# SIC-Coding Schemes for Underlay Two-Way Relaying Cognitive Networks

Authors: Pham Ngoc Son; Tran Trung Duy; Khuong Ho-Van
Journal: Wireless Communications and Mobile Computing
 (2020)

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## Abstract

In this paper, we propose an underlay two-way relaying scheme with the successive interference cancellation (SIC) solution in which two secondary sources transmit simultaneously their data to each other through secondary relays. The proposed scheme is operated in only two time slots and under an interference constraint of a primary receiver, denoted as the UTW-2TS scheme. In the UTW-2TS scheme, the secondary relays employ the SIC operation to decode successively the data from received broadcast signals and then encode these data by two techniques: digital network coding (DNC) enforced by XOR operations (denoted as the UTW-2TS-DNC protocol) and superposition coding (SC) enforced by power domain additions (denoted as the UTW-2TS-SC protocol). A selected secondary relay which subjects to maximize decoding capacities and to minimize collection time of channel state information in two protocols UTW-2TS-DNC and UTW-2TS-SC experiences residual interferences from imperfect SIC operations. Outage probabilities and throughputs are solved in terms of exact closed-form expressions to evaluate the system performance of the proposed protocols. Simulation and analysis results provide performance enhancement of the proposed protocols UTW-2TS-DNC and UTW-2TS-SC owing to increase the number of the cooperative secondary relays, the interference constraints, and the distances from the secondary network to the primary receiver. The best throughputs are pointed at optimal interference power allocation coefficients and optimal locations of the selected secondary relay. Considering the same power consumption, the UTW-2TS-DNC protocol outperforms the UTW-2TS-SC protocol. Finally, the simulation results are collected to confirm the exact analysis values of the outage probabilities and throughputs.


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## Body

## 1. Introduction

In recent years, the radio spectrum has become scarce due to the increasing bandwidth demand for mobile multimedia services and the explosive development of next-generation wireless networks such as wireless sensor networks, Internet of Things (IoT), and fifth-generation (5G) networks. On the other hand, the utilization of the licensed frequency spectrum versus time and space is low [1]. In this context, cognitive radio was proposed as an effective spectrum sharing solution in which secondary users (SUs) coexist with primary users (PUs) [2]. The SUs can operate flexibly and intelligently in (interweave, overlay, and underlay) protocols to access the licensed frequency spectra of the PUs as long as quality of service (QoS) of the primary network is maintained [3, 4]. In the interweave cognitive radio [5], the SUs use spectrum sensing methods to detect the unoccupied spectra to avoid interference to the PUs. In an opposite way, the SUs in the overlay and underlay methods can access the licensed bands at the same time with the PUs [6–9]. The overlay approach requires the cooperation between the SUs and the PUs; i.e., the secondary transmitters have to combine the data of the SUs and the PUs and then send the combined data to the intended secondary and primary receivers [6]. The SUs in the underlay approach can access the spectra at any time provided that the interferences affected on the PUs must be below a tolerable interference level [7–9]. Based on the required QoS, the PUs can calculate the tolerable interference level and send it to the secondary network so that the SUs can appropriately adjust their transmit powers.Two-way communication networks have been much interested in switching data between interactive users in which many research studies have been launched to enhance performance [10]. Two-way cooperation solutions investigated in [10] have great attractions owing to increase significantly spectrum utilization efficiency. The operation of two-way relaying is to exchange data between users with the help of other intermediate users as amplify-and-forward (AF) and decode-and-forward (DF) devices, denoted as relays. In [11], an optimum relay is selected to decode received signals from the transmit users, mix these data by XOR operation, and then broadcast back to both users. The operation of the optimum relay in [11] is named as digital network coding (DNC).


### 1.1. Related Work and Motivation

Proposals for increasing performance in the underlay two-way relaying networks have been studied in [12–18]. The authors in [12] combined DNC and opportunistic relay selection (ORS) to decrease the outage performance of the secondary two-way relaying network under the interference constraint required by the primary receiver. Moreover, the best relay selection strategy in the third time slot, which follows a max-min criterion, was proposed in [12] to significantly decrease the system outage probabilities, as compared with the traditional DNC approach [12]. By expanding the published work [12], Toan et al. in [13, 14] analyzed the performance of the underlay two-way relaying communication systems with the presence of multiple primary receivers. The authors in [15] evaluated the outage probabilities and symbol error probabilities of many primary one-way networks and a secondary two-way network operating on both the independent and identically distributed (i.i.d.) and independent but nonidentically distributed (i.n.i.d.) Nakagami-m fading channels. Imperfect channel state information (CSI) from the SUs to the PUs have been included in probability analyses [16]. The authors exploited both the direct and relaying links with appropriate diversity combinations in an underlay three-phase two-way scheme [17]. In [18], the authors considered an underlay wiretap cognitive two-way relaying network in which two SUs exchange their messages via multiple secondary DF relays in the presence of an eavesdropper. In [18], DNC, ORS, and artificial noises were used to mitigate eavesdropping attacks. However, above investigations perform on three orthogonal time slots, and hence, the bandwidth utilization efficiency is only 2/3 (two data per three time slots). This motivates us to propose new two-way relaying approaches for the underlay cognitive radio network, where only two time slots are used to obtain the data rate of 2/2.In [19], the authors applied successive interference cancellation (SIC) technique to sequentially decode signals received from multiple sources. With SIC, the spectral efficiency of the two-way relaying systems is improved because the number of time slots decreases. Indeed, SIC is one of the core technologies in nonorthogonal multiple access (NOMA) systems which can assign nonorthogonal resources such as power, time, and code to different users [20]. For the NOMA systems operating in the power domain, multiple transmit signals that are allocated with different transmit powers are merged by the superposition coding (SC) before they are sent to intended receivers. At each receiver, the signal with higher transmit power is first decoded, and it is then removed from the received signal. This process, named SIC, is repeated until the receiver obtains the desired signal [21]. The authors in [19] pointed out some implementation problems of the SIC utilization such as complexity and residual interference after performing interference cancellations. These issues will lead to lower decoding capacities than expected ones. In [22], the authors evaluated two-way relaying NOMA systems fully in terms of the outage probability, outage floor, ergodic capacity, and power allocation. The system performance of the proposed protocol in [22] outperforms that of three-time slot two-way relaying systems with orthogonal multiple access. In addition, we have applied the SIC scheme with DNC and ORS at the last time slot (the second time slot) for traditional two-way relaying networks in [23]. The results obtained in [23] presented improvements of the system performances as well as bandwidth utilization efficiencies, as compared with the corresponding scenarios without using SIC. However, the previous published works [19, 22, 23] only considered the conventional wireless networks; i.e., the underlay cognitive network was not studied.


### 1.2. Contributions

Motivated by above issues, in this paper, we propose an underlay two-way relaying scheme with the SIC solution in which two secondary sources send concurrently their data to each other through multiple secondary relays under an interference constraint of a primary receiver. The proposed scheme is operated in two time slots, denoted as the UTW-2TS scheme. In the UTW-2TS scheme, the secondary relays employ the SIC operation to decode successively the data from received broadcast signals. The data carried by the stronger channel gains is decoded firstly and will be subtracted to detect the remaining data. These decoded data are encoded by two techniques: the DNC enforced by XOR operations (denoted as the UTW-2TS-DNC protocol) and the SC enforced by power domain additions (denoted as the UTW-2TS-SC protocol). In addition, because of imperfect operations of the SIC, the secondary relays experience residual interferences. A secondary relay is selected in two protocols UTW-2TS-DNC and UTW-2TS-SC which subjects to maximize decoding capacities and to minimize collection time of CSI. Outage probabilities and throughputs are solved in terms of exact closed-form expressions to evaluate the system performance of the proposed UTW-2TS-DNC and UTW-2TS-SC protocols. These outage probability and throughput expressions are proved by doing the Monte Carlo simulations. The contributions of this paper are cataloged as follows:(1)
Proposing SIC-based underlay two-way relaying cognitive protocols which enhance the data rate, as compared with the corresponding ones without using the SIC(2)
Exactly analyzing the outage probabilities and throughputs of two secondary sources in two operation protocols UTW-2TS-DNC and UTW-2TS-SC with the same two-way relaying model in which the SIC solution in the selected secondary relay is practically considered in the perfect and imperfect cases(3)
The UTW-2TS-DNC protocol outperforms the UTW-2TS-SC protocol with the same power consumption(4)
The proposed UTW-2TS-DNC and UTW-2TS-SC protocols can achieve the best throughputs at optimal interference power allocation coefficients and optimal locations of the selected secondary relay. In addition, we examine the throughputs of the UTW-2TS-SC protocol versus the changes of the power allocation coefficients(5)
The system performances in terms of the outage probabilities and throughputs are improved when the number of the cooperative secondary relays, the interference constraints, and the distances from the secondary nodes to the primary receiver are increased as well as when the residual interference powers decrease


### 1.3. Paper Organization and Notations

This paper is organized into sections as follows. Section2 presents a system model of an underlay two-way relaying scheme with multiple secondary relays. Section 3 analyzes outage probabilities and throughputs of the proposed protocols UTW-2TS-DNC and UTW-2TS-SC. Results and discussions are shown in Section 4. Lastly, Section 5 summarizes contributions.The notations used in this paper are denoted as follows:fϒ⋅ and Fϒ⋅ denote, respectively, the probability density function (PDF) and the cumulative distribution function (CDF) of a random variable (RV) ϒ; PrΞ denotes the probability operation of an event Ξ; E· denotes the expectation operator; pM denotes the binomial coefficient pM=M!/p!M−p!; ⊕ denotes XOR math operation; and Γu,v is the upper incomplete Gamma function.


