DSpace at VNU: Algorithm for re-use of shadowed CRs as relays for improving cooperative sensing performance

Algorithm for Re-use of Shadowed CRs as Relays for Improving Cooperative Sensing Performance Dinh Thi Thai Mai, Nguyen Quoc Tuan, Lam Sinh Cong University of Engineering and Technology

Algorithm for Re-use of Shadowed CRs as Relays for Improving Cooperative Sensing Performance

Dinh Thi Thai Mai, Nguyen Quoc Tuan, Lam Sinh Cong

University of Engineering and Technology, Vietnam National

University, Hanoi - Vietnam Email: dttmai@vnu.edu.vn, tuannq@vnu.edu.vn

Dinh-Thong Nguyen Faculty of Engineering and Information Technology, University of Technology, Sydney – Australia Email: dinh-thong-nguyen@eng.uts.edu.au

Abstract – In cooperative spectrum sensing, information from

deeply faded local cognitive radios (CRs) needs to be eliminated

from contributing to the fusion pool at the fusion center Most

current works on the subject unrealistically assume that the

reporting channels between the CRs and the fusion center are free

of loss and fading In order not to waste those deeply faded CRs,

this paper proposes an efficient algorithm to re-use them by

reassigning them to act as cooperative diversity relays to assist the

surviving CRs in combatting outages due to Suzuki fading in the

reporting channel The algorithm involves the pairing of a surviving

CR to a relay CR so as to select the lowest outage probability of the

resulting cooperative diversity relaying network The paper proposes

a closed-form and accurate approximation for the outage

probability of such a network in the composite Rayleigh-lognormal

fading channel, thus rendering fast and simple execution of the

pairing algorithm

Keyword – cognitive radio, Suzuki fading, relay network

I INTRODUCTION

Cooperative spectrum sensing using cognitive radios (CRs)

has proved to be a reliable technique for combating deep

fading during the sensing a primary user [1] [2] The sensing is

carried out in two phases: in the sensing phase, the CRs

independently measure and process the signal from the

primary user, and in the reporting phase the CRs

independently report the processed information to a fusion

center (FC) which is usually a cognitive base station, to make

the final global sensing decision as to whether the primary user

is present or absent In many standard fusion rules, it is easy to

see that the inclusion of deeply faded CRs, i.e with low SNRs,

in the decision fusion at the FC diminishes the reliability of the

cooperative detection of the primary user Thus by discarding

the detection contribution from shadowed CR sensors, the

detection probability of the cooperative sensing network can

be improved However, by doing so the CRs under shadowing

are wasted Signal-to-noise ratio (SNR) is a dominant metric

of transmission quality affecting the detection performance of

a CR sensor and can be used by the FC to decide if a CR

should be rejected [4] Various techniques are available to date

in wireless communications for a CR to efficiently estimate the

SNR directly from its sensing energy samples without the

knowledge of the transmitted signal power or the noise

variance, e.g [5]

In most research papers in the literature to date on

cooperative spectrum sensing using CRs, the wireless links

between individual CRs and the fusion centre, i.e the

reporting channels, are assumed free of loss and fading In

reality, when these channels are of significant distances in suburban macrocells or under shadowing in urban microcells, loss and fading is a significant issue In this case, cooperative diversity relaying may be necessary to improve the performance of the reporting wireless channels The cooperative diversity relay can process the information it receives from the source and forward the information to the destination using either amplify-and-forward (AF) or decode-and-forward (DF) protocols

