Kasami序列的快速分類法｜國立清華大學博碩士論文庫

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研究生：	許哲鳴 Hsu, Che Ming
論文名稱：	Kasami序列的快速分類法 Efficient categorization scheme for Kasami sequences
指導教授：	黃之浩 Huang, Chih Hao
口試委員:	翁詠祿 Ueng, Yeong Luh 林澤 Lin, Che
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 通訊工程研究所 Communications Engineering
論文出版年：	2015
畢業學年度：	103
語文別：	英文
論文頁數：	63
中文關鍵詞：	TxID 、偽隨機序列、Kasami序列、浮水印、有限體
外文關鍵詞：	Transmitter identification, Pseudo-random sequences, Kasami sequences, watermarking, finite field
相關次數：	點閱：2 下載：0
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在數位電視系統中發射端識別碼（transmitter identification，簡稱Tx-ID）的重要性與日俱增，時至今日它已經變成關鍵角色。維持系統正常運作的檢測儀器需要它，電視直播節目也需要它。但是當接收端收到弱的訊號時，要識別弱訊號的來源並不容易，因此虛擬隨機序列（pseudo-random sequences，簡稱PN序列）被嵌入數位電視訊號中作為識別碼。而諸多PN序列中，Kasami序列（Kasami sequences）非常適合作為Tx-ID之用，因為它們可以產生為數眾多而且接近正交（orthogonal）的碼。未來很可能有需要對Tx-ID序列進行分類，例如將Tx-ID序列依不同的廣播公司分群。本論文的重點在於探討小集合（small set）Kasami序列的分類方式。我們設計了新的演算法，它可以很有效率的在 O(n^1.5 (logn)^2) 的時間之內完成Kasami序列的分類，其中ｎ為該序列之長度。電腦模擬結果顯示我們提出的演算法是很快的，在內建Intel i7 2.9GHz CPU的PC上，平均只要0.5秒（或8秒）就可以找出一個14位元（或16位元）Kasami序列的特徵參數組(w,d,d')。另外，如果PN序列的長度太長（16位元的Kasami序列之長度為65,535位元）會造成困擾時，我們建議採用單一個PN序列由多個Kasami序列串接構成的方式，在此情況下，第一個小集合Kasami序列的序列個數，可以視為整個PN序列的分類總類別數。

The transmitter identification (Tx-ID) of digital television systems becomes more and more important. Many things need it, such as test and measurement (T&M) equipment and live televised programs. However, identification of the signal source of a weak signal is quite difficult, and therefore the pseudo-random (PN) sequences, widely used in CDMA system, are buried beneath the ATSC signals for the purpose of identification of the emitting transmitter. Kasami sequences are one of well-known PN sequences and are good candidates for transmitter identification since they have good cross-correlation properties and can generate a large number of codes. In the future, there may be an emerging need to categorize Tx-ID sequences. For example, Tx-ID sequences may be grouped separately for different broadcasting companies. In this thesis, we are particularly interested in the Tx-ID sequences made of small set of Kasami sequences. Our main objective is to efficiently categorize and address Kasami sequences. We design a new algorithm that can efficiently classify Kasami sequences within O(n^1.5 (logn)^2)-time, where n is the sequence length. Simulations show that our proposed algorithm is very fast in practice. It will take 0.5 (or 8) seconds on average to find the parameter set (w,d,d') of a 14-bit (or 16-bit) Kasami sequence in the small set, by using a PC with an Intel i7 2.9GHz CPU. We also propose a method of categorization of a PN sequence consisting of several Kasami sequences. If the large length of a PN sequence will be a problem (16-bit Kasami sequence has a length of 65535 bits), we suggest to use two or more Kasami sequences concatenated together to form a single PN sequence. In this case, the size of the first Kasami sequences can be considered as the number of categories of the PN sequences.

