Cognitive Multihop Cluster-based Transmission under Interference Constraint

Nguyen Quang Sang, Hyunh Yun Kong Department of Electrical Engineering

University of Ulsan Ulsan, Korea

sangnq2014@mail.ulsan.ac.kr, hkong@mail.ulsan.ac.kr

Tran Trung Duy Department of Telecommunications

Post and Telecommunications of Institute of Technology HoChiMinh, VietNam

trantrungduy@ptithcm.edu.vn

Abstract— In this paper, we study multi-hop cluster-based transmission in underlay cognitive network. For performance evaluation, we derive exact and approximate expressions of end-to-end outage probability over Rayleigh fading channels. Monte-Carlo simulations are performed to verify our derivations.

Keywords—Underlay network; cluster; outage probability;

I. INTRODUCTION Multi-hop transmission is an exciting technique with the

simple idea is that relaying the information from the source to the destination via many intermediate hops between them. Combining underlay cognitive networks with multi-hop communication techniques have gained much attention, which exploit the shorter transmission range for lower path loss. As a result, lower transmit power and lower interference levels are required while guaranteeing similar data transmission quality. In most of the published research [1], the authors mainly focused on proposing algorithms to find an opportunistic route between the secondary source and the secondary destination. To the best of our knowledge, there are several works which address the diversity multi-hop transmission in cognitive underlay networks. In [2], the authors proposed a cooperative multi-hop protocol where secondary users play the role of the relays for the primary network. In [3], the authors studied the performance of multi-hop underlay cognitive radio networks using cooperative multi-hop communication.

In this paper, we investigate the outage performance of a multi-hop cluster-based transmission in underlay cognitive network. In particular, at each hop, the diversity transmission is used to relay the secondary source’s data. In addition, only partial channel state information (CSI) is used to select the next transmit node. In order to evaluate the performance of the proposed protocol, we derive exact and asymptotic expressions of end-to-end outage probability over the Rayleigh fading channels. Monte-Carlo simulations are shown to validate the mathematical derivations.

II. SYSTEM MODEL In Fig. 1, we present the system model of the cooperative multi-hop cluster-based transmission in the cognitive underlay network. In this model, the secondary source S attempts to transmit its data to the secondary destination D via K clusters from cluster 1 to cluster K. We assume that cluster j has jN

secondary nodes, where 1K > , { }1,2,...,j K∈ , and 1jN ≥ . Considering the data transmission between a transmitter T and a receiver R, the signal received at R due to the transmission of R is expressed as R T RT Ry P h s n= + , (1) where TP is the transmit power of the transmitter T, s is the signal transmitted, RTh is the channel coefficient between R and T, and Rn is the Gaussian noise at receiver R.

1 RelaysN

PU

S D

Cluster 1 Cluster 2 Cluster K

2 RelaysN RelaysKN Figure 1. Cooperative multi-hop cluster-based transmission in the cognitive underlay network.

From (1), the signal-to-noise ratio (SNR) received at R is given as

2RT T RT 0| | /P h Nψ = , (2)

where 0N is variance of the additive noise, which is assumed to be same at all receivers. In underlay network, before transmitting the data, the transmitter T has to adapt the transmit power so that it is lower than a threshold (i.e., P ), and the interference caused at the primary receiver (PR) is below an allowable levelQ .Indeed, the transmit power of node T is given as

( )2T PTmin , / | |P P Q h= , (3)

where PTh is Rayleigh fading channel between the transmitter T and the primary user PU. From (2) and (3), we rewrite RTψ as

( )( )

2 2 2RT 0 0

2 2 2RT RT PT

min | | / , | | /( | | )

min | | , | | / | | ,

RT RT PTP h N Q h N h

P h Q h h

ψ =

= Φ (4)

where 01 / NΦ = .

IEEE ISCE 2014 1569949267

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We name jN relays in cluster j as { }1 2, ,..., jNj j jR R R . We

denote cjR as the chosen relays at cluster j. In addition, random

variables (RVs) 2RT| |h and 2

PT| |h have exponential distribution with parameters RTλ and PTλ , respectively. We also assume that RVs 2

PS| |h and 2PR

| |kj

h are identical to parameters 1Ω

and 1j+Ω , respectively. Furthermore, RVs 1

2R S

| |ih and

1

2R R

| |l kj j

h+

are identical to parameters 1λ and 1jλ + , respectively.

