Известия высших учебных заведений России: Радиоэлектроника (Oct 2019)
Retrospective Review of Perfect Ternary Sequences and Their Generators
Abstract
Introduction. Perfect polyphase unimodular sequences, i.e. sequences with ideal periodic autocorrelation and single amplitude of symbols are widely used in modern radio communications and radars. Among them a special place is occupied by perfect ternary sequences (PTSs) with elements {–1, 0, 1}. PTSs are quite numerous and their length in comparison with perfect binary sequences is not limited from above. There is a well-known review of PTS families undertaken by Fan and Darnell in 1996. However, over the past two decades numerous new PTS families have been discovered. Connections between PTSs and circulant weighing matrices have been established and certain theorems on the existence of PTS existence for certain lengths have also been obtained. Therefore, there is a need for a new modern review of existing PTSs.Objective. This review of existing PTSs is intended for developers of radio electronic systems using perfect sequences. Materials and methods. Domestic and foreign sources of information (books, journal papers, conference proceedings, patents) were considered and analysed. A Web search was carried out based on keywords using resources of Yandex and Google, as well as in digital electronic libraries (Russian State Library (RSL), IEEE Xplore Digital Library), conference materials (Digital Signal Processing and its Application (DSPA), Sequences and their Applications (SETA), etc.). Results. In addition to the matter of collating an informational bibliography, the review shows the relationship between PTSs obtained at different times and their connection with circulant weighing matrices. The review also describes the generators of known PTS families (Ipatov, Hoholdt-Justensen, etc.). Conclusion. A retrospective review of PTSs is herein presented and the generators of certain known PTS families have been considered. The results of the study are relevant for use in modern radio communications and radar systems and in CW and LPI radars in particular.
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