relay selection methods in cognitive networks under ...

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RELAY SELECTION METHODS IN COGNITIVE NETWORKS UNDER INTERFERENCE AND INTERCEPT PROBABILITY CONSTRAINT IN PRESENCE OF HARDWARE NOISES Phu Tran Tin 1, 2, Tran Trung Duy 3, Miroslav Voznak 1 1

VSB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava - Poruba, Czech Republic Faculty of Electronics Technology, Industrial University of HoChiMinh City, HoChiMinh City, VietNam 3 Department of Telecommunications, Posts and Telecommunications Institute of Technology, HoChiMinh City, VietNam 2

[email protected], [email protected], [email protected]

DOI: 10.15598/aeee.v13ix.xxxx

Abstract. This paper studies physical-layer security issue in dual-hop underlay cognitive radio networks in presence of hardware impairments. We first derive the transmit power of secondary relays under interference constraint at primary user and intercept probability constraint at the eavesdropper. Then, we propose various relay selection methods to improve the outage performance of the secondary networks. For performance evaluation and comparison, we derive exact closed-form expressions of outage probability over Rayleigh fading channel. Finally, the derived expressions are verified by Monte Carlo simulations.

Keywords Hardware impairments, underlay cognitive radio, physical layer security, intercept Probability, outage Probability, Rayleigh fading channels.

1. Introduction Recently, diversity-based relaying communication [1-2] has gained much attention as a promising technique to mitigate the effect of fading environment. Moreover, this technique was widely used in underlay cognitive radio to improve performances for secondary networks [3-4]. In underlay cognitive radio networks, secondary users (SUs) can use the same licensed band as primary users (PUs) provided that interferences caused by their operations are lower than an allowable threshold required by the primary users (PUs) [5]. Physical-layer security is a simple method to guarantee

the security of wireless communications without using complex cryptographic methods [6]. Again, cooperative relaying protocols are used, in order to improve the secrecy performances for secured communication network. The authors in [7] proposed relay selection methods for cooperative networks with secrecy constraints. Published work [8] considered joint relay and jammer selection methods, where the best relay is used to forward the source data to the destination, while the optimal jammer relay generates limited interference to eavesdroppers. In [9], the authors evaluated the secrecy outage probability of secondary network with various relay jammer selection schemes at the cooperative phase. In [10], dual-hop secured multicast networks in underlay cognitive radio with partial relay selection were proposed and analyzed. The authors in [11-12] considered security versus reliability for cooperative relaying network via performance metrics such as intercept probability at the eavesdropper and outage probability at authorized nodes. However, performance analysis in [6]–[12] is based on the assumption that the transceiver hardware of the terminals is perfect. In practice, due to phase noises, nonlinear amplifier and I/Q imbalance, the transceivers are suffered from the hardware impairments [13]-[14], which degrades the performances of the wireless networks. The authors in [15] first studied the secrecy performances in the presence of the hardware imperfection. In particular, the authors in [15] considered the effects of the I/Q imbalance on the performances of OFDMA secured systems. In this paper, we propose relay selection methods to improve the outage performance of the secondary networks under the interference constraint at the primary user; the constraint of intercept probability (IP) at the eavesdropper; and the presence of hardware imperfection. In the first proposed scheme, the active relay providing

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the highest channel gain to the destination is selected to forward the source data to the destination. In the second one, the best relay is chosen to maximize the signal-tonoise ratio (SNR) obtained at the secondary destination. We derive exact closed-form expressions of outage probability for secondary networks over Rayleigh fading channel. Finally, Monte-Carlo simulations are presented to validate our derivations. Results show that the proposed methods outperform the conventional relay selection method, in which the relay is randomly selected.

Let d1 , d 2 , d 3 , d 4 and d 5 denote distances of the S  R m , R m  D , S  P , R m  P , and R m  E links, respectively. We also denote h1i , h2 i , h3 , h4i and h5i as channel coefficients of S  R m , R m  D , S  P , R m  P , and R m  E links, respectively. We assume that all of the channels follow a Rayleigh fading distribution. Hence, the channel gains and  1i | h1i |2 ,  2 i  | h2 i |2 ,  3  | h3 |2 ,  4 i | h4 i |2

The rest of the paper is organized as follows. The system model is described in Section 2. In Section 3, the performance evaluation of the protocol is described. The simulation results are presented in Section 4. Finally, conclusions of the paper are provided in Section 5.

3  d 3 , 4  d 4 , and 5  d 5 , respectively, where  is path-loss exponent.

