# Security-Reliability Tradeoff Analysis in Multisource Multirelay Cooperative Networks with Multiple Cochannel Interferers

Authors: Weilong Hu; Jiangbo Si; Hongyan Li
Journal: Wireless Communications and Mobile Computing
 (2018)

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## Abstract

Cooperative relaying communication is one of the green communication technologies since it shortens the communication distance and saves the transmit power. In this paper, the physical-layer security (PLS) of a multisource multirelay cooperative relaying communication network is investigated by considering the influence of cochannel interference from a security-reliability tradeoff (SRT) perspective. First, the SRT performance is characterized by the outage probability (OP) and the intercept probability (IP). In particular, the IP encountered at the eavesdropper is used to evaluate the security performance, while the reliability performance is analyzed in terms of the OP experienced at the destination. Then, under the impact of multiple cochannel interferers, the intercept probabilities and the outage probabilities of both the conventional direct transmission (DT) strategy and relay selection (RS) strategy are derived in closed-form expressions over Rayleigh fading channels, respectively. Simulation results are provided to validate the theoretical analysis. It is shown that when the OP (reliability) requirement is relaxed, the IP (security) performance improves and vice versa. It confirms that there is an SRT existing between the OP and the IP. Meanwhile, a better SRT performance can be achieved by increasing the number of sources, relays, and cochannel interferers. In addition, it is also shown that the RS strategy generally outperforms the conventional DT strategy in terms of the product of the IP and the OP.


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## Body

## 1. Introduction

With an explosive growth of the number of wireless devices, such as smart phones, tablet computers, and wireless sensors, more and more energy has been consumed by wireless services. According to [1], the amount of the energy consumed by the information and communication technologies accounts for about 2% to 10% of the global energy consumption, which generate nonnegligible amount of the greenhouse gases. What is worst, this percentage will grow rapidly with the development of the information and communication technologies and the increase of number of wireless devices. It will result in more greenhouse gases emission and environment pollution [2]. One promising technique to alleviate such issue is to adopt green communication technology, which can improve both the spectrum efficiency and energy efficiency of wireless communication systems. Cooperative relaying communication is an energy efficient diversity technique, which has been recognized as a green communication technology and attracts unprecedented research interest in both academic and industrial fields. A challenging issue in cooperative relaying communication is wireless security [3–5]. Because of the inherent broadcast nature of wireless channels, the destination may not successfully obtain source information, while the malicious eavesdropper may overhear and intercept the confidential information, which makes the wireless transmission insecure and vulnerable to eavesdropping attacks [6].Motivated by the above fact, physical-layer security (PLS) was proposed and has attracted increasing research attention since it is an effective paradigm of achieving information-theoretic security for protecting wireless communications against the eavesdropping attacks by utilizing the physical characteristics of wireless channels [7]. The PLS was first investigated by Shannon [8] and further developed by Wyner, who examined a classical point-to-point discrete memoryless wiretap channel (WTC) scenario consisting of a source node and a destination node as well as an eavesdropper node [9]. It was proven in [9] that perfectly secure and reliable transmission from the source node to the legitimate destination node can be achieved when the main channel from the source node to the destination node is an upgraded version of the wiretap channel from the source node to the eavesdropper node. Later on, in [10, 11], Wyner’s conclusions were, respectively, extended from the discrete memoryless wiretap channel to the nondegraded wiretap channel and the Gaussian degraded wiretap channel, where the notion of secrecy capacity (SC) was introduced. It was derived as the difference between the channel capacity of the legitimate link and that of the wiretap link. Specifically, the SC can make the transmission from the source node to the legitimate destination node secure while achieving zero mutual information between the source node and malicious eavesdropper node. Based on this idea, extensive research efforts have been devoted to improving the SC from an information-theoretic perspective under different scenarios, for example, cooperative relaying [12–15] and beamforming techniques [16, 17], cooperative jamming (CJ) methods [18–20], and multiple-input multiple-output (MIMO) schemes [21, 22].The previous works are mainly focused on enhancing wireless security without paying much attention to communication reliability. Hence, security-reliability tradeoff (SRT) was proposed to make best tradeoff between the outage probability (OP) and the intercept probability (IP). In particular, the IP encountered at the eavesdropper is used to evaluate the security performance, while the reliability performance is measured by the OP experienced at the destination. In [23], the authors studied the employment of various block cipher encryption algorithms from the perspective of both reliability and security and showed that there exists a tradeoff between communication reliability and security. Later on, the authors of [24] investigated the SRT for the downlink cloud radio access networks and the channel estimation errors were considered and the impact of the times of training on the security and reliability performance was also analyzed. The SRT of the cognitive amplify-and-forward (AF) relay network was investigated under imperfect channel estimation in [25]. As a further development, the authors of [26] characterized the SRT and quantified the benefits of opportunistic relay selection (ORS) for the purpose of improving the SRT. In [27], the authors proposed the single-relay and multirelay selection schemes for improving the SRT of general wireless networks. It was proved in [27] that in terms of the SRT the multirelay selection scheme outperformed the single-relay one.It can been seen from the above works that the PLS of multisource multirelay cooperative networks under the impact of the cochannel interferers is not considered. Motivated by this fact, the main contributions of this paper are summarized as follows: firstly, the PLS of a multisource multirelay cooperative communication network is investigated from an SRT perspective and cochannel interferers are considered. Secondly, a signal-to-interference-plus-noise ratio- (SINR-) based method is proposed and the closed-form expressions of IP and OP are derived for the direct transmission (DT) and the relay selection (RS) schemes over Rayleigh fading, respectively. Finally, simulation results are provided to validate the theoretical analysis. It is shown that when the OP (reliability) requirement is relaxed, the IP (security) performance improves and vice versa. It confirms that there is an SRT existing between the OP and the IP. Meanwhile, a better SRT performance can be achieved by increasing the number of sources, relays, and cochannel interferers. In addition, it is also shown that the RS strategy generally outperforms the conventional DT strategy in terms of the product of the IP and the OP.The remainder of this paper is organized as follows. In Section2, the system models are described. The SRT performance analysis for both the conventional DT and RS schemes over Rayleigh fading channels is presented in Section 3. Section 4 presents simulation results to corroborate the proposed studies. Section 5 concludes the paper.


