Subscribe
Issue No.11 - Nov. (2012 vol.11)
pp: 1627-1639
Cheng Wang , Tongji University, Shanghai
Shaojie Tang , Illinois Institute of Technology, Chicago
Xiang-Yang Li , Illinois Institute of Technology, Chicago
Changjun Jiang , Tongji University, Shanghai
ABSTRACT
In this paper, we study multicast capacity for cognitive networks. We consider the cognitive network model consisting of two overlapping ad hoc networks, called the primary ad hoc network (PaN) and secondary ad hoc network (SaN), respectively. PaN and SaN operate on the same space and spectrum. For PaN (or SaN, respectively), we assume that primary (or secondary, respectively) nodes are placed according to a Poisson point process of intensity n (or m, respectively) over a unit square region. We randomly choose n_s (or m_s, respectively) nodes as the sources of multicast sessions in PaN (or SaN, respectively), and for each primary source v^p (or secondary source v^s, respectively), we pick uniformly at random n_d primary nodes (or m_d secondary nodes, respectively) as the destinations of v^p (or v^s, respectively). Above all, we assume that PaN can adopt the optimal protocol in terms of the throughput. Our main work is to design the multicast strategy for SaN by which the optimal throughput can be achieved, without any negative impact on the throughput for PaN in order sense. Depending on n_d and n, we choose the optimal one for PaN from two strategies called percolation strategy and connectivity strategy, respectively. Subsequently, we design the corresponding throughput-optimal strategy for SaN. We derive the regimes in terms of n, n_d, m, and m_d in which the upper bounds on multicast capacities for PaN and SaN can be achieved simultaneously. Unicast and broadcast capacities for the cognitive network can be derived by our results as the special cases by letting n_d=1 (or m_d=1) and n_d=n-1 (or m_d=m-1), respectively, which enhances the generality of this work.
INDEX TERMS
Throughput, Ad hoc networks, Road transportation, Slabs, Routing, Lattices, Mobile computing, percolation theory, Cognitive networks, wireless ad hoc networks, multicast capacity, random networks
CITATION
Cheng Wang, Shaojie Tang, Xiang-Yang Li, Changjun Jiang, "Multicast Capacity Scaling Laws for Multihop Cognitive Networks", IEEE Transactions on Mobile Computing, vol.11, no. 11, pp. 1627-1639, Nov. 2012, doi:10.1109/TMC.2011.212
REFERENCES
 [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, pp. 2127-2159, 2006. [2] Federal Communications Commission Spectrum Policy Task Force, "Report of the Spectrum Efficiency Working Group," technical report, Nov. 2002. [3] N. Devroye, P. Mitran, and V. Tarokh, "Achievable Rates in Cognitive Radio Channels," IEEE Trans. Information Theory, vol. 52, no. 5, pp. 1813-1827, May 2006. [4] J. Mitola, "Cognitive Radio," PhD dissertation, Royal Inst. of Technology (KTH), 2000. [5] A. Keshavarz-Haddad and R. Riedi, "Multicast Capacity of Large Homogeneous Multihop Wireless Networks," Proc. Sixth Int'l Symp. Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks and Workshops (WiOpt), 2008. [6] M. Vu and V. Tarokh, "Scaling Laws of Single-Hop Cognitive Networks," IEEE Trans. Wireless Comm., vol. 8, no. 8, pp. 4089-4097, Aug. 2009. [7] S.-W. Jeon, N. Devroye, M. Vu, S.-Y. Chung, and V. Tarokh, "Cognitive Networks Achieve Throughput Scaling of a Homogeneous Network," Proc. Int'l Symp. Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), 2009. [8] M. Franceschetti, O. Dousse, D. Tse, and P. Thiran, "Closing the Gap in the Capacity of Wireless Networks via Percolation Theory," IEEE Trans. Information Theory, vol. 53, no. 3, pp. 1009-1018, Mar. 2007. [9] O. Dousse and P. Thiran, "Connectivity vs Capacity in Dense Ad Hoc Networks," Proc. IEEE INFOCOM, 2004. [10] A. Keshavarz-Haddad and R. Riedi, "Bounds for the Capacity of Wireless Multihop Networks Imposed by Topology and Demand," Proc. ACM MobiHoc, 2007. [11] K. Lu, W. Liu, J. Wang, T. Zhang, and S. Fu, "Achieving the Capacity Bounds of Multicast in Large-Scale Wireless Networks," Proc. IEEE Int'l Symp. Information Theory (ISIT), 2010. [12] Q. Peng, X. Wang, and H. Tang, "Heterogeneity Increases Multicast Capacity in Clustered Network," Proc. IEEE INFOCOM, 2011. [13] X.-Y. Li, Y. Liu, S. Li, and S. Tang, "Multicast Capacity of Wireless Ad Hoc Networks under Gaussian Channel Model," IEEE/ACM Trans. Networking, vol. 18, no. 4, pp. 1145-1157, Aug. 2010. [14] C. Wang, C. Jiang, X.-Y. Li, S. Tang, Y. He, X. Mao, and Y. Liu, "Scaling Laws of Multicast Capacity for Power-Constrained Wireless Networks under Gaussian Channel Model," IEEE Trans. Computers, vol. 61, no. 5, pp. 713-725, May 2012. [15] X.-Y. Li, "Multicast Capacity of Wireless Ad Hoc Networks," IEEE/ACM Trans. Networking, vol. 17, no. 3, pp. 950-961, June 2009. [16] R. Meester and R. Roy, Continuum Percolation. Cambridge Univ. Press, 1996. [17] Z. Kong and E.M. Yeh, "Characterization of the Critical Density for Percolation in Random Geometric Graphs," Proc. IEEE Int'l Symp. Information Theory, 2007. [18] G. Grimmett, Percolation. Springer, 1999. [19] M. Vu, N. Devroye, and V. Tarokh, "On the Primary Exclusive Regions in Cognitive Networks," IEEE Trans. Wireless Comm., vol. 8, no. 7, pp. 3380-3385, July 2009. [20] A. Özgür, O. Lév$\hat {\rm e}$ que, and D. Tse, "Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks," IEEE Trans. Information Theory, vol. 53, no. 10, pp. 3549-3572, Oct. 2007. [21] R. Zheng, "Asymptotic Bounds of Information Dissemination in Power-Constrained Wireless Networks," IEEE Trans. Wireless Comm., vol. 7, no. 1, pp. 251-259, Jan. 2008. [22] Z. Wang, H. Sadjadpour, and S. Karande, "Fundamental Limits of Information Dissemination in Wireless Ad Hoc Networks-Part I: Single-Packet Reception," IEEE Trans. Wireless Comm., vol. 8, no. 12, pp. 5749-5754, Dec. 2009. [23] B. Sirkeci-Mergen and M. Gastpar, "On the Broadcast Capacity of Wireless Networks with Cooperative Relays," IEEE Trans. Information Theory, vol. 56, no. 8, pp. 3847-3861, Aug. 2010. [24] T. Spyropoulos, K. Psounis, and C.S. Raghavendra, "Efficient Routing in Intermittently Connected Mobile Networks: The Multiple-Copy Case," IEEE/ACM Trans. Networking, vol. 16, no. 1, pp. 77-90, Feb. 2008. [25] L. Xie and P. Kumar, "A Network Information Theory for Wireless Communication: Scaling Laws and Optimal Operation," IEEE Trans. Information Theory, vol. 50, no. 5, pp. 748-767, May 2004. [26] P. Gupta and P.R. Kumar, "The Capacity of Wireless Networks," IEEE Trans. Information Theory, vol. 46, no. 2, pp. 388-404, Mar. 2000. [27] J. Li, C. Blake, D. De Couto, H. Lee, and R. Morris, "Capacity of Ad Hoc Wireless Networks," Proc. ACM MobiCom, 2001. [28] B. Tavli, "Broadcast Capacity of Wireless Networks," IEEE Comm. Letters, vol. 10, no. 2, pp. 68-69, Feb. 2006. [29] A. Keshavarz-Haddad, V. Ribeiro, and R. Riedi, "Broadcast Capacity in Multihop Wireless Networks," Proc. ACM MobiCom, 2006. [30] X. Shakkottai, S. Liu, and R. Srikant, "The Multicast Capacity of Large Multihop Wireless Networks," Proc. ACM MobiHoc, 