Some Constructions and Mathematical Properties of Zero-Correlation-Zone Sonar Sequences
Xiaoxiang Jin, Gangsan Kim, Sangwon Chae, Hong-Yeop Song
TL;DR
This paper introduces new mathematical properties and constructions for sonar sequences with zero-correlation zones, expanding their potential applications in signal processing.
Contribution
The paper introduces new optimality criteria and constructions for (m,n,r) ZCZ sonar sequences, including ZCZ-DD sequences with distinct difference properties.
Findings
An upper bound on the ZCZ radius r is derived in terms of m and n.
Constructions for (m,n,r) ZCZ sonar sequences are proposed, leading to improved lower bounds on r.
Variations of Costas arrays can construct ZCZ-DD sonar sequences with ZCZ radius r=2.
Abstract
In this paper, we propose the zero-correlation-zone (ZCZ) of radius r on two-dimensional m×n sonar sequences and define the (m,n,r) ZCZ sonar sequences. We also define some new optimality of an (m,n,r) ZCZ sonar sequence which has the largest r for given m and n. Because of the ZCZ for perfect autocorrelation, we are able to relax the distinct difference property of the conventional sonar sequences, and hence, the autocorrelation of ZCZ sonar sequences outside ZCZ may not be upper bounded by 1. We may sometimes require such an ideal autocorrelation outside ZCZ, and we define ZCZ-DD sonar sequences, indicating that it has an additional distinct difference (DD) property. We first derive an upper bound on the ZCZ radius r in terms of m and n≥m. We next propose some constructions for (m,n,r) ZCZ sonar sequences, which leads to some very good constructive lower bound on r. Furthermore, this…
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Wireless Communication Networks Research