## 2. The System Model

### 2.1. System Model Description

Consider a multisource multirelay cooperative wireless network as shown in Figure1, which consists of N sources Sn1⩽n⩽N, one eavesdropper E, one destination D, K relays Rk1⩽k⩽K, and M cochannel interferers Im1⩽m⩽M. The sources communicate with the corresponding destination via the direct link or with the help of the intermediate relays. At a specific time, only the source having the highest direct-link channel quality is viewed as the best one and is selected to transmit with the aid of relays. Meanwhile, E will intercept the information from the selected source and relays. M interferers share the same bands with D and E and cause interferences to them. It can be observed that the system model is practical and can be applied to practical scenarios [28–30]. It is assume that all nodes are equipped with single antenna and all channels are Rayleigh fading. Without loss of generality, we consider additive white Gaussian noise (AWGN) with zero mean and variance N0 at each node in networks. We assume that the sources have the global channel state information (CSI) of both the main and wiretap channels and in order to analyze the performance of the worst case, E is assumed to know all system parameters of the legitimate transmission from S to D, except for the signal. Typically, the linear minimum mean-square error (LMMSE) estimation method can be used to obtain the CSI by the destination and the eavesdropper [24, 25]. Note that this assumption has been widely used in [26, 27, 31].Figure 1
Multisource multirelay cooperative network system model.


### 2.2. Direct Transmission Strategy

In this subsection, the conventional DT strategy is considered for the purpose of performance comparison. A classical DT communication scenario consisting ofN sources, one destination, and one eavesdropper with M cochannel interferers is considered. Assuming that all sources send messages at a power PS while the interferers transmit at a power PI. Let xbE[xb2]=1 and xmE[xm2]=1, respectively, denote the source signal from the selected best source Sb and the interfering signal transmitted by the mth interferer Im. When Sb transmits xb with the rate Rs at a particular time instant, Im transmits xm with the rate Rs. Hence, under the presence of M cochannel interferers, the signals received at D and E nodes can be, respectively, presented as(1)ySbDDT=PShSbDxb+∑m=1MPIhImDxm+nD,(2)ySbEDT=PShSbExb+∑m=1MPIhImExm+nE,where hSbD, hSbE, hImD, and hImE, respectively, denote the fading gains of the channel from Sb to D, that from Sb to E, that from Im to D, and that from Im to E. nD and nE represent the AWGN encountered at D and E nodes, respectively. Using Shannon’s capacity formula, the capacity of the channel spanning from Sb to D is given by(3)CSbDDT=log2⁡1+γShSbD2∑m=1MγIhImD2+1,where γS=PS/N0 and γI=PI/N0. Similarly, the channel capacity of Sb-E transmission is obtained from (2) as(4)CSbEDT=log21+γShSbE2∑m=1MγIhImE2+1.Since fading gains hSbD, hSbE, hImD, and hImE are modeled as Rayleigh random variables, then hSbD2, hSbE2, hImD2, and hImE2 are exponentially distributed. Accordingly, σSbD2, σSbE2, σImD2, and σImE2 represent the means of hSbD2, hSbE2, hImD2, and hImE2, respectively.