In an earlier paper [6], we proposed an innovative, albeit simple, re-use of those CRs under deep fading of the sensing channels by re-assigning them to act as diversity relays to their more healthy peers in the reporting channels, thus improving the global detection reliability of the fusion center Signal-to-noise ratio in the sensing channels was used as a sole parameter in deciding which shadowed relay was to assist which surviving CR However, in realistic radio propagation scenarios, the fading characteristics in the reporting channels are different from those in the sensing channels, thus SNRs from the latter channels cannot usually be used as valid parameters for calculating the outage probability of the resulting cooperative diversity relaying networks in the reporting channels Also, in [6] the fading mechanism in the reporting channels is assumed to be Rayleigh distributed, which is rather simplistic in urban and suburban areas In this paper, we propose a more sophisticated and more reliable algorithm to select ‘surviving-rejected’ CR pairs to form cooperative diversity relaying networks in a composite Rayleigh-lognormal environment, also known as the Suzuki fading channel [7] The proposed pairing algorithm involves searching for pairs that produce lowest outage probabilities of the resulting networks However, it is well known that the infinite integral in the probability density function (pdf) of the Suzuki fading distribution makes it difficult to derive a closed-form expression for channel outage probability, thus preventing any efficient and fast search Another mathematical complexity arises in the calculation of the pdf of the sum of two lognormal random variables [8] [9] at the FC destination of the resulting cooperative diversity AF relaying network - one directly from the surviving CR and the other forwarded from the relay This pdf can be calculated using the moment generating function (MGF) technique [8] [10] followed by the inverse Laplace Transform (ILT) [10] In this paper, using a similar approach as in [10] we derive a

closed-form and accurate approximation for the outage probability of

the cooperative diversity AF relaying network, and therefore

can significantly speed up the proposed pairing search While

the main motivation of our paper is clearly to re-use the

shadowed sensing CRs which otherwise will be wasted, its

main contribution is more towards the mathematical and

computational advance for cooperative diversity relaying using

AF protocol Therefore spectral sensing and detection decision

fusion are not issues in this paper

The rest of the paper is organized as follows In Section II,

we summarize briefly the principle of cooperative spectrum

sensing and present a novel and accurate closed-form

expression for the approximation of probability of detection of

CR in a Suzuki fading channel Similarly, in Section III we

summarize the essence of a cooperative diversity AF relaying

network and present a novel and accurate closed-form

approximation for the calculation of probability of outage of

the network using moment generating function (MGF) and

inverse Laplace transform (ILT) techniques In Section IV, a

‘pairing’ algorithm is presented for efficient re-use of

shadowed CRs as relays Finally in Section V, results and

conclusions are presented

II COOPERATIVESPECTRUMSENSING

A Sensing Network Definition

Figure 1 shows a cooperative spectrum sensing CR

network in which local CRs detect signals from the primary

user, perform local processing, then send information to the

fusion centre (FC) for the latter to make the final global

sensing decision as to whether the primary user is absent (H 0)

present (H 1) In many applications, the CRs report their local

binary decision {u i} together with associated parameters-

signal to noise ratio {SNR i }, probability of detection{P Di} and

probability of false alarm {P Fi} to the fusion centre via the

reporting wireless channels These parameters adequately

characterize the reliability or the trustworthiness of the local

binary decision In this paper, we assume that while both

sensing and reporting networks are subject to composite

Rayleigh-lognormal fading, a CR can be deeply shadowed in

the sensing network, e.g by an obstacle, but still is clear in the

reporting network

B Detection and False Alarm Probabilities over Fading

Channels

There are two probabilities that are most commonly used

as performance metrics for spectrum sensing: probability of a

false alarm P F which is the probability that a signal is detected

while it does not exist, and probability of detection P D which is

the probability that the presence of a signal is correctly

detected

Probabilities of false alarm is given in [1] as

( )

m

λ

Γ (1)

where λ is the power detection threshold, Γ(.) and Γ(.,.) are complete and incomplete gamma functions, respectively

P D in fading conditions is obtained by averaging its value in

the AWGN case over the SNR fading distribution f(γ), while

P F remains the same under all fading conditions since it is calculated under Η hypothesis, i.e no signal, hence 0 independent of SNR, i.e

1

P =∞f γ Q γ G− P dγ (2) where γ is the SNR, Q m (.,.) is the generalized Marcum’s Q function of 2m degree of freedom

In a Rayleigh fading channel with average SNRγ , the probability of detection of a local CR is given in [3] as

1

1

m P

m m m

m

γ

γ

λ γ γ γ

Γ −

  (3)

