Signal & System Theory Group

Professor Peter Schreier

M.S.E.E. (Notre Dame, USA), 1999
Ph.D. (Colorado at Boulder, USA), 2003

Room: P1.7.01.2
Phone: +49 (0)5251 60-2213

Student consultation hours: by prior appointment with Ms. Merle


I am Professor and Head of the Signal and System Theory Group in the Department of Electrical Engineering and Information Technology at the Universität Paderborn, Germany.

I was born in Munich, Germany, in 1975. I received a Master of Science from the University of Notre Dame, Indiana, USA, in 1999, and a Ph.D. from the University of Colorado at Boulder, USA, in 2003, both in electrical engineering. In the Fall semester of 1998, I was a visiting research student with the Coding Group at the University of Hawaii at Manoa, USA. In the Spring semester of 2004, I was a Postdoctoral Research Associate, and in the Spring semester of 2008, a Visiting Associate Professor with the Department of Electrical and Computer Engineering at Colorado State University, Ft. Collins, USA. From 2004 until January 2011, I was on the faculty of the University of Newcastle, Australia.

I have received fellowships from the State of Bavaria, the Studienstiftung des deutschen Volkes (German National Academic Foundation), and the Deutsche Forschungsgemeinschaft (German Research Foundation). I currently serve as Area Editor and Associate Editor of the IEEE Transactions on Signal Processing, and on the IEEE Technical Committee Machine Learning for Signal Processing. I am a Senior Member of the IEEE.

Peter J. Schreier and Louis L. Scharf

Statistical Signal Processing of Complex-Valued Data:

The Theory of Improper and Noncircular Signals
330 pages, Cambridge University Press, 2010

Complex-valued random signals are embedded in the very fabric of science and engineering, yet the usual assumptions made about their statistical behavior are often a poor representation of the underlying physics. This book deals with improper and noncircular complex signals, which do not conform to classical assumptions, and it demonstrates how correct treatment of these signals can have significant payoffs.

The book begins with detailed coverage of the fundamental theory and presents a variety of tools and algorithms for dealing with improper and noncircular signals. It provides a comprehensive account of the main applications, covering detection, estimation, and signal analysis of stationary, nonstationary, and cyclostationary processes.

Providing a systematic development from the origin of complex signals to their probabilistic description makes the theory accessible to newcomers. This book is ideal for graduate students and researchers working with complex data in a range of research areas from communications to oceanography.

J. Tong, P. J. Schreier, and S. R. Weller, "Design and analysis of large MIMO systems with Krylov subspace receivers," IEEE Trans. Signal Processing, vol. 60, no. 5, pp. 2482-2493, May 2012

T. Adali, P. J. Schreier, and L. L. Scharf, "Complex-valued signal processing: the proper way to deal with impropriety" (overview paper), IEEE Trans. Signal Processing, vol. 59, no. 11, pp. 5101-5125, Nov. 2011

P. Wahlberg and P. J. Schreier, "Locally stationary harmonizable complex improper stochastic processes," J. Time Series Analysis, vol. 32, no. 1, pp. 33-46, Jan. 2011

P. Wahlberg and P. J. Schreier, "On Wiener filtering of certain locally stationary stochastic processes," Signal Processing, vol. 90, no. 3, pp. 885-890, Mar. 2010

P. Wahlberg and P. J. Schreier, "Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes," Applied and Computational Harmonic Analysis, vol. 26, no. 1, pp. 97-120, Jan. 2009 

P. J. Schreier, "Polarization ellipse analysis of nonstationary random signals," IEEE Trans. Signal Processing, vol. 56, no. 9, pp. 4330-4339, Sep. 2008

P. Wahlberg and P. J. Schreier, "Spectral relations for multidimensional complex improper stationary and (almost) cyclostationary processes," IEEE Trans. Information Theory, vol. 54, no. 4, pp. 1670-1682, Apr. 2008

P. J. Schreier, "Bounds on the degree of impropriety of complex random vectors," IEEE Signal Processing Lett., vol. 15, pp. 190-193, 2008

