會合演算法(rendezvous)是運作在無線感知網路(Cognitive Radio Networks, CRN)中的一項重要技術，用於使用者之間以相同的頻道來建立通訊。在過去大多數文獻假設每位使用者只配備了一根天線(radio)。但是實際情況使用者可能有多根天線(multi-radio)。在此論文中，我們針對具有多根天線的情境提出了兩個會合跳頻(channel hopping)演算法以解決會合問題。
在第一個快速會合(Fast Multi-Radio Rendezvous, FMRR)跳頻演算法中，我們將多個時隙(time slots) 形成一個時間區間。在此時間區間中每個使用者的行為就相當於它具有至少兩根天線。假設總共有N個頻道、時間區間為M個時隙組成，時間區間的長度M = 2⌈lg ⌈lg N⌉⌉ + 7。我們後續證明了FMRR演算法的最大會合時間(Maximum Time To Rendezvous, MTTR)會在(9MN_1 N_2)/(m_1 m_2 )個時隙以內，其中n1及n2是使用者1及2可用頻道的數量，而m1及m2是使用者1及2的天線數量。當每個使用者僅配備一根天線和兩個可用頻道時，我們的MTTR範圍僅為2⌈lg ⌈lg N⌉⌉ + 7，這與過去文獻中的16(⌈lg⌈lgN⌉⌉ + 1)有很大的改進，並且相較於過去多天線的研究，FMRR還能兼容單根天線，在模擬中，FMRR演算法的MTTR及ETTR比文獻中的多天線演算法效能好。
在第二個會合算法中，我們解決了多天線場域情況中的另一個問題，改善了平均會合的rendezvous時間(Expected Time To Rendezvous, ETTR)。我們提出了類隨機(Quasi-Random, QR)跳頻演算法，該算法具有與隨機算法相當的ETTR，而無需使用者標誌(identifier)，並且可以在對稱、異質、不同步等困難環境中執行。
在QR演算法中，當每個使用者具有單根天線時，ETTR將收斂在M = (n_1 n_2)/G+Mn_1 n_2·(1 - 〖G/(n_1 n_2 ))〗^M，其中G是這兩個使用者共同頻道的數量。除此之外QR演算法的MTTR與FMRR演算法一樣皆為(9MN_1 N_2)/(m_1 m_2 )個時段，但M的長度卻是更短的⌈lgN⌉ + 1。在模擬中，儘管FMRR的MTTR可以到達O(lglgN)，而QR則為O(lgN)。當N小於256時，QR的ETTR和MTTR優於FMRR。

Rendezvous is a fundamental operation in cognitive radio networks (CRNs) for establishing a communication link on a commonly-available channel between cognitive users. Commonly, most of the existing works assume that each cognitive user is equipped with one radio. However, it is possible that users may have multiple radios. In this dissertation, we address two rendezvous problems by proposing rendezvous algorithms for the scenario of users having multiple radios.
We have proposed two algorithms. In the first fast multi-radio rendezvous (FMRR) algorithm, we construct the channel hopping (CH) sequence by grouping several time slots of a single radio into an interval. By this, at the interval level, each user behaves as if it had at least two radios. By assuming N commonly available channels, the interval length is chosen to be M time slots, where M = 2⌈lg ⌈lg N⌉⌉ + 7. In the second rendezvous algorithm, we solve another problem with the multiple radio rendezvous scenario to improve the expected time to-rendezvous (ETTR). We propose the quasi-random (QR) CH algorithm that has a comparable ETTR to the random algorithm, without the need of a unique identifier (ID). Therefore, it is straightforward to implement in the symmetric, asynchronous, and heterogeneous setting.
We show that the maximum time-to-rendezvous (MTTR) of our FMRR algorithm is bounded above by (9MN_1 N_2)/(m_1 m_2 ) time slots, where (resp. n2) is the number of available channels to user 1 (resp. 2), and m1 (resp. m2) is the number of radios for user 1 (resp. 2). When each user is equipped with only one radio and two available channels, our MTTR bound is only M which is a significant improvement over the existing work having MTTR 16(⌈lg⌈lgN⌉⌉ + 1). Our algorithm is yet backward compatible to single radios. Additionally, in the second algorithm, when each secondary user (SU) has a single radio, the ETTR is bounded above by M = (n_1 n_2)/G+Mn_1 n_2·(1 - 〖G/(n_1 n_2 ))〗^M, where G is the number of common channels between these two users. Additionally, our method has the best bound to MTTR, which is (9MN_1 N_2)/(m_1 m_2 ) time slots, where M = ⌈lgN⌉ + 1. In the simulations, although the MTTR of FMRR can reach O(lglgN) while that of QR is O(lgN). The ETTR and MTTR of QR are better than FMRR when N is less than 256.

