acoust. Speech Signal Process..

[3]  Boualem Boashash,et al.  Time-Frequency Distributions Based on Compact Support Kernels: Properties and Performance Evaluation , 2012, IEEE Transactions on Signal Processing.

[4]  Jiří Jan,et al.  Digital signal filtering, analysis and restoration , 2000 .

[5]  Boualem Boashash,et al.  Time-Frequency Signal Analysis and Processing: A Comprehensive Reference , 2015 .

[6]  Boualem Boashash,et al.  Use of the cross Wigner-Ville distribution for estimation of instantaneous frequency , 1993, IEEE Trans. Signal Process..

[7]  E. Krouk,et al.  Modulation and Coding Techniques in Wireless Communications , 2011 .

[8]  Soo-Chang Pei,et al.  Modulation signal classification by the Wigner distribution , 1987 .

[9]  Antonia Papandreou-Suppappola,et al.  Quadratic Time-Frequency Representations with Scale Covariance and Generalized Time-Shift Covariance: A Unified Framework for the Affine, Hyperbolic, and Power Classes , 1998, Digit. Signal Process..

[10]  Jin Bae Park,et al.  Application of cross time-frequency analysis to postural sway behavior: the effects of aging and visual systems , 2005, IEEE Transactions on Biomedical Engineering.

[11]  Boualem Boashash,et al.  Polynomial Wigner-Ville distributions and their relationship to time-varying higher order spectra , 1994, IEEE Trans. Signal Process..

[12]  William Moran,et al.  Cramer-Rao lower bounds for QAM phase and frequency estimation , 2001, IEEE Trans. Commun..

[13]  Z. Zenn Bien,et al.  A Variable Bandwidth Filter for Estimation of Instantaneous Frequency and Reconstruction of Signals With Time-Varying Spectral Content , 2011, IEEE Transactions on Signal Processing.

[14]  B. Boashash,et al.  Instantaneous frequency estimation using the cross Wigner-Ville distribution with application to nonstationary transient detection , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[15]  Mj Martin Bastiaans.  Time-frequency signal analysis , 2008 .

[16]  Antonia Papandreou-Suppappola,et al.  Time-varying techniques for multisensor signal detection , 2006, IEEE Transactions on Signal Processing.

[17]  V. Sucic,et al.  A separable kernel filter design procedure for signal time-frequency analysis , 2008, 2008 6th International Symposium on Communication Systems, Networks and Digital Signal Processing.

[18]  Ahmad Zuri Shaameri,et al.  Use of the cross time-frequency distribution for the analysis of the class of PSK signals , 2010, International Conference on Computer and Communication Engineering (ICCCE'10).

[19]  Walter Fischer,et al.  Digital Video and Audio Broadcasting Technology: A Practical Engineering Guide , 2008 .

[20]  Bijan G. Mobasseri,et al.  Digital modulation classification using constellation shape , 2000, Signal Process..

[21]  Boualem Boashash,et al.  Analytic signal generation-tips and traps , 1994, IEEE Trans. Signal Process..

[22]  Guillaume Gelle,et al.  Time varying higher order statistics for FM signals analysis and decision , 2004, Digit. Signal Process..

[23]  Yu Huang,et al.  Time-Frequency Representation Based on an Adaptive Short-Time Fourier Transform , 2010, IEEE Transactions on Signal Processing.

[24]  William G. Cowley,et al.  Phase and frequency estimation for PSK packets: bounds and algorithms , 1996, IEEE Trans. Commun..

[25]  Mostefa Mesbah,et al.  IF estimation for multicomponent signals using image processing techniques in the time-frequency domain , 2007, Signal Process..

[26]  Jin Jiang,et al.  Time-frequency feature representation using energy concentration: An overview of recent advances , 2009, Digit. Signal Process..

[27]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.

[28]  Giulio Colavolpe,et al.  On the Cramer-Rao bound for carrier frequency estimation in the presence of phase noise , 2007, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[29]  T. Thayaparan.  Time-Frequency Signal Analysis , 2014 .

[30]  Jiri Jan.  Digital Signal Filtering, Analysis and Restoration (Telecommunications Series) , 2000 .

[31]  P. S. Moharir,et al.  A Signal-Dependent Evolution Kernel for Cohen Class Time-Frequency Distributions , 1998, Digit. Signal Process..

[32]  Pradip Sircar,et al.  A new technique to reduce cross terms in the Wigner distribution , 2007, Digit. Signal Process..

[33]  Boualem Boashash,et al.  Note on the use of the Wigner distribution for time-frequency signal analysis , 1988, IEEE Trans. Acoust. Speech Signal Process..

[34]  Boualem Boashash,et al.  Optimisation algorithm for selecting quadratic time-frequency distributions: performance results and calibration , 2001, Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467).

[35]  Ljubisa Stankovic,et al.  Performance of quadratic time-frequency distributions as instantaneous frequency estimators , 2003, IEEE Trans. Signal Process..

[36]  Jo Lynn Tan,et al.  Adaptive optimal kernel smooth-windowed Wigner-Ville bispectrum for digital communication signals , 2011, Signal Process..

[37]  Boualem Boashash,et al.  Adaptive instantaneous frequency estimation of multicomponent FM signals using quadratic time-frequency distributions , 2002, IEEE Trans. Signal Process..

[38]  Ahmad Zuri bin Sha'ameri.  Analysis of HF data communication signals using the lag-windowed Wigner-Ville distribution , 2001, ISSPA.

[39]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. II. A/lgorithms and applications , 1992, Proc. IEEE.

[40]  J. Drake,et al.  Cramer-Rao bounds for M-PSK packets with random phase , 1999, ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359).

[41]  Boualem Boashash,et al.  Use of the cross polynomial Wigner-Ville distribution for instantaneous frequency estimation of non-linear FM signals , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.