University of Minnesota

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Applications of Cyclostationarity in Signal Processing and Communications

Modeling and estimation problems involving nonstationary signals and time-varying systems are challenging and solutions are not possible in the most general case. However, structured nonstationarities such as those entailing periodic and (almost) periodic variations in their statistical descriptors, are tractable. The resulting random signals are called (almost) cyclostationary and their study in signal processing and communications related applications is the theme of this project. Research in this project has pursued two broad directions:

  1. polynomial phase signal (PPS) modeling, estimation algorithms, radar, sonar, and SAR related applications, and
  2. exploitation of cyclostationarity for linear and nonlinear system identification with applications to speech modeling, image motion estimation, source separation, synchronization, genralized differential encoding, and equalization of communication channels.

Our results are detailed in the journal and conference papers listed below (see also the book chapter for an overview).

Our basic-research results have established:

  • 1a. identifiability, blind estimation, and direct adaptive (LMS and RLS) deconvolution approaches for FIR systems (MA processes); the resulting algorithms rely on cyclostationary statistics induced by fractionally sampling the continuous-time output and/or by deploying multiple sensors (outputs); asymptotic statistical analysis and extensive simulations have also been performed.
  • 1b. identifiability, blind estimation and deconvolution algorithms for FIR and pole-zero systems (MA and ARMA processes) relying on input cyclostationarity induced by modulating the stationary random input with (almost) periodic deterministic sequences; thorough performance analysis yielded optimal modulating sequences and revealed superiority of input-induced cyclic identification over high-order statistics based methods as well as over the methods in 1a) that capitalize on output-induced cyclostationarity; in contrast to existing second-order cyclic approaches, our methods impose no restrictions on the underlying system zeros.
  • 1c. development of the product multilag high-order ambiguity function -- a valuable tool when it comes to reliable estimation and separation of multicomponent polynomial phase signals; simulations and analytical performance evaluation based on perturbation techniques showed distinct advantages over existing estimators not only in terms of identifiability but also in SNR gains.
  • 1d. modeling and linear parameter estimation techniques of time series described as the product of frequency-modulated (FM) and polynomial phase signals (PPS); derivation of Cramer-Rao bounds for such hybrid FM-PPS estimators and extensive simulations to assess performance vs complexity tradeoffs.

Our application-oriented results have included:

  • 2a. Communications: self-recovering online equalization algorithms of FIR frequency-selective communication channels relying on output cyclic statistics; blind channel estimators using modulation induced cyclostationarity that do not introduce input redundancy, operate irrespective of the channel zero locations, and are capable of handling jointly carrier frequency-offsets arising due to oscillator drifts and Doppler effects; exploitation of cyclostationarity for blind subspace based channel estimators in the increasingly popular orthogonal frequency-division multiplexing transmission systems for broadcasting; application of the product multilag high-order ambiguity function in 1b. to encode and decode information symbol transmissions through flat fading channels while compensating for unknown phase, Doppler, and general PPS distortions; a cyclostationary framework for estimating frequency offset and timing ambiguities in communication signal transmissions over flat fading channels.
  • 2b. Radar-Sonar: application of hybrid FM-PPS modeling for estimating kinematic parameters of moving targets with vibrating or rotating components;
  • 2c. Speech Processing: blind separation of multiple speech signals using (cyclic) polyspectra of their superposition recorded at several sensors; the algorithm yields the FIR coupling systems as well as the (possibly colored) input signals which are allowed to be (almost) periodic and with overlapping spectra.
  • 2d. Image Processing: spatio-temporal approach to time-varying (TV) image motion estimation; TV motion is described using PPS or FM models and the results are corroborated with real data acquired from a moving or vibrating camera;
  • 2e. Synthetic Aperture Radar (SAR): autofocusing of SAR imagery relying on PPS modeling for the instantaneous phase shift induced by the relative radar/scene motion; the resulting algorithm is capable of discriminating moving target echoes from stationary background by exploiting the different phase modulation arising due to the different motion laws; experimental comparisons with real images (from ERIM's database) confirm superiority over phase gradient techniques.