Chapter 1 Introduction 1
1.1 Introduction to Channel hopping in CRN 1
1.2 Classification of Channel hopping schemes 3
1.3 Motivation 5
1.4 Contributions 6
Chapter 2 Related Works 8
Chapter 3 Multi-Radio Rendezvous Algorithm in Heterogeneous Cognitive Radio Networks 14
3.1 Problem Background and Scenario 14
3.2 THE GENERIC CH SEQUENCES 16
3.3 The Enhanced CH Sequences 28
3.4 Simulation results 38
Chapter 4 Quasi Random Rendezvous Algorithm in Heterogeneous Cognitive Radio Networks 46
4.1 Background and problem scenario 46
4.2 The Generic CH Sequences 48
4.3 The Enhanced CH Sequences 61
4.4 Simulation results of quasi-random CH algorithm 70
Chapter 5 Conclusion and Future work 76
5.1 Conclusion 76
5.2 Future Work 77
References 79

[1] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, “NeXt Generation/Dynamic Spectrum Access Cognitive Radio Wireless Networks: A Survey,” Computer Networks, Vol. 50, No. 13, pp. 2127-2159, Sep. 2006.
[2] S. Alpern and S. Gal. The Theory of Search Games and Rendezvous. Dordrecht: Kluwer Academic Publishers, Jan. 2003.
[3] C. O. de Sousa, D. Passos, R. C. Carrano, and C. Albuquerque, “Multi-Channel Continuous Rendezvous in Cognitive Networks,” Proceedings of the ACM International Conference on Modelling, Analysis and Simulation of Wireless and Mobile Systems (MSWiM), pp. 63-70, NY, USA, Nov. 2017.
[4] J. Jia, Q. Zhang, and X. Shen, “HC-MAC: A Hardware-Constrained Cognitive MAC for Efficient Spectrum Management,” IEEE Journal on Selected Areas in Communications, Vol. 26, No. 1, pp. 106-117, Jan. 2008.
[5] B. Hamdaoui and K. G. Shin, “OS-MAC: An Efficient MAC Protocol for Spectrum-Agile Wireless Networks,” IEEE Transactions on Mobile Computing, Vol. 7, No. 8, pp. 915-930, Aug. 2008.
[6] B. F. Lo, I. F. Akyildiz, and A. M. Al-Dhelaan, “Efficient Recovery Control Channel Design in Cognitive Radio Ad Hoc Networks,” IEEE Transactions on Vehicular Technology, Vol. 59, No. 9, pp. 4513-4526, Sep. 2010.
[7] M. Kim and S. Yoo, “Distributed Coordination Protocol for Ad Hoc Cognitive Radio Networks,” Journal of Communications and Networks, Vol. 14, No. 1, pp. 51-62, Jan. 2012.
[8] Z. Htike, C. S. Hong, and S. Lee, “The Life Cycle of the Rendezvous Problem of Cognitive Radio Ad Hoc Networks: A Survey,” Journal of Computing Science and Engineering, Vol. 7, No. 2, pp. 81-88, June 2013.
[9] L. Yu, H. Liu, Y.-W. Leung, X. Chu, and Z. Lin, “Channel-Hopping Based on Available Channel Set for Rendezvous of Cognitive Radios,” Proceedings of the IEEE International Conference on Communications (ICC), pp. 1573-1579, Sydney, Australia, June 2014.
[10] Y.-W. Chen, P.-Y. Liao, and Y.-C. Wang, “A Channel Hopping Scheme for Continuous Rendezvous and Data Delivery in Cognitive Radio Networks,” Peer-to-Peer Networking and Applications, Vol. 9, No. 1, pp. 16-27, Jan. 2016.
