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

[1] ATSC, ATSC A/110: Standard for Transmitter Synchronization, April 2011.
[2] X. Wang, Y. Wu, and B. Caron, “Transmitter identification using embedded pseudo-random sequences,” IEEE Transactions on Broadcasting, vol. 50, no. 3, pp. 244–252, September 2004.
[3] X. Feng and H.-C. Wu, “Injection-level optimization for digital television transmitter identification systems using Kasami sequences,” IET Communications, vol. 5, no. 16, pp. 2397–2406, November 2011.
[4] X. Feng, H.-C. Wu, and S. Y. Chang, “On the injection-level optimization for digital television transmitter identification systems using Kasami sequences,” in Proceedings of IEEE International Conference on Communications (ICC), June 2011, pp. 1–5.
[5] X. Feng, H.-C. Wu, and Y. Wu, “New identification sequence analysis for multiple transmitters subject to arbitrary topologies,” in Proceedings of IEEE Global Telecommunications Conference, December 2010, pp.1–5.
[6] X. Feng, H.-C. Wu, and Y. Wu, “Geometric capacity studies for DTV transmitter identification using Kasami sequences,” in Proceedings of IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB), March 2010, pp. 1–6.
[7] S. I. Park, H. Lim, H. M. Kim, Y. Wu, and W. Oh, “Augmented data transmission for the ATSC terrestrial DTV system,” IEEE Transactions on Broadcasting, vol. 58, no. 2, pp. 261–268, June 2012.
[8] S. I. Park, J. Kim, D. Choi, H. M. Kim, and W. Oh, “RF watermark backward compatibility tests for the ATSC terrestrial DTV receivers,”IEEE Transactions on Broadcasting, vol. 57, no. 2, pp. 246–252, June 2011.
[9] F. Yang, L. N. Hu, L. Gui, Z. Wang, and W. Zhang, “Transmitter identification with watermark signal in DVB-H signal frequency network,”IEEE Transactions on Broadcasting, vol. 55, no. 3, pp. 663–667, September 2009.
[10]ATSC, ATSC A/111: ATSC Recommended Practice: Design Of Multiple Transmitter Networks, September 2009.
[11]H.-C. Wu, T. Xia, and Y. Wu, “Novel channel-estimation based transmitter-identification for digital television signals,” in Proceedings of IEEE International Symposium on Broadband Multimedia Systems and Broadcasting, June 2013, pp. 1–8.
[12]X. Feng, H.-C. Wu, Y. Wu, and X. Wang, “Kasami sequence studies for DTV transmitter identification,” IEEE Transactions on Consumer Electronics, vol. 58, no. 4, pp. 1138–1146, November 2012.
[13]H.-C. Wu and Y. Wu, “Novel robust transmitter identification technique for digital television signals,” in Proceedings of IEEE Global Telecommunications Conference (GLOBECOM), December 2013, pp. 1–6.
[14]T. Kasami, “Weight distribution formula for some class of cyclic codes,”Report 0475236 at Coordinated Science Lab, University of Illinois at Urbana, April 1966.
[15]Scott C.-H. Huang and Hsiao-Chun Wu, Efficient Addressing Algorithm for Categorizing Kasami Sequences, IEEE Wireless Communications and Networking Conference (WCNC), pp. 440–445, March 2015.
[16]HU Lingna, JIANG Lingge, HE Chen and YANG Feng, Transmitter Identification in DVB-H System with Steganography Signal, Chinese Journal of Electronics, Vol.19, No.1, Jan. 2010.
[17]Helleseth, T. & Kumar, P.V., Mobile Communications Handbook, CRC Press LLC, 1999.
[18]Mosa Ali Abu-Rgheff, Introduction to CDMA Wireless Communications, Academic Press, 2007.
[19]Dr Alison Griffiths & Amr El-HELW, Building a Dircet sequence spread spectrum Model, Staffordshire University.
[20]Amol Shah, Code Division Multiple Access: A Tutorial, Wireless Communications, Rowan University, November 24, 1999.