## 1.1. Related Work and Motivation

Proposals for increasing performance in the underlay two-way relaying networks have been studied in [12–18]. The authors in [12] combined DNC and opportunistic relay selection (ORS) to decrease the outage performance of the secondary two-way relaying network under the interference constraint required by the primary receiver. Moreover, the best relay selection strategy in the third time slot, which follows a max-min criterion, was proposed in [12] to significantly decrease the system outage probabilities, as compared with the traditional DNC approach [12]. By expanding the published work [12], Toan et al. in [13, 14] analyzed the performance of the underlay two-way relaying communication systems with the presence of multiple primary receivers. The authors in [15] evaluated the outage probabilities and symbol error probabilities of many primary one-way networks and a secondary two-way network operating on both the independent and identically distributed (i.i.d.) and independent but nonidentically distributed (i.n.i.d.) Nakagami-m fading channels. Imperfect channel state information (CSI) from the SUs to the PUs have been included in probability analyses [16]. The authors exploited both the direct and relaying links with appropriate diversity combinations in an underlay three-phase two-way scheme [17]. In [18], the authors considered an underlay wiretap cognitive two-way relaying network in which two SUs exchange their messages via multiple secondary DF relays in the presence of an eavesdropper. In [18], DNC, ORS, and artificial noises were used to mitigate eavesdropping attacks. However, above investigations perform on three orthogonal time slots, and hence, the bandwidth utilization efficiency is only 2/3 (two data per three time slots). This motivates us to propose new two-way relaying approaches for the underlay cognitive radio network, where only two time slots are used to obtain the data rate of 2/2.In [19], the authors applied successive interference cancellation (SIC) technique to sequentially decode signals received from multiple sources. With SIC, the spectral efficiency of the two-way relaying systems is improved because the number of time slots decreases. Indeed, SIC is one of the core technologies in nonorthogonal multiple access (NOMA) systems which can assign nonorthogonal resources such as power, time, and code to different users [20]. For the NOMA systems operating in the power domain, multiple transmit signals that are allocated with different transmit powers are merged by the superposition coding (SC) before they are sent to intended receivers. At each receiver, the signal with higher transmit power is first decoded, and it is then removed from the received signal. This process, named SIC, is repeated until the receiver obtains the desired signal [21]. The authors in [19] pointed out some implementation problems of the SIC utilization such as complexity and residual interference after performing interference cancellations. These issues will lead to lower decoding capacities than expected ones. In [22], the authors evaluated two-way relaying NOMA systems fully in terms of the outage probability, outage floor, ergodic capacity, and power allocation. The system performance of the proposed protocol in [22] outperforms that of three-time slot two-way relaying systems with orthogonal multiple access. In addition, we have applied the SIC scheme with DNC and ORS at the last time slot (the second time slot) for traditional two-way relaying networks in [23]. The results obtained in [23] presented improvements of the system performances as well as bandwidth utilization efficiencies, as compared with the corresponding scenarios without using SIC. However, the previous published works [19, 22, 23] only considered the conventional wireless networks; i.e., the underlay cognitive network was not studied.


## 1.2. Contributions

Motivated by above issues, in this paper, we propose an underlay two-way relaying scheme with the SIC solution in which two secondary sources send concurrently their data to each other through multiple secondary relays under an interference constraint of a primary receiver. The proposed scheme is operated in two time slots, denoted as the UTW-2TS scheme. In the UTW-2TS scheme, the secondary relays employ the SIC operation to decode successively the data from received broadcast signals. The data carried by the stronger channel gains is decoded firstly and will be subtracted to detect the remaining data. These decoded data are encoded by two techniques: the DNC enforced by XOR operations (denoted as the UTW-2TS-DNC protocol) and the SC enforced by power domain additions (denoted as the UTW-2TS-SC protocol). In addition, because of imperfect operations of the SIC, the secondary relays experience residual interferences. A secondary relay is selected in two protocols UTW-2TS-DNC and UTW-2TS-SC which subjects to maximize decoding capacities and to minimize collection time of CSI. Outage probabilities and throughputs are solved in terms of exact closed-form expressions to evaluate the system performance of the proposed UTW-2TS-DNC and UTW-2TS-SC protocols. These outage probability and throughput expressions are proved by doing the Monte Carlo simulations. The contributions of this paper are cataloged as follows:(1)
Proposing SIC-based underlay two-way relaying cognitive protocols which enhance the data rate, as compared with the corresponding ones without using the SIC(2)
Exactly analyzing the outage probabilities and throughputs of two secondary sources in two operation protocols UTW-2TS-DNC and UTW-2TS-SC with the same two-way relaying model in which the SIC solution in the selected secondary relay is practically considered in the perfect and imperfect cases(3)
The UTW-2TS-DNC protocol outperforms the UTW-2TS-SC protocol with the same power consumption(4)
The proposed UTW-2TS-DNC and UTW-2TS-SC protocols can achieve the best throughputs at optimal interference power allocation coefficients and optimal locations of the selected secondary relay. In addition, we examine the throughputs of the UTW-2TS-SC protocol versus the changes of the power allocation coefficients(5)
The system performances in terms of the outage probabilities and throughputs are improved when the number of the cooperative secondary relays, the interference constraints, and the distances from the secondary nodes to the primary receiver are increased as well as when the residual interference powers decrease


## 1.3. Paper Organization and Notations

This paper is organized into sections as follows. Section2 presents a system model of an underlay two-way relaying scheme with multiple secondary relays. Section 3 analyzes outage probabilities and throughputs of the proposed protocols UTW-2TS-DNC and UTW-2TS-SC. Results and discussions are shown in Section 4. Lastly, Section 5 summarizes contributions.The notations used in this paper are denoted as follows:fϒ⋅ and Fϒ⋅ denote, respectively, the probability density function (PDF) and the cumulative distribution function (CDF) of a random variable (RV) ϒ; PrΞ denotes the probability operation of an event Ξ; E· denotes the expectation operator; pM denotes the binomial coefficient pM=M!/p!M−p!; ⊕ denotes XOR math operation; and Γu,v is the upper incomplete Gamma function.


