IDEAL 2007: Intelligent Data Engineering and Automated Learning - IDEAL 2007 pp 268-276 | Cite as
Reproducing Kernel Hilbert Space Methods to Reduce Pulse Compression Sidelobes
Abstract
Since the development of pulse compression in the mid-1950’s the concept has become an indispensable feature of modern radar systems. A matched filter is used on reception to maximize the signal to noise ratio of the received signal. The actual waveforms that are transmitted are chosen to have an autocorrelation function with a narrow peak at zero time shift and the other values, referred to as sidelobes, as low as possible at all other times. A new approach to radar pulse compression is introduced, namely the Reproducing Kernel Hilbert Space (RKHS) method. This method reduces sidelobe levels significantly. The paper compares a second degree polynomial kernel RKHS method to a least squares and L 2P -norm mismatched filter, and concludes with a presentation of the representative testing results.
Keywords
Reproduce Kernel Hilbert Space Polynomial Kernel Pulse Compression Chirp Pulse Sidelobe LevelPreview
Unable to display preview. Download preview PDF.
References
- 1.Cook, C.E.: The early history of pulse compression radar-the history of pulse compression at Sperry Gyroscope Company. IEEE Transactions on Aerospace and Electronic Systems 24, 825–833 (1988)CrossRefGoogle Scholar
- 2.Siebert, W.M.: The early history of pulse compression radar-the development of AN/FPS-17 coded-pulse radar at Lincoln Laboratory. IEEE Transactions on Aerospace and Electronic Systems 24, 833–837 (1988)CrossRefGoogle Scholar
- 3.Cilliers, J.E., Smit, J.C.: Pulse Compression Sidelobe Reduction by Minimization of Lp-norms. Accepted for publication in IEEE Transactions on Aerospace and Electronic Systems (2007)Google Scholar
- 4.Lewis, B.L., Kretschmer, F.F., Shelton, W.W.: Aspects of Radar Signal Processing. Artech House, Norwood, MA (1986)Google Scholar
- 5.Aronszajn, N.: Theory of Reproducing Kernels. Transactions of the American Mathematical Society 68, 337–404 (1950)MATHCrossRefMathSciNetGoogle Scholar
- 6.Parzen, E.: Statistical Inference on Time Series by Hilbert Space Methods. Technical report, Department of Statistics, Stanford University, Technical Report No. 24 (1959)Google Scholar
- 7.Parzen, E.: Regression Analysis of Continuous Parameter Time Series. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability Theory, pp. 469–489. University of California Press, Berkeley, CA (1961)Google Scholar
- 8.Parzen, E.: An Approach to Time Series Analysis. The Annals of Mathematical Statistics 32, 337–404 (1961)MathSciNetGoogle Scholar
- 9.Kailath, T.: RKHS Approach to Detection and Estimation Problems—Part I: Deterministic Signals in Gaussian Noise. IEEE Transactions on Information Theory IT-17, 530–549 (1971)CrossRefMathSciNetGoogle Scholar
- 10.Kailath, T., Duttweiler, D.: An RKHS Approach to Detection and Estimation Problems—Part II: Gaussian Signal Detection. IEEE Transactions on Information Theory IT-21, 15–23 (1975)CrossRefGoogle Scholar
- 11.Kailath, T., Duttweiler, D.: An RKHS Approach to Detection and Estimation Problems—Part III: Generalized Innovations Representations and a Likelihood-Ratio Formula. IEEE Transactions on Information Theory IT-18, 730–745 (1972)CrossRefMathSciNetGoogle Scholar
- 12.van Wyk, M.A., Durrani, T.S.: A Framework for Multi-Scale and Hybrid RKHS-Based Approximators. IEEE Transactions on Signal Processing 48, 3559–3568 (2000)CrossRefGoogle Scholar
- 13.van Wyk, M.A., Durrani, T.S., van Wyk, B.J.: A RKHS Interpolator-Based Graph Matching Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 988–995 (2002)CrossRefGoogle Scholar
- 14.van Wyk, M.A.: Hilbert Space Methods for Non-linear Function Approximation and Filtering. Technical report, Tshwane University of Technology, CSIR / LEDGER, South Africa (2006)Google Scholar
- 15.Luenberger, D.G.: Optimization by Vector Space Methods. John Wiley and Sons, New York, NY (1969)MATHGoogle Scholar
- 16.van Wyk, B.J., van Wyk, M.A., Noel, G.: Kernel-based Non-linear Template Matching. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A., de Ridder, D. (eds.) SSPR 2004. LNCS, vol. 3138, pp. 831–839. Springer, Heidelberg (2004)Google Scholar
- 17.Mathworks: MATLAB Documentation - Neural Network Toolbox. Version 6.5.0.180913a Release 13 edn. Mathworks Inc., Natick, MA (2002)Google Scholar