In this paper we consider a composite Rayleigh-lognormal

fading channel with power gain Y R-Ln =e Z where Z is a Gaussian

RV with distribution N (µz, σz2) The pdf of its power gain is

dx

x x

x

p x

p f

Z

Z Z

Ln R

















=

2 ) (ln exp 2

1 )

exp(

0

1 ) (

σ

μ π

σ

(4) Thus by inserting (4) into (2), it can be shown that the probability of detection in the composite Rayleigh-lognormal (also known as Suzuki) fading channel, can be approximated

in terms of its corresponding probability of detection in a Rayleigh channel, is [10]



N

z n z Rayleigh

D n Suzuki

D

P

, ,

σ μ γ π

(5)

in which w n and a n are, respectively the weights and the abscissas of the Gauss-Hermite polynomial The approximation becomes more and more accurate with

increasing approximation order N p, and high accuracy is

achieved for N p > 6 [8][9]

The behavior of the curve of P D in (5) versus P F in (1) represents the receiver operating characteristics (ROC) in a Suzuki fading channel

C Cooperative Spectrum Sensing

Let u i = [0,1], i=1,2,…,n, denote the 1-bit decision from

the ith CR There are many different decision fusion rules, but

if the individual measurements are mutually independent, then

the k-out-of-n rule is most popular by which hypothesis Η is 1

chosen if k or more individual decisions are 1, and Η is 0

chosen otherwise Under this rule the global average

probabilities are

1

i

n

=

−

 (6) and

1 1

( ) (1i ) i i

n n



Figure 1 : A decentralized cooperative spectrum sensing network with the Nth

CR sensor eliminated from the fusion process

III COOPERATIVE DIVERSITY RELAYING

A AF Cooperative Relaying Protocol Definition

Figure 2 shows a simple cooperative diversity relay

network using M relaying branches, where x s , P s , y ij , h ij and n ij,

are, respectively the normalized transmit signal, the power

from the source, i.e ( )2

1

E x = , the received signal, the channel gain (or loss), and the additive noise on the channel

link from i to j The additive noise is modeled as a circularly

symmetric complex Gaussian random variable with zero mean

and variance σ2 at the receiver, i.e n ~ N(0,σ2 )

In the application for CR reuse in this paper we use only

one relay (M=1); the Source is a reliable CR, the Destination is

the FC and a Relay is an unreliable CR being reused.The relay

is assumed to use the amplify-and-forward (AF) protocol and operates in the time division mode having two phases: the relay-receive phase and the relay-transmit phase; each phase or

sub-block is of duration T/2 In the relay-receive phase, the

source transmits the complete message to both the destination and the relay (broadcast mode), and the received signal at the relay and at the destination, respectively is

) ( ) ( )

(t P s h sr s t n sr t sr

y = + (8a)

) ( ) ( )

( t P h x t n t

ysd = s sd s + sd (8b)

In the relay-transmit phase, the relay with power P r sends a

signal x r and the destination receives

) 2 / ( ) 2 / ( )

2 / (t T P r h rd r t T n rd t T rd

which is an amplified version of the signal it receives in (11a)

to the destination, i.e

) 2 / ( )}

( ) ( {

) 2 / (t T h rd r P s h sr x s t n sr t n rd t T rd

By equating the expectations of (9a) and (9b), we obtain

2 ] 2 [h sr sr E

s P r P r

σ

α

+

=

(10)

Figure 2: Diagram of an M-relay cooperative diversity relaying network

From (9b) the SNR at the destination of the relayed signal can be obtained with α r from (10), as

1 2

2 2

2

+ +

= +

=

rd sr rd sr rd

sr rd h r

s P rd h sr h r

γ γ σ

σ α

α

2

2

, 2 2

rd

r P rd h rd sr

s P sr h sr

σ

γ σ

d rd

Phenomenon

0 1 {H H, }

Fusion Center

i i

i P P SNR D F i

δ =

u 0 {0,1}

P D1 P D2 … P DN

d sr

d sd

Sensing channel

Reporting channel

For simplicity we assume that unfaded SNR is the same

on all channels, i.e P/σ 2 =SNRo, then the power gain of the

relay channel corresponding to (11) is

SNRo h

h

h h

h

rd

sr

rd sr

R

/ 1

2 2

2 2 2

+ +

Finally, the end-to-end power gain of the AF relay

wireless network is

2 2

2

R sd

B System Outage Definition

The outage probability, i j ( )

ou

P μ of the wireless channel

between two points i and j having instantaneous channel gain

h ij for a given outage information rate threshold, R th is defined

as

) ( )