 5i | h5i |2 follow exponential distributions. To take pathloss into account, we can model the parameters of  1i ,  2 i ,  3 ,  4 i , and  5i as [17] 1  d1 , 2  d 2 ,

Similar to [18], the maximum transmit power of the source S under the interference constraint and hardware impairments can be given as

2. System Model

P0 

Data Link

RM

Interference Link Eavesdropping Link

Rm

I th .  3 1   

(1)

where  is the constant characterizes the total level of hardware impairments at the transmitters and the receivers. Then, the instantaneous signal-to-noise ratio (SNR) of the S  R m link can be obtained as

E

R1

D

S

P Fig. 1: Fig. 1. System model of the proposed protocols in underlay cognitive radio.

In Fig. 1, we present the system model of the proposed protocol, in which a secondary source (S) communicates with the secondary destination (D) with help from M secondary relays, i.e., R m  m  1, 2,..., M  . Assume that there does not exist a direct link between S and D due to the far distance and deep fading. The secondary transmitters such as the source and relays must adapt their transmit power to satisfy a maximum interference threshold, i.e., I th , at the primary user (P). In the secondary network, an eavesdropper E tries to overhear the data transmitted to the destination. We assume that eavesdropper is near the destination and cannot overhear the data transmitted by the source. It is also assumed that the secondary relays are close together, which form a cluster [16]. All of the terminals are equipped with a single antenna and operate in half-duplex mode. Hence, the data transmission is realized through a time division technique over orthogonal channels.

1m 

P0 1m Q 1m /  3  .  P0 1m  N 0  Q 1m /  3  1

(2)

where N 0 is variance of Gaussian noise which is assumed to be the same at all of the receivers, i.e., the relay, destination and eavesdropper and Q  I th / N 0 / 1    . Next, we describe the operation of the proposed protocol: at the first time slot, the source S broadcasts its data to all of the relays. Then, the relays try to decode the source's data from the received data. Let us denote W1 and W2 as the set of the relays that decode the signal successfully and unsuccessfully, respectively. Without loss of generality, we can assume that W1   R1 , R2 ,..., RN  and W2   RN 1 , RN  2 ,..., RM  , where N is the cardinality of

the set W1 , N  0,1, 2,..., M  . Particularly, if N=0, there is no relay that can relay the source data to the destination. If N  1 , the system can choose a relay to forward the source data. Assume that a relay is in outage if the received SNR at that node is below an outage threshold  th . Otherwise, it is assumed that the relay successfully receives the data. Therefore, we calculate the probability that the number of active relay equals to N as follows:

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 11   th ,..., 1N   th ,  P | W1 | N   CMN Pr    1N 1   th ,..., 1M   th  (3)       CMN Pr  11   ,..., 1N   , 1N 1   ,..., 1M    , 3 3 3  3  where CMN 

 th M! and   . N ! M  N ! 1   th  Q

  Pj  5 j IP=Pr  ej   th   Pr    th   P   N  0  j 5j   N 0 th  Pr   5 j   1   th  Pj  

level is small; and hence the condition of  th  1 is assumed to be satisfied [19].

2.2. Transmit Power Formulation The IP at the eavesdropper must be lower than a predetermined value, i.e.,  . Hence, the constraint of the transmit power Pj can be found by

Next, we can rewrite (3) under the following form:

IP    Pj  (4)

F1  y   1  exp  1 y  , we obtain

power at the relay Pj is given as

(5)

M N

M N

  1

j

j 0

CMj  N CMN 3 . 3   j  N  1 

(6)

More specially, when N  0 , it can be obtained that M

P | W1 | 0     1 CMj j

j 0

3 . 3  j1 

(7)

2.1. Intercept Probability (IP) at the Eavesdropper Let us denote P j as the transmit power of the relay R j . At first, the received SNR at the eavesdropper due to the transmission of the relay R j can be formulated as

 ej 

Pj  5 j  Pj  5 j  N 0

.

(8)

  , (11) 

where W  5 / ln 1/   . With the transmit power in (11), the received SNR at the destination D can be provided by

and after calculating the integrals, an exact closed-form expression for P | W1 | N  can be given by

P | W1 | N  

(10)

that P j  I th /  4 j / 1    . Hence, the maximum transmit

 N   I th Q Pj  min  5 0 ,  N 0 min  W ,  ln 1/    1       4j 4j   

P | W1 | N  

Using the binomial expansion for 1  exp  1  x  

5 N 0 . ln 1/  

In addition, to satisfy the interference constraint at the primary user, the transmit power Pj must be adjusted so

Using the PDF and CDF of the exponential random f 3  x   3 exp  3 x  variables, i.e., and

M N     exp  3 x  1  exp  1  x   dx. CMN   3 0  exp   N 1  x  

(9)

where    th / 1   th  .