### 2.3. Relay Selection Strategy

As shown in Figure1, this subsection presents a multisource multirelay cooperative wireless network with multiple cochannel interferers existing at relays, D and E. Specifically, all sources share the relay nodes and the relays employ the decode-and-forward (DF) relaying protocol. Without loss of generality, the total cooperative communication procedure is divided into two time slots. It can also be seen from Figure 1 that the solid and dash lines represent the transmission in the first time slot and that in the second time slot, respectively. In the first time slot, the selected best source node Sb transmits its signals xb to D and all relays, and meanwhile E intercepts the transmission of the source. Under the presence of M cochannel interferers, the signals received at D, E, and Rk nodes can be, respectively, presented as(5)ySbDRS=PShSbDxb+∑m=1MPIhImDxm+nD,(6)ySbERS=PShSbExb+∑m=1MPIhImExm+nE,(7)ySbRkRS=PShSbRkxb+∑m=1MPIhImRkxm+nRk,where hSbRk and hImRk, respectively, denote the fading gains of the channel from Sb to Rk and that from Im to Rk. nRk represents the AWGN encountered at Rk node. Similar to [7], according to (5), (6), and (7), the capacities of the channel spanning from Sb to D, that spanning from Sb to Rk, and that spanning from Sb to E can, respectively, be obtained as(8)CSbDRS=12log2⁡1+γShSbD2∑m=1MγIhImD2+1,(9)CSbRkRS=12log2⁡1+γShSbRk2∑m=1MγIhImRk2+1,(10)CSbERS=12log2⁡1+γShSbE2∑m=1MγIhImE2+1,where 1/2 arises from the fact that two orthogonal slots are needed for completing the overall transmission. Similarly, hSbRk2 and hImRk2 are exponentially distributed and accordingly, and σSbRk2 and σImRk2 represent the means of hSbRk2 and hImRk2, respectively.According to the DF protocol, only those relays that succeed in perfectly decoding the source signalxb form a decoding set denoted by D. Thus, in the second time slot, when D is a nonempty set, a specific relay is chosen from D for forwarding its received signal to D node with PS denoting the transmit power. In particular, Rk is regarded as the selected relay node. Then, the signal received at D node can be presented as(11)yRkDRS=PShRkDxb+∑m=1MPImhImDxm+nD,where hRkD represents the fading gain of the channel from Rk to D. Similarly, according to (11), the capacity of the channel spanning from Rk to D is given by(12)CRkDRS=12log2⁡1+γShRkD2∑m=1MγIhImD2+1,where hRkD2 is exponentially distributed and σRkD2 represents the mean of hRkD2. Based on the obtained capacity of the channel spanning from Rk to D, the selected relay node with the largest channel capacity is chosen from D, that is,(13)Rbest=argmaxRk∈DCRkDRS,where Rbest represents the selected best relay node. It can be seen from (12) that the interferers and noise terms are same for the channel capacities of different relays. Then, (13) is simplified as Rbest=argmaxRk∈D⁡hRkD2. Thus, the signal received at E node with the best relay node can be presented as(14)yRbestERS=PShRbestExb+∑m=1MPImhImExm+nE,where hRbestE denotes the fading gain of the channel from Rbest to E. Thus, according to (14), the capacity of the channel spanning from Rbest to E is given by(15)CRbestERS=12log2⁡1+γShRbestE2∑m=1MγIhImE2+1, where hRbestE2 is exponentially distributed and σRbestE2 represents the mean of hRbestE2.Across this paper, for ease of discussion, we assume thatσSbD2=σSbRk2=σRkD2=σS2,σSbE2=σRbestE2=σE2 and σImRk2=σImD2=σImE2=σI2. This assumption can be valid in a statistical sense when all relays are mobile and uniformly distributed around S and D nodes [7].


## 2.1. System Model Description

Consider a multisource multirelay cooperative wireless network as shown in Figure1, which consists of N sources Sn1⩽n⩽N, one eavesdropper E, one destination D, K relays Rk1⩽k⩽K, and M cochannel interferers Im1⩽m⩽M. The sources communicate with the corresponding destination via the direct link or with the help of the intermediate relays. At a specific time, only the source having the highest direct-link channel quality is viewed as the best one and is selected to transmit with the aid of relays. Meanwhile, E will intercept the information from the selected source and relays. M interferers share the same bands with D and E and cause interferences to them. It can be observed that the system model is practical and can be applied to practical scenarios [28–30]. It is assume that all nodes are equipped with single antenna and all channels are Rayleigh fading. Without loss of generality, we consider additive white Gaussian noise (AWGN) with zero mean and variance N0 at each node in networks. We assume that the sources have the global channel state information (CSI) of both the main and wiretap channels and in order to analyze the performance of the worst case, E is assumed to know all system parameters of the legitimate transmission from S to D, except for the signal. Typically, the linear minimum mean-square error (LMMSE) estimation method can be used to obtain the CSI by the destination and the eavesdropper [24, 25]. Note that this assumption has been widely used in [26, 27, 31].Figure 1
Multisource multirelay cooperative network system model.


## 2.2. Direct Transmission Strategy

In this subsection, the conventional DT strategy is considered for the purpose of performance comparison. A classical DT communication scenario consisting ofN sources, one destination, and one eavesdropper with M cochannel interferers is considered. Assuming that all sources send messages at a power PS while the interferers transmit at a power PI. Let xbE[xb2]=1 and xmE[xm2]=1, respectively, denote the source signal from the selected best source Sb and the interfering signal transmitted by the mth interferer Im. When Sb transmits xb with the rate Rs at a particular time instant, Im transmits xm with the rate Rs. Hence, under the presence of M cochannel interferers, the signals received at D and E nodes can be, respectively, presented as(1)ySbDDT=PShSbDxb+∑m=1MPIhImDxm+nD,(2)ySbEDT=PShSbExb+∑m=1MPIhImExm+nE,where hSbD, hSbE, hImD, and hImE, respectively, denote the fading gains of the channel from Sb to D, that from Sb to E, that from Im to D, and that from Im to E. nD and nE represent the AWGN encountered at D and E nodes, respectively. Using Shannon’s capacity formula, the capacity of the channel spanning from Sb to D is given by(3)CSbDDT=log2⁡1+γShSbD2∑m=1MγIhImD2+1,where γS=PS/N0 and γI=PI/N0. Similarly, the channel capacity of Sb-E transmission is obtained from (2) as(4)CSbEDT=log21+γShSbE2∑m=1MγIhImE2+1.Since fading gains hSbD, hSbE, hImD, and hImE are modeled as Rayleigh random variables, then hSbD2, hSbE2, hImD2, and hImE2 are exponentially distributed. Accordingly, σSbD2, σSbE2, σImD2, and σImE2 represent the means of hSbD2, hSbE2, hImD2, and hImE2, respectively.