[21]Anil Kumar, Abhijit Mitra and S.R. Mahadeva Prasanna, “On the Effectivity of Different Pseudo-Noise and Orthogonal sequences for Speech Encryption from Correlation Properties”, International journal of information technology, 2007.
[22]P. Desain, J. Farquhar, J. Blankespoor, and S. Gielen, Detecting spread spectrum pseudo random noise tags in EEG/MEG using a structure-based decomposition, Radbound University, Nijmegen, The Netherlands.
[23]Mark Goresky and Andrew Klapper, Pseudo-noise Sequences based on Algebraic Feedback Shift Registers, IEEE Transactions on Information Theory, April 2006.
[24]ir .J.Meel, "Spread Spectrum (SS)", DE NAYER instituut, Sint-Katelijne-Waver, Belgium, Dec.1999.
[25]Md. Alamgir Hossain, Md. Shariful Islam, and Md. Sadek Ali, Performance Analysis of Barker Code Based on Their Correlation Property in Multiuser Environment, International Journal of Information Sciences and Techniques (IJIST), Vol.2, No.1, January 2012.
[26]林福林, 顏楠源, 沈義順, 陳曉華, 展頻通訊與CDMA, Principles of Spread Spectrum Communications and CDMA, 滄海書局, 2006.
[27]Edfors, Molisch, Tufvesson, Spread Spectrum, Slides for "Wireless Communications".
[28]G.VENKAT REDDY, Performance Evaluation of Different DS-CDMA Receivers Using Chaotic Sequences, National Institute of Technology, Rourkela, 2007.
[29]A. Ahmad1, S. S. Al-Busaidi1, A. Al Maashri1, M. Awadalla1, M. A. K. Rizvi and N. Mohanan, Computing and Listing of Number of Possible m-sequence Generators of Order n, Indian Journal of Science and Technology, 2013.
[30]V. Anil Kumar, Abhijit Mitra, and S. R. M. Prasanna, Performance Analysis of Different Pseudo Noise Sequences for Speech Encryption, IIT Guwahati, India.
[31]R.Gold, “Optimal Binary Sequences for Spread Spectrum Multiplexing,” IEEE. Trans. Inform. Theory.vol. IT-13 , pp.619-621.October 1967.
[32]D. V. Sarwate and M. B. Pursley, “Correlation properties of pseudo random and related sequences,” Proc. IEEE, vol. 68, no. 5, pp. 593-619, May 1980.
[33]Zartash Afzal Uzmi, Simplified Multiuser Detection for CDMA Systems, Stanford University, 2003.
[34]J.G. Proakis, Digital Communications, McGraw-Hill, 1989.
[35]S. Golomb, Shift Register Sequences, Revised Edition. Laguna Hills, CA: Aegean Park, 1982.
[36]CDMA Online. (1999). CMDA Online. <http://www.cdmaonline.com>
[37]Digital watermarking, Wikipedia, https://en.wikipedia.org/wiki/Digital_watermarking
[38]Wendy Russell, What is a Watermark? http://presentationsoft.about.com/od/uvw/g/080221watermark.htm
[39]Watermarks, Georgia Institute of Technology, Atlanta, Georgia, http://www.ipst.gatech.edu/amp/education/watermark/watermarks.htm
[40]Frank Y. Shih: Digital watermarking and steganography: fundamentals and techniques. Taylor & Francis, Boca Raton, FL, USA, 2008.
[41]Gerrit Cornelis Langelaar, Real-time Watermarking Techniques for Compressed Video Data, 2000.
[42]Ned Soseman, Synchronized digital television, August 5, 2012.
[43]Meintel, Sgrignoli, and Wallace, DTV DTx Field Test Report, 2008.
[44]Yiyan Wu, Xianbin Wang and Bernard Caron, DTV Transmitter Identification Using Embedded Pseudo Random Sequences, Communications Research Centre, Canada.
[45]ATSC, ATSC A/82: Automatic Transmitter Power Control (ATPC) Data Return Link (DRL) Standard, February 2008.
[46]Ayse Kortun, Spreading Codes in CDMA Detection, Eastern Mediterranean University, July 2003.
[47]R. Lidl and H. Niederreiter, Finite Fields, ser. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1997, vol. 20.