分碼多重存取系統中二元數列的一些特性

Abstract

二元數列是展頻通訊與CDMA系統中的關鍵因素。對二元數列的研究也是通訊理□中的重要課題。在這篇論文□，會複習並研究一些二元數列的特性。 本篇論文包含兩個部分，第一部分著重於如何以位移暫存器達成多項式除法以產生數列，一個多項式的許多狀態環，m數列的奇妙特性，與m數列所衍生出來，相關值很小的數列集。 第二部分討論二元數列的正交性，將會討論正交數列的特性，其中有些特性只存在於二元數列。可變長度正交數列的觀念也會被介紹，並提出一個用來產生可變長度正交數列的新方法。

Binary sequences are a key element in spread spectrum communication and CDMA systems. The research of binary sequences is also an important issue in communication theory. In this thesis, some properties about binary sequences are reviewed and investigated. This thesis consists of two parts. The first part addressing how shift-registers implement polynomial division to generate sequences, different state cycles of a polynomial, marvelous properties of m-sequences and some sequence sets derived from m-sequences whose correlation values are small. The second part discusses the orthogonality of binary sequences. We will discuss the properties of orthogonal sequences, some of which exist only in the binary cases. Concept of variable length orthogonal sequences will be introduced. And a new algorithm to generate more variable length orthogonal sequences will be proposed.