Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users

Transcription

1 Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users Y.Li, X.Wang, X.Tian and X.Liu Shanghai Jiaotong University Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 1

2 Outline Introduction System Model Routing and Scheduling Scheme Capacity and Delay Scaling Perfomrance Conclusion Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 2

3 Outline Introduction System Model Routing and Scheduling Scheme Capacity and Delay Scaling Performance Conclusion Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 3

4 Introduction-CRN Cognitive Radio Network (CRN) The conflict between spectrum scarcity and the underutilization of licensed spectrum propels the study of Cognitive Radio technology. Cognitive Radio Network consists of the primary users licensed to the spectrum, and the secondary users which access the spectrum opportunistically. The secondary network coexists with the licensed primary network. The secondary users access the spectrum opportunistically without causing harmful interference to the primary users. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 4

5 Introduction-CRN The secondary network coexist with the licensed primary network The number of primary users and secondary users n primary users and m secondary users, and m ( n ) Whether 1, 1, 1? How cognitive are the secondary users? How much information the secondary users know about the primary users? Are the secondary users willing to relay the packets for the primary users? Static or mobile? ad-hoc or hybrid network? Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 5

6 Introduction-CRN The secondary users could access the spectrum opportunistically How to limit the interference of secondary users to primary users? The existence of secondary network should not degrade the performance of primary network How to guarantee the transmission opportunity for the secondary users? The secondary network should not suffer severe outage probability (i.e., the fraction of secondary users that cannot be served) Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 6

7 Introduction-Previous Works [S.Jeon, 2009] Basic assumptions: Dense network with n static primary users and m static secondary users with ( ), and m n 1 The secondary nodes know the location of all the primary nodes Define the preservation region around each primary user to limit the interference from secondary users Results: 1 1 Primary network- p ( ) Secondary network- s ( nlog n [C. Yin, 2010]: m Basic assumptions: The secondary users only know the location of primary transmitters Define the preservation region around each active primary transmitters. Results: Primary network: 1 p( n) ( ), and Dp( n) ( n p ( n)) nlog n 1 Secondary network: s ( m) ( ), and Ds m) ( m s ( mlog m ( m)) ) log m [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 Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 7

8 Introduction-Previous Works The cooperation between PU and SU could improve the capacity and delay scaling in the CRN. [L. Gao, 2009]: Basic Assumptions: The secondary users are willing to relay the primary packets. There are n static primary users and m secondary users, either static or mobile, with m ( n ), 2 Results1: SUs are static 1 Primary network: p( n) ( ), and Dp( n) ( n log n p( n)) log n Secondary network: Results2: SUs are mobile(i.i.d. mobility model) Primary network: p( n) ( ), ( n) (1) Secondary network: ( m) (1), 1 s ( m) ( ), Ds ( m) ( m s ( m)) mlog m s 1 log n D p ( m) ( m) D s [L.Gao, 2009]: L. Gao, R. Zhang, C. Yin, and S. Cui, Throughput and Delay Scaling in Supportive Two-tier Networks, to appear in JSAC Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 8

9 Introduction-Previous Works [X. Wang, 2011]: Basic Assumptions: There are n static primary users and m mobile secondary users, with m ( n ), 1 Cooperation is considered in this work. Secondary users move under the hierarchical i.i.d. mobility model. Results: Primary network: p( n) ( ), Secondary network:, 1 D ( n) (log 2 n) log n p 1 s ( ) D s (log 2 n) n [X. Wang, 2011]: X.Wang, L.Fu, Y.Li, Z.Cao, X.Gan, L. Gao, Mobility Reduces the Number of Secondary Users in Cognitive Radio Network, in proceedins of IEEE GLOBECOM Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 9

10 Introduction-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). All the previous works have some limitations in terms of system models and scaling laws. We study: A more general and representative mobility model which reflects the mobility heterogeneity. The routing and scheduling scheme which utilize the mobility heterogeneity of secondary users. The impact of mobility heterogeneity on the scaling laws of Cognitive Radio Network Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 10

11 Outline Introduction System Model Hierarchical Relay Algorithm Performance Of The Hierarchical Relay Algorithm Conclusion Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 11

12 System model I/III Network Model: The primary network consists of n static, randomly and evenly distributed primary users in the unit area, which are grouped into S-D pairs one-by-one. 1 The secondary network consists of m ( h 1) n heterogeneous mobile secondary users, where h O(log n), which are also grouped into S-D pairs one-by-one. 0 The unit square is divided into non-overlapping small square 2log N 1 cells, with side length r, N n. Nodes can N communicate with each other only when they are in the same cell. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 12

13 System model II/III Channel Model: Path Loss Only: r Normalized channel gain is g( d) d, where r 2. We apply the Gaussian Channel Model to regulate the transmission rate, which is a continuous function to the SINR. The data rate from primary transmitter to primary receiver P D(i) : Pp g( Pi PD ( i) ) R( Pi, PD ( i) ) log(1 ) N I I : the ambient noise power N 0 0 p I p : the interference from all the other primary transmitters I sp : the interference from all the secondary transmitters sp P i Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 13

