Zero Correlation Zone Sequences With Flexible Block-Repetitive Spectral Constraints

TL;DR

This paper introduces a flexible method for constructing zero correlation zone sequences with spectral constraints, enabling customizable correlation properties and PAPR control through a novel block-repetitive DFT structure.

Contribution

It presents a new construction of ZCZ sequences with a block-repetitive spectral structure, allowing flexible design under spectral and PAPR constraints, including a unified method for MCAZAC sequences.

Findings

Sequences exhibit multiple zero correlation zones with sparse autocorrelation.

The spectral structure allows independent control of ZCZ size and spectral properties.

0 dB PAPR sequences are achievable using MCAZAC sequences.

Abstract

A general construction of a set of time-domain sequences with sparse periodic correlation functions, having multiple segments of consecutive zero-values, i.e. multiple zero correlation zones (ZCZs), is presented. All such sequences have a common and block-repetitive structure of the positions of zeros in their Discrete Fourier Transform (DFT) sequences, where the exact positions of zeros in a DFT sequence do not impact the positions and sizes of ZCZs. This property offers completely new degree of flexibility in designing signals with good correlation properties under various spectral constraints. The non-zero values of the DFT sequences are determined by the corresponding frequency-domain modulation sequences, constructed as the element-by-element product of two component sequences: a "long" one, which is common to the set of time-domain sequences, and which controls the peak-to-average power ratio (PAPR) properties of the time-domain sequences; and a "short" one, periodically extended to match the length of the "long" component sequence, which controls the non-zero crosscorrelation values of all time-domain sequences. It is shown that 0 dB PAPR of time-domain sequences can be obtained if the "long" frequency-domain component sequence is selected to be a modulatable constant amplitude zero autocorrelation (MCAZAC) sequence. A generalized and simplified unified construction of MCAZAC sequences is presented.