## 2.3. Relay Selection Strategy

As shown in Figure1, this subsection presents a multisource multirelay cooperative wireless network with multiple cochannel interferers existing at relays, D and E. Specifically, all sources share the relay nodes and the relays employ the decode-and-forward (DF) relaying protocol. Without loss of generality, the total cooperative communication procedure is divided into two time slots. It can also be seen from Figure 1 that the solid and dash lines represent the transmission in the first time slot and that in the second time slot, respectively. In the first time slot, the selected best source node Sb transmits its signals xb to D and all relays, and meanwhile E intercepts the transmission of the source. Under the presence of M cochannel interferers, the signals received at D, E, and Rk nodes can be, respectively, presented as(5)ySbDRS=PShSbDxb+∑m=1MPIhImDxm+nD,(6)ySbERS=PShSbExb+∑m=1MPIhImExm+nE,(7)ySbRkRS=PShSbRkxb+∑m=1MPIhImRkxm+nRk,where hSbRk and hImRk, respectively, denote the fading gains of the channel from Sb to Rk and that from Im to Rk. nRk represents the AWGN encountered at Rk node. Similar to [7], according to (5), (6), and (7), the capacities of the channel spanning from Sb to D, that spanning from Sb to Rk, and that spanning from Sb to E can, respectively, be obtained as(8)CSbDRS=12log2⁡1+γShSbD2∑m=1MγIhImD2+1,(9)CSbRkRS=12log2⁡1+γShSbRk2∑m=1MγIhImRk2+1,(10)CSbERS=12log2⁡1+γShSbE2∑m=1MγIhImE2+1,where 1/2 arises from the fact that two orthogonal slots are needed for completing the overall transmission. Similarly, hSbRk2 and hImRk2 are exponentially distributed and accordingly, and σSbRk2 and σImRk2 represent the means of hSbRk2 and hImRk2, respectively.According to the DF protocol, only those relays that succeed in perfectly decoding the source signalxb form a decoding set denoted by D. Thus, in the second time slot, when D is a nonempty set, a specific relay is chosen from D for forwarding its received signal to D node with PS denoting the transmit power. In particular, Rk is regarded as the selected relay node. Then, the signal received at D node can be presented as(11)yRkDRS=PShRkDxb+∑m=1MPImhImDxm+nD,where hRkD represents the fading gain of the channel from Rk to D. Similarly, according to (11), the capacity of the channel spanning from Rk to D is given by(12)CRkDRS=12log2⁡1+γShRkD2∑m=1MγIhImD2+1,where hRkD2 is exponentially distributed and σRkD2 represents the mean of hRkD2. Based on the obtained capacity of the channel spanning from Rk to D, the selected relay node with the largest channel capacity is chosen from D, that is,(13)Rbest=argmaxRk∈DCRkDRS,where Rbest represents the selected best relay node. It can be seen from (12) that the interferers and noise terms are same for the channel capacities of different relays. Then, (13) is simplified as Rbest=argmaxRk∈D⁡hRkD2. Thus, the signal received at E node with the best relay node can be presented as(14)yRbestERS=PShRbestExb+∑m=1MPImhImExm+nE,where hRbestE denotes the fading gain of the channel from Rbest to E. Thus, according to (14), the capacity of the channel spanning from Rbest to E is given by(15)CRbestERS=12log2⁡1+γShRbestE2∑m=1MγIhImE2+1, where hRbestE2 is exponentially distributed and σRbestE2 represents the mean of hRbestE2.Across this paper, for ease of discussion, we assume thatσSbD2=σSbRk2=σRkD2=σS2,σSbE2=σRbestE2=σE2 and σImRk2=σImD2=σImE2=σI2. This assumption can be valid in a statistical sense when all relays are mobile and uniformly distributed around S and D nodes [7].


## 3. SRT Performance Analysis over Rayleigh Fading Channels

In this section, the SRT performance analysis of the conventional DT strategy as well as of the RS strategy with the presence of multiple cochannel interferers communicating over Rayleigh fading channels is presented. As discussed in [7], the tradeoff between the security and reliability, characterized by the intercept probability and by the outage probability, is analyzed. In particular, the outage probability represents the probability that the capacity of the main channel is lower than the data rate and the intercept probability represents the probability that the capacity of the wiretap channel is higher than the data rate. Then, the two performance metrics can be expressed as(16)Pout=PrCd<Rs,(17)Pint=PrCe>Rs,where Cd and Ce represent, respectively, the capacity of the main channel achieved at the destination and that of the wiretap channel experienced by the eavesdropper. Rs is the data rate.


