Design, Analysis And Application Of Complementary Sequences With Generalized Orthogonal Zone

In code-division multiple-access (CDMA) systems, the auto-correlation and cross-correlation (including periodic/aperiodic correlation) function of the spreading sequences employed play an critical role on the level of the multipath interference (MI) multiple access-interference (MAI) and adjacent cell interference (ACI), therefore directly influence the performance and capacity of the CDMA systems. Existing research on spreading sequences mainly focuses on two aspects, i.e. the design and application respectively. In this thesis, sequences and arrays with zero correlation zone (ZCZ) are investigated concretely. The ZCZ concept is also referred as generalized orthogonality (GO). Different methods of constructing sequences and arrays with favorable correlation properties are obtained. The potential applications of these sequences and arrays in multicarrier CDMA systems^ indoor wireless infrared communications and muti-input multi-output (MIMO) are also investigated. Meanwhile, the logic function representation of Golay sequences and complete complementary sequences are analyzed.Based on the extension of ZCZ concept to complementary sequences, general construction methods of ZCZ aperiodic complementary sequences (ZACS), ZCZ periodic complementary sequences (ZPCS) and their mates are presented. In addition, by performing shift operation on periodic complementary sequences (PCS), a new method of generating ZPCS is obtained. The resultant ZPCS not only processes ideal cross-correlation properties inside of ZCZ but also good correlation properties outside of ZCZ. By employing PCS and shift sequences together with interleaving technique, inter-group periodic complementary sequences are obtained. The resultant sequences can be divided into several groups, the CCF of two sequences in the same group has ZCZ and the CCF of two sequences from two different groups is perfect as well.Based on perfect array and shift sequences together with interleaving technique, optimal or near optimal ZCZ arrays are obtained. This method not only produces ZCZ arrays with new parameter combination but also provides flexible choices of different parameters. Meanwhile, the rectangular ZCZ of the resultant ZCZ arrays reaches its maximum value in column direction or row direction depending on whether row-by-row interleaving or columm-by-column is performed. Besides, the number of arrays and the size of rectangular ZCZ provide a tradeoff to meet different requirements on parameters in different applications.Based on the extension of ZCZ concept to complementary array, a new concept called complementary array with ZCZ is proposed. It includes complementary array and ZCZ array as special cases. The extension enriches the existence pattern of array, which not only provides more choices for the possible applications but also make it possible to investigate arrays under a unified framework. Three methods for constructing complementary arrays with the desired ZCZ are given. The first method uses aperiodic complementary array as initial array together with orthogonal expansion to generate aperiodic complementary array with ZCZ. The second method uses ZCZ array as initial array together with orthogonal expansion to generate periodic complementary array with ZCZ. The third method uses ZCZ array as initial array together with recursive bit interleaving to generate periodic complementary array with ZCZ. The resultant complementary arrays with ZCZ obtained from these three methods have two kinds of rectangular ZCZ, one is the general rectangular ZCZ, the other is perfect rectangular ZCZ. The classification of these two kinds of rectangular ZCZ corresponding to the three methods is determined by initial array, orthogonal expansion and recursive bit interleaving respectively.Based on the simple logic operations of AND,OR and NOT, specific logic function representation of Golay sequences and complete complementary sequences, which are two important kinds of sequences with wide applications, are obtained from mathematic induction. Logic functions of sequences not only facilitates the simple engineering generation of sequences but also throw light on the characteristics of sequences from a different angle, thus helps to construct similar kind of sequences.Three possible applications for complementary sequences with ZCZ are investigated concretely. The first one is serving as spreading sequences in quasi-synchronous multicarrier CDMA systems to eliminate MI and MAI so long as the maximum multipath delay and inter-user delay falls within ZCZ. The second application is indoor wireless infrared communications to improve complementary sequence keying (CSK), thereby avoids the unnecessary interference caused by the cross-correlation of two element sequences from binary complementary pair (BCP) and simplify the selection of BCP. The third one is to employ ZCZ complementary sequences as training sequences in multi-input mulit-output (MIMO) channel estimation to achieve optimal estimation results.