It is noted from (3) that we only consider the case that  th  1 . Indeed, in practice, the hardware impairment

M N      f 3  x   F 1   x   N   dx. P | W1 | N   CM  N  0    1  F   x   1    

  N   exp   5 0  , Pj   

2 j 

Pj  2 j  Pj  2 j  N 0



min W , Q /  4 j   2 j

 min W , Q /  4 j   2 j  1

. (12)

2.3. Relay Selection Methods At first, we consider the conventional relay selection protocol, named PR0, in which an active relay, e.g., R a is selected randomly to forward the source data to the destination. In the second proposed protocol, named PR1, the active relay which has the highest channel gain to the destination is selected for the cooperation. Let us denote R b as the chosen relay, the relay selection strategy can be given as

R b : 2b  max   2 j  . j 1,2,..., N

(13)

Finally, we propose an optimal relay selection method, where the best relay R c is chosen to maximize the SNR received at the destination, i.e.

Similar to [11]-[12], the intercept probability can be computed by

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R c :  2 c  max

j 1,2,..., N

  . 2j

(14)

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3. Performance Evaluation

I2  



Q /W

In this section, the outage probability (OP) of the considered protocols is derived. Generally, the OP of the PRX protocol (X = 0, 1, 2) can be formulated as follows:

N

I 2    1 CNt

OPX  P | W1 | 0    P | W1 | N  Pr   2 y   th  , (15)

t

t 0

N 1

By applying [20, (eq. (A.1))], the Pr   2 a   th  in (15) can be expressed as

M

OP1    1 CMj j

j 0

Pr   2 a

M M N

M

j

j 0

M M N



  1

N 1 j  0

j

3 3  j1 

  1

N 1 j  0

j

(17)

CMj  N CMN 3 3   j  N  1 

(23)

N   Q       1  exp  4    1  exp  2    W  W      .   N   Q t     Q t   t 4 4     1 CN  exp   2   t  0 t 2  4 Q W   

Pr   2 c   th   Pr

 max   j 1,2,..., N

2j



th

   Pr  

2a

  th  

N

N

 2         4 Q     1  exp   2   exp   2  . W     Q W      2 4 (24)

2   2  4 Q         Q exp    . W    2 4

For the PR1 protocol, we first consider the probability Pr   2b   th  , which can be formulated by

Hence, an exact closed-form expression of the OP for the PR2 protocol can be expressed as in (25) below:

 min W , Q /  4b   2b  Pr   2b   th   Pr    th   min W , Q /    1   4b 2b  

OP2    1 CMj

  Q  Pr  min  W ,   4b  



    2b     

M

j

j 0

M M N

(18)

  1

N 1 j  0

j

3 3  j1 

CMj  N CMN 3 3   j  N  1 

(25) N

 2         4 Q    1  exp   2   exp   2  . W  W  2   4 Q   

 Q   Q     Pr   4b  ,  2b    Pr   4b  , 2b   . W W W  Q   4b        I1

3 3  j1 

Next, from the relay selection method proposed in (14), it is obvious that

CMj  N CMN 3 3   j  N  1 

    1  exp   2  W 



(16)

Combining (6), (7), (15) and (16) together, an exact closed-form expression of the OP for the PR0 protocol can be provided by

OP0    1 CMj

4 Q  t    4 Q  exp   2 . (22) t 2  4 Q W  

From the results obtained above, an exact closed-form expression of the OP for the PR1 protocol is given as

probability

    th   1  exp   2   W  2     4 Q   exp   2 . 2  4 Q W  

(21)

Plugging (19) and (21) together, and after some careful manipulation, we obtain that

M

where y  a, b, c , corresponds to X = 0, 1, 2, respectively.

  f 4 b  x  F 2 b  x  dx. Q 

I2

Moreover, the CDF of  2b can be given as in [10]:

4. Performance Evaluation

F 2 b  y   Pr   2b  y   1  exp  2 y   , N

N

(19)

   1 CNt exp  t 2 y  . t

t 0

From (18) and (19), we obtain the probability I1 as

 0.5,0  ,

Q     I1  Pr   4b   Pr   2b   W  W   Q      1  exp  4    1  exp  2 W  W   

In this section, we present various Monte Carlo simulations to verify the theoretical results derived above. In a two-dimensional network, we assume that the coordinates of the source, the destination, the relay, the primary user and the eavesdropper, are  0,0  , 1,0  ,

N

  . 

(20)

 0.5,0.5 

and

1, 0.5  respectively. In the

simulations, we assume that the path-loss exponent    equals 3 and the outage threshold   th  equals 1.

Next, the probability I 2 in (18) can be formulated by

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the best performance while the performance of the PR1 protocol is between those of the PR0 and PR2 protocols.

Fig. 2: Outage probability (OP) as a function of Q in dB when M  4 ,   0.1 and   0.3 .