[11] N. C. Theis, R. W. Thomas, and L. A. DaSilva, “Rendezvous for Cognitive Radios,” IEEE Transactions on Mobile Computing, Vol. 10, No. 2, pp. 216-227, Feb. 2011.
[12] Z. Lin, H. Liu, X. Chu, and Y.-W. Leung, “Jump-Stay Based Channel Hopping Algorithm with Guaranteed Rendezvous for Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), pp. 2444-2452, Shanghai, China, April 2011.
[13] H. Liu, Z. Lin, X. Chu, and Y.-W Leung, “Jump-Stay Rendezvous Algorithm for Cognitive Radio Networks,” IEEE Transactions on Parallel and Distributed Systems, Vol. 23, No. 10, pp. 1867-1881, Oct. 2012.
[14] Z. Lin, H. Liu, X. Chu, and Y. W. Leung, “Enhanced Jump-Stay Rendezvous Algorithm for Cognitive Radio Networks,” IEEE Communications Letters, Vol. 17, No. 9, pp. 1742-1745, Sep. 2013.
[15] I. Chuang, H.-Y. Wu, K.-R. Lee, and Y.-H Kuo, “Alternate Hop-and-Wait Channel Rendezvous Method for Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), pp. 746-754, Turin, Italy, April 2013.
[16] J. Li, H. Zhao, J. Wei, D. Ma, and L. Zhou, “Sender-Jump Receiver-Wait: A Simple Blind Rendezvous Algorithm for Distributed Cognitive Radio Networks,” IEEE Transactions on Mobile Computing, Vol. 17, No. 1, pp. 183-196. Jan. 2018.
[17] L. DaSilva and I. Guerreiro, “Sequence Based Rendezvous for Dynamic Spectrum
Access,” Proceedings of the IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), pp. 1-7, Chicago, USA, Oct. 2008.
[18] J. Shin, D. Yang, and C. Kim, “A Channel Rendezvous Scheme for Cognitive Radio Networks,” IEEE Communications Letters, Vol. 14, No. 10, pp. 954-956, Oct. 2010.
[19] Z. Gu, Q.-S. Hua, and W. Dai, “Local Sequence Based Rendezvous Algorithms for Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Sensing, Communication, and Networking (SECON), pp. 194-202, Singapore, July 2014.
[20] K. Bian, J.-M. Park, and R. Chen, “A Quorum-Based Framework for Establishing Control Channels in Dynamic Spectrum Access Networks,” Proceedings of the ACM Mobile Computing and Networking (MobiCom), pp. 216-230, Beijing, China, Sep. 2009.
[21] K. Bian and J.-M. Park, “Asynchronous Channel Hopping for Establishing Rendezvous in Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), pp. 236-240, Shanghai, China, April 2011.
[22] K. Bian, J.-M. Park, and R. Chen, “Control Channel Establishment in Cognitive Radio Networks Using Channel Hopping,” IEEE Journal on Selected Areas in Communications, Vol. 29, No. 4, pp. 689-703, April 2011.
[23] K. Bian and J.-M. Park, “Maximizing Rendezvous Diversity in Rendezvous Protocols for Decentralized Cognitive Radio Networks,” IEEE Transactions on Mobile Computing, Vol. 12, No. 7, pp. 1294-1307, July 2013.
[24] C. Chao, H. Fu, and L. Zhang, “A Fast Rendezvous Guarantee Channel Hopping Protocol for Cognitive Radio Networks,” IEEE Transactions on Vehicular Technology, Vol. 64, No. 12, pp. 1-13, Dec. 2014.
[25] J.-P. Sheu, C.-W. Su, and G.-Y. Chang, “Asynchronous Quorum-based Channel Hopping Schemes for Cognitive Radio Networks,” IEEE Transactions on Communications, Vol. 64, No. 3, pp. 918-930, March 2016.
[26] J.-F. Huang, G.-Y. Chang, and G.-X. Hung, “A Quorum-based Channel Hopping Scheme for Jamming Resilience,” Proceedings of IEEE International Conference on Parallel and Distributed Systems (ICPADS), pp. 896-899, Hsinchu, Taiwan, Dec. 2014.