### 3.1. Direct Transmission Strategy

In what follows, the SRT performance of the conventional DT strategy is first analyzed as a benchmark. According to (16), using the law of total probability, the OP of the conventional DT strategy can be formulated as(18)PoutDT=∑b=1NPrhSbD2>max1⩽n⩽N,n≠b⁡hSnD2,CSbDDT<Rs,where CSbDDT is given by (3). Substituting CSbDDT into (18), the OP is given by (19)PoutDT=∑b=1NPrhSbD2>max1⩽n⩽N,n≠b⁡hSnD2,γShSbD2Y+1<Δ︸P1,where Y=∑m=1MγIhImD2 and Δ=(2Rs-1). Note that, due to the common term hSbD2, P1 cannot be calculated as the conventional analysis directly. Hence, upon assuming hSbD2=x, P1 can be expressed as(20)P1=∫0∞Prmax1⩽n⩽N,n≠bhSnD2<x∣x×PrγSxY+1<Δ∣xfhSbD2xdx,in which the first term can be obtained as(21)Prmax1⩽n⩽N,n≠bhSnD2<x∣x=∏1⩽n⩽N,n≠bPrhSnD2<x∣x=∑n=0N-1CN-1n-1nexp⁡-nxσSnD2.In (20), it can be found that, for x<Δ/γS, the second-term PrγSx/Y+1<Δ∣x=1. Therefore, there are two cases for the term PrγSx/Y+1<Δ∣x; that is,(22)PrγSxY+1<Δ∣x=1x<ΔγSexp⁡Δ-γSxγIσImD2Δ∑m1=0M-1γSx-Δ/γIσImD2Δm1m1!x>ΔγS.Then substituting (21) and (22) into (20) yields(23)P1=∫0Δ/γS∑n=0N-1CN-1n-1nexp-nxσSnD2+∫Δ/γS∞∑n=0N-1CN-1n-1nexp-nxσSnD2×exp1γIσImD2-γSxγIσImD2Δ×∑m1=0M-1γSx/γIσImD2Δ-1/γIσImD2m1m1!fhSbD2xdx.Proceeding as in Appendix A, one has (24)P1=∑n=0N-1CN-1n-1n1-exp-n+1Δ/σS2γSn+1+∑m1=0M-1exp⁡-n+1ΔγSσS2γIσI2ΔσS2γSn+1γIσI2Δ/σS2γS+1m1+1.Similarly, according to (4) and (17), the IP of the conventional DT strategy is formulated as(25)PintDT=∑b=1NPrhSbD2>max1⩽n⩽N,n≠bhSnD2,CSbEDT>Rs.With the aid of CSbEDT, the IP can be expressed as (26)PintDT=∑b=1NPrhSbD2>max1⩽n⩽N,n≠b⁡hSnD2,γShSbE2T+1>Δ︸P2,where T=∑m=1MγIhImE2. Similar to the analysis of P1, P2 can be rewritten as(27)P2=∫0∞Prmax1⩽n⩽N,n≠bhSnD2<x∣x×PrγShSbE2T+1>Δ∣xfhSbD2xdx,where the term PrγShSbE2/T+1>Δ∣x can be readily derived as(28)PrγShSbE2T+1>Δ∣x=exp⁡-ΔγSσSbE2σSbE2MσSbE2+γIσImE2Δ/γSM.Then substituting (21) and (28) into (27), one has(29)P2=∫0∞∑n=0N-1CN-1n-1nexp⁡-nxσSnD2×exp⁡-ΔγSσSbE2σSbE2MσSbE2+γIσImE2θ/γSM×fhSbD2xdx.After some appropriate incorporations and necessary mathematical manipulations, P2 can be obtained as(30)P2=∑n=0N-1CN-1n-1nσE2Mn+1σE2+γIσI2Δ/γSMexp-ΔγSσE2.


### 3.2. Relay Selection Strategy

This subsection focuses on the SRT performance analysis of the RS strategy. According to (16) and using the theory of total probability, the OP of the RS strategy is formulated as(31)PoutRS=∑b=1N∑k=0K∑D⊂RPrD=k,CDRS<Rs,where D represents the number of elements in successful decoding set D and R={R1,R2,…,RK} denotes the relay set. As can be observed, when D is an empty set (i.e., D=0), it shows that no relay can be chosen for forwarding the received signal. In this case, only the direct link is available, that is, CDRS=CSbDRS, where D is a nonempty set and selection combining is considered to combine the received signal copies at D from the selected best source Sb and the selected best relay Rbest during the two time slots. In this case, the capacity achieved by D is the higher one between CSbDRS and CRbestDRS, that is, CDRS=max⁡CSbDRS,CRbestDRS. Substituting these results into (31), one has(32)PoutRS=∑b=1NPrD=∅P3+∑k=1K∑D⊂RPrD=kP4,where the terms P3 and P4 are, respectively, given by(33)P3=PrhSbD2>max1⩽n⩽N,n≠bhSnD2,CSbDRS<Rs,(34)P4=PrhSbD2>max1⩽n⩽N,n≠bhSnD2,CDRS<Rs.In (32), the term Pr(D=k) denotes the probability that there exist k relays decoding the source signal xs successfully. Thus, considering σSbRi2=σSbRj2=σS2 and σImRi2=σImRj2=σI2, one has(35)PrD=k=∏Ri∈DPrCSbRiRS>Rs×∏Rj∈D¯PrCSbRjRS<Rs=exp-θγSσS2σS2MσS2+γIσI2θ/γSMk×1-exp-θγSσS2σS2MσS2+γIσI2θ/γSMK-k,where θ=22Rs-1 and D¯ is the complementary set of the successful decoding set D. By utilizing a similar way, the term PrD=∅ is calculated as(36)PrD=∅=∏Rk∈RPrCSbRkRS<Rs=1-exp-θγSσS2σS2MσS2+γIσI2θ/γSMK.As discussed before, by utilizing a similar way as P1, P3 can be obtained as(37)P3=∑n=0N-1CN-1n-1n1-exp-n+1θ/σS2γSn+1+∑m1=0M-1exp-n+1θγSσS2×γIσI2θσS2γSn+1γIσI2θ/σS2γS+1m1+1.Similar to (20), the term P4 is expressed as(38)P4=∫0∞Prmax1⩽n⩽N,n≠bhSnD2<x∣x×PrmaxγSxY+1,γShRbestD2Y+1<θ∣x×fhSbD2xdx.Proceeding as in Appendix B, P4 can be obtained as(39)P4=∑n=0N-1∑k1=0DCN-1n-1nCDk1-1k1exp-k1θσS2γS×1-exp-n+1θ/σS2γSn+11+k1θσI2γI/σS2γSM+∑m1=0M-1exp-n+1θσS2γSγIσI2θ1+k1θσI2γI/σS2γSm1-MσS2γS1+k1γIσI2θ/σS2γS+n+1γIσI2θ/σS2γSm1+1.On the other hand, similarly, according to (17) and using the theory of total probability, the IP of the RS strategy is formulated as(40)PintRS=∑b=1N∑k=0K∑D⊂RPrD=k,CERS>Rs.During the two slots, note that E will intercept the message transmitted by both the selected best source Sb and the selected best relay Rbest and perform detection using both received signal copies. Thus, (40) can be rewritten as(41)PintRS=∑b=1NPrD=∅P5+∑k=1K∑D⊂RPrD=kP6in which the terms P5 and P6 are, respectively, given by(42)P5=PrhSbD2>max1⩽n⩽N,n≠bhSnD2,CSbERS>Rs,(43)P6=PrhSbD2>max1⩽n⩽N,n≠bhSnD2,CERS>Rs.As discussed before, similar to P2, P5 can be obtained as(44)P5=∑n=0N-1CN-1n-1nσE2Mn+1σE2+γIσI2θ/γSMexp-θγSσE2.Similar to (38), the term P6 can be rewritten as(45)P6=∫0∞Prmax1⩽n⩽N,n≠bhSnD2<x∣x×PrmaxγShSbE2T+1,γShRbestE2T+1>θ∣x×fhSbD2xdx.After some appropriate substitutions and via utilizing a similar derivation for P4, P6 can be obtained as(46)P6=∑n=0N-1CN-1n-1n1+n×2exp-θγSσE2σE2MσE2+γIσI2θ/γSM-exp-2θγSσE2σE2σE22MσE2+γIσI2θ/γS2M.Therefore, after some incorporations and iterations, the closed-form outage probability and intercept probability expressions of both the DT and RS schemes with multiple cochannel interferers can be achieved.