## 2. System Model

Figure1 presents a system model of an underlay two-way relaying scheme. In this scheme, secondary sources S1 and S2 own data x1 and x2 (x1∈S1 and x2∈S2), respectively. The exchange of information is achieved between the S1 and the S2 through a cluster of M intermediate secondary relays Ri, where i=1,2,⋯,M [12]. More specifically, the data x1 of S1 is exchanged with the data x2 of S2. The secondary network including S1, S2, and Ri suffers an interference constraint of a primary receiver (PR), denoted as I. The secondary relays can perform the SIC technique to decode the received data-carried signals successively in an interval of a time slot.Figure 1
System model of an underlay two-way relaying scheme.We assume that a direct link between the secondary sourcesS1 and S2 does not exist due to the far distance or deep shadow fading [18, 23, 24]. It is also assumed that the secondary and primary nodes are installed with a single antenna, and additive noises at all the receivers are zero-mean Gaussian random variables (RVs) whose mean is zero, and variance is σ2.In Figure1, hXY and dXY denote the flat-block Rayleigh fading channel coefficient and the normalized link distance of link X-Y, respectively, where X,Y∈S1,S2,Ri,PR. Because the secondary relays Ri are located in the cluster, where the secondary relays Ri are close to each other, the normalized distances can be assumed to be identical, i.e., dS1Ri=dRiS1=d1, dS2Ri=dRiS2=d2, dRiPR=d3, dS1PR=d4, and dS2PR=d5 [25, 26]. Because hXY have Rayleigh distributions, the channel gains gXY=hXY2 are exponential RVs with the PDFs fgXYy=λXYe−λXYy and the CDFs FgXYy=1−e−λXYy, where λXY=dXYη, and η is a path loss exponent (see [23, 27, 28]). Moreover, we have λS1Ri=λRiS1=λ1, λS2Ri=λRiS2=λ2, λRiPR=λ3, λS1PR=λ4, and λS2PR=λ5.In the underlay cognitive radio network, the secondary network coexisted in the same frequency with the primary network and satisfies that the interference power at the primary receiver (PR) is less than or equal the constraintI [29, 30]. We have the inequality(1)PS1gS1PR+PS2gS2PR≤I,PRigRiPR≤I,i=1,2,⋯,M,where PS1, PS2, and PRi are transmit powers of the secondary source S1, the secondary source S2, and the secondary relays Ri, respectively.From (1), the transmit powers of the secondary transmitters can be set as PS1=α1I/gS1PR, PS2=α2I/gS2PR, and PRi=I/gRiPR, where α1 and α2 are interference power allocation coefficients, 0<α1, α2<1, and α1+α2=1.Comment 1.
In practice, the transmit powersPX must be below a maximum power (denoted by PX,max), where X∈S1,S2,Ri. Therefore, PX should be formulated as PX=minPX,max,uI/gXPR, where u∈α1,α2,1. Suppose that PX,max≫I (e.g., the X nodes are near the PR node); hence, we can approximate PX by PX≈uI/gXPR. It is worth noting that this assumption is used in many published literatures, i.e., [12, 26, 30–36].The operation principle of the UTW-2TS schemes happens in two time slots as follows. In the first time slot, secondary sourcesS1 and S2 transmit simultaneously the data-carried signals x1 and x2, respectively, to all secondary relays under interference constraint of the primary receiver (PR). A selected secondary relay, denoted as Rm, where m=1,2,⋯,M, decodes the desired data by applying the SIC process. In the second time slot (last time slot), the Rm creates the new data x by the DNC technique, denoted as the UTW-2TS-DNC protocol, or by the SC technique, denoted as the UTW-2TS-SC protocol. The new data will be transmitted back to two secondary sources S1 and S2. Collection of CSI and system parameters for decoding data, cancelling interferences, subtracting self-interference components, and selecting the cooperative relay are performed by the medium access control (MAC) protocol as specified in [37].The secondary sourcesS1 and S2 transmit simultaneously the data x1 and x2, respectively, to the secondary relays Ri at the same time (the first time slot) and the same frequency as the uplink NOMA operation, where i=1,2,⋯,M. The received signal at the Ri is expressed as(2)yRi=PS1x1hS1Ri+PS2x2hS2Ri+nRi,where Ex12=Ex22=1, and nRi presents the Gaussian noises at the secondary relays Ri with the same variance σ2.The secondary relaysRi can compute the distances dS1Ri and dS2Ri by taking coordinate parameters in received request-to-send (RTS) messages of the secondary sources S1 and S2 in the setup phase [37]. Coordinates of the nodes can be received from the navigation systems. Hence, the secondary relays Ri can make decoding decisions of the signals x1 and x2 in (2) by the SIC technique as follows.Case 1.
(dS1Ri≤dS2Ri or EgS1Ri≥EgS2Ri (Ri is closer S1 than S2)).
In this case, the datax1 in (2) is decoded by the secondary relay Ri firstly whereas a signal PS2x2hS2Ri containing x2 is treated as interference. The received signal-to-interference-plus-noise ratios (SINRs) at the Ri to decode x1 are obtained from (2) as(3)γRi→x11=PS1gS1RiPS2gS2Ri+σ2=α1QgS1RigS2PRα2QgS2RigS1PR+gS1PRgS2PR,where Q=I/σ2.
In (3), to increase the decoding capacity for the data x1, decrease the collection of the CSI, and minimize help of the cooperative secondary relays, we only select one secondary relay among M secondary relays. Indeed, the selected secondary relay Rm is obtained as Rm=argmaxi=1,2,⋯,MgS1Ri. Then, the CDF and PDF of the RV gS1Rm are correspondingly expressed as ([28], eqs. 7–14)(4)FgS1Rmy=1−e−λ1yM=∑p=0MpM−1pe−pλ1y,(5)fgS1Rmy=Mλ1e−λ1y1−e−λ1yM−1.
After decodingx1 successfully, the inference component PS1x1hS1Rm in (2) can be cancelled completely or partly by the SIC technique in which the transmit power PS1 and the channel coefficient hS1Rmwere known in the setup phase [37]. The remaining received SINR at the selected secondary relay Rm to decode x2 is inferred as(6)γRm→x21=PS2gS2RmεIrm2+σ2,where rm is a residual interference part at the secondary relay Rm due to the imperfect SIC operations and can be modeled as an identical complex normal distribution rm∼CN0,Ψ [19] with zero mean and same variance Ψ (Ψ is also the power of the residual interference part), and hence, gm=rm2 are also exponentially distributed RVs with the PDF as fgmy=Ωe−Ωy and the CDF as Fgmy=1−e−Ωy ([28], eqs. 6–68), where Ω=1/Ψ; ε=0 and ε=1 denote perfect and imperfect interference cancellation at the secondary relay Rm, respectively.
SubstitutingPS2=α2I/gS2PR into (6), γRm→x21 is expressed as(7)γRm→x21=α2QgS2RmgS2PRεQgm+1.Case 2.
(dS1Ri>dS2Ri or EgS1Ri<EgS2Ri (Ri is closer S2 than S1)).
Similarly, the secondary relayRi decodes the data x2 firstly with the interference signal PS1x1hS1Ri, where i=1,2,⋯,M. The SINRs at the Ri for decoding x2 and x1 are expressed, respectively, as(8)γRi→x22=PS2gS2RiPS1gS1Ri+σ2=α2QgS2RigS1PRα1QgS1RigS2PR+gS1PRgS2PR,(9)γRi→x12=PS1gS1RiεIgi+σ2=α1QgS1RigS1PRεQgi+1.In the second time slot, if the selected secondary relayRm decodes successfully both data x1 and x2 in the first time slot, the Rm creates a new data x as(10)x=x1⊕x2,digitalnetworkcodingtheUTW‐2TS‐DNCprotocol,β1x1+β2x2,superpositioncodingtheUTW‐2TS‐SCprotocol,where β1 and β2 are power allocation coefficients to data x1 and x2, respectively, and satisfy conditions as [21](11)β1+β2=1,0≤β1≤1,0≤β2≤1,β1≥β2,dS1Rm≤dS2RmCase1,β1<β2,dS1Rm>dS2RmCase2.We remark that for the UTW-2TS-SC protocol as in (10) and (11), the selected secondary relay Rm performs the downlink NOMA operation to allocate powers to data x1 and x2 as x=β1x1+β2x2 in which x1 and x2 are the desired data of the secondary sources S2 and S1, respectively [21]. If the Sk is closer to the Rm, the Rm will allocate the lower power for the data xl, where k,l=1,2 and l≠k and vice versa. More specifically, in Case 1 (dS1Rm≤dS2Rm), the S1 is the nearby user and the S2 is the distant user. Hence, the Rm uses the lower power allocation coefficient β2 (β2≤β1) to transmit the data x2 to the S1 and the higher power allocation coefficient β1 to transmit the data x1 to the S2. In addition, we note that the secondary relay Rm in Case 2 is selected by Rm=argmaxi=1,2,⋯,MgS2Ri.The coded datax in (10) will be broadcasted back to two secondary sources S1 and S2, and then the received signals at the secondary sources Sk are expressed as(12)ySk=PRmxhRmSk+nSk=PRmhRmSkx1⊕x2+nSktheUTW‐2TS‐DNCprotocolPRmhRmSkβ1x1+β2x2+nSktheUTW‐2TS‐SCprotocol=PRmhRmSkx1⊕x2+nSktheUTW‐2TS‐DNCprotocolβlPRmhRmSkxl+βkPRmhRmSkxk+nSktheUTW‐2TS‐SCprotocol.where nSk presents the Gaussian noises at the secondary sources Sk with the same variance σ2.For the UTW-2TS-DNC protocol withx=x1⊕x2 in (12), the received SINRs at the secondary sources Sk can be obtained from (12) to take x as(13)γSk→xUTW‐2TS‐DNC=PRmhRmSk2σ2=QgRmSkgRmPR.The decoding method of the secondary sourcesSk to take the desired data is performed by decoding operations of the network coding; i.e., the S1 takes the data x2 by XOR operations of its data x1 with the compressed data x as x1⊕x=x1⊕x1⊕x2=x2.For the UTW-2TS-SC protocol, the received signals at the secondary sourcesSk are shown more clearly as(14)ySk=βlPRmhRmSkxl⏟desiredcomponent+βkPRmhRmSkxk⏟self‐interferencecomponent+nSk.In (14), the secondary source Sk owns the data xk and does not decode this data. In addition, the Sk can estimate the fading channel coefficient hRmSk from receiving the setup messages of the selected secondary relay Rm and takes the system parameters as the transmit power PRm and the power allocation coefficient βk during the setup time, where k=1,2, [37]. Hence, the Sk knows the parameters xk, hRmSk, PRm, and βk, which then can cancel out the self-interference component βkPRmhRmSkxk in (14) [38, 39]. The received signals at the Sk after subtracting the known self-interference components are obtained as(15)ySk^=βlPRmhRmSkxl⏟desiredcomponent+nSk.The received SINRs at the secondary sourcesSk can be computed to take the desired data xl as(16)γSk→xlUTW‐2TS‐SC=PRmβlhRmSk2σ2=QβlgRmSkgRmPR.


## 3. Outage Probability and Throughput Analyses

In this paper, it is assumed that an outage event occurs when the received SINR is less than a threshold SINRγth [30, 40]. In addition, the data transmission in the secondary network is fixed to the delay-limited mode in which the secondary receivers such as the selected secondary relay Rm and the secondary sources S1 and S2 decode the desired data block by block without using buffers [30, 40]. Throughput has been considered to characterize the spectrum utilization of the communication systems [30, 40, 41] (known as the mean spectral efficiency) and is related to outage analyses as(17)TPZl=121−OPZ−S1lRth+121−OPZ−S2lRth=122−OPZ−S1l−OPZ−S2lRth,where 1/2 denotes that the Z protocol operates in the two time slots, Z∈UTW‐2TS‐DNC,UTW‐2TS‐SC; Rth is the threshold data rate and is given by Rth=log21+γth (bits/s/Hz) [30, 38, 40, 41]; OPZ−Skl is the outage probability at the secondary source Sk in the case l (l,k=1,2) and is defined as probability that the secondary source Sk cannot decode successfully the desired data.


