發(fā)布時(shí)間：2018-03-13 08:55

  本文選題：二維　切入點(diǎn)：光正交碼　出處：《北京交通大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：光正交碼是為碼分多址(CDMA)光纖信道設(shè)計(jì)的一種專用碼,是一種具有良好自相關(guān)性和互相關(guān)性的序列族.碼分多址技術(shù)現(xiàn)已成功用于衛(wèi)星通信和移動(dòng)通信等領(lǐng)域.由于受到寬帶的限制,碼分多址技術(shù)的優(yōu)點(diǎn)難以得到最大限度的發(fā)揮.而光碼分多址(OCDMA)技術(shù)是光纖寬帶資源與CDMA技術(shù)的有機(jī)結(jié)合,有效解決了這一問(wèn)題.為了進(jìn)一步提高光碼分多址系統(tǒng)的性能,G.C.Yang等人提出了二維光正交碼(2-DOOC)的概念.一個(gè)參數(shù)為(n×m,k,λ_a,λ_c)的二維光正交碼(2-D(n×m,k,λ_a,λ_c)-OOC),C,是一族漢明重量為k的n×m(0,1)-陣列(稱為碼字).C滿足下述兩個(gè)性質(zhì):(1)自相關(guān)性:對(duì)任意正整數(shù)r(?)0(modm),任意A =(a_(ij))_(n×m)∈C,有(?)a_(ij)a_i,j+r≤λ_a;(2)互相關(guān)性:對(duì)任意正整數(shù)r,任意兩個(gè)不同的矩陣A =(aij)n× ∈ C,B=(b_(ij))_(n×m) ∈C,有(?)ijbi,j+r≤λ_c,其中j+r在模m下計(jì)算.本文對(duì)自相關(guān)系數(shù)為λ_a、互相關(guān)系數(shù)為1的最優(yōu)二維光正交碼進(jìn)行研究.通過(guò)利用w-循環(huán)可分組設(shè)計(jì)和半循環(huán)不完全帶洞可分組設(shè)計(jì),給出了最優(yōu)二維(n×m,k,λ_a,1)-光正交碼的組合構(gòu)造方法.利用這些構(gòu)造,對(duì)于任意正整數(shù)n,任意正整數(shù)m = 2(mod4),k=3,λ_a = 2且λ_c=1時(shí),我們完全確定了最優(yōu)二維(n× m,3,2,1)-光正交碼的碼字個(gè)數(shù).本文的結(jié)構(gòu)組織如下:第一章,簡(jiǎn)要介紹OCDMA系統(tǒng)的研究背景與現(xiàn)狀、二維光正交碼的概念、簡(jiǎn)述本文的主要結(jié)果.第二章,給出利用半循環(huán)帶洞可分組設(shè)計(jì)構(gòu)造g-正則2-D(n ×n,λ_a,l)-OOC的遞推構(gòu)造方法,并利用w-循環(huán)可分組設(shè)計(jì)和半循環(huán)不完全帶洞可分組設(shè)計(jì)構(gòu)造2-D([n:r]× m,k,λ_a,l)-OOC.第三章,介紹,n∈{4,5,7,88,1}時(shí),最優(yōu)22-D(n×m,k,λ_a,1)-OOC的直接構(gòu)造方法.第四章,證明本文的主要結(jié)論,即確定Φ(n×m,3,2,1)的精確值,并提出可能的進(jìn)一步的研究問(wèn)題。
[Abstract]:Optical orthogonal code is a kind of special code designed for code division multiple access (CDMA) optical fiber channel. Code division multiple access (CDMA) is a family of sequences with good autocorrelation and interrelated.Code division multiple access (CDMA) technology has been successfully used in areas such as satellite communications and mobile communications. The advantages of code division multiple access (CDMA) are difficult to be maximized. Optical CDMA (Optical Code Division multiple access) (OCDMA) technology is an organic combination of optical fiber broadband resources and CDMA technology. In order to improve the performance of optical code division multiple access (OCDMA) system, G.C. Yang et al put forward the concept of 2-DOOC. A 2-D optical orthogonal code 2-DX n 脳 mkk, 位, 位 c) is a family of n 脳 m01m01s with hamming weight k. A column (called codeword. C satisfies the following two properties: 1) autocorrelation: for any positive integer rn? C? Interrelation: for any positive integer r, any two different matrices A / T n 脳 鈭，

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