零相關區域序列之研究

Abstract

在許多的通訊與雷達系統裡常常需要用到有著良好自相關性(Autocorrelation)跟良好的交互相關性(Crosscorrelation)之序列。在有延遲的情況下，非零的自相關性會導致符元間干擾(Intersymbol Interference)，而在許多使用者的情況下，非零的交互相關性會導致多重路徑干擾(Multiple-access Interference)。在一個多重路徑衰弱(Multi-path Fading)的環境下，如果已知延遲的邊界，那序列必須在延遲的時間裡面，滿足良好的相關性。這一有良好關係的延遲範圍稱做零相關區域(Zero-Correlation Zone)。 在本論文中，我們提出四種有系統的架構法，去架構出零相關區域序列。這些方法更有彈性的去選擇序列的長度和零相關區域的長度，也可以產生出有限訊號群集點(Finite Constellation Points)之序列。 我們舉了許多用數值表示的零相關區域序列並且展示了一些應用例子去證實我們的方法是有效的。

Sequences with desired autocorrelation (AC) and cross-correlation (CC) properties are often needed in many communication and radar systems applications. Nonzero AC values at nonzero lags result in intersymbol or self interference (ISI) while nonzero CC values give rise to multiuser or multiple-access interference (MAI). For use in a multi-path fading enviroment with known a delay spread bound, a family of sequences needs to meet these desired correlation requirements for only those correlation lags that lie within a range called zero-correlation zone (ZCZ) or interference free window (IFW). This thesis presents four systematic methods for constructing families of ZCZ sequences. The proposed methods unify various existing ZCZ sequence-generating algorithms. They provides more °exibility in choosing the sequence length, the ZCZ size, and the signal constellation. We give various numerical sequences and show several application examples to demonstrate the usefulness of our approaches.