Barker Sequences Theory and Applications

A Barker sequence is a finite length binary sequence using the minimal possible aperiodic autocorrelation. Presently, only 8 known Barker sequences exist and it has been conjectured that these are the only Barker sequences which exist. This dissertation shows that long sequences (having length more than thirteen) should have an even length and be a perfect square. Barker sequences are then utilized to explore flatness problems associated with Littlewood polynomials. These theorems can be employed to figure out the existence or non-existence of longer sequences. Finally, an application of Barker sequences is offered. Barker sequences had been initially investigated for the purposes of pulse compression in radar systems. This method leads to better range and Doppler resolution without having to shorten a radar pulse, nor raise the power…

Contents: Barker Sequences Theory and Applications

1 Introduction and Motivation
1.1 Introduction
1.2 Motivation
2 Even and Odd Length Sequences
2.1 Even Length
2.2 Odd Length
3 Flat Polynomials
3.1 Definitions and Rudin-Shapiro Polynomials
3.2 Littlewood’s Problem
3.3 Mahler’s Problem
4 Physical Application to Radars
4.1 Introduction to Radar Systems
4.2 Matched Filter
4.3 Development of the Ambiguity Function
4.4 Properties of the Ambiguity Function
4.5 Basic Radar Signals and Ambiguity of the Signals…

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Source: University of Maryland

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