Construction of sparse representations of perfect polyphase sequences in Zak space with applications to radar and communications

Authors:
Andrzej K. Brodzik
Affiliations:
The MITRE Corporation, Emerging Technologies, Bedford, MA
Venue:
EURASIP Journal on Advances in Signal Processing - Special issue on recent advances in theory and methods for nonstationary signal analysis
Year:
2011

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Abstract

Sparse representations of sequences facilitate signal processing tasks in many radar, sonar, communications, and information hiding applications. Previously, conditions for the construction of a compactly supported finite Zak transform of the linear FM chirp were investigated. It was shown that the discrete Fourier transform of a chirp is, essentially, a chirp, with support similar to the support of the time-domain signal. In contrast, the Zak space analysis produces a highly compactified chirp, with support restricted to an algebraic line. Further investigation leads to relaxation of the original restriction to chirps, permitting construction of a wide range of polyphase sequence families with ideal correlation properties. This paper contains an elementary introduction to the Zak transform methods, a survey of recent results in Zak space sequence design and analysis, and a discussion of the main open problems in this area.