On a class of optimal nonlinear binary sequences

• Main Author: S. S. Yudachev
• Format: Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 2014-01-01
• Series: Nauka i Obrazovanie
• Subjects: correlation properties; spread spectrum systems; nonlinear binary sequences; Galois fields; primitive field element
• Online Access: http://technomag.edu.ru/jour/article/view/579

<p>Investigated class of binary sequences is designed for use in advanced spread spectrum radio systems for various purposes, based on the application of code sequences. The paper considers the class of nonlinear binary sequences that are optimal in the sense of the boundaries of packaging. The idea of such sequences development and mathematical method of their construction first were proposed by B.J. Kamaletdinov. These sequences differ favorably from those widely used now by large variety of ways of forming the fine structure of the code, representative set of lengths, and difficulty of deciphering. However, the properties of these sequences and methods of their generating insufficiently investigated.</p><p>The paper presents a practical algorithm for the formation of ensembles of two subclasses of Kamaletdinov N and Di-sequences. Based on this algorithm and its software implementation in C #, ensemble samples of various lengths are obtained and their periodic and aperiodic correlation functions and statistical characteristics are thoroughly investigated. Some of the most significant correlation functions are provided as illustrations and the most notable characteristics of the ensemble sequences are considered. Boundaries of package for ensembles of various lengths are given. The statistical characteristics of N and Di-sequences are compared and specific differences of characteristics are highlighted. Based on the study of cross correlation characteristics of combined ensemble and Di-N sequences it was concluded that application of such an ensemble is unreasonable. The annex contains the three first samples of sequences from each test ensemble of the length L = 342.</p><p>On the basis of the calculations performed the conclusion can be made about the prospects of studied classes of sequences application which allows to reduce intersystem interference in the projected spread spectrum systems with code division multiple channels.</p>