[27] G. Li, Z. Gu, X. Lin, H. Pu, and Q.-S. Hua, “Deterministic Distributed Rendezvous Algorithms for Multi-Radio Cognitive Radio Networks,” Proceedings of the ACM International Conference on Modelling, Analysis and Simulation of Wireless and Mobile Systems (MSWiM), pp. 313-320, Montreal, Canada, Sep. 2014.
[28] L. Yu, H. Liu, Y. W. Leung, X. Chu, and Z. Lin, “Adjustable Rendezvous in Multi-Radio Cognitive Radio Networks,” Proceedings of the IEEE Global Communications Conference (GLOBECOM), pp. 1-7, San Diego, CA, Dec. 2015.
[29] J.-P. Sheu and J.-J. Lin, “A Multi-Radio Rendezvous Algorithm Based on Chinese Remainder Theorem in Heterogeneous Cognitive Radio Networks,” IEEE Transactions on Mobile Computing, Vol. 17, No. 9, pp. 1980-1990, Sep. 2018.
[30] L. Yu, H. Liu, Y.-W. Leung, X. Chu, and Z. Lin, “Multiple Radios for Fast Rendezvous in Cognitive Radio Networks,” IEEE Transactions on Mobile Computing, Vol. 14, No. 9, pp. 1917-1931, Sep. 2015.
[31] A. Li, G. Han, and T. Ohtsuki, “Multiple Radios for Fast Rendezvous in Heterogeneous Cognitive Radio Networks,” IEEE Access, Vol. 7, pp. 37342-37359, March 2019.
[32] T.-H. Lin, G.-C. Yang, and W. C. Kwong, “A Homogeneous Multi-Radio Rendezvous Algorithm for Cognitive Radio Networks,” IEEE Communications Letters, Vol. 23, No. 4, pp. 736-739, April 2019.
[33] J. Li and J. Xie, “Practical Fast Multiple Radio Blind Rendezvous Schemes in Ad-Hoc Cognitive Radio Networks,” Proceedings of Resilience Week (RWS), pp. 1-6, Philadelphia, PA, USA, Aug. 2015.
[34] R. N. Yadav and R. Misra, “Periodic Channel-Hopping Sequence for Rendezvous in Cognitive Radio Networks,” Proceedings of the International Conference on Advances in Computing, Communications and Informatics (ICACCI), pp. 1787-1792, Kochi, India, Aug. 2015.
[35] C.-F. Shih, T. Y. Wu, and W. Liao, “DH-MAC: A Dynamic Channel Hopping MAC Protocol for Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Communications (ICC), pp. 1-5, Cape Town, South Africa, May 2010.
[36] I. Chuang, H.-Y. Wu, K.-R. Lee, and Y.-H. Kuo, “A Fast Blind Rendezvous Method by Alternate Hop-and-Wait Channel Hopping in Cognitive Radio Networks,” IEEE Transactions on Mobile Computing, Vol. 13, No. 99, pp. 2171-2184, Jan. 2014.
[37] L. Chen, K. Bian, L. Chen, C. Liu, J. M. J. Park, and X. Li, “A Group Theoretic Framework for Rendezvous in Heterogeneous Cognitive Radio Networks,” Proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 165-174, PA, USA, Aug. 2014.
[38] C.-S. Chang, C.-Y. Chen, D.-S. Lee, and W. Liao, “Efficient Encoding of User IDs for Nearly Optimal Expected Time-To-Rendezvous in Heterogeneous Cognitive Radio Networks,” IEEE/ACM Transactions on Networking, Vol. 25, No. 6, pp. 3323-3337, June 2017.
[39] L. Chen, K. Bian, L. Chen, C. Liu, J.-M. J. Park, and X. Li, “A Group-Theoretic Framework for Rendezvous in Heterogeneous Cognitive Radio Networks,” Proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 165-174, Philadelphia, PA, USA, Aug. 2014.
[40] S. Chen, A. Russell, A. Samanta, and R. Sundaram, “Deterministic Blind Rendezvous in Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Distributed Computing Systems (ICDCS), pp. 358-367, Madrid, Spain, June 2014.
[41] Z. Gu, H. Pu, Q.-S. Hua, and F. C. M. Lau, “Improved Rendezvous Algorithms for Heterogeneous Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), pp. 154-162, Hong Kong, May 2015.