2007. [31] C. Hu, X. Wang, D. Nie, and J. Zhao, "Multicast Scaling Laws with Hierarchical Cooperation," Proc. IEEE INFOCOM, 2010. [32] M. Grossglauser and D. Tse, "Mobility Increases the Capacity of Ad Hoc Wireless Networks," IEEE/ACM Trans. Networking, vol. 10, no. 4, pp. 477-486, Aug. 2002. [33] C. Hu, X. Wang, and F. Wu, "Motioncast: On the Capacity and Delay Tradeoffs," Proc. ACM MobiHoc, 2009. [34] A. El Gamal, J. Mammen, B. Prabhakar, and D. Shah, "Throughput-Delay Trade-Off in Wireless Networks," Proc. IEEE INFOCOM, 2004. [35] G. Sharma and R. Mazumdar, "Scaling Laws for Capacity and Delay in Wireless Ad Hoc Networks with Random Mobility," Proc. IEEE Int'l Conf. Comm., 2004. [36] X. Lin, G. Sharma, R. Mazumdar, and N. Shroff, "Degenerate Delay-Capacity Tradeoffs in Ad-Hoc Networks with Brownian Mobility," IEEE/ACM Trans. Networking, vol. 52, no. 6, pp. 2777-2784, June 2006. [37] G. Sharma and R. Mazumdar, "Delay and Capacity Trade-Off in Wireless Ad Hoc Networks with Random Way-Point Mobility," technical report, Dept. of Electrical Computer Eng., Purdue Univ., http://ece.purdue.edugsharma, 2005. [38] G. Sharma, R. Mazumdar, and N. Shroff, "Delay and Capacity Trade-Offs in Mobile Ad Hoc Networks: A Global Perspective," IEEE/ACM Trans. Networking, vol. 15, no. 5, p. 992, Oct. 2007. [39] T. Spyropoulos, K. Psounis, and C.S. Raghavendra, "Performance Analysis of Mobility-Assisted Routing," Proc. ACM MobiHoc, pp. 49-60, 2006. [40] H. Luo, R. Ramjee, P. Sinha, L. Li, and S. Lu, "UCAN: A Unified Cellular and Ad-Hoc Network Architecture," Proc. ACM MobiCom, 2003. [41] B. Liu, P. Thiran, and D. Towsley, "Capacity of a Wireless Ad Hoc Network with Infrastructure," Proc. ACM MobiHoc, 2007. [42] O. Dousse, P. Thiran, and M. Hasler, "Connectivity in Ad Hoc and Hybrid Networks," Proc. IEEE INFOCOM, 2002. [43] X. Mao, X.-Y. Li, and S. Tang, "Multicast Capacity for Hybrid Wireless Networks," Proc. ACM MobiHoc, 2008. [44] C. Wang, X.-Y. Li, C. Jiang, S. Tang, and Y. Liu, "Multicast Throughput of Hybrid Wireless Networks Under Gaussian Channel Model," IEEE Trans. Mobile Computing, vol. 10, no. 6, pp. 839-852, June 2011. [45] Y. Lin and Y. Hsu, "Multihop Cellular: A New Architecture for Wireless Communications," Proc. IEEE INFOCOM, 2000. [46] H. Hsieh and R. Sivakumar, "On Using the Ad-hoc Network Model in Cellular Packet Data Networks," Proc. ACM MobiHoc, 2002. [47] B. Liu, Z. Liu, and D. Towsley, "On the Capacity of Hybrid Wireless Networks," Proc. IEEE INFOCOM, 2003. [48] U.C. Kozat and L. Tassiulas, "Throughput Capacity of Random Ad Hoc Networks with Infrastructure Support," Proc. ACM MobiCom, 2003. [49] A. Agarwal and P. Kumar, "Capacity Bounds for Ad Hoc and Hybrid Wireless Networks," ACM SIGCOMM Computer Comm. Rev., vol. 34, no. 3, pp. 71-81, 2004. [50] W. Huang, X. Wang, and Q. Zhang, "Capacity Scaling in Mobile Wireless Ad Hoc Network with Infrastructure Support," Proc. IEEE 30th Int'l Conf. Distributed Computing Systems (ICDCS '10), 2010. [51] S. Jafar and S. Srinivasa, "Capacity Limits of Cognitive Radio with Distributed and Dynamic Spectral Activity," IEEE J. Selected Areas in Comm., vol. 25, no. 3, pp. 529-537, Apr. 2007. [52] C. Wang, C. Jiang, X.-Y. Li, and Y. Liu, "Multicast Throughput for Large Scale Cognitive Networks," ACM/Springer Wireless Networks, vol. 16, no. 7, pp. 1945-1960, 2010. [53] C. Wang, S. Tang, X.-Y. Li, and C. Jiang, "Multicast Capacity of Multihop Cognitive Networks," Proc. IEEE Sixth Int'l Conf. Mobile Ad Hoc and Sensor Systems (MASS '09), 2009.