Contents
Chapter 1. Introduction    1
Chapter 2. Pseudo-Random Noise Sequences    3
2.1 Introduction    3
2.2 PN Sequence Generation    3
2.3 Arithmetic of Binary Polynomial    6
2.4 Correlation between PN Sequences    6
2.5 Maximal Length Sequences (m-sequences)    6
2.6 PN Sequence in Direct Sequence Spread Spectrum    9
2.7 Gold Sequences    12
2.8 Kasami Sequences    13
Chapter 3. Transmitter Identification    20
3.1 Watermarking    20
3.1.1 What is a Watermark    20
3.1.2 Digital Watermarking    20
3.1.3 RF Watermarking    21
3.2 The Need for Transmitter Identification    22
3.3 Categorization of Transmitter Identification    22
3.3.1 Categorization of nominal numbers    22
3.3.2 Categorization of PN Sequences    22
3.3.3 Categorization of Kasami Sequences    23
3.4 How to Obtain Numerous Kasami Sequences    23
Chapter 4. Addressing Algorithm    25
4.1 Addressing Kasami Sequences    25
4.2 Blind Detection of Addressing Parameters    26
4.3 Truncated Subroutines for Linear Recurring Sequences    30
4.4 Enhanced Blind Detection Algorithm    34
4.4.1 Creation of the Cyclotomic Cosets Table    36
4.4.2 Store the Trace Function in Table    36
4.4.3 Elucidating Our Proposed Algorithm    38
4.4.4 Check if Two Numbers Are Co-prime    38
4.4.5 32-bit vs. 64-bit Arithmetic    39
4.4.6 Improvement of the Checking of the Recurrence Relation    40
4.4.7 Prove the Uniqueness of the Parameter set (w, d, d’) by Exhaustive Search.    44
4.4.8 Comparison of Algorithm Performance    44
4.4.9 Analysis of Computation Time    48
Chapter 5. Conclusions    58
References    59

 
List of Tables
Table 2.2.1 Time-shifted versions of PN sequence    4
Table 2.5.1 Some primitive polynomials for generating m-sequences    7
Table 2.8.1 Some m-sequences and corresponding Kasami sequences    14
Table 2.8.2 Comparison between Kasami and Gold sequences    15
Table 2.8.3 Comparison of m-sequences and Kasami sequences    16
Table 2.8.4 Different polynomials generate same Kasami sequences    18
Table 4.1.1 Examples of Kasami sequence    26
Table 4.4.1 Comparison of the simulation result of Blind Detection and Enhanced Blind    40
Table 4.4.2 Average running time of Brute Force, Blind Detection and Truncated Blind with different m’s    45
Table 4.4.3 Average running time of Blind Detection and Enhanced Blind with different m’s    46
Table 4.4.4 Average running time of Truncated Blind and Enhanced Truncated with different m’s    47
Table 4.4.5 Average running time of Brute Force, Enhanced Blind and Enhanced Truncated with different m’s    48
Table 4.4.6 Comparison of the simulation result of Enhanced Blind and Parallel Blind    54
 
List of Figures
Figure 2.2.1 PN sequence generator    4

Figure 2.2.2 A PN sequence generator with 15-stage shift register     5

Figure 2.6.1 Block diagram of a DSSS system        9

Figure 2.8.1 A sequence u to be decimated by 9 to generate w    13

Figure 2.8.2 An example generator of a small set of Kasami sequence    14

Figure 4.4.1 Comparison of Blind Detection and Enhanced Blind for m = 16    43

Figure 4.4.2 Comparison of Brute Force, Blind Detection and Truncated Blind    45

Figure 4.4.3 Comparison of Blind Detection and Enhanced Blind    46

Figure 4.4.4 Comparison of algorithm Truncated Blind and Enhanced Truncated    47

Figure 4.4.5 Comparison of Brute Force, Enhanced Blind and Enhanced Truncated    48

Figure 4.4.6 Comparison of Enhanced Blind and Parallel Blind (test case #1)     53

Figure 4.4.7 Comparison of Enhanced Blind and Parallel Blind (test case #2)     54

Figure 4.4.8 Comparison of Enhanced Blind and Parallel Blind        57

                                

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