Cooperative Cognitive Radio with Obstacles on the Sensing ...

Cooperative Cognitive Radio with Obstacles on the Sensing

Channels

Abdul Haris Junus Ontowirjo1,2

, Wirawan1, and Adi Soeprijanto

1

1Department of Electrical Engineering, Faculty of Electrical Technology, Institut Teknologi Sepuluh Nopember,

Surabaya 60111, Indonesia 2Department of Electrical Engineering, Faculty of Engineering, Universitas Sam Ratulangi, Manado 95115, Indonesia

Email: [email protected]; {wirawan, adisup}@ee.its.ac.id

Abstract—This paper investigates the performance of

cooperative cognitive radio with obstacles on the sensing

channels. The analysis focuses on weighted summation

combining in the fusion center. In this paper we propose

Rayleigh, Rician, and Nakagami-m channel models to handle

the presence of obstacles in the sensing channels. The analysis

is based on the central limit theorem. The results are presented

in the form of relation between detection probability and SNR

with decision threshold as the parameter and the relation

between detection probability and decision threshold with SNR

as the parameter. Index Terms—Cooperative cognitive radio, spectrum sensing,

fusion center, weighted summation, decision threshold, energy

detection.

I. INTRODUCTION

Measurements show that spectrum utilization by

licensed Primary Users (PUs) is inefficient [1]. Cognitive

radio [2], [3] is a technology which has inherent

capability to increase the efficiency of inefficient

spectrum utilization by allowing unlicensed Secondary

Users (SUs) access the spectrum band during idle time.

The Cognitive Radio Network (CRN), all the SUs, must

release the spectrum band as soon as the PU be active. It

means the SUs do not interfere the PU and it is said the

SUs utilize the spectrum band in opportunistic fashion. In

order to keep the SUs from interfering the primary

network, the network of PU, spectrum sensing is essential

to detect the spectrum holes, the idle licensed spectrum

sub-bands. Different spectrum sensing techniques have

been proposed. Among them are matched filter detection

[4], the cyclostationary detection [5], the energy detection

[6]-[9], and covariance based detection [10]. Among the

proposed detection techniques for spectrum sensing, the

energy detection is the most common practical one due to

its simplicity.

With a single SU, the instantaneous Signal-to-Noise

Ratio (SNR) of the received signal may become too low

to make the sensing result due to the fading, shadowing,

and the hidden node problem. Cooperative approach has

been introduced to overcome this challenge. Several

Manuscript received August 1, 2018; revised April 2, 2019. Corresponding author email: [email protected].

doi:10.12720/jcm.14.5.396-401

different SUs cooperatively detect the spectrum holes. As

the number of involved SUs increases, the probability

that all of the cooperating SUs are simultaneously in a

deep shadowing or fading is reduced [11]. Furthermore,

the multiple distributed SUs provide the diversity gain.

The diversity gain, in turn, greatly improves the global

performance and efficiency [12].

We consider the Cooperative Cognitive Radio (CCR)

of Fig. 1. The model consists of one PU, K SUs, and a

Fusion Center (FC). The black thick vertical lines

represent the obstacles on the related channels. Each SU

senses the spectrum band of interest through an

individual sensing channel, applies energy detection

technique, that is, computes the amount of energy of the

signal received from PU for specified time interval, and

sends it to the FC via perfect (error-free) reporting

channel. The FC collects the information on the energy of

PU's signal received by all SUs, combines them, and

applies some rule to make the global decision considering

the occupancy of the spectrum band. If the messages sent

by the SUs are in form of local binary decision about the

present or the absent of the PU, then the FC combining

rule is called hard combining method [9]. If the messages

sent to the FC are the local test statistics, the FC

combining rule will be a soft combining method [4], [13].

If every SU forwards the signal from PU to FC and the

test statistics is computed by the FC then it is still said

that the FC performs soft combining method [14]-[16].

Fig. 1. Cooperative cognitive radio with obstacles

Even if only binary decisions are transmitted by the

SUs to the FC for hard combining, there may be

significant communication overhead related to the

protocol used in transmitting the sensing results.

