Study of Optical Code Division Multiple Access Communication Systems

在本論文中，吾人提出三種應用在光分碼多工通訊系統之技術；在同步光分碼多工系統中，吾人提出一個使用完美相差碼應用於被動式乙太光網路之系統，此系統可以真正達到寬頻接取的服務。根據完美相差碼的同步特性，吾人分析其在時脈擾動下之效能；並且設計一個交互時脈擾動估測與消除電路，研究分析結果顯示此電路可以有效降低時間偏差對系統效能之影響。 在非同步光分碼多工系統中，吾人提出兩種建構可變權重光正交碼之演算法；第一個方式根據成對平衡設計而建構，成對平衡設計屬於組合數學理論中的一門，根據此設計吾人找出一組不同尺寸的集合，在將這組集合經過映射而得到可變權重之光正交碼。第二個方式稱為劃分包裝設計，吾人將一組較大權重的光正交碼進行劃分，劃分之後的尺寸屬於可變的，如此以來便可以得到不同權重之光正交碼；本論文針對此兩種新的可變權重光正交碼進行效能分析，研究結果顯示由第一種演算法所得到的編碼效能與傳統的理想編碼相同；然而第二種演算法則是在編碼尺寸上優於傳統的理想編碼。 在二維波長/時間光分碼多工系統中，吾人提出一組新的二維光正交碼，此二維光正交碼根據組合數學理論中的相差族群建構而成，吾人證明這組二維編碼滿足了光正交碼所需要的自我相關以及交互相關條件；此外，吾人所提出的二維光正交編碼可以根據不同的系統將編碼維度做彈性的調整，此特性改進了傳統的二維光分碼多工編碼之限制。在本論文中，吾人採用馬可夫鍊模型來分析此二維光分碼多工編碼之效能，並且研究發現在同時考慮編碼權重以及交互相關特性之下可以使得光分碼多工系統達到最大的容量。In this thesis, we propose three novel techniques for the optical code division multiple access (OCDMA) communication systems. For the synchronous OCDMA (SOCDMA) systems, we analyze the jitter performance of SOCDMA-based Ethernet passive optical network (EPON) communication systems using perfect difference codes (PDC). We propose the joint jitter estimator and canceller (JJEC) to reduce the impact of jitter and multiple-user interference (MUI). The bit error rate (BER) of the system with JJEC is formulated analytically based on the correlator and the simple sampler receiver structures. The numerical results show that the proposed scheme can significantly suppress the MUI and improve the system performance. For asynchronous OCDMA (ASOCDMA) systems, we propose two construction schemes of variable weight optical orthogonal codes. The first scheme uses pairwise balanced design (PBD) which is a research topic in the combinatorial theory. PBD produces a family of blocks with unequal block size. Therefore we can use PBD to construct codewords with variable code weights. The lower bound of code size of the codes from PBD is derived in this thesis. A second scheme employs packing design with partition to generate blocks with unequal block sizes. The variable weight optical orthogonal codes can be constructed by partitioning a larger weight codeword into a family of codes with smaller code weight. The upper bound and lower bound of code size of the second scheme is discussed in this thesis. The BER performances of the two proposed codes are evaluated analytically. The simulation results show that the codes from the first scheme have the same BER performance as that of conventional code while the second scheme has larger maximum number of simultaneous users than that of conventional codes. For the two-dimensional (2-D) wavelength/time OCDMA systems, we propose a new family of 2-D wavelength/time optical orthogonal codes. The construction scheme uses the difference family (DF) which is an assemblage of difference sets in the combinatorial theory. We prove that the proposed 2-D optical orthogonal codes satisfy the correlation properties required for the asynchronous OCDMA systems. The code dimension of the proposed codes is more flexible than that of the conventional 2-D optical orthogonal codes. We analyze the performance of the system with the proposed codes by using Markov chain method. Numerical results show that the BER has a minimal value given the number of simultaneous users. We also observe that the maximum number of simultaneous users of the OCDMA system can be achieved by properly choosing both the code weight and cross correlation of the optical orthogonal codes1 Introduction of the OCDMA Communication Systems 1.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Transmitters of OCDMA Systems . . . . . . . . . . . . . . . . 5 1.2.1 1-D encoder using fiber delay line . . . . . . . . . . . . 5 1.2.2 2-D encoder using FBG . . . . . . . . . . . . . . . . . 6 1.3 Receivers of OCDMA Systems . . . . . . . . . . . . . . . . . . 7 1.3.1 Asynchronous OCDMA systems . . . . . . . . . . . . . 8 1.3.2 Synchronous OCDMA systems . . . . . . . . . . . . . . 11 1.3.3 Two-dimensional OCDMA systems . . . . . . . . . . . 14 1.4 Application and Discussion . . . . . . . . . . . . . . . . . . . . 15 1.4.1 GMPLS . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4.2 Ring Network . . . . . . . . . . . . . . . . . . . . . . . 17 1.4.3 EPON . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . 22 2 Overview of the Optical Orthogonal Codes 25 2.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 Asynchronous Optical Orthogonal Codes . . . . . . . . . . . . 28 2.2.1 Prime Sequence Codes . . . . . . . . . . . . . . . . . . 28 2.2.2 Quadratic Congruence Codes . . . . . . . . . . . . . . 30 2.2.3 OOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3 Synchronous Optical Orthogonal Codes . . . . . . . . . . . . . 37 2.3.1 Modified Prime Sequence Codes . . . . . . . . . . . . . 37 2.3.2 Modified Quadratic Congruence Codes . . . . . . . . . 38 2.3.3 M-sequence Codes . . . . . . . . . . . . . . . . . . . . 42 2.3.4 Perfect Difference Codes . . . . . . . . . . . . . . . . . 43 2.4 2-D Optical Orthogonal Codes . . . . . . . . . . . . . . . . . . 45 2.4.1 MWOOC from 1-D OOC . . . . . . . . . . . . . . . . . 47 2.4.2 MWOOC from frequency hopping sequences . . . . . . 48 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3 Jitter Performance Analysis of SOCDMA-based EPON Using Perfect Difference Code 53 3.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2 System Description . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3 Jitter Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3.1 The receiver with correlator . . . . . . . . . . . . . . . 61 3.3.2 The receiver using simple sampler . . . . . . . . . . . . 66 3.3.3 The receiver using JJEC . . . . . . . . . . . . . . . . . 69 3.4 System Performance Analysis . . . . . . . . . . . . . . . . . . 70 3.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4 VariableWeight Optical Orthogonal Codes for Asynchronous Optical CDMA Systems 81 4.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 Construction Schemes of Variable Weight OOC . . . . . . . . 84 4.2.1 The construction scheme using pairwise balanced design 84 4.2.2 The construction scheme using packing design with partition . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . 93 4.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5 Construction of Two-Dimensional Wavelength/Time Optical Orthogonal Codes Using Di¤ erence Family 105 5.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2 Di¤erence Family in Galois Fields . . . . . . . . . . . . . . . . 108 5.2.1 Properties of pairwise balanced design . . . . . . . . . 110 5.2.2 Construction of DF from projective plane using PBD . 111 5.2.3 Construction of DF from a¢ ne plane using PBD . . . . 112 5.2.4 Recursive construction of DF . . . . . . . . . . . . . . 113 5.3 Design of MWOOC Using DF . . . . . . . . . . . . . . . . . . 113 5.4 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . 116 5.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6 Conclusion 12