### 3.1. The UTW-2TS-DNC Protocol

#### 3.1.1. Case1: dS1Ri≤dS2Ri,i=1,2,⋯,M

The outage probability of the secondary sourceS1 occurs when the secondary source S1 cannot successfully decode the data x2 of the opposite secondary source S2. Due to the exploitation of the SIC technique at the selected secondary relay Rm which was set up in the initial phase, the outage probability of the secondary source S1 happens when (1) the Rm fails to decode the data x1; or (2) the Rm decodes the data x1 successfully but does not decode the data x2; or (3) the Rm decodes both x1 and x2 successfully, but the S1 cannot decode the DNC-coded data x to get the desired data x2 in the second time slot. We express the outage probability of the secondary source S1 by the mathematical expression(18)OPUTW‐2TS‐DNC−S11=PrγRm→x11<γth⏟Φ1+PrγRm→x11≥γth∩γRm→x21<γth⏟Φ2+PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→xUTW‐2TS‐DNC<γth.In (18), the probability Φ1=PrγRm→x11<γth is considered when the secondary relay Rm fails to decode the data x1 while applying the SIC technique. The probability Φ2=PrγRm→x11≥γth∩γRm→x21<γth is the decoding error of the data x2 at the secondary relay Rm. Finally, the probability PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→xUTW‐2TS‐DNC<γth measures the decoding error of the coded data x at the secondary source S1. The event γS1→xSIC‐DNC<γth occurs independently with the events γRm→x11≥γth and γRm→x21≥γth; thus, we have an equivalent representation of (18) as(19)OPUTW‐2TS‐DNC‐S11=Φ1+Φ2+PrγRm→x11≥γth∩γRm→x21≥γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ2+PrγRm→x11≥γth−PrγRm→x11≥γth∩γRm→x21<γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ2+1−PrγRm→x11<γth−PrγRm→x11≥γth∩γRm→x21<γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ21−PrγS1→xUTW‐2TS‐DNC<γth+PrγS1→xUTW‐2TS‐DNC<γth.To analyze the probabilitiesΦ1, Φ2, and PrγS1→xUTW‐2TS‐DNC<γth, we define GX1Y1/X2Y2=gX1Y1/gX2Y2, where X1,X2,Y1,Y2∈S1,S2,Ri,PR, gX1Y1≠gX2Y2, and i=1,2,⋯,M; then, by referring from [30] (eqs. 24–25), the CDF and PDF of the RV GX1Y1/X2Y2 are obtained as(20)FGX1Y1/X2Y2z=λX1Y1zλX2Y2+λX1Y1z,(21)fGX1Y1/X2Y2x=dFGX1Y1/X2Y2xdx=λX1Y1λX2Y2λX2Y2+λX1Y1x2.For the selected secondary relayRm from the S1‐Ri links (m,i=1,2,⋯,M), the CDF of the RV GS1Rm/S1PR is given as(22)FGS1Rm/S1PRz=PrGS1Rm/S1PR<z=PrgS1RmgS1PR<z=PrgS1Rm<zgS1PR=∫0∞fgS1PRt×FgS1Rmztdt.Substituting the CDF of the RVgS1Rm in (4) and the PDF of the RVgS1PR into (22), we have a final result as(23)FGS1Rm/S1PRz=∫0∞λ4e−λ4t∑p=0MpM−1pe−pλ1ztdt=λ4∑p=0MpM−1p∫0∞e−tλ4+pλ1zdt=λ4∑p=0MpM−1pλ4+pλ1z.The probabilitiesΦ1 and Φ2 are solved by Lemmas 1 and 2 as follows.Lemma 1.
The probabilityΦ1 is solved as(24)Φ1=1+λ2λ4λ5∑p=1MpM−1pλ2υ3p−λ5υ4p1λ5−υ4pλ2υ3p−λ5υ4plnλ2υ3pλ5υ4p,where υ1=γthα2/α1, υ2=γth/α1Q, υ3p, and υ4p are functions versus count variable p and are defined, respectively, as υ3p=λ4+pλ1υ2 and υ4p=pλ1υ1.Proof.
(proven in AppendixA).Lemma 2.
The probabilityΦ2 is given in two cases of ε as follows:
Caseε=0 (perfect SICs):(25)Φ2=λ2υ5λ5+λ2υ5−λ2λ4λ5∑p=0MpM−1pλ2υ3p−λ5υ4p×λ2υ5λ5λ5+λ2υ5−υ4pλ2υ3p−λ5υ4plnλ5+λ2υ5×υ3pλ5×υ3p+υ5υ4p.
Casε=1 (imperfect SICs):(26)Φ2=1−λ5eλ5+λ2υ5Ω/λ2υ6Γ0,λ5+λ2υ5Ωλ2υ6Ωλ2υ6−∑p=0MpM−1pλ2υ3p−λ5υ4pΩλ4υ6+λ2λ4υ4pλ2υ3p−λ5υ4p−λ2λ4∑p=0MpM−1pλ2υ3p−λ5υ4p1−λ5υ4pλ2υ3p−λ5υ4p×lnλ5+λ2υ5υ3pλ5υ3p+υ5υ4p−eυ3p+υ5υ4pΩ/υ6υ4pΓ0,υ3p+υ5υ4pΩυ6υ4p,where Γu,v is the upper incomplete Gamma function Γu,v=∫v∞e−ttu−1dt ([42], eq. 8.350.2).Proof.
(see the proof and notations in AppendixB).The last probabilityPrγS1→xUTW‐2TS‐DNC<γth in (19) is obtained by using formula (13) with k=1 as(27)PrγS1→xUTW‐2TS‐DNC<γth=PrQgRmS1gRmPR<γth=PrGRmS1/RmPR<γthQ=FGRmS1/RmPRγthQ=λ1γth/Qλ3+λ1γth/Q=λ1γthλ3Q+λ1γth.Substituting (27) into (19), the outage probability of the secondary source S1 is obtained by the closed-form expression(28)OPUTW‐2TS‐DNC‐S11=Φ1+Φ2λ3Q+λ1γthλ3Q+λ1γth,where Φ1 and Φ2 are given by closed-form expressions in Lemmas 1 and 2, respectively.The secondary sourceS2 expects to receive the desired data x1 of the secondary source S1. Hence, the outage probability of the secondary source S2 occurs when (1) the selected secondary relay Rm cannot decode the data x1 or (2) the S2 fails to decode the data transmitted by the Rm after the data x1 is decoded successfully. We formulate the outage probability of the secondary source S1 as(29)OPUTW‐2TS‐DNC‐S21=PrγRm→x11<γth+PrγRm→x11≥γth∩γS2→xUTW‐2TS‐DNC<γth.In (29), the probability part PrγRm→x11≥γth∩γS2→xUTW‐2TS‐DNC<γth shows transmission errors of the data x1 from the selected secondary relay Rm to the desired secondary source S2. Because the event γS2→xUTW‐2TS‐DNC<γth occurs independently, and with the help of (13) with k=1, the outage probability of the secondary source S2 is manipulated and solved as(30)OPUTW‐2TS‐DNC‐S21=Φ1+PrγRm→x11≥γth×PrγS2→xUTW‐2TS‐DNC<γth=Φ1+1−Φ1×PrQgRmS2gRmPR<γth=Φ1+1−Φ1×FGRmS2/RmPRγthQ=Φ1+1−Φ1×λ2γthλ3Q+λ2γth,where Φ1 is given exactly by Lemma 1.Next, the throughput of the UTW-2TS-DNC protocol as in (17) is solved in Case 1 (dS1Ri≤dS2Ri) by(31)TPUTW‐2TS‐DNC1=122−OPUTW‐2TS‐DNC‐S11−OPUTW‐2TS‐DNC‐S21log21+γth=log21+γth22−2Φ1−1−Φ1λ1γthλ3Q+λ1γth+λ2γthλ3Q+λ2γth−λ3QΦ2λ3Q+λ1γth,where Φ1 and Φ2 are taken from Lemmas 1 and 2, respectively.


#### 3.1.2. Case2: dS1Ri>dS2Ri

In this case, a selected secondary relayRm must decode the data x2 firstly. Because the system model of the UTW-2TS-DNC protocol in Figure 1 is symmetric, we can model the outage probabilities in Case 1 as functions versus symmetric parameters as OPUTW‐2TS‐DNC‐S11≡OPUTW‐2TS‐DNC‐S11λ1,α1,λ2,α2 and OPUTW‐2TS‐DNC‐S21≡OPUTW‐2TS‐DNC‐S21λ1,α1,λ2,α2. Hence, in Case 2 (dS1Ri>dS2Ri), the outage probability of the secondary sources S1 and S2 can be inferred from Case 1 as follows:(32)OPUTW‐2TS‐DNC‐S12=OPUTW‐2TS‐DNC‐S21λ2,α2,λ1,α1,(33)OPUTW‐2TS‐DNC‐S22=OPUTW‐2TS‐DNC‐S11λ2,α2,λ1,α1,where OPUTW‐2TS‐DNC‐S21λ2,α2,λ1,α1 and OPUTW‐2TS‐DNC‐S11λ2,α2,λ1,α1 are closed-form outage probability expressions of the secondary sources S2 and S1 in Case 1 with replacing λ1↔λ2 and α1↔α2.The throughput of the UTW-2TS-DNC protocol as in (17) is obtained in Case 2 by(34)TPUTW‐2TS‐DNC2=log21+γth22−OPUTW‐2TS‐DNC‐S12−OPUTW‐2TS‐DNC‐S22,where OPUTW‐2TS‐DNC‐S12 and OPUTW‐2TS‐DNC‐S22 are presented in (32) and (33), respectively.


### 3.2. The UTW-2TS-SC Protocol

Operation of the UTW-2TS-SC protocol is different to the UTW-2TS-DNC protocol in the time slot 2 (the last time slot) with power allocation coefficientsβ1 and β2 to decoded data x1 and x2. Similar to the UTW-2TS-DNC protocol for Case 1 (dS1Ri≤dS2Ri) and Case 2 (dS1Ri>dS2Ri), the outage probability and corresponding throughput of the secondary sources S1 and S2 will be obtained briefly in the next subsections.


#### 3.2.1. Case1: dS1Ri≤dS2Ri

The decoding operation of the UTW-2TS-SC protocol is similar to that of the UTW-2TS-DNC protocol. One difference is that the secondary sourceS1 expects to decode the desired data x2 directly from the received signal yS1 as in (14) where k=1 and l=2. Hence, the outage probability of the secondary source S1 (denoted as OPUTW‐2TS‐SC‐S11) is expressed in Case 1 (dS1Ri≤dS2Ri) as(35)OPUTW‐2TS‐SC‐S11=PrγRm→x11<γth+PrγRm→x11≥γth∩γRm→x21<γth+PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→x2UTW‐2TS‐SC<γth=Φ1+Φ2×1−PrγS1→x2UTW‐2TS‐SC<γth+PrγS1→x2UTW‐2TS‐SC<γth,where Φ1 and Φ2 are obtained from Lemmas 1 and 2.In (35), the probability PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→x2UTW‐2TS‐SC<γth directly calculates the decoding error of the data x2 at the secondary source S1.Substituting (16) with k=1 and l=2 into the probability PrγS1→x2UTW‐2TS‐SC<γth in (35) and performing similarly as (27), we have a result as(36)PrγS1→x2UTW‐2TS‐SC<γth=PrQβ2gRmS1gRmPR<γth=PrGRmS1/RmPR<γthβ2Q=FGRmS1/RmPRγthβ2Q=λ1γth/β2Qλ3+λ1γth/β2Q=λ1γthλ3β2Q+λ1γth.Hence, the outage probabilityOPUTW‐2TS‐SC‐S11 is solved in a closed-form expression with Φ1, Φ2, and PrγS1→x2UTW‐2TS‐SC<γth from Lemmas 1 and 2 and (36).We see that becauseβ2≤1, then PrγS1→x2UTW‐2TS‐SC<γth≥PrγS1→xUTW‐2TS‐DNC<γth which leads to OPUTW‐2TS‐SC‐S11≥OPUTW‐2TS‐DNC‐S11.Similarly, the remaining outage probability of the secondary sourceS2 is obtained as(37)OPUTW‐2TS‐SC‐S21=PrγRm→x11<γth+PrγRm→x11≥γth∩γS2→x1UTW‐2TS‐SC<γth=Φ1+1−Φ1×λ2γthλ3β1Q+λ2γth.Then, the throughput of the UTW-2TS-SC protocol is solved in Case1 (dS1Ri≤dS2Ri) by(38)TPUTW‐2TS‐SC1=122−OPUTW‐2TS‐SC‐S11−OPUTW‐2TS‐SC‐S21log21+γth=log21+γth22−2Φ1−1−Φ1λ1γthλ3β2Q+λ1γth+λ2γthλ3β2Q+λ2γth−λ3β2QΦ2λ3β2Q+λ1γth.