P. J. Schreier, "A unifying discussion of correlation analysis for complex random vectors," IEEE Trans. Signal Processing, vol. 56, no. 4, pp. 1327-1336, Apr. 2008

M. S. Spurbeck and P. J. Schreier, "Causal Wiener filter banks for periodically correlated time series," Signal Processing, vol. 87, no. 6, pp. 1179-1187, June 2007

P. J. Schreier and L. L. Scharf, "Higher order spectral analysis of complex signals," Signal Processing, vol. 86, no. 11, pp. 3321-3333, Nov. 2006

P. J. Schreier, L. L. Scharf, and A. Hanssen, "A generalized likelihood ratio test for impropriety of complex signals," IEEE Signal Processing Lett., vol. 13, no. 7, pp. 433-436, July 2006

P. J. Schreier and L. L. Scharf, "Canonical coordinates for transform coding of noisy sources," IEEE Trans. Signal Processing, vol. 54, no. 1, pp. 235-243, Jan. 2006

L. L. Scharf, P. J. Schreier and A. Hanssen, "The Hilbert space geometry of the Rihaczek distribution for stochastic analytic signals," IEEE Signal Processing Lett., vol. 12, no. 4, pp. 297-300, April 2005

P. J. Schreier, L. L. Scharf, and C. T. Mullis, "Detection and estimation of improper complex random signals," IEEE Trans. Information Theory, vol. 51, no. 1, pp. 306-312, Jan. 2005

P. J. Schreier and L. L. Scharf, "Stochastic time-frequency analysis using the analytic signal: why the complementary distribution matters," IEEE Trans. Signal Processing, vol. 51, no. 12, pp. 3071-3079, Dec. 2003

P. J. Schreier and L. L. Scharf, "Second-order analysis of improper complex random vectors and processes," IEEE Trans. Signal Processing, vol. 51, no. 3, pp. 714-725, Mar. 2003

J. Tong, P. J. Schreier, and S. R. Weller, "Precoder design and convergence analysis of MIMO systems with Krylov subspace receivers," in Intl. Symposium Inform. Theory (ISIT), St. Petersburg, Russia, Aug. 2011

J. Tong, P. J. Schreier, S. R. Weller, and L. L. Scharf, "Linear precoding for time-varying MIMO channels with low-complexity receivers," in Proc. Intl. Conf. Acoustics, Speech, Signal Processing (ICASSP), Prague, Czech Republic, May 2011

P. Wahlberg and P. J. Schreier, "The Wiener filter for locally stationary stochastic processes is rarely locally stationary," in Proc. European Signal Processing Conf., Glasgow, UK, Aug. 2009

P. J. Schreier, T. Adali, and L. L. Scharf, "On ICA of improper and noncircular sources", in Proc. Intl. Conf. Acoust., Speech, Signal Processing (ICASSP), Taipei, Taiwan, Apr. 2009

P. Wahlberg and P. J. Schreier, "A time-frequency formula for LMMSE filters for nonstationary underspread continuous-time stochastic processes," in Proc. European Signal Processing Conf., Lausanne, Switzerland, Aug. 2008

P. J. Schreier, "The degree of impropriety (noncircularity) of complex random vectors," in Proc. Intl. Conf. Acoust., Speech, Signal Processing (ICASSP), Las Vegas, NV, Apr. 2008

V. D. Trajkovic, M. Fu, and P. J. Schreier, "Near-capacity turbo equalization using optimized turbo codes," in Proc. Australasian Telecomm. Networks Appl. Conf. (ATNAC), Christchurch, New Zealand, Dec. 2007

P. J. Schreier, "Correlation coefficients for complex random vectors," in Proc. 41st Asilomar Conf. Signals, Systems, Computers, pp. 577-581, Pacific Grove, CA, Nov. 2007

P. Wahlberg and P. J. Schreier, "Frequency-domain properties of locally stationary improper second-order stochastic processes," in Proc. 41st Asilomar Conf. Signals, Systems, Computers, pp. 1093-1097, Pacific Grove, CA, Nov. 2007