In Fig. 2, we present the outage probability of the secondary network as a function of Q in dB. In this simulation, the number of relays is 4  M  4  , the

Fig. 4: Outage probability (OP) as a function of M when   0.4 ,   0.1 and Q  0 dB.

hardware impairment level is 0.1    0.1 and the IP threshold is set by 0.3    0.3  . It can be observed from Fig. 2 that the OP of the PR2 protocol is lowest, while that of the PR0 protocol is highest. It is because that the PR1 and PR2 protocols use the diversity transmission which enhances the reliability for the data transmission. Moreover, it is also seen that the OP decreases with the increasing of the Q value.

Fig. 5: Outage probability (OP) as a function of  when   0.1 , M  3 and Q  0 dB.

Figure 4 illustrates the outage probability as a function of the number of relays when   0.4 ,   0.1 and Q  0 dB. As we can see, the OP of the PR1 and PR2 protocols significantly decreases with the increasing of the number of relays, while the outage performance of the PR0 protocol slightly decreases. Fig. 3: Outage probability (OP) as a function of  when M  5 ,   0 and Q  0 dB.

Figure 3 shows the outage probability as a function of the IP threshold when M  5 ,   0 and Q  0 dB. As we can see, the outage performance of three protocols decreases with the increasing of  . It is due to the fact that the transmit power of the selected relay increases with higher value of  . Again, the PR2 protocol obtains

In Fig. 5, we investigate the impact of the hardware impairment level on the outage performance when   0.1 , M  3 and Q  0 dB. As illustrated in this figure, the OP of three protocols rapidly increases when the level  increases. From Figs. 2-5, we can see that the simulation results (simulation) match very well with the theoretical results (theory), which validates our derivations.

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System Technical Journal 1975, vol. 54, no. 8, p. 1355–1387. ISSN: 0005-8580. DOI:10.1002/j.15387305.1975.tb02040.x

5. Conclusion In this paper, we studied the physical layer security in underlay cognitive radio networks. We proposed two relay selection methods to improve the outage performance of the secondary network under the interference constraint at the primary user and intercept probability constraint at the eavesdropper. The exact closed-form expressions of the outage probability were presented and verified by Monte Carlo simulations. Results showed that the proposed protocols outperform the random relay selection protocol. In addition, both methods obtain higher performance when the number of relays increases. Moreover, the hardware impairments significantly impact on the system performance.

Acknowledgement This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.01-2014.33 and by the SGS grant No. SP2016/170, VSB-Technical University of Ostrava, Czech Republic.

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[18] P. K. Sharma, P. K. Upadhyay, “Cognitive Relaying with Transceiver Hardware Impairments under Interference Constraints”, IEEE Communications Letters, vol. 20, no. 4, pp. 820 – 823, 2016. [19] E. Bjornson, M. Matthaiou and M. Debbah, “A New Look at Dual-hop Relaying: Performance Limits with Hardware Impairments,” IEEE Trans. Commun., vol. 61, no. 11, pp. 4512–4525, Nov. 2013. [20] T. T. Duy and H.Y. Kong, "On Performance Evaluation of Hybrid Decode-Amplify-Forward Relaying Protocol with Partial Relay Selection in Underlay Cognitive Networks", Journal of Communications and Networks (JCN), vol. 16, no. 5, pp. 502-511, Oct. 2014

About Authors Phu Tran Tin was born in Khanh Hoa, Vietnam, in 1979. He received the Bachelor degree (2002) and Master degree (2008) from Ho Chi Minh City University of Science. In 2007, he was lecturer at the Faculty of Electronics Technology (FET), Industrial University of Ho Chi Minh City. Since 2015, he has been participating in Ph.D program that had been linked between Technical University of Ostrava, Czech Republic and Ton Duc Thang University, Ho Chi Minh City. His major research interests are wireless communication in 5G, energy harvesting, performance of cognitive radio and physical layer security. Tran Trung Duy (corresponding author) was born in Nha Trang city, Vietnam, in 1984. He received the B.E. degree in Electronics and Telecommunications Engineering from the French-Vietnamese training program for excellent engineers (PFIEV), Ho Chi Minh City University of Technology, Vietnam in 2007. In 2013, he received the Ph.D degree in electrical engineering from University of Ulsan, South Korea. In 2013, he joined the Department of Telecommunications, Posts and Telecommunications Institute of Technology (PTIT), as a lecturer. His major research interests are cooperative communications, cognitive radio, and physical layer security. Miroslav Voznak was born in Czech Republic. He received the master degree in Electronics and Telecommunication Technology from the Technical University of Ostrava, Czech Republic, in 1995. In 2002, he received the Ph.D degree in Telecommunication Engineering from Technical University of Ostrava, Czech Republic. In 2009, he appointed an Associate professor in Electronics and Communication Engineering from Technical University of Ostrava. He is member of the Scientific Board of FEI VSB-TU Ostrava, several editorial committees of journals, several scientific committees of international conferences, the IEEE.

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