( Pr ) ,

2

2

th h th ij th

out

(14)

where F (.) is the cdf of the fading distribution and the channel

gain threshold is defined as

SNRo

th

R M th

1

2( 1 )

−

μ (15)

and M is the number of relays which is 1 in this paper

C AF Cooperative Relaying Outage Calculation

Since the end-to-end power gain in (13) is a continuous

function, the outage probability of an AF cooperative diversity

relaying network is defined simply as

) ( )

Pr(

)

2

th h th

AF th

out

AF

AF

F h

To calculate (16), we require the pdf of hAF 2 In [10] it

has been justified that the power gain hR2 in (12) of the

diversity relaying channel can be represented by a single

Suzuki RV with estimated Gaussian distribution

parameters( ˆ , ˆ2)

R

μ Thus, hAF 2in (13) can be considered

as the power sum of two Suzuki RVs, and in [10] an elegant

method is presented to calculate its pdf using moment

generating function (MGF) and inverse Laplace transform

(ILT) The result given in [10] is





































=

p N p

N

AF

h

m k m R s k m R

m

n k n sd s k n sd

n w

s

M

1 , (.)[ 1 , (.)]

1 , (.)[ 1 , (.)]

1

)

2

π

Therefore















−

−

−

=

p

N N p

AF h AF

h

R m k p e sd n k p e m n w

s M InvLaplace p

f

) , / ,

/ ( 1

) )

2

π

(17)

where

)

) ,

;

,

ξ

μ σ

σ

sd n

) ˆ ˆ 2 exp(

ˆ , ˆ

ξ

μ σ σ

m

R m

Therefore the outage probability of the AF cooperating diversity relaying network is

))

/ 1 ( )

/ 1 ( (

(.)]

(.) [ 1

) (

, ,

, ,

) (

R m R

m sd n sd

n

p N m

p N

m n

AF h th

out AF

k p e k k p e k

k k

w w

dp p f

th P

−

−

−

−

−



−

=

= =



π

μ μ

(18)

Figure 3: Probability of outage versus given channel power gain threshold defined in (15) for an AF cooperative diversity relay network Figure 3 confirms the accuracy of the closed form expression for the probability of outage in (18)

IV ALGORITHM FOR RE-USE OF SHADOWED CRs

In this section we propose a method that utilizes eliminated CRs by assigning them to act as cooperative diversity relays for the surviving CRs that still stay in the fusion pool In Figure 1 we illustrate an example in which

CR N suffers from deep fading and its reported information is

discarded by the fusion center The FC then reassigns CR N to

act as a relay for CR1 to improve the transmission reliability of

the CR1-to-FC reporting channel, thus forming a 3-terminal

relay network with the surviving CR1 as the source (S), the

eliminated CR N as the relay (R), and the FC as the destination

(D)

Figure 4 below represents the simulation model used in

this paper for the reporting network to illustrate the proposed

pairing algorithm to select which relay (eliminated CR) to

assist which source (CR retained in the fusion pool) We

assume that Suzuki fading channels all have σ =8dB and that µ

is proportional to a negative exponent of the propagation

distance, d -α In the simulation we normalize µ sd =µ rd=5dB, then

µ s1r1 =2dB, µ s1r2 =4dB, µ s1r3=6dB, similarly for other values of

μ sjri Relative values are important but precise values of µ are

not important for the objective of this paper

From these simulation data, the Gaussian parameters

)

ˆ

,

Rji

Rji σ

μ are found for each cooperative diversity relay

network (Sj,Ri,D). The outage probability of all the networks

(Sj,Ri,D) required to complete Table 1 for rate threshold

μth=0.1 and Table 2 for rate threshold μth=0.5 is calculated from

(18)