Therefore, hard combining method does not significantly

decrease the bandwidth requirement comparing its soft

counterpart. The difference in the resource usage between

hard combining strategy and the soft combining one may

Journal of Communications Vol. 14, No. 5, May 2019

©2019 Journal of Communications 396

be small [17]. Complex coupling relation between the

local quantization rule and the fusion combining rule is

the most important task in hard combining technique and

that is not present in soft combining technique. The soft

combining technique (soft-fusion policy) can achieve

optimal diversity, providing a higher diversity gain and

better detection accuracy compared with the hard

combining one (decision-fusion policy) [18].

Obstacles can considerably reduce the performance of

cognitive radio in practice. Hence, the fading channel that

occurs in most of the realistic wireless environments,

degrade the performance of the channels. CSS is analyzed

superficially by [19]. In [15] the performance analysis of

CSS in CR over Nakagami-m channels is studied. In [20]

the performance analysis of CSS is examined for

multipath fading channels based on energy detection. In

[6] the analysis is based on fast-fading and block-fading

channels where only the average SNR is available. In [9]

block flat-fading channels are assumed in the model for

analyzing the CSS and in [7] Nakagami-m fading

channels are assumed with MRC reception.

This paper describes the effect of the presence of

obstacles on the sensing channels. The work presents a

performance analysis of spectrum sensing over multipath

fading for a system with obstacles between PU and SUs

as depicted in [21]. Specifically, we suggest the use of

available channel models as Rayleigh channels, Rician

channels, and Nakagami-m channels and the use of

Central Limit Theorem (CLT) to derive the closed-form

expression of the performance measures.

II. SYSTEM AND CHANNEL MODELS

We consider a CCR with K secondary users, {𝑆𝑈𝑘}𝑘=1𝐾 ,

which cooperatively observe the presence and the

absence of the primary signal, 𝑠[𝑛], transmitted by PU,

with a specified frequency, via independent sensing

channels, in certain successive observation intervals.

Each interval consists of N samples which is selected

based on the bandwidth-observation time product. The n-

th received signal sample at 𝑆𝑈𝑘 , 𝑦𝑘[𝑛] , for 𝑘 =1,2,⋯ , 𝐾 and 𝑛 = 1,2,⋯ ,𝑁, can be written as

𝑦𝑘[𝑛] = {𝑤𝑘[𝑛] 𝐻0

ℎ𝑘𝑠[𝑛] + 𝑤𝑘[𝑛] 𝐻1 (1)

where the null hypothesis, 𝐻0, represents the absence of

PU and the alternative hypothesis, 𝐻1 , represents the

presence of PU. Noise samples are zero mean complex

Gaussian random variables with variance 𝜎𝑘2.

𝑤𝑘[𝑛]~𝐶𝑁(0, 𝜎𝑘2) (2)

where ℎ𝑘 is the flat fading channel gain between PU and

𝑆𝑈𝑘 . The energy of the primary signal, 𝑠[𝑛], from PU,

during observation, is

𝐸𝑠 =∑|𝑠[𝑛]|2𝑁

𝑛=1

(3)

The channels with obstacles have no line-of-sight

(LOS) component in their propagation paths. The fading

amplitude of each channel, |ℎ𝑘|, can be approximated by

Rayleigh distribution. The SNR, 𝛾, distribution is [22]

𝑓𝛾(𝛾) =

1

𝛾𝑒𝑥𝑝 (−

𝛾

�̅�) , 𝛾 ≥ 0,

(4)

where �̅� = 𝐸[𝛾] is the expectation value of 𝛾 . The

channels with no obstacle have one strong direct LOS

component in their paths. They can be considered as

Rician channels approximately. The SNR distribution is

[22]

𝑓𝛾(𝛾) =𝜅 + 1

�̅�𝐼0 (

𝛾𝜅(𝜅 + 1)

�̅�) 𝑒𝑥𝑝 (−

𝛾(𝜅 + 1)

�̅�− 𝜅),

𝛾 ≥ 0 (5)

where the function 𝐼0 is the modified Bessel function of

0-th order and 𝜅 is the ratio of the power in the LOS

component to the power in the non-LOS multipath

components. It can be seen that for 𝜅 = 0 , Ricean

distribution becomes Rayleigh distribution so it can be

used to approximate the channels without LOS

component as well.