The parameters are modeled as 1 PSdβΩ = ,

1 PRkjj d β+Ω =

11 R Sd βλ = , and 1

1 R Rl kj j

j d βλ+

+ = , where d and

β denotes the distance and the path-loss exponent. Now, we describe the operation of the proposed scheme. At hop j, where { }2,..., 1j K∈ − , the chosen relay 1

cjR − of the

cluster j-1 will forward the signal to the relays of cluster j if it decodes the signal correctly. At that point, only the relay c

jR

which has the best channel to relay 1cjR − receives and decodes

the received signal. Moreover, similar to the protocol proposed in [4], we apply the cooperative transmission strategy for the last two hops to enhance the diversity gain of these hops.

III. PERFORMANCE ANALYSIS In this section, we presented the expressions of end-to-end outage probability and diversity order. In this paper, it is assumed that The data transmission between two nodes R and T is in outage if the SNR at T is lower than a threshold thγ , and the data is unsuccessfully received by the receiver T if the instantaneous received SNR is lower than a threshold thγ . Let us denote 1D as the set of secondary relays which successfully decode the source’s data, we formulate a probability for the decoding set 1D as follows:

[ ]1 2 11 1 1

11 11 1

1

, ,..., ,Pr Pr

,..., ,

k

k N

th th thR S R S R S

th thR S R S

Dψ γ ψ γ ψ γ

ψ γ ψ γ+

≥ ≥ ≥=

< <. (5)

After some manipulation, we can obtain

[ ] ( )

( ) ( )( )

( )1 1

1 1

1 1 1 1

1 1 11

0 1 1 1

exp

Pr 1

exp

N kt t

N kt

t k t kP Q t k

D Ct k QP P

λ ρ λ ρλ ρ

λ ρ

−

−=

+ +− −

Ω + += −

+ Ω− −

. (6)

In the case where 1 0k = , (6) can be rewritten as

[ ] ( )

1

110

1 1 1 1

1 1

Pr 1

exp exp .

Nt t

Nt

D C

t t t QP Q t P P

λ ρ λ ρ λ ρλ ρ

=

= −

Ω− − − −

Ω +

(7)

Considering the transmission between cjR and 1

cjR + , where

{ }0,1,..., 2j K∈ − and 0cR S≡ . As mentioned above, the relay

1cjR + in this case is chosen by the following strategy:

{ } ( )

1 11

2 2

1,2,...,: | | max | | .c c i c

j j j jj

cj R R R Ri NR h h

+ ++∈= (8)

We can observe that (7) is equivalent to (8), which is expressed as follows:

{ }( )

1 111

1,2,...,: max .c c i c

j j j jj

cR R R Ri N

R ψ ψ+ ++∈

= (9)

From (9), the outage probability of the 1c cj jR R +− link can be

calculated by

{ } ( )

1 1 111,2,...,

Pr Pr max .c c c c i cR Rjj j j j jj

outth thR R R Ri N

P ψ γ ψ γ+ + +

+∈= < = < (10)

Using the result got in (7), The 1

c cR R jj

outP+

can given as

( )1

110

1 1 1 1

1 1

1

exp exp

j

c cR R jjj

Ntout t

Nt

j j j j

j j

P C

t t t QP Q t P P

λ ρ λ ρ λ ρλ ρ

+

++=

+ + + +

+ +

= −

Ω− − − −

Ω +

,(11)

where /thρ γ= Φ . Furthermore, at high Φ values ( 0ρ → ), we have

( ) ( )( )( ) ( )

1 1

1

1 1

1 10

1 1 1 1

/ 1 exp /

/ 1, /

j jc cR Rjj

j j

N Noutj j

N Nj j j j

P P Q P

Q N Q P

ρλ ρ

λ ρ

+ +

+

+ +

+ +→

+ + + +

= − −Ω

+ Ω Γ + Ω, (12)

where ( ).,.Γ is the incomplete upper gamma function. Considering the transmission at the two last hops, we can calculate the outage probability for the 1

c cK KR R D− − − link as

( )

( )( )( )

( )( )

( )( )

11

111

1

0 0

1

1 1

1

1 1 11

1 1

1

exp /

exp

exp /1 exp .