V. D. Trajkovic, M. Fu, and P. J. Schreier, "Turbo equalization with irregular turbo codes," in Proc. IEEE Intl. Symposium on Wireless Communication Systems (ISWCS), pp. 153-157, Trondheim, Norway, Oct. 2007

P. Wahlberg and P. J. Schreier, "Spectra of multidimensional complex improper (almost) cyclostationary processes," in Proc. Intl. Symposium on Inform. Theory (ISIT), pp. 971-975, Nice, France, June 2007

P. J. Schreier, "A new interpretation of bilinear time-frequency distributions," in Proc. Intl. Conf. Acoust., Speech, Signal Processing (ICASSP), pp. III-1133-1136, Honolulu, HI, Apr. 2007

M. S. Spurbeck, P. J. Schreier, and L. L. Scharf, "Causal cyclic Wiener filtering" (invited paper), in Proc. 40th Asilomar Conf. on Signals, Systems, Computers, pp. 1425-1429, Pacific Grove, CA, Nov. 2006

P. J. Schreier, L. L. Scharf, and A. Hanssen, "A statistical test for impropriety of complex random signals," in Proc. Intl. Conf. Acoust., Speech, Signal Processing (ICASSP), pp. III-796-799, Toulouse, France, May 2006

P. J. Schreier, L. L. Scharf, and A. Hanssen, "A geometric interpretation of the Rihaczek time-frequency distribution for stochastic signals," in Proc. Intl. Symposium on Inform. Theory (ISIT), pp. 966-969, Adelaide, SA, Australia, Sep. 2005

P. J. Schreier, "A note on aliasing in higher-order spectra," in Proc. Australian Commun. Theory Workshop (AusCTW), pp. 171-174, Brisbane, Qld., Australia, Feb. 2005

P. J. Schreier and L. L. Scharf, "Polyspectra of analytic signals," in Proc. Intl. Conf. Acoust., Speech, Signal Processing (ICASSP), pp. II-473-476, Montréal, QC, Canada, May 2004

T. McWhorter and P. Schreier, "Widely linear beamforming," in Proc. 37th Asilomar Conf. Signals, Systems, Computers, pp. 753-759, Pacific Grove, CA, Nov. 2003

P. J. Schreier, L. L. Scharf, T. Hu, and S. D. Voran, "Canonical coordinates are the right coordinate system for transform coding of noisy sources," in Proc. IEEE Workshop on Statistical Signal Processing, pp. 221-224, St. Louis, MO, Sep. 2003

P. J. Schreier, L. L. Scharf, and C. T. Mullis, "A unified approach to performance comparisons between linear and widely linear processing," in Proc. IEEE Workshop on Statistical Signal Processing, pp. 105-108, St. Louis, MO, Sep. 2003

P. J. Schreier and L. L. Scharf, "The Karhunen-Loève expansion of improper complex random signals with applications in detection," in Proc. Intl. Conf. Acoust., Speech, Signal Processing (ICASSP), pp. VI-717-720, Hong Kong, Apr. 2003

P. J. Schreier and L. L. Scharf, "Reducing interference in stochastic time-frequency analysis without losing information," in Proc. 36th Asilomar Conf. Signals, Systems, Computers, pp. 1565-1570, Pacific Grove, CA, Nov. 2002

P. J. Schreier and L. L. Scharf, "Canonical coordinates for reduced-rank estimation of improper complex random vectors," in Proc. Intl. Conf. Acoust., Speech, Signal Processing (ICASSP), pp. 1153-1156, Orlando, FL, May 2002

P. J. Schreier and L. L. Scharf, "Low-rank approximation of improper complex random vectors," in Proc. 35th Asilomar Conf. Signals, Systems, Computers, pp. 597-601, Pacific Grove, CA, Nov. 2001

P. J. Schreier and D. J. Costello Jr., "MAP decoding of linear block codes based on a sectionalized trellis of the dual code," in Proc. Intl. Zurich Seminar Broadband Commun. (IZS), pp. 271-278, Zurich, Switzerland, Feb. 2000