The problem of obstacles also can be approached by

Nakagami-m distribution which has SNR distribution as

[22]

𝑓𝛾(𝛾) =

𝑚𝑚𝛾𝑚−1

�̅�𝑚Γ(𝑚)𝑒𝑥𝑝 (−

𝑚𝛾

�̅�) , 𝛾 ≥ 0 (6)

where Γ(⋅) is the Gamma function and m is the

Nakagami-m fading parameter. We can see that for m = 1

the distribution reduces to Rayleigh fading so it can be

used to model the channels with obstacles. For𝑚 =(𝜅 + 1)2/(2𝜅 + 1) the distribution is approximately

Rician fading which can be used to represent the channels

without obstacle.

The instantaneous SNR at the k-th secondary user is

𝛾𝑘 =

𝐸𝑠|ℎ𝑘|2

𝜎𝑘2 (7)

and its average value is

�̅�𝑘 = 𝐸[|ℎ𝑘|

2]𝐸𝑠

𝜎𝑘2 (8)

Each secondary user, 𝑆𝑈𝑘 , performs energy detection

on the received signal, 𝑦𝑘[𝑛], to produce test statistics, 𝑌𝑘,

𝑌𝑘 = ∑|𝑦𝑘[𝑛]|2

𝑁−1

𝑛=0

(9)

According to the central limit theorem (CLT) [23], for

a large 𝑁 (the number of samples), 𝑌𝑘 is asymptotically

normally distributed,

𝑌𝑘~𝑁(𝜇𝑌𝑘 , 𝜎𝑌𝑘2 ) (10)



The probability distribution function (PDF) of 𝑌𝑘 then

can be expressed as

𝑓𝑌𝑘(𝑥) =

1

𝜎𝑌𝑘√2𝜋𝑒𝑥𝑝 (−

1

2[𝑥 − 𝜇𝑌𝑘𝜎𝑌𝑘

]

2

) (11)

where the local test statistics mean, 𝜇𝑌𝑘, and the local test

statistics variance, 𝜎𝑌𝑘, are [24]

𝐸[𝑌𝑘] = 𝜇𝑌𝑘 = {

𝑁𝜎𝑘2 𝐻0

𝑁(1 + 𝛾𝑘)𝜎𝑘2 𝐻1

(12)

and

𝑉𝑎𝑟[𝑌𝑘] = 𝜎𝑌𝑘

2 = {𝑁𝜎𝑘

4 𝐻0𝑁(1 + 2𝛾𝑘)𝜎𝑘

4 𝐻1 (13)

respectively.

All SUs send their local test statistics to FC via

independent and perfect reporting channels. FC applies

weighted summation rule and combines linearly all 𝑌𝑘 to

generate a single global test statistics 𝑍,

𝑍 =∑𝛽𝑘𝑌𝑘

𝐾

𝑘=1

(14)

where 𝛽𝑘 is the weight applied to each channel. Since all

𝑌𝑘 are normal random variables, their linear combination

is normal too. We can see that equal gain combining

(EGC) and maximum ratio combining (MRC) are two

special cases of weighted summation combining. If all

weights are unity, 𝛽𝑘 = 1 for all 𝑘, then we have EGC

and if each weight is proportional to the SNR at 𝑆𝑈𝑘 ,

𝛽𝑘 ∝ 𝛾𝑘 , then we have MRC. The distribution of the

global test statistics can be expressed as

𝑍~𝑁(𝜇𝑍, 𝜎𝑍2) (15)