#### 3.2.2. Case2: dS1Ri>dS2Ri

We can also model the outage probabilities in Case1 as functions versus parameters as OPUTW‐2TS‐SC‐S11λ1,α1,β1,λ2,α2,β2 and OPUTW‐2TS‐SC‐S21λ1,α1,β1,λ2,α2,β2. Because of the symmetry model of the UTW-2TS-SC protocol in Figure 1, the outage probability of the secondary sources S1 and S2 in Case 2 can be concluded from Case 1 as follows:(39)OPUTW‐2TS‐SC‐S12=OPUTW‐2TS‐SC‐S21λ2,α2,β2,λ1,α1,β1,(40)OPUTW‐2TS‐SC‐S22=OPUTW‐2TS‐SC‐S11λ2,α2,β2,λ1,α1,β1,where OPUTW‐2TS‐SC‐S21λ2,α2,β2,λ1,α1,β1 and OPUTW‐2TS‐SC‐S11λ2,α2,β2,λ1,α1,β1 are closed-form outage probability expressions of the secondary sources S2 and S1 in Case 1 with replacing λ1↔λ2, α1↔α2, and β1↔β2.The corresponding throughput of the UTW-2TS-SC protocol is obtained in Case2 as(41)TPUTW‐2TS‐SC2=log21+γth22−OPUTW‐2TS‐SC‐S12−OPUTW‐2TS‐SC‐S22,where OPUTW‐2TS‐SC‐S12 and OPUTW‐2TS‐SC‐S22 are given in (39) and (40), respectively.


## 3.1. The UTW-2TS-DNC Protocol

### 3.1.1. Case1: dS1Ri≤dS2Ri,i=1,2,⋯,M

The outage probability of the secondary sourceS1 occurs when the secondary source S1 cannot successfully decode the data x2 of the opposite secondary source S2. Due to the exploitation of the SIC technique at the selected secondary relay Rm which was set up in the initial phase, the outage probability of the secondary source S1 happens when (1) the Rm fails to decode the data x1; or (2) the Rm decodes the data x1 successfully but does not decode the data x2; or (3) the Rm decodes both x1 and x2 successfully, but the S1 cannot decode the DNC-coded data x to get the desired data x2 in the second time slot. We express the outage probability of the secondary source S1 by the mathematical expression(18)OPUTW‐2TS‐DNC−S11=PrγRm→x11<γth⏟Φ1+PrγRm→x11≥γth∩γRm→x21<γth⏟Φ2+PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→xUTW‐2TS‐DNC<γth.In (18), the probability Φ1=PrγRm→x11<γth is considered when the secondary relay Rm fails to decode the data x1 while applying the SIC technique. The probability Φ2=PrγRm→x11≥γth∩γRm→x21<γth is the decoding error of the data x2 at the secondary relay Rm. Finally, the probability PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→xUTW‐2TS‐DNC<γth measures the decoding error of the coded data x at the secondary source S1. The event γS1→xSIC‐DNC<γth occurs independently with the events γRm→x11≥γth and γRm→x21≥γth; thus, we have an equivalent representation of (18) as(19)OPUTW‐2TS‐DNC‐S11=Φ1+Φ2+PrγRm→x11≥γth∩γRm→x21≥γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ2+PrγRm→x11≥γth−PrγRm→x11≥γth∩γRm→x21<γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ2+1−PrγRm→x11<γth−PrγRm→x11≥γth∩γRm→x21<γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ21−PrγS1→xUTW‐2TS‐DNC<γth+PrγS1→xUTW‐2TS‐DNC<γth.To analyze the probabilitiesΦ1, Φ2, and PrγS1→xUTW‐2TS‐DNC<γth, we define GX1Y1/X2Y2=gX1Y1/gX2Y2, where X1,X2,Y1,Y2∈S1,S2,Ri,PR, gX1Y1≠gX2Y2, and i=1,2,⋯,M; then, by referring from [30] (eqs. 24–25), the CDF and PDF of the RV GX1Y1/X2Y2 are obtained as(20)FGX1Y1/X2Y2z=λX1Y1zλX2Y2+λX1Y1z,(21)fGX1Y1/X2Y2x=dFGX1Y1/X2Y2xdx=λX1Y1λX2Y2λX2Y2+λX1Y1x2.For the selected secondary relayRm from the S1‐Ri links (m,i=1,2,⋯,M), the CDF of the RV GS1Rm/S1PR is given as(22)FGS1Rm/S1PRz=PrGS1Rm/S1PR<z=PrgS1RmgS1PR<z=PrgS1Rm<zgS1PR=∫0∞fgS1PRt×FgS1Rmztdt.Substituting the CDF of the RVgS1Rm in (4) and the PDF of the RVgS1PR into (22), we have a final result as(23)FGS1Rm/S1PRz=∫0∞λ4e−λ4t∑p=0MpM−1pe−pλ1ztdt=λ4∑p=0MpM−1p∫0∞e−tλ4+pλ1zdt=λ4∑p=0MpM−1pλ4+pλ1z.The probabilitiesΦ1 and Φ2 are solved by Lemmas 1 and 2 as follows.Lemma 1.
The probabilityΦ1 is solved as(24)Φ1=1+λ2λ4λ5∑p=1MpM−1pλ2υ3p−λ5υ4p1λ5−υ4pλ2υ3p−λ5υ4plnλ2υ3pλ5υ4p,where υ1=γthα2/α1, υ2=γth/α1Q, υ3p, and υ4p are functions versus count variable p and are defined, respectively, as υ3p=λ4+pλ1υ2 and υ4p=pλ1υ1.Proof.
(proven in AppendixA).Lemma 2.
The probabilityΦ2 is given in two cases of ε as follows:
Caseε=0 (perfect SICs):(25)Φ2=λ2υ5λ5+λ2υ5−λ2λ4λ5∑p=0MpM−1pλ2υ3p−λ5υ4p×λ2υ5λ5λ5+λ2υ5−υ4pλ2υ3p−λ5υ4plnλ5+λ2υ5×υ3pλ5×υ3p+υ5υ4p.
Casε=1 (imperfect SICs):(26)Φ2=1−λ5eλ5+λ2υ5Ω/λ2υ6Γ0,λ5+λ2υ5Ωλ2υ6Ωλ2υ6−∑p=0MpM−1pλ2υ3p−λ5υ4pΩλ4υ6+λ2λ4υ4pλ2υ3p−λ5υ4p−λ2λ4∑p=0MpM−1pλ2υ3p−λ5υ4p1−λ5υ4pλ2υ3p−λ5υ4p×lnλ5+λ2υ5υ3pλ5υ3p+υ5υ4p−eυ3p+υ5υ4pΩ/υ6υ4pΓ0,υ3p+υ5υ4pΩυ6υ4p,where Γu,v is the upper incomplete Gamma function Γu,v=∫v∞e−ttu−1dt ([42], eq. 8.350.2).Proof.
(see the proof and notations in AppendixB).The last probabilityPrγS1→xUTW‐2TS‐DNC<γth in (19) is obtained by using formula (13) with k=1 as(27)PrγS1→xUTW‐2TS‐DNC<γth=PrQgRmS1gRmPR<γth=PrGRmS1/RmPR<γthQ=FGRmS1/RmPRγthQ=λ1γth/Qλ3+λ1γth/Q=λ1γthλ3Q+λ1γth.Substituting (27) into (19), the outage probability of the secondary source S1 is obtained by the closed-form expression(28)OPUTW‐2TS‐DNC‐S11=Φ1+Φ2λ3Q+λ1γthλ3Q+λ1γth,where Φ1 and Φ2 are given by closed-form expressions in Lemmas 1 and 2, respectively.The secondary sourceS2 expects to receive the desired data x1 of the secondary source S1. Hence, the outage probability of the secondary source S2 occurs when (1) the selected secondary relay Rm cannot decode the data x1 or (2) the S2 fails to decode the data transmitted by the Rm after the data x1 is decoded successfully. We formulate the outage probability of the secondary source S1 as(29)OPUTW‐2TS‐DNC‐S21=PrγRm→x11<γth+PrγRm→x11≥γth∩γS2→xUTW‐2TS‐DNC<γth.In (29), the probability part PrγRm→x11≥γth∩γS2→xUTW‐2TS‐DNC<γth shows transmission errors of the data x1 from the selected secondary relay Rm to the desired secondary source S2. Because the event γS2→xUTW‐2TS‐DNC<γth occurs independently, and with the help of (13) with k=1, the outage probability of the secondary source S2 is manipulated and solved as(30)OPUTW‐2TS‐DNC‐S21=Φ1+PrγRm→x11≥γth×PrγS2→xUTW‐2TS‐DNC<γth=Φ1+1−Φ1×PrQgRmS2gRmPR<γth=Φ1+1−Φ1×FGRmS2/RmPRγthQ=Φ1+1−Φ1×λ2γthλ3Q+λ2γth,where Φ1 is given exactly by Lemma 1.Next, the throughput of the UTW-2TS-DNC protocol as in (17) is solved in Case 1 (dS1Ri≤dS2Ri) by(31)TPUTW‐2TS‐DNC1=122−OPUTW‐2TS‐DNC‐S11−OPUTW‐2TS‐DNC‐S21log21+γth=log21+γth22−2Φ1−1−Φ1λ1γthλ3Q+λ1γth+λ2γthλ3Q+λ2γth−λ3QΦ2λ3Q+λ1γth,where Φ1 and Φ2 are taken from Lemmas 1 and 2, respectively.


### 3.1.2. Case2: dS1Ri>dS2Ri

In this case, a selected secondary relayRm must decode the data x2 firstly. Because the system model of the UTW-2TS-DNC protocol in Figure 1 is symmetric, we can model the outage probabilities in Case 1 as functions versus symmetric parameters as OPUTW‐2TS‐DNC‐S11≡OPUTW‐2TS‐DNC‐S11λ1,α1,λ2,α2 and OPUTW‐2TS‐DNC‐S21≡OPUTW‐2TS‐DNC‐S21λ1,α1,λ2,α2. Hence, in Case 2 (dS1Ri>dS2Ri), the outage probability of the secondary sources S1 and S2 can be inferred from Case 1 as follows:(32)OPUTW‐2TS‐DNC‐S12=OPUTW‐2TS‐DNC‐S21λ2,α2,λ1,α1,(33)OPUTW‐2TS‐DNC‐S22=OPUTW‐2TS‐DNC‐S11λ2,α2,λ1,α1,where OPUTW‐2TS‐DNC‐S21λ2,α2,λ1,α1 and OPUTW‐2TS‐DNC‐S11λ2,α2,λ1,α1 are closed-form outage probability expressions of the secondary sources S2 and S1 in Case 1 with replacing λ1↔λ2 and α1↔α2.The throughput of the UTW-2TS-DNC protocol as in (17) is obtained in Case 2 by(34)TPUTW‐2TS‐DNC2=log21+γth22−OPUTW‐2TS‐DNC‐S12−OPUTW‐2TS‐DNC‐S22,where OPUTW‐2TS‐DNC‐S12 and OPUTW‐2TS‐DNC‐S22 are presented in (32) and (33), respectively.