Table 1: Matrix of Probability of Outage of Cooperative Relay Network (Sj, R i, D)

with µ th = 0.1

CR S1 S2 S3 S4 S5

R1 0.0182 0.0198 0.0182 0.0154 0.0122

R2 0.0154 0.0182 0.0198 0.0182 0.0154

Table 2: Matrix of Probability of Outage of Cooperative Relay Network (Sj, R i, D)

with µ th = 0.5

CR S1 S2 S3 S4 S5

R1 0.1262 0.1296 0.1262 0.1152 0.0963

R2 0.1152 0.1262 0.1296 0.1262 0.1152

Figure 4: Simulation model of reporting network to illustrate the proposed

pairing algorithm

Because the reporting channels between the CRs and the

FC are subjected to fading and hence link outages, the reported

parameters received at the FC are usually deteriorated The

effective probability of detection received from the jth CR by

the FC is

P (j) P {1 P out(j)}

Dj

De = −

(19)

where P Dj is probability of detection from (5) and P out (j) is the outage probability of the channel between the jth CR and the

FC either with (using (18)) or without (when all terms involving m are omitted) diversity relaying It can be easily

observed that the outage probability in (18) is lower with the use of the relay compared to that without the relay, hence improving the local effective probability of detection in (19) received by the fusion center

A Eliminating Algorithm

• Step 1: Local CRs calculate the SNR {SNR i ;i=1,2, N }

from their respective raw sensed signal {y i}from the primary user and calculate the probability of detection

{P Di}using (5)

• Step 2: The fusion center receives the processed information in Step 1 from the local CRs Note that having received individual SNRs (of the sensing channels)

from the CRs, the FC can evaluate the individual P Ds

instead of the CRs However, such evaluated P D s will be unreliable due to fading in the reporting channels

• Step 3: The FC ranks the CRs in the descending order of

their SNR and eliminates those CRs with lowest SNR

B Pairing Algorithm

The pairing algorithm is based on the minimum

probability of outage of the entire reporting network

• Step 1: Calculate P AFj out (μ th ), (j=1,2,3,4,5; i=1,2,3) using

(18) of the resulting cooperative diversity relay networks using AF protocol, and complete Table 1 (or Table 2)

• Step 2: Rank and select three pairs (i=1,2,3) with lowest

P AFj out (μ th) from Table 1 (or Table 2) as the optimal solution for pairing The pairing result is shown in red

V RESULTS AND CONCLUSIONS

The paper has successfully presented an accurate analysis

of the proposed strategy for the re-use of discarded CR sensors

as diversity relays to improve the performance of surviving peers against Suzuki fading in the reporting network The most significant contribution of this paper is the derivation of closed-form and accurate expressions for the probability of

detection P D of the primary user and the probability of outage

P out of the resulting three-terminal cooperative diversity relaying wireless network These closed-form and accurate expressions greatly speed up the execution of the proposed re-use algorithm, giving us the incentive to research into a more sophisticated and efficient algorithm The effectiveness of the strategy was judged on the basis of resulting global ROC

curves, i.e global probability of detection, Q D, versus global

probability of false alarm, Q F Figures 5a and 5b show the simulation results of the receiver operating characteristic (ROC) curves of the

cooperative sensing network in three operating environments:

transparent reporting channels (no fading), Suzuki fading

reporting channels without re-use of eliminated CRs as

diversity relays, and Suzuki fading reporting channels with

re-use of eliminated CRs as diversity relays All ROC curves are

for the simulation model in Figure 4 The outage power gain

threshold µ th is much lower, i.e much healthier SNR, in Figure

5a than in Figure 5b giving much higher global probability of

detection, and therefore the benefit of re-use of deeply faded

CRs is not as pronounced in Figure 5a compared to Figure 5b

However, in both cases the benefit of the proposed re-use of

poor sensing CRs as diversity relays is very convincing

(a)

(b) Figure 5: Sensing performance of the cooperative spectrum sensing network

under fading with and without re-use of poor CRs as diversity relays,

(a) Outage threshold µ th =0.1 and (b) Outage threshold µ th = 0.5

ACKNOWLEDGEMENTS This work was supported by research grants from QG.2012 (Projects of the University of Engineering and Technology, Vietnam National University Hanoi) and NAFOSTED (National Foundation for Science and Technology Development)

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