where the global test statistics mean, 𝜇𝑍 = ∑ 𝛽𝑘𝜇𝑌𝑘𝐾𝑘=1 ,

and the global test statistics variance, 𝜎𝑍2 = ∑ 𝛽𝑘

2𝜎𝑌𝑘2𝐾

𝑘=1

are expressed in detail as

𝐸[𝑍] = 𝜇𝑍 =

{

𝑁∑𝛽𝑘

𝐾

𝑘=1

𝜎𝑘2 𝐻0

𝑁∑𝛽𝑘

𝐾

𝑘=1

(1 + 𝛾𝑘)𝜎𝑘2 𝐻1

(16)

and

𝑉𝑎𝑟[𝑍] = 𝜎𝑍2 =

{

𝑁∑𝛽𝑘

2

𝐾

𝑘=1

𝜎𝑘4 𝐻0

𝑁∑𝛽𝑘2

𝐾

𝑘=1

(1 + 2𝛾𝑘)𝜎𝑘4 𝐻1

(17)

respectively.

The FC makes a decision based on the global test

statistics, 𝑍,

𝐻1𝑍 ≷ 𝜆

𝐻0

(18)

where 𝜆 is the decision threshold.

The performance measures of the cooperative

cognitive radio under consideration, in this case, are the

probability of false alarm, 𝑃𝑓 , and the probability of

detection, 𝑃𝑑 , then can be derived. The probability of

false alarm is the probability that the system detects the

presence of PU while in fact, it is absent. The probability

of false alarm can also be viewed as a complementary

cumulative distribution function for null hypothesis. The

probability of detection is the probability that the system

detects the presence of PU and indeed it is present. The

detection probability can also be considered as

complementary cumulative distribution function for the

alternative hypothesis.

𝑃𝑓 = 𝑃𝑟(𝑍 > 𝜆|𝐻0)

= ∫ 𝑓𝑍(𝑥|𝐻0)𝑑𝑥

∞

𝜆

= 1 − 𝐹(𝜆|𝐻0)

(19)

and

𝑃𝑑 = 𝑃𝑟(𝑍 > 𝜆|𝐻1)

= ∫ 𝑓𝑍(𝑥|𝐻1)𝑑𝑥

∞

𝜆

= 1 − 𝐹(𝜆|𝐻1)

(20)

where 𝐹(⋅) is the cumulative distribution function (CDF)

of the global test statistics, 𝑍 . In terms of the AWGN

noise, the channel SNR, the number of samples, the

weighting constant, and the decision threshold, the

probabilities of false alarm and detection can be

expressed as

𝑃𝑓 = 𝑄(

𝜆 − 𝐸[𝑍|𝐻0]

√𝑉𝑎𝑟[𝑍|𝐻0])

= 𝑄(𝜆 − 𝑁∑ 𝛽𝑘𝜎𝑘

2𝐾𝑘=1

√𝑁∑ 𝛽𝑘2𝜎𝑘

4𝐾𝑘=1

)

(21)

and

𝑃𝑑 = 𝑄(

𝜆 − 𝐸[𝑍|𝐻1]

√𝑉𝑎𝑟[𝑍|𝐻1])

= 𝑄(𝜆 − 𝑁∑ 𝛽𝑘(1 + 𝛾𝑘)𝜎𝑘

2𝐾𝑘=1

√𝑁∑ 𝛽𝑘2(1 + 2𝛾𝑘)𝜎𝑘

4𝐾𝑘=1

)

(22)

respectively. where 𝑄(⋅) is the Q-function defined as the

tail distribution function of the standard normal

distribution,

𝑄(𝑥) =1

√2𝜋∫ 𝑒𝑥𝑝 (−

1

2𝑥) 𝑑𝑥

∞

𝑥



The Q-function can be expressed in term of the error

function or the complementary error function.

III. SIMULATION

The performance of the CCR is analyzed by means of

detection probability vs. SNR (𝑃𝑑 vs. 𝛾) curves for

several values of threshold (𝜆),

detection probability vs. threshold (𝑃𝑑 vs. 𝜆) curves

for several values of SNR (𝛾),

For simulation purpose, the system is set up for 𝐾 = 4

users. All SUs take their local test statistics over a sensing

interval of 𝑁 = 100 samples.