## 3.1. Direct Transmission Strategy

In what follows, the SRT performance of the conventional DT strategy is first analyzed as a benchmark. According to (16), using the law of total probability, the OP of the conventional DT strategy can be formulated as(18)PoutDT=∑b=1NPrhSbD2>max1⩽n⩽N,n≠b⁡hSnD2,CSbDDT<Rs,where CSbDDT is given by (3). Substituting CSbDDT into (18), the OP is given by (19)PoutDT=∑b=1NPrhSbD2>max1⩽n⩽N,n≠b⁡hSnD2,γShSbD2Y+1<Δ︸P1,where Y=∑m=1MγIhImD2 and Δ=(2Rs-1). Note that, due to the common term hSbD2, P1 cannot be calculated as the conventional analysis directly. Hence, upon assuming hSbD2=x, P1 can be expressed as(20)P1=∫0∞Prmax1⩽n⩽N,n≠bhSnD2<x∣x×PrγSxY+1<Δ∣xfhSbD2xdx,in which the first term can be obtained as(21)Prmax1⩽n⩽N,n≠bhSnD2<x∣x=∏1⩽n⩽N,n≠bPrhSnD2<x∣x=∑n=0N-1CN-1n-1nexp⁡-nxσSnD2.In (20), it can be found that, for x<Δ/γS, the second-term PrγSx/Y+1<Δ∣x=1. Therefore, there are two cases for the term PrγSx/Y+1<Δ∣x; that is,(22)PrγSxY+1<Δ∣x=1x<ΔγSexp⁡Δ-γSxγIσImD2Δ∑m1=0M-1γSx-Δ/γIσImD2Δm1m1!x>ΔγS.Then substituting (21) and (22) into (20) yields(23)P1=∫0Δ/γS∑n=0N-1CN-1n-1nexp-nxσSnD2+∫Δ/γS∞∑n=0N-1CN-1n-1nexp-nxσSnD2×exp1γIσImD2-γSxγIσImD2Δ×∑m1=0M-1γSx/γIσImD2Δ-1/γIσImD2m1m1!fhSbD2xdx.Proceeding as in Appendix A, one has (24)P1=∑n=0N-1CN-1n-1n1-exp-n+1Δ/σS2γSn+1+∑m1=0M-1exp⁡-n+1ΔγSσS2γIσI2ΔσS2γSn+1γIσI2Δ/σS2γS+1m1+1.Similarly, according to (4) and (17), the IP of the conventional DT strategy is formulated as(25)PintDT=∑b=1NPrhSbD2>max1⩽n⩽N,n≠bhSnD2,CSbEDT>Rs.With the aid of CSbEDT, the IP can be expressed as (26)PintDT=∑b=1NPrhSbD2>max1⩽n⩽N,n≠b⁡hSnD2,γShSbE2T+1>Δ︸P2,where T=∑m=1MγIhImE2. Similar to the analysis of P1, P2 can be rewritten as(27)P2=∫0∞Prmax1⩽n⩽N,n≠bhSnD2<x∣x×PrγShSbE2T+1>Δ∣xfhSbD2xdx,where the term PrγShSbE2/T+1>Δ∣x can be readily derived as(28)PrγShSbE2T+1>Δ∣x=exp⁡-ΔγSσSbE2σSbE2MσSbE2+γIσImE2Δ/γSM.Then substituting (21) and (28) into (27), one has(29)P2=∫0∞∑n=0N-1CN-1n-1nexp⁡-nxσSnD2×exp⁡-ΔγSσSbE2σSbE2MσSbE2+γIσImE2θ/γSM×fhSbD2xdx.After some appropriate incorporations and necessary mathematical manipulations, P2 can be obtained as(30)P2=∑n=0N-1CN-1n-1nσE2Mn+1σE2+γIσI2Δ/γSMexp-ΔγSσE2.