14 System model III/III Mobility Model for Secondary Users: The secondary users are uniformly and randomly distributed at the beginning. Each secondary user would move within a circular region centered at its initial position, according to the i.i.d. mobility model. The moving area of each mobile SU is follows the discrete uniform distribution: 2 0 0, 0,,..., with equal probability 0 h h 0 h=o(log n) and is a random positive value. (h and determine the mobility heterogeneity together) We call the SUs with i 0 h, where the i-th type secondary user. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 14 n 1 p h 1 0

15 System model III/III Mobility Model: Denote the k-th secondary user of type i as i k, and its initial 1 position as X i, k, where 0 i h, 1 k N n. Under the proposed mobility model: S X R, where R i ( n i 0 / 2h ) S, i, k i, k i Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 15

16 Outline Introduction System Model Routing and Scheduling Scheme Capacity and Delay Scaling Performance Conclusion Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 16

17 Primary Network Routing Scheme The secondary users are willing to act as the relay nodes for primary users. The primary routing scheme would utilize the mobility heterogeneity of SUs to make the packet approach its destination progressively. Since the SUs with larger type would correspond to smaller moving area, thus 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: h max{ i R 2 2r}, where i 0,1,2,... h i h * Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 17

18 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 relay the packet to a 0-type SU. In the intermediate relay steps, the (i-1)-th type SU the packet would relay it to a i-th type SU S i, S i 1, ui 1 which holds, whose moving area contains the primary destination node. ( ) In the final step, the h*-type SU u i 1 i h which holds the packet would relay the packet to the primary receiver. * Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 18

19 Primary Relay Algorithm Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 19

20 Secondary Network Relay Algorithm For the secondary source node i k i and its destination node S j, k j, the secondary relay algorithm would utilize SU relay nodes from type 0 to type h =min{ j,h* } : In the first step, the secondary source node would relay its packet to a 0-type SU In the intermediate relay steps, the k-th type SU k u k which holds the packet would relay it to a (k+1)-th type SU S k 1, u, whose k 1 moving area contains the initial position of destination node. ( ) 0 k h' 1 In the final step, the h -the type SU which holds the packet ', uh' would relay it to the destination node S, when they are j, k j encountered in the same cell. S, S h S, Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 20

21 Secondary Network Relay Algorithm Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 21

22 Scheduling Scheme 25-TDMA scheme is adopted: All the cells are divided into 25 sub-slots by a 5*5 pattern. The cells in different subsets would be activated with a round-robin fashion within one time slot. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 22

23 Scheduling Scheme- Preservation Region We define preservation region to control the interference from SUs to PUs: The 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. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 23

24 Scheduling Scheme The scheduling scheme would guarantee transmission opportunity for both primary network and secondary network. The scheduling scheme consists of 2h*+3 phases, the first h*+1 phases would transmit the primary packets: Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 24

25 Scheduling Scheme The next h*+2 phases would transmit secondary packets Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 25

26 Outline Introduction System Model Routing and Scheduling Scheme Capacity and Delay Scaling Performance Conclusion Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 26

27 Scaling Laws of Primary Network Lemma 5&6: In any cell, there are at most SUs of each type with high probability. (1) PUs and (log n) 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: 1 p ( ) h Theorem 2: Under the proposed primary relay algorithm, the primary network can achieve the following average delay with high probability: D p ( hn * 0 0 ( 1 h ) h 2 h h n log 2 n) Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 27

28 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 1 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: D s, j O( h 2 log n h 2 n 0 h log h 0 (1 ) h log n), where j is the type of destination node. 2 n h 2 n ' s ( h 2 log n Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 28

29 Optimal Performance of Primary Network The effect of mobility heterogeneity (i.e., h and ) on the capacity and delay scaling laws of primary network: 1 2log log n / log n h (1) th If, denote, the primary network could achieve the following average delay: 0 h 2 D ( n log n), if 0 th p 1 0 ( n ), if 0 th with the per-node throughput p 1 1/ h (1) 0 Despite the throughput performance is optimal, but the delay performance is still suboptimal, since ( poly log n) D p Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 29

30 Optimal Performance of Primary Network 1 3log log n / log n 1 1/ h If h (log n), denote, the primary network can achieve the following average delay: D p (log 1 ( n 4 n), if 0 log n), if 0 th' 1 with the per-node throughput p ( ). log n 0 th' th' 0 In this case, the delay performance can be improved when increase from 0 to th', until near-optimal delay performance is achieved. Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 30

31 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 31

32 Optimal Performance of Secondary Network Similar to primary network, the secondary network can also achieve the optimal performance when h (log n) 1 and : 0 The secondary network can achieve the following average delay: 4 * (log n), if j h Dp j 0 1 h 3 * ( n log n), if j h 1 with per-node throughput of s ( ) log 3 n The secondary network can achieve the near-optimal delay-capacity * tradeoff for the when the type of destination SUs satisfies: j h Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 32

33 Comparison with Previous Works Compared with [13], this paper achieves better delay scaling for secondary network while requires less secondary users Compared with [14], this paper adopts more general mobility model and better scaling for secondary netork Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 33

34 Outline Introduction System Model Routing and Scheduling Scheme Capacity and Delay Scaling Performance Conclusion Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 34

35 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 Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 35

36 Thank you! Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 36

37 Introduction-Previous Work [S.Jeon, 2009]-Preservation region Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 37