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
Outline
 Introduction
 Background
 Motivation
 Objectives
 System Model
 Routing and Scheduling Scheme
 Capacity and Delay Scaling Performance
 Conclusion
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
2
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.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
3
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.
4
Background
 [X. Wang, 2011] studies a static primary network and a multilayer 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
1

(
n
)


(
)
can be achieved, i.e. p
log n
2
and Dp (n)  (log n).
[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.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
5
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
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
6
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
7
System model – I/VI
 Network Model:
 n static primary users are randomly and evenly distributed in
the unit square area.
1
 m  (h  1)n mobile secondary users, where h  O(logn),  0
 Source and destination are randomly grouped one by one in
each network.
 The unit square is divided into non-overlapping small square
2 log N
cells, with side length r 
, where N  n1 .
N
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
8
System model – II/VI
 Channel Model:
 We apply the Gaussian Channel Model to regulate the
transmission rate.
• The data rate from primary transmitter Pi to primary
receiver PD(i ) :
Pp g (|| Pi  PD (i ) ||)
R( Pi , PD (i ) )  log(1 
)
N 0  I p  I sp
•
I p : interference from other primary transmitters
• I sp : interference from all the secondary transmitters
• The data rate from secondary transmitter to secondary
receiver is defined similarly.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
9
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.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
10
System model – IV/VI
 Mobility Model for Secondary Users:
1
 Among all the m  (h  1)n secondary users, the moving
area of each mobile SU is n , where  follows the
discrete uniform distribution:
1
 0 2 0
p



0
,
,
,...,

•
0 with equal probability

h
h
h 1
.
• h=O(log n) and  0 are random positive values, h and  0
would determine the mobility heterogeneity together.
i 0
 We call the SUs with  
the i-th type secondary user,
h
and each type consists of N  n1 mobile secondary
users.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
11
System model – V/VI
 Mobility Model for Secondary Users:
• Denote the k-th secondary user of type i as S i ,k , and its initial
position as X i ,k , where 0  i  h , 1  k  N  n1 .
• Under the proposed mobility model: || Si ,k  X i,k || Ri , where
Ri  (ni0 / 2h )
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
12
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
Outline
 Introduction
 System Model
 Routing and Scheduling Schemes
 Primary Network Routing Scheme
 Secondary Network Routing Scheme
 Scheduling Scheme
 Capacity and Delay Scaling Performance
 Conclusion
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
14
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 h*
is defined as: h*  max{i | Ri  2 2r} , where i  0,1,2,...h
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
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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 Si 1,ui1 which holds
the packet would relay it to an
i-th type SU Si ,ui , whose moving
area contains the primary
*
destination node. ( 1  i  h )
 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
Secondary Network Routing Scheme
 For i-th type secondary source node Si ,ki and j-th type
destination node S j ,k j , 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 Si 1,ui1
which holds the packet would relay it to an i-th type SU Si ,u
i
,whose moving area contains the initial position of
destination node. ( 0  i  h'1 )
 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.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
17
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
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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
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
19
Scaling Laws of Primary Network
 Lemma 5&6: In any cell, there are at most (1) PUs and (logn)
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 per1
node throughput with high probability:  p  ( )
h
 Theorem 2: Under the proposed primary relay algorithm,
the primary network can achieve the following
average
0
* 0
(1 h
)
h
delay with high probability: Dp  (hn
 h2n h log2 n)
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
20
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: s  ( 2
h log n
 Theorem 4: Under the proposed secondary relay
algorithm, the secondary network can achieve the following
average delay with high probability:
0
Ds , j  O (h 2 log n  h 2 n h log 2 n  h 2 n
h ' 0
(1 
)
h
log n),
where j is the type of destination node.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
21
Optimal Performance of Primary Network
 The effect of mobility heterogeneity (i.e., h and 0 ) on the
capacity and delay scaling laws of primary network:
1    2 log log n / log n
 If h  (1) , denote  th 
, the primary
11/ h
network could achieve the following average delay:
0

(n h log2 n), if  0   th
Dp  
1  0


(
n
),
if  0   th

with the per-node throughput p  (1)
 Despite the throughput performance is optimal, but the
delay performance is still suboptimal, since Dp  ( polylog n)
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
22
Optimal Performance of Primary Network
 If h  (logn), denote th' 
1    3 log log n / log n
, the
11/ h
primary network can achieve the following average delay:
4

if  0   th'
(log n),
Dp  
1  0

log n), if  0   th'
(n
1
).
with the per-node throughput  p  (
log n
 In this case, the delay performance can be improved when
 0 increase from 0 to  th' , until near-optimal delay
performance is achieved.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
23
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
Optimal Performance of Secondary Network
 Similar to primary network, the secondary network can
also achieve the optimal performance when h  (logn)
and  0 1   :
 The secondary network can achieve the following average
delay:
(log4 n),
if j  h*

Dp  
j
1  0
3
*
h


(
n
log
n
),
if
j

h

with per-node throughput of s  (
1
)
3
log n
 The secondary network can achieve the near-optimal
delay-capacity tradeoff when the type of destination SUs
satisfies: j  h*
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
25
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.
[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.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
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
27
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
28
Thank you !
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
29