Research ArticleOpen AccessGoogle Scholar indexed
Construction of Zero Autocorrelation Stochastic Waveforms
Department of Mathematics, University of Idaho, Moscow, USA
- 1 Department of Mathematics, University of Idaho, Moscow, USA
Advances in Pure Mathematics·Volume 02 (2012)·Pages 428–440·Published 9 November 2012·DOI10.4236/apm.2012.26065
Copy link · social · email
Abstract
Stochastic waveforms are constructed whose expected autocorrelation can be made arbitrarily small outside the origin. These waveforms are unimodular and complex-valued. Waveforms with such spike like autocorrelation are desirable in waveform design and are particularly useful in areas of radar and communications. Both discrete and continuous waveforms with low expected autocorrelation are constructed. Further, in the discrete case, frames for C d are constructed from these waveforms and the frame properties of such frames are studied.
KeywordsAutocorrelationFramesStochastic Waveforms
- L. Auslander and P. E. Barbano, “Communication Codes and Bernoulli Transformations,” Applied and Computational Harmonic Analysis, Vol. 5, No. 2, 1998, pp. 109-128. doi:10.1006/acha.1997.0222
- J. J. Benedetto and J. J. Donatelli, “Ambiguity Function and Frame Theoretic Properties of Periodic Zero Autocorrelation Waveforms,” IEEE Journal of Selected Topics in Signal Processing, Vol. 1, 2007, pp. 6-20.
- T. Helleseth and P. V. Kumar, “Sequences with Low Correlation,” Handbook of Coding Theory, North-Holland, Amsterdam, 1998, pp. 1765-1853.
- N. Levanon and E. Mozeson, “Radar Signals,” Wiley Interscience, New York, 2004. doi:10.1002/0471663085
- M. L. Long, “Radar Reflectivity of Land and Sea,” Artech House, 2001.
- W. H. Mow, “A New Unified Construction of Perfect Root-of-Unity Sequences,” Proceedings of IEEE 4th International Symposium on Spread Spectrum Techniques and Applications, Sun City, 22-25 September 1996, pp. 955-959. doi:10.1109/ISSSTA.1996.563445
- F. E. Nathanson, “Radar Design Principles: Signal Processing and the Environment,” SciTech Publishing Inc., Mendham, 1999.
- G. W. Stimson, “Introduction to Airborne Radar,” SciTech Publishing Inc., Mendham, 1998.
- S. Ulukus and R. D. Yates, “Iterative Construction of Optimum Signature Sequence Sets in Synchronous CDMA Systems,” IEEE Transactions on Information Theory, Vol. 47, No. 5, 2001, pp. 1989-1998. doi:10.1109/18.930932
- S. Verdú, “Multiuser Detection,” Cambridge University Press, Cambridge, 1998.
- J. J. Benedetto and S. Datta, “Construction of Infinite Unimodular Sequences with Zero Autocorrelation,” Advances in Computational Mathematics, Vol. 32, No. 2, 2010, pp. 191-207. doi:10.1007/s10444-008-9100-9
- D. Cochran, “Waveform-Agile Sensing: Opportunities and Challenges,” IEEE International Conference on Acoustics, Speech, and Signal Processing, Pennsylvania, 18-23 March 2005, pp. 877-880.
- M. R. Bell, “Information Theory and Radar Waveform Design,” IEEE Transactions on Information Theory, Vol. 39, No. 5, 1993, pp. 1578-1597. doi:10.1109/18.259642
- S. P. Sira, Y. Li, A. Papandreou-Suppappola, D. Morrell, D. Cochran and M. Rangaswamy, “Waveform-Agile Sensing for Tracking,” IEEE of Signal Processing Magazine, Vol. 26, No. 1, 2009, pp. 53-64.
- H. Boche and S. Stanczak, “Estimation of Deviations between the Aperiodic and Periodic Correlation Functions of Polyphase Sequences in Vicinity of the Zero Shift,” IEEE 6th International Symposium on Spread Spectrum Techniques and Applications, Parsippany, 6-8 September 2000, pp. 283-287.