K K

c cK KK K

N N ktkout t

N N kR R Dk t

K

K K K

K K

k

K K KK

K K

P C C

t k P

t k t k QQ t k P P

Q PP Q

λ ρ

λ ρ λ ρλ ρ

λ ρ λ ρλ ρλ ρ

−

−

−= =

+ + ++

+ +

= −

− +

+ + Ω− − −Ω + +

− + Ω− − +

+ Ω

(13)

Also, we can obtain 1

11

1 111

1

00

1

1 1 1

1 1

1 exp

1,

exp .

K

c c KK K

K

N kK K

NkoutN N kR R D

kK K

KK

k

NK K K

K K

QP P

P CQ

N kQ P

QP Q

ρ

λ

λ

λ λ ρλ

−

−

−→=

+ + +

+ +

Ω− −

=Ω+ Γ − +

Ω

Ω× + −Ω

(14)

2

Due to the independence of the hops, the end-to-end outage probability of the proposed protocol is calculated as

( ) ( )1 1

1

1

1 1 1c c c cK K j j

Kout out out

R R D R Rj

P P P− +

−

=

= − − −∏ . (15)

Moreover, from (11), (14) and (15), we determine the diversity gain of the proposed protocol as

( ) ( )1 2

loglim min , ,...,

log

out

K

PL N N N

Φ→+∞= − =

Φ. (16)

IV. SIMULATION RESULTS In the simulation environment, we consider a two-dimensional plane in which the coordinates of the source S , the relays

{ }( )1,2,...,kjR j K∈ , the destination D , and the primary user

are (0,0), ( )( )/ 1 ,0j K + , (1,0), and ( Px , Py ), respectively. In all simulations, we assume that a path-loss exponential β is equal to 3, and the threshold thγ is equal to 1.

Figure 2. End-to-end outage probability as a function of 1K + when

0.3Px = , 0.4Py = , 5dBΦ = , and 2 .jN j= ∀

In Fig. 2, we present presents the outage probability as a function of the number of hops 1K + . We change the threshold values of P and Q , while fixing the number of relays at each cluster to 2, 0.3Px = , 0.4Py = , 5dBΦ = . It can be seen from this figure the outage performance in the case of P=Q=0.3 is better that of P=Q=0,1. This is due to the fact that, the higher threshold values of P and Q, the lower outage probability. Furthermore, the outage probability decreases when increasing the number of clusters (hops) .

Figure 3. Outage probability as a function of Φ in dB.

In Fig. 3, we present the end-to-end outage probability of the proposed protocol as a function of Φ in dB. In this simulation, we fix values K, P, and Q as 2, 0.5, and 0.5, respectively. In addition, we fix the position of the primary user at ( )0.4,0.4 , while changing the number of relays at each cluster. In this figure, vector [1 2] implies that the number of relays at clusters 1, and 2 are 1, 2, respectively. As we can observe, the outage performance is worst when the number of relays in each cluster is equal to 1. Moreover, when the number of relays at the last cluster is 2, the performance is better than the case that the number of relays at the first cluster is 3. Finally, the theoretical results and simulation results are in excellent agreement.

V. CONCLUSION In this paper, we evaluated the performance of the multi-hop cluster-based transmission protocol in underlay network. Results showed that the simulation results match very well with the theoretical results, which verifies our derivations.

REFERENCE [1] Shi, Y., Hou, Y.T.; Kompella, S. ; Sherali, H.D., “Maximizing Capacity

in Multihop Cognitive Radio Networks under the SINR Model”, IEEE Trans. Mobile Computing, vol. 10, no. 7, pp. 954 – 967, 2011.

[2] T. T. Duy and H.Y. Kong, "Cooperative Multi-relay Scheme for Secondary Spectrum Access", KSII Transactions on Internet and Information Systems (TIIS), vol. 4, no. 3, pp. 273-288, June 2010.

[3] T. T. Duy and V.N.Q. Bao, "Outage performance of cooperative multihop transmission in cognitive underlay networks", ComManTel, HCM City, Viet Nam, Jan. 2013.

[4] Q. Deng, A.G. Klein, “Diversity of multi-hop cluster-based routing with arbitrary relay selection”, IET Communications, vol. 6, no. 9, pp. 1054–1060, 2012.

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