## 3.2. Relay Selection Strategy

This subsection focuses on the SRT performance analysis of the RS strategy. According to (16) and using the theory of total probability, the OP of the RS strategy is formulated as(31)PoutRS=∑b=1N∑k=0K∑D⊂RPrD=k,CDRS<Rs,where D represents the number of elements in successful decoding set D and R={R1,R2,…,RK} denotes the relay set. As can be observed, when D is an empty set (i.e., D=0), it shows that no relay can be chosen for forwarding the received signal. In this case, only the direct link is available, that is, CDRS=CSbDRS, where D is a nonempty set and selection combining is considered to combine the received signal copies at D from the selected best source Sb and the selected best relay Rbest during the two time slots. In this case, the capacity achieved by D is the higher one between CSbDRS and CRbestDRS, that is, CDRS=max⁡CSbDRS,CRbestDRS. Substituting these results into (31), one has(32)PoutRS=∑b=1NPrD=∅P3+∑k=1K∑D⊂RPrD=kP4,where the terms P3 and P4 are, respectively, given by(33)P3=PrhSbD2>max1⩽n⩽N,n≠bhSnD2,CSbDRS<Rs,(34)P4=PrhSbD2>max1⩽n⩽N,n≠bhSnD2,CDRS<Rs.In (32), the term Pr(D=k) denotes the probability that there exist k relays decoding the source signal xs successfully. Thus, considering σSbRi2=σSbRj2=σS2 and σImRi2=σImRj2=σI2, one has(35)PrD=k=∏Ri∈DPrCSbRiRS>Rs×∏Rj∈D¯PrCSbRjRS<Rs=exp-θγSσS2σS2MσS2+γIσI2θ/γSMk×1-exp-θγSσS2σS2MσS2+γIσI2θ/γSMK-k,where θ=22Rs-1 and D¯ is the complementary set of the successful decoding set D. By utilizing a similar way, the term PrD=∅ is calculated as(36)PrD=∅=∏Rk∈RPrCSbRkRS<Rs=1-exp-θγSσS2σS2MσS2+γIσI2θ/γSMK.As discussed before, by utilizing a similar way as P1, P3 can be obtained as(37)P3=∑n=0N-1CN-1n-1n1-exp-n+1θ/σS2γSn+1+∑m1=0M-1exp-n+1θγSσS2×γIσI2θσS2γSn+1γIσI2θ/σS2γS+1m1+1.Similar to (20), the term P4 is expressed as(38)P4=∫0∞Prmax1⩽n⩽N,n≠bhSnD2<x∣x×PrmaxγSxY+1,γShRbestD2Y+1<θ∣x×fhSbD2xdx.Proceeding as in Appendix B, P4 can be obtained as(39)P4=∑n=0N-1∑k1=0DCN-1n-1nCDk1-1k1exp-k1θσS2γS×1-exp-n+1θ/σS2γSn+11+k1θσI2γI/σS2γSM+∑m1=0M-1exp-n+1θσS2γSγIσI2θ1+k1θσI2γI/σS2γSm1-MσS2γS1+k1γIσI2θ/σS2γS+n+1γIσI2θ/σS2γSm1+1.On the other hand, similarly, according to (17) and using the theory of total probability, the IP of the RS strategy is formulated as(40)PintRS=∑b=1N∑k=0K∑D⊂RPrD=k,CERS>Rs.During the two slots, note that E will intercept the message transmitted by both the selected best source Sb and the selected best relay Rbest and perform detection using both received signal copies. Thus, (40) can be rewritten as(41)PintRS=∑b=1NPrD=∅P5+∑k=1K∑D⊂RPrD=kP6in which the terms P5 and P6 are, respectively, given by(42)P5=PrhSbD2>max1⩽n⩽N,n≠bhSnD2,CSbERS>Rs,(43)P6=PrhSbD2>max1⩽n⩽N,n≠bhSnD2,CERS>Rs.As discussed before, similar to P2, P5 can be obtained as(44)P5=∑n=0N-1CN-1n-1nσE2Mn+1σE2+γIσI2θ/γSMexp-θγSσE2.Similar to (38), the term P6 can be rewritten as(45)P6=∫0∞Prmax1⩽n⩽N,n≠bhSnD2<x∣x×PrmaxγShSbE2T+1,γShRbestE2T+1>θ∣x×fhSbD2xdx.After some appropriate substitutions and via utilizing a similar derivation for P4, P6 can be obtained as(46)P6=∑n=0N-1CN-1n-1n1+n×2exp-θγSσE2σE2MσE2+γIσI2θ/γSM-exp-2θγSσE2σE2σE22MσE2+γIσI2θ/γS2M.Therefore, after some incorporations and iterations, the closed-form outage probability and intercept probability expressions of both the DT and RS schemes with multiple cochannel interferers can be achieved.


