1. Riheng Jia, Jinbei Zhang, Xinbing Wang, Xiaohua Tian
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Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users
Riheng Jia, Jinbei Zhang, Xinbing Wang, Xiaohua Tian
Department of Electronic Engineering Shanghai Jiao Tong University, China
Qian Zhang
Department of Computer Science and Engineering
Hong Kong University of Science and Technology, China

2. Outline Introduction System Model &Traffic Locality Network Protocols
Background
Motivation
Objectives
System Model &Traffic Locality
Network Protocols
Throughput and Delay Scaling Performance
Conclusion
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users 2

3. Background Cognitive Radio Network (CRN)
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Cognitive Radio Network (CRN)
Cognitive radio (CR) technique is considered an effective mechanism to relieve the spectrum scarcity issue.
Cognitive Radio Network consists of primary users (PUs) and secondary users (SUs), where SUs can utilize the idle spectrum of the PUs.
The impact of CR technique on the performance of wireless networks has been attracting much attention in past years.
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users 3

4. Background
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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.
[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
[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
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The heterogeneous distribution of source and destination (S-D)
A common assumption in most previous works of CRN is that the S-D is homogeneously distributed, where the distance of S-D is of the same order as the network extension.
In the real word, source would prefer the closer rather than the further destination to communicate, which is often considered as the small-world phenomenon.
The small-world phenomenon will certainly cause the heterogeneity of S-D distribution, as well as the different traffic patterns.

6. Background
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The rank based model which well captures the characteristic of S-D was investigated in [Y.-Y. Ahn, 2007].
Study the rank-based model where the probability of any source node finding a designated destination node is inversely proportional to the α-th power of the number of closer nodes.
The rank based model was incorporated into wireless networks in [L. Fu, 2011]
Incorporate the rank based model into wireless networks and explored the impact of traffic locality on capacity over the network under different traffic patterns.
[Y. -Y. Ahn, 2007]: Y. -Y. Ahn, S. Han, H. Kwak, S. Moon, and H. Jeong, “Analysis of Topological Characteristics of Huge Online Social Networking Services,” in 16th International Conference on World Wide Web, New York, US, pp , 2007.
[L. Fu, 2011]: L. Fu, W. Huang, and X. Wang, “Capacity of Wireless Social Networks,” Shanghai Jiao Tong university, Tech. Rep., [Online]. Available:

7. Motivation & Objectives
Motivated by the fact that:
The impact of heterogeneous S-D distribution on performance of CRN is very limited.
Cooperation between the PUs and SUs can significantly improve the scaling performance of CRN.
We study:
A more realistic S-D distribution which is generated by the rank based model and explore the corresponding traffic flow.
The network protocols and cooperation scheme under the new network settings.
The impact of S-D heterogeneity on the scaling laws of Cognitive Radio Network
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users 7

8. Outline Introduction System Model & Traffic Locality Network Protocols
Throughput and Delay Scaling Performance
Conclusion
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users 8

9. System model – I/III Network Geometry:
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System model – I/III
Network Geometry:
Static primary users are randomly and evenly distributed in the unit square area according to a P.P.P. of density .
Static secondary users are randomly and evenly distributed
in the unit square area according to a P.P.P. of density ,
where
Source and destination (S-D) are randomly grouped one by one in both primary and secondary networks following a rank based model.
The unit square is divided into non-overlapping small square
cells, with each area of and for primary and secondary networks, respectively. (achieving full connectivity)
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users 9

10. System model – II/III Rank Based Model
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System model – II/III
Rank Based Model
For simplicity, we consider a single network with nodes randomly distributed in a given area. For arbitrary two nodes
and , then define the rank of with respect to as:
then, the probability that is the destination of is modeled
as:
where is the S-D heterogeneity exponent and ,
denoting for short , the distribution law is:
Unicast!!
Nodes can communicate with each other only when they are in the same cell.
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11. System model – III/III Definition of Throughput: Definition of Delay:
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 fluid model [A. E. Gamal, 2006] is utilized for delay analysis and the delay is defined as the average time slots a packet takes to be delivered from source to destination.
[A. E. Gamal, 2006]: A. E. Gamal, J. Mammen, B. Prabhakar, and D. Shah, “Optimal Throughput-delay Scaling in Wireless Networks-part I: the Fluid Model,” in IEEE Trans. Inform. Theory, vol. 52, no. 6, pp , Jun
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

12. Traffic Locality
Since we adopt the rank based model to determine the destination for each source node, a source node tends to choose a closer node as its destination and therefore results in a certain degree of traffic locality:
and denote the location of source and destination
As increases, the distribution of S-D tends to be
localized !
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