Related Journal papers:

  1. G. B. Giannakis and G. Zhou, "Harmonics in multiplicative and additive noise: parameter estimation using cyclic statistics," IEEE Transactions on Signal Processing, pp. 2217-2221, September 1995.
  2. A. V. Dandawate and G. B. Giannakis, "Modeling (almost) periodic moving average processes using cyclic statistics," IEEE Transactions on Signal Processing, vol. 44, pp. 673-684, March 1996.
  3. A. Delopoulos and G. B. Giannakis, "Cumulant based identification of noisy closed loop systems," International Journal of Adaptive Control and Signal Processing, vol. 10, no. 2/3, pp. 303-317, March 1996.
  4. G. Zhou, G. B. Giannakis and A. Swami, "On polynomial phase signals with time-varying amplitudes," IEEE Trans. on Signal Processing, vol. 44, no. 4, pp. 848-861, April 1996.
  5. G. Zhou and G. B. Giannakis "Polyspectral analysis of mixed processes and coupled harmonics," IEEE Transactions on Information Theory,} pp. 943-958, May 1996.
  6. W. Chen, G. B. Giannakis, and N. Nandhakumar, "Spatio-temporal approach for time-varying image motion estimation," IEEE Transactions on Image Processing}, pp. 1448-1461, Oct. 1996.
  7. G. . B. Giannakis and E. Serpedin, "Linear multichannel blind equalizers of nonlinear FIR Volterra channels," IEEE Transactions on Signal Processing, pp. 67-81, January 1997.
  8. G. B. Giannakis, "Filterbanks for blind channel identification and equalization," IEEE Signal Processing Letters, vol. 4, pp. 184-187, June 1997.
  9. G. B. Giannakis and S. D. Halford, "Asymptotically Optimal Blind Fractionally-Spaced Channel Estimation and Performance Analysis," IEEE Transactions on Signal Processing, vol. 45, pp. 1815-1830, July 1997.
  10. A. Swami, G. B. Giannakis, and G. Zhou, "Bibliography on Higher-Order Statistics," Signal Processing, vol. 60, pp. 65-126, Elsevier Science Publ. B.V., July 1997.
  11. G. B. Giannakis, and S. Halford, "Blind fractionally-spaced equalization of noisy FIR channels: direct and adaptive solutions," IEEE Transactions on Signal Processing, vol. 45, pp. 2277-2292, September 1997.
  12. S. Shamsunder and G. B. Giannakis, "Multichannel blind signal separation and reconstruction," IEEE Transactions on Speech and Audio Processing, vol. 5, pp. 515-528, November 1997.
  13. S. Barbarossa, A. Scaglione, and G. B. Giannakis, "Product multilag high-order ambiguity function for multicomponent polynomial phase signal modeling," IEEE Transactions on Signal Processing, vol. 46, pp. 691-708, March 1998.
  14. F. Gini and G. B. Giannakis, "Frequency Offset and Symbol Timing Recovery in Flat Fading Channels: A Cyclostationary Approach," IEEE Transactions on Communications, vol. 46, pp. 400-411, March 1998.
  15. T. J. Endres, S. D. Halford, C. R. Johnson Jr., and G. B. Giannakis, "Simulated comparisons of blind equalization algorithms for cold start-up applications," International Journal of Adaptive Control and Signal Processing, vol. 12, no. 3, pp. 283-301, May 1998.
  16. E. Serpedin and G. B. Giannakis, "Blind Channel Identification and Equalization using Modulation Induced Cyclostationarity," IEEE Transactions on Signal Processing, vol. 46, pp. 1930-1944, July 1998.
  17. W. Chen, G. B. Giannakis, and N. Nandhakumar, "A harmonic retrieval framework for discontinuous motion estimation," IEEE Transactions on Image Processing}, vol. 7, pp. 1242-1257, September 1998.
  18. F. Gini and G. B. Giannakis, "Generalized differential encoding: A nonlinear signal processing framework," IEEE Transactions on Signal Processing, pp. 2967-2974, Nov. 1998.
  19. G. B. Giannakis and E. Serpedin, "Blind Identification of ARMA Models with Periodically Modulated Inputs," IEEE Transactions on Signal Processing, pp. 3099-3104, November 1998.
  20. F. Gini and G. B. Giannakis, "Hybrid FM-Polynomial Phase Signal Modeling: Estimation and Performance Analysis," IEEE Transactions on Signal Processing, pp. 363-377, February 1999.
  21. E. Serpedin and G. B. Giannakis, "A simple proof of a known blind channel identifiability result," IEEE Transactions on Signal Processing, pp. 591-593, February 1999.
  22. R. W. Heath and G. B. Giannakis, "Exploiting Input Cyclostationarity for Blind Channel Identification in OFDM Systems," IEEE Transactions on Signal Processing, vol. 47, pp. 848-856, March 1999.
  23. A. Kambanellas and G. B. Giannakis, "Modulo pre-equalization of nonlinear communication channels," Proc. of IEEE-SP Workshop on Signal Proc. Advances in Wireless Comm., Annapolis, MD, May 9-12, 1999.

Tutorial (Book Chapter)

  1. G. B. Giannakis, "Cyclostationary Signal Analysis" Chapter in the Statistical Signal Processing Section of Digital Signal Processing Handbook, V. K. Madisetti, D. Williams, Editors-in-Chief, CRC Press, 1998.

 

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