## 4. Simulation Evaluations

In this section, the SRT performances of the DT and RS schemes are evaluated by simulations. The simulation parameters are set as follows:Rs=1bit/s/Hz, σSbD2=σSbRk2=σRkD2=σS2=1, σImRk2=σImD2=σImE2=σI2=0.1, and σSbE2=σRbestE2=σE2=0.2.Figures2–4 show the curves of the theoretical SRT analysis. As can be seen from the figures the intercept probability is presented as a function of the outage probability. Obviously, it can be seen that the simulation results match well with the theoretical analysis. Figure 2 shows the intercept probabilities versus the outage probabilities of the conventional DT strategy as well as the RS strategy at different K (K=4,8,12). Figure 2 also shows that as the outage probabilities increase, the intercept probabilities of the conventional DT and the RS schemes decrease. This confirms that there exists a tradeoff between the intercept probability and the outage probability. Another phenomenon can be observed in Figure 2; that is, the SRT of the RS strategy always outperforms that of the conventional DT strategy. Moreover, the SRT of the RS strategy is also improved with increasing K (from 4 to 12). This is due to the reason that the diversity gain can be obtained with the increase of the number of relays.Figure 2
SRTs of the conventional DT strategy and RS strategy for different numbers of relaysK with γI=15dB, N=3, and M=4.Figure 3
SRTs of the conventional DT strategy and RS strategy for different numbers of cochannel interferersM with γI=15dB, N=3, and K=4.Figure 4
SRTs of the conventional DT strategy and RS strategy for different numbers of sourcesN with γI=15dB, M=4, and K=4.Figure3 depicts the intercept probabilities versus the outage probabilities of the conventional DT strategy as well as the RS strategy at different M (M=4,8,12). Figure 3 also shows that when the outage probabilities change from 10-4 to 100, the intercept probabilities of the conventional DT and the RS schemes decrease correspondingly. Moreover, for a given M, the SRT of the RS strategy performs better than that of the conventional DT strategy. It is also seen that the SRTs of the conventional DT and the RS schemes are also improved with increasing M (from 4 to 12).Figure4 shows the intercept probabilities versus the outage probabilities of the conventional DT strategy as well as the RS strategy at different N (N=2,3). Similar to Figure 3, the intercept probabilities of the conventional DT and the RS schemes decrease correspondingly, as the outage probabilities increase from 10-4 to 100. Moreover, for a given N, the SRT of the RS strategy always outperforms that of the conventional DT strategy. The SRTs of the conventional DT and the RS schemes are also improved with increasing N (from 2 to 3). By jointly considering Figures 2–4, it is found that as the outage probabilities increase, the intercept probabilities of the conventional DT and the RS schemes decrease, implying that the SRT indeed exists between the intercept probability and the outage probability. Meanwhile, the improvement of the SRT is obtained with increasing the number of sources, relays, and cochannel interferers. Moreover, it is also shown that the SRT of the RS strategy consistently outperforms that of the conventional DT strategy.In order to further evaluate the SRT, the products of the intercept probabilities and the outage probabilities of the conventional DT strategy as well as the RS strategy are plotted in Figures5–7. Figure 5 shows the IP×OP products of the conventional DT strategy as well as the RS strategy against the transmit SNR γS at different numbers of available relays K (K=4,8,12). Figure 5 also shows that there exists an IP×OP peak with the increase of the transmit SNR γS. This is due to the reason that the IP in the low SNR regime comes close to 0, and the OP in the high SNR regime comes close to 0. Particularly, the presence of the IP×OP peak is another perspective that the SRT indeed exists between the intercept probability and the outage probability. Clearly, it is also seen from Figure 5 that the maximum IP×OP product of the RS strategy is smaller than that of the conventional DT strategy, which means the RS strategy is always better than the conventional DT strategy in terms of the IP×OP product. Moreover, the maximum IP×OP product decreases significantly with increasing K (from 4 to 12). It implies the SRT of the RS strategy is improved accordingly.Figure 5
I P × O P versus the transmit SNR γS of the conventional DT strategy and RS strategy for different numbers of relays K with γI=15dB, N=3, and M=4.Figure 6
I P × O P versus the transmit SNR γS of the conventional DT strategy and RS strategy for different numbers of cochannel interferers M with γI=15dB, N=3, and K=4.Figure 7
I P × O P versus the transmit SNR γS of the conventional DT strategy and RS strategy for different numbers of sources N with γI=15dB, M=4, and K=4.Figure6 shows the IP×OP products of the conventional DT strategy as well as the RS strategy against the transmit SNR γS at different M (M=4,8,12). Similar to Figure 5, there also exists an IP×OP peak with the increase of the transmit SNR γS. Figure 6 also shows that, for a given M, the RS strategy outperforms the DT strategy in terms of the IP×OP product. Moreover, the SRTs of the conventional DT and the RS schemes are also improved with increasing M (from 4 to 12).Figure7 shows the IP×OP products of the conventional DT strategy as well as the RS strategy versus the transmit SNR γS at different N (N=2,3). Similar to Figure 5, there also exists an IP×OP peak with the increase of the transmit SNR γS. Meanwhile, for a given N, the RS strategy outperforms the conventional DT strategy in terms of the IP×OP product, and when the number of sources increases from N=2 to N=3, the maximum IP×OP product can be minimized so that the SRTs of the conventional DT and the RS schemes are improved. By jointly considering Figures 5–7, the improvement of the SRT performance in terms of the IP×OP product can be achieved by increasing the number of relays, sources, and cochannel interferers. Moreover, it is also shown that the SRT performance of the RS strategy is better than that of the conventional DT strategy in terms of the product of the IP and the OP.


## 5. Conclusions

In this paper, we presented the PLS of a multisource multirelay cooperative communication network by considering the influence of cochannel interference from an SRT perspective. Under impact of cochannel interferers, we adopted an SINR-based method to analyze the SRT performance characterized by the OP and the IP. We derived the closed-form IP and OP expressions of both the conventional DT strategy and RS strategy over Rayleigh fading channels, respectively. We showed that when the OP (reliability) requirement is relaxed, the IP (security) performance improves and vice versa. It confirms that there is an SRT existing between the OP and the IP. We also showed that a better SRT performance can be achieved by increasing the number of sources, relays, and cochannel interferers. In addition, the RS strategy generally outperforms the conventional DT strategy in terms of the product of the OP and the IP.



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*Source: 2379427-2018-06-28.xml*