13. Outline Introduction System Model & Traffic Locality Network Protocols
Primary Protocol
Secondary Protocol
Throughput and Delay Scaling Performance
Conclusion
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users 13

14. Primary Protocol Every 64 primary cells are grouped into a
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Every 64 primary cells are grouped into a
primary cluster and a round-robin fashion
to activate the cells in each primary cluster.
Define the horizontal data path (HDP) and
the vertical data path (VDP) which connect
source and its corresponding destination.
Each source transmits data to its destination
by first hopping to the adjacent cells on its
HDP and then the VDP.
When a primary cell is active, each primary
source node will transmit its own packet in
order
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15. Secondary Protocol The secondary nodes are providing relay service
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The secondary nodes
are providing relay service
for primary nodes and the
secondary time frame is
divided into 3 phases.
Phase 1: When a active secondary cell is outside the preservation regions, each secondary source node first transmits one own packet and then serve each secondary S-D path passing through the cell.
Preservation Region
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16. Secondary Protocol Phase 2: Only the secondary nodes who
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Phase 2: Only the
secondary nodes who
buffered the primary
packets are permitted
to access the spectrum
and each secondary
node is assigned to
relay portion of the
primary packet to the intermediate destination by a multi-hop
scheme.
Phase 3: The intermediate destination is responsible for delivering the primary packet to the final destination.
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17. Outline Introduction System Model & Traffic Locality Network Protocols
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Introduction
System Model & Traffic Locality
Network Protocols
Throughput and Delay Scaling Performance
Throughput Analysis for Multi-hop Scheme
Throughput Analysis for Single-hop Scheme
Delay Analysis for Multi-hop Scheme
Delay Analysis for Single-hop Scheme
Conclusion
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18. Throughput Analysis for Multi-hop Scheme
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Lemma 3. With the primary protocol defined previously, an active primary cell can support a constant data rate of , the intermediate destination node can deliver the primary packets
to the intended primary destination at a constant rate of .
Lemma 2. The probability that a randomly selected designated
relay node is a secondary node in a primary cell approaches
one w.h.p..
Based on different traffic patterns, the value of is set as:
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

19. Throughput Analysis for Multi-hop Scheme
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Theorem 1. With the protocols given previously, the primary
network can achieve the following per-node throughput w.h.p.:
The range of is to guarantee that there are more than
secondary nodes in each primary cell !
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

20. Throughput Analysis for Multi-hop Scheme
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Lemma 5. With the secondary protocol defined previously, each Tx in a secondary cell can support a constant data rate of , which is independent of .
Lemma 6. The number of secondary S-D paths (including
HDPs and VDPs) passing through or originating from
each secondary cell is bounded as
for
Theorem 2. With the predefined model and secondary protocol, the secondary network can achieve the per-node throughput:
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

21. Throughput Analysis for Single-hop Scheme
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When increases beyond , the S-D tends to be distributed in a cell. Since we remain the scheduling scheme unchanged, the S-D pair in both primary and secondary networks can transmit data at a constant data rate.
Theorem 3. In our proposed sing-hop scheme, the primary and secondary network can achieve the following per-node throughput w.h.p.:
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

22. Delay Analysis for Multi-hop Scheme
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Let and denote the durations of the primary and secondary time slot, respectively. According to the proposed protocols, we have Since each secondary time frame is split into three phases and one of them is used for relaying the primary packets, thus each primary packet suffers from the following delay:
Theorem 5. Based on the predefined secondary protocol, the delay is given by:
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

23. Delay Analysis for Single-hop Scheme
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When increases beyond , each S-D is located in a particular cell w.h.p.. Therefore in this case, the packet delay is the time for each packet to reach the destination through single-hop transmission.
Theorem 6. Based on the predefined protocols, the primary and secondary network can achieve the following delays,
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

24. Outline Introduction System Model & Traffic Locality Network Protocols
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Introduction
System Model & Traffic Locality
Network Protocols
Throughput and Delay Scaling Performance
Conclusion
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25. Conclusion Throughput of primary networks VS secondary networks
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

26. Conclusion
The impact of S-D heterogeneity on throughput and delay of CRN, as well as the number of SUs required to aid the transmission of PUs.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users

27. Conclusion
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We explored the heterogeneous distribution of S-D upon the rank-based model, as well as the corresponding traffic patterns.
We propose the cooperative routing scheme among the PUs and SUs, based on which the throughput and delay of CRN are derived. We show that the heterogeneous S-D distribution do affect the scaling performance of both primary and secondary networks, except the throughput of PUs (see page 25).
We reveal that the number of required SUs can be dramatically reduced due to the heterogeneous distribution of S-D.
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users

28. Thank you !
Scaling Laws for Heterogeneous Cognitive Radio Networks with Cooperative Secondary Users