Abstract
In this survey a novel system, called the oscillator system, consisting of order of p 3 functions (signals) on the finite field \(\mathbb{F}_{p},\) is described and studied. The new functions are proved to satisfy good auto-correlation, cross-correlation and low peak-to-average power ratio properties. Moreover, the oscillator system is closed under the operation of discrete Fourier transform. Applications of the oscillator system for discrete radar and digital communication theory are explained. Finally, an explicit algorithm to construct the oscillator system is presented.
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References
Golomb, S.W., Gong, G.: Signal design for good correlation. For wireless communication, cryptography, and radar. Cambridge University Press, Cambridge (2005)
Howard, S.D., Calderbank, A.R., Moran, W.: The finite Heisenberg-Weyl groups in radar and communications. EURASIP J. Appl. Signal Process (2006)
Viterbi, A.J.: CDMA: Principles of Spread Spectrum Communication. Addison-Wesley Wireless Communications (1995)
Paterson, K.G., Tarokh, V.: On the existence and construction of good codes with low peak-to-average power ratios. IEEE Trans. Inform. Theory 46 (2000)
Howe, R.: Nice error bases, mutually unbiased bases, induced representations, the Heisenberg group and finite geometries. Indag. Math (N.S.) 16(3-4), 553–583 (2005)
Gurevich, S., Hadani, R., Sochen, N.: The finite harmonic oscillator and its applications to sequences, communication and radar. IEEE Trans. on Inform. Theory (accepted March 2008) (to appear)
Weil, A.: Sur certains groupes d’operateurs unitaires. Acta Math. 111, 143–211 (1964)
Chang, R.W.: Synthesis of Band-Limited Orthogonal Signals for Multichannel Data Transmission. Bell System Technical Journal 45 (1966)
Woodward, P.M.: Probability and Information theory, with Applications to Radar. Pergamon Press, New York (1953)
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Gurevich, S., Hadani, R., Sochen, N. (2008). Group Representation Design of Digital Signals and Sequences. In: Golomb, S.W., Parker, M.G., Pott, A., Winterhof, A. (eds) Sequences and Their Applications - SETA 2008. SETA 2008. Lecture Notes in Computer Science, vol 5203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85912-3_14
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DOI: https://doi.org/10.1007/978-3-540-85912-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85911-6
Online ISBN: 978-3-540-85912-3
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