Fig. 2 shows how the detection probability varies as

the average SNR varies for three decision threshold

values. It is evident that better SNR leads to improvement

in the performance of spectrum sensing.

Fig. 2. Detection probability vs. SNR

The quasilinear segments of the graphs show that their

slopes are nearly close to each other. For decision

threshold 𝜆 = 2.0 , the detection probability increases

0.38 as the average SNR increases 1 dB from 0.5 dB to

1.5 dB. The detection probability increases 0.36 as the

average SNR increases with the same increment from 2.5

dB to 3.5 dB for decision threshold 𝜆 = 2.5. With the

decision threshold 𝜆 = 3.0 and with the same increment

of the average SNR, the detection probability increases

0.25 as the average SNR increases from 5.5 dB to 6.5 dB.

With this evidence, the same performance can be

achieved within different average SNR intervals by

adjusting the decision threshold value. For example if a

level of performance can be achieved when average SNR

varies between 0 dB to 4 dB by setting the decision

threshold of 𝜆 = 2.0, then the same performance can be

achieved within the interval of SNR from 2 dB to 6 dB by

adjusting threshold value 𝜆 = 2.5 and the same

performance can be achieved within the interval of SNR

from 4 dB to 8 dB by adjusting threshold value 𝜆 = 3.0,

as long as the detection probability is concerned.

Fig. 3 depicts the variation of detection probability due

to the variation of the decision threshold for several SNR

values. It is evident that the performance decreases as the

decision threshold increases as long as decision

probability is concerned.

Fig. 3. Detection probability vs. decision threshold



With different channel qualities, the system shows

different performance degradations. For average SNR of

4 dB, the detection probability decreases 0.52 (from 0.78

to 0.26) as decision threshold value increases 0.61 (from

2.46 to 3.07). With the same increment of decision

threshold value, the detection probability decreases 0.32

for SNR of 5 dB and decreases 0.16 when SNR is 6 dB.

IV. CONCLUSIONS

This paper has analyzed the performance of CCR with

diversity reception and obstacles on the sensing channels.

Through extensive elaboration of analytical formulas and

simulation models, we have shown that numerical results

from analytical expressions of detection probability and

false alarm probability are close to the numerical

simulation results. The closeness of analytical and

simulation results has been presented in graphical relation

between the detection probability and the SNR with

decision threshold as the parameter and graphical relation

between the detection probability and the decision

threshold with SNR as the parameter.

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Abdul Haris Junus Ontowirjo received

the B.Eng. degree in electrical

engineering from the Institut Teknologi

Bandung (ITB), Bandung, Indonesia, in

1991, M.Eng. degree in electrical

engineering from the Institut Teknologi

Sepuluh Nopember (ITS), Surabaya,

Indonesia, in 2010, where he is currently

pursuing the Ph.D. degree in electrical engineering.

Wirawan received the B.Eng. degree in

electrical engineering from the Institut

Teknologi Sepuluh Nopember (ITS),

Surabaya, Indonesia, in 1987, the D.E.A.

degree in signal and image processing

from the Ecole Superieure en Sciences

Informatiques, Sophia Antipolis, France,

in 1996, and the Ph.D. degree in image

processing from Telecom ParisTech, Paris, France, in 2003. He

has been with the Electrical Engineering Department, ITS, as a

Lecturer since 1989. His current research interests include

statistical signal processing, underwater acoustic

communication, and various aspects of wireless sensor networks.

Adi Soeprijanto received the B.Eng.

degree in electrical engineering and

M.Eng. Degree in control system from

the Institut Teknologi Bandung (ITB),

Bandung, Indonesia, in 1989 and 1995

respectively, and the Ph.D. degree in

power system stability from Hiroshima

University in 2001. He has been with the

Electrical Engineering Department, ITS, as a Lecturer and

Researcher since 2001. His current research interests include

power system analysis.



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