On cross-ambiguity properties of welch-costas arrays

Svitislav V. Marić; Ivan Seskar; Edward L. Titlebaum

doi:10.1109/7.328760

On cross-ambiguity properties of welch-costas arrays

Svitislav V. Marić, Ivan Seskar, Edward L. Titlebaum

School of Engineering, Wireless Information Network Lab (WINLAB)

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

22 Scopus citations

Abstract

We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar systems, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross-ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers.

Original language	English (US)
Pages (from-to)	1063-1071
Number of pages	9
Journal	IEEE Transactions on Aerospace and Electronic Systems
Volume	30
Issue number	4
DOIs	https://doi.org/10.1109/7.328760
State	Published - Oct 1994

All Science Journal Classification (ASJC) codes

Aerospace Engineering
Electrical and Electronic Engineering

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title = "On cross-ambiguity properties of welch-costas arrays",

abstract = "We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar systems, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross-ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers.",

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note = "Funding Information: This work was supported in part by a grant from BMDODST and managed by the Office of Naval Research under Contract NOOO14-92-J-1933.",

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AU - Marić, Svitislav V.

AU - Seskar, Ivan

AU - Titlebaum, Edward L.

N1 - Funding Information: This work was supported in part by a grant from BMDODST and managed by the Office of Naval Research under Contract NOOO14-92-J-1933.

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N2 - We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar systems, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross-ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers.

AB - We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar systems, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross-ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers.

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On cross-ambiguity properties of welch-costas arrays

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