## 3.1.1. Case1: dS1Ri≤dS2Ri,i=1,2,⋯,M

The outage probability of the secondary sourceS1 occurs when the secondary source S1 cannot successfully decode the data x2 of the opposite secondary source S2. Due to the exploitation of the SIC technique at the selected secondary relay Rm which was set up in the initial phase, the outage probability of the secondary source S1 happens when (1) the Rm fails to decode the data x1; or (2) the Rm decodes the data x1 successfully but does not decode the data x2; or (3) the Rm decodes both x1 and x2 successfully, but the S1 cannot decode the DNC-coded data x to get the desired data x2 in the second time slot. We express the outage probability of the secondary source S1 by the mathematical expression(18)OPUTW‐2TS‐DNC−S11=PrγRm→x11<γth⏟Φ1+PrγRm→x11≥γth∩γRm→x21<γth⏟Φ2+PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→xUTW‐2TS‐DNC<γth.In (18), the probability Φ1=PrγRm→x11<γth is considered when the secondary relay Rm fails to decode the data x1 while applying the SIC technique. The probability Φ2=PrγRm→x11≥γth∩γRm→x21<γth is the decoding error of the data x2 at the secondary relay Rm. Finally, the probability PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→xUTW‐2TS‐DNC<γth measures the decoding error of the coded data x at the secondary source S1. The event γS1→xSIC‐DNC<γth occurs independently with the events γRm→x11≥γth and γRm→x21≥γth; thus, we have an equivalent representation of (18) as(19)OPUTW‐2TS‐DNC‐S11=Φ1+Φ2+PrγRm→x11≥γth∩γRm→x21≥γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ2+PrγRm→x11≥γth−PrγRm→x11≥γth∩γRm→x21<γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ2+1−PrγRm→x11<γth−PrγRm→x11≥γth∩γRm→x21<γth×PrγS1→xUTW‐2TS‐DNC<γth=Φ1+Φ21−PrγS1→xUTW‐2TS‐DNC<γth+PrγS1→xUTW‐2TS‐DNC<γth.To analyze the probabilitiesΦ1, Φ2, and PrγS1→xUTW‐2TS‐DNC<γth, we define GX1Y1/X2Y2=gX1Y1/gX2Y2, where X1,X2,Y1,Y2∈S1,S2,Ri,PR, gX1Y1≠gX2Y2, and i=1,2,⋯,M; then, by referring from [30] (eqs. 24–25), the CDF and PDF of the RV GX1Y1/X2Y2 are obtained as(20)FGX1Y1/X2Y2z=λX1Y1zλX2Y2+λX1Y1z,(21)fGX1Y1/X2Y2x=dFGX1Y1/X2Y2xdx=λX1Y1λX2Y2λX2Y2+λX1Y1x2.For the selected secondary relayRm from the S1‐Ri links (m,i=1,2,⋯,M), the CDF of the RV GS1Rm/S1PR is given as(22)FGS1Rm/S1PRz=PrGS1Rm/S1PR<z=PrgS1RmgS1PR<z=PrgS1Rm<zgS1PR=∫0∞fgS1PRt×FgS1Rmztdt.Substituting the CDF of the RVgS1Rm in (4) and the PDF of the RVgS1PR into (22), we have a final result as(23)FGS1Rm/S1PRz=∫0∞λ4e−λ4t∑p=0MpM−1pe−pλ1ztdt=λ4∑p=0MpM−1p∫0∞e−tλ4+pλ1zdt=λ4∑p=0MpM−1pλ4+pλ1z.The probabilitiesΦ1 and Φ2 are solved by Lemmas 1 and 2 as follows.Lemma 1.
The probabilityΦ1 is solved as(24)Φ1=1+λ2λ4λ5∑p=1MpM−1pλ2υ3p−λ5υ4p1λ5−υ4pλ2υ3p−λ5υ4plnλ2υ3pλ5υ4p,where υ1=γthα2/α1, υ2=γth/α1Q, υ3p, and υ4p are functions versus count variable p and are defined, respectively, as υ3p=λ4+pλ1υ2 and υ4p=pλ1υ1.Proof.
(proven in AppendixA).Lemma 2.
The probabilityΦ2 is given in two cases of ε as follows:
Caseε=0 (perfect SICs):(25)Φ2=λ2υ5λ5+λ2υ5−λ2λ4λ5∑p=0MpM−1pλ2υ3p−λ5υ4p×λ2υ5λ5λ5+λ2υ5−υ4pλ2υ3p−λ5υ4plnλ5+λ2υ5×υ3pλ5×υ3p+υ5υ4p.
Casε=1 (imperfect SICs):(26)Φ2=1−λ5eλ5+λ2υ5Ω/λ2υ6Γ0,λ5+λ2υ5Ωλ2υ6Ωλ2υ6−∑p=0MpM−1pλ2υ3p−λ5υ4pΩλ4υ6+λ2λ4υ4pλ2υ3p−λ5υ4p−λ2λ4∑p=0MpM−1pλ2υ3p−λ5υ4p1−λ5υ4pλ2υ3p−λ5υ4p×lnλ5+λ2υ5υ3pλ5υ3p+υ5υ4p−eυ3p+υ5υ4pΩ/υ6υ4pΓ0,υ3p+υ5υ4pΩυ6υ4p,where Γu,v is the upper incomplete Gamma function Γu,v=∫v∞e−ttu−1dt ([42], eq. 8.350.2).Proof.
(see the proof and notations in AppendixB).The last probabilityPrγS1→xUTW‐2TS‐DNC<γth in (19) is obtained by using formula (13) with k=1 as(27)PrγS1→xUTW‐2TS‐DNC<γth=PrQgRmS1gRmPR<γth=PrGRmS1/RmPR<γthQ=FGRmS1/RmPRγthQ=λ1γth/Qλ3+λ1γth/Q=λ1γthλ3Q+λ1γth.Substituting (27) into (19), the outage probability of the secondary source S1 is obtained by the closed-form expression(28)OPUTW‐2TS‐DNC‐S11=Φ1+Φ2λ3Q+λ1γthλ3Q+λ1γth,where Φ1 and Φ2 are given by closed-form expressions in Lemmas 1 and 2, respectively.The secondary sourceS2 expects to receive the desired data x1 of the secondary source S1. Hence, the outage probability of the secondary source S2 occurs when (1) the selected secondary relay Rm cannot decode the data x1 or (2) the S2 fails to decode the data transmitted by the Rm after the data x1 is decoded successfully. We formulate the outage probability of the secondary source S1 as(29)OPUTW‐2TS‐DNC‐S21=PrγRm→x11<γth+PrγRm→x11≥γth∩γS2→xUTW‐2TS‐DNC<γth.In (29), the probability part PrγRm→x11≥γth∩γS2→xUTW‐2TS‐DNC<γth shows transmission errors of the data x1 from the selected secondary relay Rm to the desired secondary source S2. Because the event γS2→xUTW‐2TS‐DNC<γth occurs independently, and with the help of (13) with k=1, the outage probability of the secondary source S2 is manipulated and solved as(30)OPUTW‐2TS‐DNC‐S21=Φ1+PrγRm→x11≥γth×PrγS2→xUTW‐2TS‐DNC<γth=Φ1+1−Φ1×PrQgRmS2gRmPR<γth=Φ1+1−Φ1×FGRmS2/RmPRγthQ=Φ1+1−Φ1×λ2γthλ3Q+λ2γth,where Φ1 is given exactly by Lemma 1.Next, the throughput of the UTW-2TS-DNC protocol as in (17) is solved in Case 1 (dS1Ri≤dS2Ri) by(31)TPUTW‐2TS‐DNC1=122−OPUTW‐2TS‐DNC‐S11−OPUTW‐2TS‐DNC‐S21log21+γth=log21+γth22−2Φ1−1−Φ1λ1γthλ3Q+λ1γth+λ2γthλ3Q+λ2γth−λ3QΦ2λ3Q+λ1γth,where Φ1 and Φ2 are taken from Lemmas 1 and 2, respectively.


## 3.1.2. Case2: dS1Ri>dS2Ri

In this case, a selected secondary relayRm must decode the data x2 firstly. Because the system model of the UTW-2TS-DNC protocol in Figure 1 is symmetric, we can model the outage probabilities in Case 1 as functions versus symmetric parameters as OPUTW‐2TS‐DNC‐S11≡OPUTW‐2TS‐DNC‐S11λ1,α1,λ2,α2 and OPUTW‐2TS‐DNC‐S21≡OPUTW‐2TS‐DNC‐S21λ1,α1,λ2,α2. Hence, in Case 2 (dS1Ri>dS2Ri), the outage probability of the secondary sources S1 and S2 can be inferred from Case 1 as follows:(32)OPUTW‐2TS‐DNC‐S12=OPUTW‐2TS‐DNC‐S21λ2,α2,λ1,α1,(33)OPUTW‐2TS‐DNC‐S22=OPUTW‐2TS‐DNC‐S11λ2,α2,λ1,α1,where OPUTW‐2TS‐DNC‐S21λ2,α2,λ1,α1 and OPUTW‐2TS‐DNC‐S11λ2,α2,λ1,α1 are closed-form outage probability expressions of the secondary sources S2 and S1 in Case 1 with replacing λ1↔λ2 and α1↔α2.The throughput of the UTW-2TS-DNC protocol as in (17) is obtained in Case 2 by(34)TPUTW‐2TS‐DNC2=log21+γth22−OPUTW‐2TS‐DNC‐S12−OPUTW‐2TS‐DNC‐S22,where OPUTW‐2TS‐DNC‐S12 and OPUTW‐2TS‐DNC‐S22 are presented in (32) and (33), respectively.


