Higher Order Statistics and Cyclostationary Signal Analysis

Summary

Processes encountered in radar, sonar, and communications are often assumed stationary. The huge amount of available algorithms testifies to the need for processing and spectral analysis of stationary signals. Nevertheless, signal processing problems dealing with linear non-Gaussian signals, nonlinearities, and nonstationarities, cannot be addressed completely using time-invariant second-order statistical descriptors. Traditional correlation and spectral analysis are currently generalized to higher-order moments, cumulants, and polyspectra. At the same time there is an effort to cope with structured nonstationarities and in particular with cyclostationary processes which are signals exhibiting periodicity in their statistical behavior.

The success of higher order statistics (HOS) based methods depends upon the degree of non-Gaussianity and nonlinearity present in the data. The drawbacks of HOS methods are due to their heavier computational load and increase in the statistical variance of the sample estimators involved. Relatively unexplored areas of HOS research include efficient algorithms for non-linear signals and systems analysis with emphasis on robust estimation methods and potential applications to chaotic time series. Man made communication signals are clearly non-Gaussian, and beyond the already successful HOS based blind equalization, they offer additional areas for research especially in topics related to synchronization, multi-user systems, and sensor arrays.

Cyclostationary processes constitute the most common class of nonstationary signals encountered in engineering. Cyclostationarity appears in signals and systems exhibiting repetitive variations and allows for separation of components on the basis of their cycles. The diversity offered by such a structured variation can be exploited for suppression of stationary noise with unknown spectral characteristics and for blind parameter estimation using single data record. Cyclostationarity appears also with nonlinear systems and certain signals exhibit periodicity in their higher- than second order statistics. Topics of current interest and future trends include algorithms for nonlinear signal processing, theoretical performance evaluation, and analysis of cyclostationary point processes. As far as applications, exploitation of cyclostationarity is expected to further improve algorithms in manufacturing problems involving vibrating and rotating components, and will continue to contribute in the design of single- and multi-user digital communications systems especially in the presence of fading and time-varying multipath environments.

Research topics:

  • Non-Gaussian signal detection and estimation using HOS (with applications to radar &SAR)
  • Cyclostationary signal analysis for radar target classification
  • Synchronization parameters estimation in time-selective and frequency-selective channels
  • Parameter estimation of non-linear FM and polynomial phase signals in non-Gaussian noise
  • Publications

    1. F. Gini, "A Cumulant-Based Adaptive Technique for Coherent Radar Detection in a Mixture of K-Distributed Clutter and Gaussian Disturbance," IEEE Trans. on Signal Processing (to appear, June 1997).
    2. F. Berizzi, G. Corsini, F.Gini, "A HOS based algorithm for autofocusing of spotlight SAR images," Electronics Letters (to appear, 1997).
    3. F. Gini and G. B. Giannakis, "Frequency offset and timing estimation in slowly-varying fading channels: A cyclostationary approach," Proceedings of the 1st IEEE Signal Processing Workshop on Wireless Communications, Paris, France, April 16-18, 1997 (to appear).
    4. F. Gini and G. B. Giannakis, "Generalized differential encoding: A nonlinear signal processing framework," Proceedings of the 1st IEEE Signal Processing Workshop on Wireless Communications, Paris, France, April 16-18, 1997 (to appear).
    5. F. Gini and G. B. Giannakis, "Hybrid FM-Polynomial Phase Signal Modeling: Parameter Estimation and Performance Analysis," Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, Banff, Alberta, Canada, July 21-23, 1997 (to appear).
    6. F. Gini and G. B. Giannakis, "Parameter estimation of hybrid hyperbolic FM and polynomial phase signals using multi-lag high-order ambiguity function," Proceedings of the 31st Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, Nov. 1997 (invited paper).
    7. F. Gini, "Estimation Strategies in the Presence of Nuisance Parameters," Signal Processing, vol. 55, No. 2, pp. 241-245, 1996.
    8. F. Berizzi, G. Corsini, F. Gatti, F. Gini, "Cumulant Based Algorithms for Autofocusing in ISAR/SAR Systems," Proceedings of the 1996 International Conference on Image Processing, Lausanne, Switzerland, September 1996.
    9. F. Gini, M. Luise, R. Reggiannini, "Analysis and Design of a DPSK Optical Heterodyne Receiver in the Presence of Laser Phase Noise and Frequency Detuning," International Journal of Communication Systems, vol.8, pp. 129-141 (1995), by John Wiley & Sons.
    10. F. Gini, L. Verrazzani, "A HOS Technique for Coherent Radar Detection in Mixed Clutter Environment," Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing, Neos Marmaras, Halkidiki, Greece, June 1995.
    11. F. Gini, M. Luise, "Asynchronous Polarization Diversity Receivers for Coherent Optical Communications: A Performance Review," European Trans. on Telecommunications, vol ETT-5, No.3, pp. 307-318, May-June 1994.
    12. F. Berizzi, E. Dalle Mese, F. Gini, G. Pinelli, "An Adaptive Non Linear Filtering Technique for the Initialisation of ISAR Autofocusing Algorithms," Proceedings of the EUSIPCO-94 Conference, Edinburgh, Scotland, U.K., September 1994.

    Contact persons

    Ing. Fulvio GINI

    Dipartimento di Ingegneria dell'Informazione
    Universita` di Pisa
    via Diotisalvi 2 -- 56126 PISA
    Tel. +39-50-568550 Fax +39-50-568522
    email: gini@iet.unipi.it

    Prof. Lucio VERRAZZANI

    Dipartimento di Ingegneria dell'Informazione
    Universita` di Pisa
    via Diotisalvi 2 -- 56126 PISA
    Tel. +39-50-568532 Fax +39-50-568545
    email: lucio@iet.unipi.it