[42] L. Chen, S. Shi, K. Bian, and Y. Ji, “Optimizing Average-Maximum TTR Trade-off for Cognitive Radio Rendezvous,” Proceedings of the IEEE International Conference on Communications (ICC), pp. 7707-7712, London, UK, June 2015.
[43] X. J. Tan, J. Wang, and Y. Yuan, “Difference-Set-Based Channel Hopping for Minimum-Delay Blind Rendezvous in Multi-Radio Cognitive Radio Networks,” IEEE Transactions on Vehicular Technology, Vol. 68, No. 5, pp. 4918-4932, May 2019.
[44] G.-Y. Chang, J.-F. Huang, and Y.-S. Wang, “Matrix-Based Channel Hopping Algorithms for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, Vol. 14, No. 5, pp. 2755-2768, May 2015.
[45] G.-Y. Chang and J.-F. Huang, “A Fast Rendezvous Channel-Hopping Algorithm for Cognitive Radio Networks,” IEEE Communications Letters, Vol. 17, No. 7, pp. 1475-1478, July 2013.
[46] G.-Y. Chang, S.-Y. Wang, and Y.-X. Liu, “A Jamming-Resistant Channel Hopping Scheme for Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, Vol. 16, No. 10, pp. 6712-6725, Oct. 2017.
[47] J.-F. Huang, G.-Y. Chang, and J.-X. Huang, “Anti-Jamming Rendezvous Scheme for Cognitive Radio Networks,” IEEE Transactions on Mobile Computing, Vol. 16, No. 3, pp. 648-661, March 2017.
[48] C.-S. Chang, D.-S. Lee, and W. Liao, “A Tutorial on Multichannel Rendezvous in Cognitive Radio Networks,” Chapter 1 of Cognitive Radio Networks: Performance, Applications and Technology. Nova Science Publisher, Jan. 2018.
[49] P. Bahl, R. Chandra, and J. Dunagan, “SSCH: Slotted Seeded Channel Hopping for Capacity Improvement in IEEE 802.11 Ad Hoc Wireless Networks,” Proceedings of the Annual International Conference on Mobile Computing and Networking (MobiCom), pp. 216-230, NY, USA, Oct. 2004.
[50] P. K. Sahoo, S. Mohapatra, and J.-P. Sheu, “Dynamic Spectrum Allocation Algorithms for Industrial Cognitive Radio Networks,” IEEE Transactions on Industrial Informatics, Vol. 14, No. 7, pp. 3031-3043, July 2017.
[51] Y. R. Kondareddy and P. Agrawal, “Synchronized MAC Protocol for Multi-hop Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Communications (ICC), Beijing, China, May 2008.
[52] M. El Bachraoui, “Primes in the interval [2n, 3n],” International Journal of Contemporary Mathematical Sciences, Vol. 1, No. 13, pp. 617-621, Jan. 2006.
[53] Z. Gu, Q.-S. Hua, Y. Wang, and F. C. M. Lau, “Nearly Optimal Asynchronous Blind Rendezvous Algorithm for Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Sensing, Communication, and Networking (SECON), pp. 371-379, New Orleans, USA, Dec. 2013.
[54] J. Singer, “A Theorem in Finite Projective Geometry and Some Applications to Number Theory,” Transactions of the American Mathematical Society, Vol. 43, No. 3, pp. 377-385, May 1938.
[55] Y.-C. Chang, C.-S. Chang, and J.-P. Sheu, “An Enhanced Fast Multi-Radio Rendezvous Algorithm in Heterogeneous Cognitive Radio Networks,” IEEE Transactions on Cognitive Communications and Networking, Vol. 4, No. 4, Dec. 2018.
[56] Z. Zhang, B. Yang, M. Liu, Z Li, and X. Guo, “A Quaternary-Encoding-Based Channel Hopping Algorithm for Blind Rendezvous in Distributed IoTs,” IEEE Transactions on Communications, Vol. 67, No. 10, Oct. 2019.
[57] Y. Fu, Y. Wang, Z. Gu, X. Zheng, T. Wei, Z. Cao, H. Cui, and F. C. M. Lau, “How Local Information Improves Rendezvous in Cognitive Radio Networks,” Proceedings of the IEEE International Conference on Sensing, Communication, and Networking (SECON), pp. 1-9, Hong Kong, June 2018.