## 3.2. The UTW-2TS-SC Protocol

Operation of the UTW-2TS-SC protocol is different to the UTW-2TS-DNC protocol in the time slot 2 (the last time slot) with power allocation coefficientsβ1 and β2 to decoded data x1 and x2. Similar to the UTW-2TS-DNC protocol for Case 1 (dS1Ri≤dS2Ri) and Case 2 (dS1Ri>dS2Ri), the outage probability and corresponding throughput of the secondary sources S1 and S2 will be obtained briefly in the next subsections.


### 3.2.1. Case1: dS1Ri≤dS2Ri

The decoding operation of the UTW-2TS-SC protocol is similar to that of the UTW-2TS-DNC protocol. One difference is that the secondary sourceS1 expects to decode the desired data x2 directly from the received signal yS1 as in (14) where k=1 and l=2. Hence, the outage probability of the secondary source S1 (denoted as OPUTW‐2TS‐SC‐S11) is expressed in Case 1 (dS1Ri≤dS2Ri) as(35)OPUTW‐2TS‐SC‐S11=PrγRm→x11<γth+PrγRm→x11≥γth∩γRm→x21<γth+PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→x2UTW‐2TS‐SC<γth=Φ1+Φ2×1−PrγS1→x2UTW‐2TS‐SC<γth+PrγS1→x2UTW‐2TS‐SC<γth,where Φ1 and Φ2 are obtained from Lemmas 1 and 2.In (35), the probability PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→x2UTW‐2TS‐SC<γth directly calculates the decoding error of the data x2 at the secondary source S1.Substituting (16) with k=1 and l=2 into the probability PrγS1→x2UTW‐2TS‐SC<γth in (35) and performing similarly as (27), we have a result as(36)PrγS1→x2UTW‐2TS‐SC<γth=PrQβ2gRmS1gRmPR<γth=PrGRmS1/RmPR<γthβ2Q=FGRmS1/RmPRγthβ2Q=λ1γth/β2Qλ3+λ1γth/β2Q=λ1γthλ3β2Q+λ1γth.Hence, the outage probabilityOPUTW‐2TS‐SC‐S11 is solved in a closed-form expression with Φ1, Φ2, and PrγS1→x2UTW‐2TS‐SC<γth from Lemmas 1 and 2 and (36).We see that becauseβ2≤1, then PrγS1→x2UTW‐2TS‐SC<γth≥PrγS1→xUTW‐2TS‐DNC<γth which leads to OPUTW‐2TS‐SC‐S11≥OPUTW‐2TS‐DNC‐S11.Similarly, the remaining outage probability of the secondary sourceS2 is obtained as(37)OPUTW‐2TS‐SC‐S21=PrγRm→x11<γth+PrγRm→x11≥γth∩γS2→x1UTW‐2TS‐SC<γth=Φ1+1−Φ1×λ2γthλ3β1Q+λ2γth.Then, the throughput of the UTW-2TS-SC protocol is solved in Case1 (dS1Ri≤dS2Ri) by(38)TPUTW‐2TS‐SC1=122−OPUTW‐2TS‐SC‐S11−OPUTW‐2TS‐SC‐S21log21+γth=log21+γth22−2Φ1−1−Φ1λ1γthλ3β2Q+λ1γth+λ2γthλ3β2Q+λ2γth−λ3β2QΦ2λ3β2Q+λ1γth.


### 3.2.2. Case2: dS1Ri>dS2Ri

We can also model the outage probabilities in Case1 as functions versus parameters as OPUTW‐2TS‐SC‐S11λ1,α1,β1,λ2,α2,β2 and OPUTW‐2TS‐SC‐S21λ1,α1,β1,λ2,α2,β2. Because of the symmetry model of the UTW-2TS-SC protocol in Figure 1, the outage probability of the secondary sources S1 and S2 in Case 2 can be concluded from Case 1 as follows:(39)OPUTW‐2TS‐SC‐S12=OPUTW‐2TS‐SC‐S21λ2,α2,β2,λ1,α1,β1,(40)OPUTW‐2TS‐SC‐S22=OPUTW‐2TS‐SC‐S11λ2,α2,β2,λ1,α1,β1,where OPUTW‐2TS‐SC‐S21λ2,α2,β2,λ1,α1,β1 and OPUTW‐2TS‐SC‐S11λ2,α2,β2,λ1,α1,β1 are closed-form outage probability expressions of the secondary sources S2 and S1 in Case 1 with replacing λ1↔λ2, α1↔α2, and β1↔β2.The corresponding throughput of the UTW-2TS-SC protocol is obtained in Case2 as(41)TPUTW‐2TS‐SC2=log21+γth22−OPUTW‐2TS‐SC‐S12−OPUTW‐2TS‐SC‐S22,where OPUTW‐2TS‐SC‐S12 and OPUTW‐2TS‐SC‐S22 are given in (39) and (40), respectively.


## 3.2.1. Case1: dS1Ri≤dS2Ri

The decoding operation of the UTW-2TS-SC protocol is similar to that of the UTW-2TS-DNC protocol. One difference is that the secondary sourceS1 expects to decode the desired data x2 directly from the received signal yS1 as in (14) where k=1 and l=2. Hence, the outage probability of the secondary source S1 (denoted as OPUTW‐2TS‐SC‐S11) is expressed in Case 1 (dS1Ri≤dS2Ri) as(35)OPUTW‐2TS‐SC‐S11=PrγRm→x11<γth+PrγRm→x11≥γth∩γRm→x21<γth+PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→x2UTW‐2TS‐SC<γth=Φ1+Φ2×1−PrγS1→x2UTW‐2TS‐SC<γth+PrγS1→x2UTW‐2TS‐SC<γth,where Φ1 and Φ2 are obtained from Lemmas 1 and 2.In (35), the probability PrγRm→x11≥γth∩γRm→x21≥γth∩γS1→x2UTW‐2TS‐SC<γth directly calculates the decoding error of the data x2 at the secondary source S1.Substituting (16) with k=1 and l=2 into the probability PrγS1→x2UTW‐2TS‐SC<γth in (35) and performing similarly as (27), we have a result as(36)PrγS1→x2UTW‐2TS‐SC<γth=PrQβ2gRmS1gRmPR<γth=PrGRmS1/RmPR<γthβ2Q=FGRmS1/RmPRγthβ2Q=λ1γth/β2Qλ3+λ1γth/β2Q=λ1γthλ3β2Q+λ1γth.Hence, the outage probabilityOPUTW‐2TS‐SC‐S11 is solved in a closed-form expression with Φ1, Φ2, and PrγS1→x2UTW‐2TS‐SC<γth from Lemmas 1 and 2 and (36).We see that becauseβ2≤1, then PrγS1→x2UTW‐2TS‐SC<γth≥PrγS1→xUTW‐2TS‐DNC<γth which leads to OPUTW‐2TS‐SC‐S11≥OPUTW‐2TS‐DNC‐S11.Similarly, the remaining outage probability of the secondary sourceS2 is obtained as(37)OPUTW‐2TS‐SC‐S21=PrγRm→x11<γth+PrγRm→x11≥γth∩γS2→x1UTW‐2TS‐SC<γth=Φ1+1−Φ1×λ2γthλ3β1Q+λ2γth.Then, the throughput of the UTW-2TS-SC protocol is solved in Case1 (dS1Ri≤dS2Ri) by(38)TPUTW‐2TS‐SC1=122−OPUTW‐2TS‐SC‐S11−OPUTW‐2TS‐SC‐S21log21+γth=log21+γth22−2Φ1−1−Φ1λ1γthλ3β2Q+λ1γth+λ2γthλ3β2Q+λ2γth−λ3β2QΦ2λ3β2Q+λ1γth.


## 3.2.2. Case2: dS1Ri>dS2Ri

We can also model the outage probabilities in Case1 as functions versus parameters as OPUTW‐2TS‐SC‐S11λ1,α1,β1,λ2,α2,β2 and OPUTW‐2TS‐SC‐S21λ1,α1,β1,λ2,α2,β2. Because of the symmetry model of the UTW-2TS-SC protocol in Figure 1, the outage probability of the secondary sources S1 and S2 in Case 2 can be concluded from Case 1 as follows:(39)OPUTW‐2TS‐SC‐S12=OPUTW‐2TS‐SC‐S21λ2,α2,β2,λ1,α1,β1,(40)OPUTW‐2TS‐SC‐S22=OPUTW‐2TS‐SC‐S11λ2,α2,β2,λ1,α1,β1,where OPUTW‐2TS‐SC‐S21λ2,α2,β2,λ1,α1,β1 and OPUTW‐2TS‐SC‐S11λ2,α2,β2,λ1,α1,β1 are closed-form outage probability expressions of the secondary sources S2 and S1 in Case 1 with replacing λ1↔λ2, α1↔α2, and β1↔β2.The corresponding throughput of the UTW-2TS-SC protocol is obtained in Case2 as(41)TPUTW‐2TS‐SC2=log21+γth22−OPUTW‐2TS‐SC‐S12−OPUTW‐2TS‐SC‐S22,where OPUTW‐2TS‐SC‐S12 and OPUTW‐2TS‐SC‐S22 are given in (39) and (40), respectively.


