The finite harmonic oscillator and its applications to sequences, communication, and radar

Shamgar Gurevich; Ronny Hadani; Nir Sochen

doi:10.1109/TIT.2008.926440

The finite harmonic oscillator and its applications to sequences, communication, and radar

Shamgar Gurevich^*, Ronny Hadani, Nir Sochen

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

A novel system, called the oscillator system, consisting of order of p³ functions (signals) on the finite field F_p with p an odd prime, is described and studied. The new functions are proved to satisfy good autocorrelation, 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.

Original language	English
Pages (from-to)	4239-4253
Number of pages	15
Journal	IEEE Transactions on Information Theory
Volume	54
Issue number	9
DOIs	https://doi.org/10.1109/TIT.2008.926440
State	Published - 2008

Keywords

Commutative subgroups
Eigenfunctions
Explicit algorithm
Fourier invariance
Good correlations
Low supremum
Radar communication
Weil representation

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10.1109/TIT.2008.926440

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abstract = "A novel system, called the oscillator system, consisting of order of p3 functions (signals) on the finite field Fp with p an odd prime, is described and studied. The new functions are proved to satisfy good autocorrelation, 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.",

keywords = "Commutative subgroups, Eigenfunctions, Explicit algorithm, Fourier invariance, Good correlations, Low supremum, Radar communication, Weil representation",

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AU - Gurevich, Shamgar

AU - Hadani, Ronny

AU - Sochen, Nir

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AB - A novel system, called the oscillator system, consisting of order of p3 functions (signals) on the finite field Fp with p an odd prime, is described and studied. The new functions are proved to satisfy good autocorrelation, 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.

KW - Commutative subgroups

KW - Eigenfunctions

KW - Explicit algorithm

KW - Fourier invariance

KW - Good correlations

KW - Low supremum

KW - Radar communication

KW - Weil representation

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JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 9

ER -

The finite harmonic oscillator and its applications to sequences, communication, and radar

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Keywords

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