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
- 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).
- F. Berizzi, G. Corsini, F.Gini, "A HOS based algorithm for autofocusing
of spotlight SAR images," Electronics Letters (to appear,
1997).
- 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).
- 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).
- 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).
- 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).
- F. Gini, "Estimation Strategies in the Presence of Nuisance
Parameters,"
Signal Processing, vol. 55, No. 2, pp. 241-245, 1996.
- 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.
- 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.
- 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.
- 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.
- 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