1. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users Yingzhe Li, Xinbing Wang, Xiaohua Tian Department of Electronic Engineering Shanghai Jiao Tong University, China Xue Liu School of Computer Science McGill University, CA 1

2. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 22 Outline Introduction Background Motivation Objectives System Model Routing and Scheduling Scheme Capacity and Delay Scaling Performance Conclusion

3. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 33 Background  Cognitive Radio Network (CRN)   The underutilization of limited spectral resource motivates the study of cognitive radio network.   Cognitive Radio Network consists of primary users (PUs) licensed to the spectrum, and secondary users (SUs) which access the spectrum opportunistically.   Due to the characteristics of cognitive radio network, the study of throughput and delay scaling laws in cognitive radio network is challenging.

4. 4 Background  The throughput scaling of cognitive radio network is investigated in [S. Jeon, 2009] and [C. Yin, 2010].  Study overlapping static primary and secondary network, where secondary network has higher node density.  Both networks can achieve the same throughput scaling as the stand-alone network.  [L. Gao, 2011] proves that cooperation among PUs and SUs can improve the throughput and delay scaling in CRN.  Secondary users are willing to relay the primary packets.  When SUs are mobile (i.i.d. mobility model), primary network can achieve near constant throughput and delay scaling. [S. Jeon, 2009]: S. Jeon, N. Devroye, M. Vu, S. Chung, and V. Tarokh, “Cognitive networks achieve throughput scaling of a homogeneous network, ” IEEE Trans. Info. Theory, to appear. [C. Yin, 2010]: C. Yin, L. Gao, and S. Cui, “Scaling laws for overlaid wireless networks: A cognitive radio network vs. a primary network,” IEEE Trans. Networking, vol. 18, no. 4, Aug. 2010. [L. Gao, 2011]: L. Gao, R. Zhang, C. Yin, and S. Cui, “Throughput and Delay Scaling in Supportive Two-tier Networks ” to appear in JSAC 2011.

5. Background  [X. Wang, 2011] studies a static primary network and a multi- layer mobile secondary network coexist in the network.  The secondary network follows a special-designed hierarchical i.i.d. mobility model, where SUs of different layer have different moving areas.  Near constant capacity and delay scaling laws for primary network can be achieved, i.e. and. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 5 [X. Wang, 2011]: X. Wang, L. Fu, Y. Li, Z. Cao and X. Gan, “Mobility Reduces the Number of Secondary Users in Cognitive Radio Network” in Proc. of IEEE GLOBECOM, 2011.

6. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 66 Motivation & Objectives  Motivated by the fact that:   Cooperation and Mobility could significantly improve the scaling laws in Cognitive Radio Network.   Different mobile secondary nodes could have different moving areas in Cognitive Radio Network (Mobility Heterogeneity).  We study:   A more general and representative mobility model which reflects the mobility heterogeneity.   The routing and scheduling schemes which utilize the mobility heterogeneity of secondary users.   The impact of mobility heterogeneity on the scaling laws of Cognitive Radio Network

7. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 77 Outline Introduction System Model Hierarchical Relay Algorithm Performance Of The Hierarchical Relay Algorithm Conclusion

8. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 88 System model – I/VI  Network Model:   n static primary users are randomly and evenly distributed in the unit square area.   mobile secondary users, where   Source and destination are randomly grouped one by one in each network.   The unit square is divided into non-overlapping small square cells, with side length, where.

9. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 99 System model – II/VI  Channel Model:   We apply the Gaussian Channel Model to regulate the transmission rate. The data rate from primary transmitter to primary receiver : : interference from other primary transmitters : interference from all the secondary transmitters The data rate from secondary transmitter to secondary receiver is defined similarly.

10. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 10 System model – III/VI  Mobility Model for Secondary Users:  SUs are uniformly and randomly distributed at the beginning.  Each secondary user moves within a circular region centered at its initial position according to i.i.d. mobility model. 10

11. System model – IV/VI  Mobility Model for Secondary Users:  Among all the secondary users, the moving area of each mobile SU is, where follows the discrete uniform distribution: with equal probability. h=O(log n) and are random positive values, h and would determine the mobility heterogeneity together.  We call the SUs with the i-th type secondary user, and each type consists of mobile secondary users. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 11

12. System model – V/VI  Mobility Model for Secondary Users: Denote the k-th secondary user of type i as, and its initial position as, where,. Under the proposed mobility model:, where Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 12

13. System model – VI/VI  Definition of Throughput:   The throughput per S-D pair is defined as the average data rate (in bits/time-slot) that each source node can transmit to its chosen destination.  Definition of Delay:  The delay of a packet is defined as the average number of time-slots passed before the packet reaches its destination, after it leaves the source node. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 13

14. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 14 Outline Introduction System Model Routing and Scheduling Scheme Routing and Scheduling Schemes  Primary Network Routing Scheme  Secondary Network Routing Scheme  Scheduling Scheme Capacity and Delay Scaling Performance Conclusion

15. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 15 Primary Network Routing Scheme   Secondary users are willing to act as the relay nodes for primary packets.   Primary routing scheme utilizes the mobility heterogeneity of SUs to make the packet relayed by a chain of different type SUs.   We define the maximum type of SU that can be exploited to relay the primary packets.   Definition 1: (Critical Relay Type) The critical relay type is defined as:, where

16. Primary Network Routing Scheme  The primary relay algorithm would utilize the SU relay nodes from type 0 to type h*:  In the first step, the primary source node would transmit the packet to a 0-type SU.  In the intermediate relay steps, the (i-1)-th type SU which holds the packet would relay it to an i-th type SU, whose moving area contains the primary destination node. ( )  In the final step, the h*-type SU which holds the packet would relay the packet to the primary receiver. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 16

17. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 17 Secondary Network Routing Scheme  For i-th type secondary source node and j-th type destination node, the secondary relay algorithm utilizes SU relay nodes from type 0 to type h’=min{ j,h* } :  In the first step, the i-th type secondary source node would transmit its packet to a 0-type SU.  In the intermediate relay steps, the (i-1)-th type SU which holds the packet would relay it to an i-th type SU,whose moving area contains the initial position of destination node. ( )  In the final step, the h’-the type SU which holds the packet would relay it to the j-th type destination node, when they are encountered in the same cell.

18. Scheduling Scheme  25-TDMA scheme is adopted.  We define preservation region to limit interference from SUs to PUs :  Preservation region is a square that contains 9 cells, with the active primary transmitter in the center cell.  Only SUs outside the current preservation region could transmit or relay packets.  The scheduling scheme consists of 2h*+3 phases, the first h*+1 phases would transmit the primary packets, the next h*+2 phases would transmit secondary packets. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 18

19. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 19 Outline Introduction System Model Routing and Scheduling Scheme Capacity and Delay Scaling Performance  Scaling Laws of Primary Network  Scaling Laws of Secondary Network  Optimal Performance of Primary Network  Optimal Performance of Secondary Network  Comparison with Previous Works Conclusion

20. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 20 Scaling Laws of Primary Network  Lemma 5&6: In any cell, there are at most PUs and SUs of each type with high probability.  Lemma 7: During the routing process of primary packets, the primary transmitters and secondary relay nodes can support constant data rate in each cell.  Theorem 1: Under the proposed relay algorithm, the primary network can achieve the following average per- node throughput with high probability:  Theorem 2: Under the proposed primary relay algorithm, the primary network can achieve the following average delay with high probability:

21. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 21 Scaling Laws of Secondary Network  Lemma 9: During the routing process of secondary packets, the secondary transmitters and relay nodes can support a constant data rate in each cell.  Theorem 3: Under the proposed secondary relay algorithm, the secondary network can achieve the following per-node throughput with high probability:  Theorem 4: Under the proposed secondary relay algorithm, the secondary network can achieve the following average delay with high probability: where j is the type of destination node.

22. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 22  The effect of mobility heterogeneity (i.e., h and ) on the capacity and delay scaling laws of primary network:  If, denote, the primary network could achieve the following average delay: with the per-node throughput  Despite the throughput performance is optimal, but the delay performance is still suboptimal, since Optimal Performance of Primary Network

23.  If, denote, the primary network can achieve the following average delay: with the per-node throughput.  In this case, the delay performance can be improved when increase from 0 to, until near-optimal delay performance is achieved. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 23

24. Optimal Performance of Primary Network  Curve for the relation between Delay/Capacity tradeoff and mobility heterogeneity: Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 24

25. Optimal Performance of Secondary Network  Similar to primary network, the secondary network can also achieve the optimal performance when and :  The secondary network can achieve the following average delay: with per-node throughput of  The secondary network can achieve the near-optimal delay-capacity tradeoff when the type of destination SUs satisfies: Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 25

26. Comparison with Previous Works  Under optimal condition, this paper achieves near-constant capacity and delay scaling for primary and secondary network.  Compared with [13], this paper achieves better delay scaling for secondary network and requires less secondary users.  Compared with [14], this paper achieves better capacity and delay scaling for secondary network and adopts a more general and flexible mobility model. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 26 [13]: L. Gao, R. Zhang, C. Yin, and S. Cui, “Throughput and Delay Scaling in Supportive Two-tier Networks ” to appear in JSAC 2011. [14]: X. Wang, L. Fu, Y. Li, Z. Cao and X. Gan, “Mobility Reduces the Number of Secondary Users in Cognitive Radio Network” in Proc. of IEEE GLOBECOM, 2011.

27. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 27 Outline Introduction System Model Routing and Scheduling Scheme Capacity and Delay Scaling Performance Conclusion

28. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 28 Conclusion  We propose a more general mobility model which reflects the mobility heterogeneity of secondary users in CRN.  We show the increase of mobility heterogeneity could improve the delay-capacity tradeoff for both primary network and secondary network.  Under optimal condition, the proposed algorithm can achieve near-constant capacity and delay scaling for primary network and part of secondary network

29. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 29 Thank you !