## 4. Results and Discussions

This section presents analysis and simulation results in terms of outage probabilities and throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC in the two-dimensional plane. These proposed protocols are considered in two cases of perfect SICs (ε=0, denoted by pSIC) and imperfect SICs (ε=1, denoted by ipSIC). The simulation results are performed by the Monte Carlo method to validate the analysis ones which are shown from exact closed-form expressions. Coordinates of the nodes S1, S2, PR, and the cluster with M secondary relay Ri are set as S10,0, S21,0, PRxPR,yPR, and RixR,yR, where 0<xR<1 and i=1,2,⋯,M. The normalized distances are calculated from the coordinates as d1=xR2+yR2, d2=1−xR2+yR2, d3=xPR−xR2+yPR−yR2, d4=xPR2+yPR2, and d5=1−xPR2+yPR2. It is assumed that the threshold SINR and the path loss exponent are fixed by γth=3 and η=3, and Q (dB) on the x-axis is defined as Q=10×log10I/σ2 (dB). Markers denote simulated results, and solid lines present analyzed ones.Figure2 shows the outage probabilities of the secondary sources S1 and S2 in the protocols UTW-2TS-DNC and UTW-2TS-SC versus Q (dB) when xR=0.3, yR=0, xPR=yPR=0.5, Ψ=0dB, M=3, and interference allocation coefficients α1=α2=0.5 [19, 30]. The normalized distances are calculated as d1=0.3, d2=0.7, d3=0.54, d4=0.71, and d5=0.71; hence, the results are presented following Case 1 (dS1Ri≤dS2Ri). The power allocation coefficients β1 and β2 at the selected secondary relay are suitably set as β1=0.7 and β2=1−β1=0.3. We note that the power allocation coefficients β1 and β2 to carry the desired data x1 and x2 from the selected relay to the S2 and S1, respectively. Simulated results are performed from equations (18) and (29) by making RVs in (3), (7), and (13), whereas exact theory values are calculated by closed-form expressions in (28) and (30) for the secondary sources S1 and S2, respectively. From Figure 2, some findings are watched as follows. Firstly, the outage probabilities of the secondary source S1 and S2 in both protocols with the perfect SICs and imperfect SICs decrease when the interference constraint parameters Q increase. Secondly, the system performances of the secondary source S1 with the perfect SICs are always better than those with the imperfect SICs. We note that the outage probabilities of the secondary source S2 in both protocols are not affected by SIC operations, and thus, the system performances of the secondary source S2 with the perfect SICs and the imperfect SICs are identical (markers and solid line are merged in Figure 2). Thirdly, in this case, the outage probabilities of the secondary source S2 are almost smaller than those of the secondary source S1. Finally, the results (solid lines) from the theory expressions of the outage probabilities are exact to the Monte Carlo simulations. These findings can be reasoned that the received SINRs in (3) and (7) to decode the data x1 and x2 declined by more interferences from transmittance of the data-carried signal x2, affecting of the residual interference signal and interference constraints as in (1). In addition, with large values of Q, the transmit powers of the nodes S1, S2, and Rm increase as in (1) which correspond to large SINRs to decode the data x1, x2, and x as in (3), (7), (13), and (16), where m=1,2,⋯,M.Figure 2
Outage probabilities of the secondary sourcesS1 and S2 versus Q (dB) when α1=α2=0.5, β1=0.7, β2=1−β1=0.3, Ψ=0 (dB), xR=0.3, yR=0, xPR=yPR=0.5, and M=3.Figure3 compares the throughputs of the UTW-2TS-DNC and UTW-2TS-SC protocols versus Q (dB) when xR=0.3, yR=0, xPR=yPR=0.5, Ψ=0 (dB), α1=α2=0.5, β1=0.7, β2=1−β1=0.3, and the number of intermediate secondary relays is set as M∈3,12. Exact throughput curves of the UTW-2TS-DNC and UTW-2TS-SC protocols are obtained by theoretic analyses in (31) and (38). Simulation markers are carried out by (17) with separate outage probabilities for each protocol. From Figure 3, the throughputs of the UTW-2TS-DNC protocol are larger than those of the UTW-2TS-SC protocol with all the cases of SICs and M. In addition, the throughputs of both protocols increase when the UTW-2TS systems use more secondary relays (M is increased). These contributions are based on observations from SINRs (13) and (16). With 0≤β1 and β2≤1, the SINRs in (13) of the UTW-2TW-DNC protocol are always larger than those in (16) of the UTW-2TW-SC protocol. Furthermore, with more cooperative secondary relays, the diversity capacity of both protocols will be increased by the relay selection methods.Figure 3
Throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versusQ (dB) when α1=α2=0.5, β1=0.7, β2=1−β1=0.3, Ψ=0 (dB), xR=0.3, yR=0, xPR=yPR=0.5, and M=3,12.Figure4 presents the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versus α1 when Q=10 (dB), β1=0.7, β2=1−β1=0.3, Ψ=−5 (dB), xR=0.3, yR=0, xPR=yPR=0.5, M=3, and α2 can be set as α2=1−α1. In Figure 4, the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC achieve the large values at an approximate interference power allocation coefficient α1≈0.6 for both cases (perfect SICs and imperfect SICs). The value α1≈0.6 is to balance constraints such as interferences from the secondary network to the primary network, locations of the secondary relays, and perfect/imperfect SIC operations.Figure 4
Throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versusα1 when Q=10 (dB), β1=0.7, β2=1−β1=0.3, Ψ=−5 (dB), xR=0.3, yR=0, xPR=yPR=0.5, M=3, and α2=1−α1.Figure5 shows the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versus β1 when Q=10 (dB), α1=0.6, α2=1−α1=0.4, Ψ=−5 (dB), xR=0.3, yR=0, xPR=yPR=0.5, M=3, and β2 is changed as β2=1−β1. As observed from Figure 5, the UTW-2TS-DNC protocol is not affected by the power allocation coefficients β1 and β2, and the UTW-2TS-SC protocol reaches the largest throughputs at approximate values β1=0.7 and β1=0.8 corresponding to perfect SICs and imperfect SICs, respectively. These values β1=0.7 and β1=0.8 are to equalize the SINR qualities between two hops from the selected secondary relay to the secondary sources.Figure 5
Throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versusβ1 when Q=10 (dB), α1=0.6, α2=1−α1=0.4, Ψ=−5 (dB), xR=0.3, yR=0, xPR=yPR=0.5, M=3, and β2=1−β1.Figure6 shows the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versus α1 and β1 in the three-dimensional plane when Q=10 (dB), Ψ=−5 (dB), xR=0.3, yR=0, xPR=yPR=0.5, M=3, and α2 and β2 are set as α2=1−α1 and β2=1−β1. The value ranges of α1 and β1 are established between 0.1 and 0.9. The results from Figure 6 confirm the contributions from Figures 4 and 5.Figure 6
Throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versusα1 and β1 when Q=10 (dB), Ψ=−5 (dB), xR=0.3, yR=0, xPR=yPR=0.5, M=3, α2=1−α1, and β2=1−β1.Figure7 presents the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versus xR when Q=10 (dB), α1=α2=0.5, β1=β2=0.5, Ψ=−5 (dB), xPR=yPR=0.5, M=3, and yR is fixed as yR=0. In this simulation, the normalized distances d4 and d5 are fixed at the same value 0.7 and the remaining normalized distances d1, d2, and d3 are changed from 0.1 to 0.9 for d1, 0.9 to 0.1 for d2 (the distance d2 has a reverse change versus the distance d1), and 0.64 to 0.5 and back to 0.64 for d3. From Figure 7, these proposed protocols UTW-2TS-DNC and UTW-2TS-SC achieve the largest throughputs at asymmetric locations of the selected secondary relay as xR≈0.2d1=0.2,d2=0.8 and xR≈0.8d1=0.8,d2=0.2 because of decoding the received data sequentially (SIC operations). In addition, at the symmetric location xR=0.5d1=d2=0.5, the throughputs of both protocols again have the lowest values.Figure 7
Throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versusxR when Q=10 (dB), α1=α2=0.5, β1=β2=0.5, Ψ=−5 (dB), xPR=yPR=0.5, M=3, and yR=0.Figure8 presents the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versus yPR when Q=10 (dB), α1=α2=0.5, β1=0.7, β2=1−β1=0.3, Ψ=−5 (dB), xR=0.3, yR=0, M=3, and xPR is fixed at xPR=0.5. In this case, the normalized distances d1 and d2 are fixed to 0.3 and 0.7, respectively, and the primary receiver (PR) is moving farther the secondary network characterized by changing the normalized distances d3, d4, and d5 from 0.22 to 0.92 for d3 and from 0.51 to 1.03 for d4 and d5. As shown in Figure 8, the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC are enhanced when the value of yPR increases because of low influence of the interference constraint to the sources and relays in the secondary network. Therefore, the secondary sources and relays can transmit with the maximum power, and interference cancelling and decoding capacity at the secondary relays and the secondary sources increase.Figure 8
Throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versusyPR when Q=10 (dB), α1=α2=0.5, β1=0.7, β2=1−β1=0.3, Ψ=−5 (dB), xR=0.3, yR=0, M=3, and xPR=0.5.Figure9 presents the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versus the residual interference powers Ψ when Q=10 (dB), α1=α2=0.5, β1=0.7, β2=1−β1=0.3, xR=0.3, yR=0, xPR=yPR=0.5, and M=3. Considering the case of the imperfect SICs for both protocols, the throughput performances decrease when the residual interference powers increase. Furthermore, the throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC in the perfect SICs are upper limitations (expectations) of the ones in the imperfect SICs when Ψ→−∞ (dB).Figure 9
Throughputs of the protocols UTW-2TS-DNC and UTW-2TS-SC versusΨ when Q=10 (dB), α1=α2=0.5, β1=0.7, β2=1−β1=0.3, xR=0.3, yR=0, xPR=yPR=0.5, and M=3.


## 5. Conclusions

In this paper, we proposed and analyzed the underlay two-way relaying scheme with two secondary sources and multiple secondary relays, known as the UTW-2TS scheme. The UTW-2TS scheme with the SIC solution operated in only two time slots and under an interference constraint of the primary receiver. The secondary relays decode successively the data transmitted by two secondary sources and then encode these data by two techniques: the DNC enforced by XOR operations (known as the UTW-2TS-DNC protocol) and the SC enforced by power domain additions (known as the UTW-2TS-SC protocol). A selected secondary relay which subjects to maximize the decoding capacities and to minimize the collection time of CSI in the proposed protocols UTW-2TS-DNC and UTW-2TS-SC suffered the residual interferences from the imperfect SIC operations. Exact outage probabilities and throughputs were derived to evaluate the system performance of the proposed UTW-2TS-DNC and UTW-2TS-SC protocols. Simulation and analysis results provided discoveries of the performance improvements by increasing of the number of the cooperative secondary relays, the interference constraints, and the distances from the secondary network to the primary receiver. In addition, the proposed UTW-2TS-DNC and UTW-2TS-SC protocols achieved the best throughputs at optimal interference power allocation coefficients and optimal locations of the selected secondary relay. Considering the same power consumption, the UTW-2TS-DNC protocol performed better than the UTW-2TS-SC protocol. Finally, the analysis results of the outage probabilities and throughputs were validated by the Monte Carlo simulations.



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*Source: 8860551-2020-08-24.xml*