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Article overview
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Optimal ambiguity functions and Weil's exponential sum bound | | John J. Benedetto
; Robert L. Benedetto
; Joseph T. Woodworth
; | | Date: |
10 Jul 2011 | | Abstract: | Complex-valued periodic sequences, u, constructed by Goran Bjorck, are
analyzed with regard to the behavior of their discrete periodic narrow-band
ambiguity functions A_p(u). The Bjorck sequences, which are defined on Z/pZ for
p>2 prime, are unimodular and have zero autocorrelation on (Z/pZ){0}. These
two properties give rise to the acronym, CAZAC, to refer to constant amplitude
zero autocorrelation sequences. The bound proven is |A_p(u)| leq 2/sqrt{p} +
4/p outside of (0,0), and this is of optimal magnitude given the constraint
that u is a CAZAC sequence. The proof requires the full power of Weil’s
exponential sum bound, which, in turn, is a consequence of his proof of the
Riemann hypothesis for finite fields. Such bounds are not only of mathematical
interest, but they have direct applications as sequences in communications and
radar, as well as when the sequences are used as coefficients of phase-coded
waveforms. | | Source: | arXiv, 1107.1887 | | Services: | Forum | Review | PDF | Favorites | |
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