Secrecy Enhancement of Cooperative NOMA Networks With Two-Way Untrusted Relaying

The two-way relaying (TWR) technique has been confirmed to achieve higher spectral efficiency and average sum rate compared with the one-way relaying (OWR) technique in ultra-dense next generation networks with limited spectal resources. In this paper, an enhanced secrecy cooperative TWR scheme for cooperative non-orthogonal multiple access (NOMA) networks against untrusted relaying is highlighted. Specifically, with the application of NOMA principle, a base station (Bs) communicates with two trusted users, i.e., namely a near and a far users, where the communication with the far user takes place only via an untrusted relay (UR) employing both TWR and analog network coding (ANC) mechanisms. To minimize information leakage at the UR, the far user transmits its uplink signal simultaneously with Bs’s downlink signal to confuse the eavesdropping capability of the UR by increasing inter-user interference (IUI). To investigate the benefits of the proposed scheme, asymptotic lower bound expressions of the ergodic secrecy sum rate (ESSR) of uplink/downlink rates and their scaling law are derived to characterize the secrecy performance. The system parameters have been carefully studied to maitain the desired ESSR performance where we obtain an optimal value for the uplink power sharing coefficient with an arbitrary known value of the downlink one. Analytical and simulation results show that the proposed scheme can achieve scaling gain of $\boldsymbol {\frac {1}{8}\ln {\rho }}$ of positive ESSR over the untrusted OWR scheme with adaptive uplink/downlink jamming and a significant gain over the other conventional NOMA uplink/downlink schemes in two time slots of communication.


I. INTRODUCTION
The ever-extending massive connectivity, low latency, high spectral efficiency demands makes non-orthogonal multiple access (NOMA) techniques having the urgent necessity to be performed to break the orthogonality requirement in time/frequency/code resources by partially overlapping wireless signals with a tolerable level of interference [1]. In the context of increasing the multiplexing gain by exploiting different domains, NOMA have been recently classified into power-domain and code-domain NOMA. The key concept of the power-domain NOMA is to enable the The associate editor coordinating the review of this manuscript and approving it for publication was Xingwang Li . signals of multiple users to occupy the same resource block (time/frequency/code) but with different power levels. In particular, NOMA exploits superposition coding (SC) at the transmitters to transmit superimposed signals within the same resource while the receivers of better channel conditions carry out successive interference cancellation (SIC) technique to separate superimposed signals of the poorer ones before decoding their own signals [2]. Thus, NOMA can support massive connectivity [3], [4], achieve higher spectral efficiency [5]- [8] and improve the user fairness [9]- [11].
Cooperative NOMA is an effective approach to enhance the network coverage extension and the reception reliability of the users of poor channel conditions by exploiting the spatial diversity. Particularly, cooperative NOMA can VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ be classified in terms of the elements of the network into: user-aided and relay-aided cooperative NOMA. In user-aided cooperative NOMA, the users of better channel conditions act as a relay to enhance the reception capability of the users of poorer channel conditions as they previously have to decode the signals intended to the poorer users. There exist several studies concerning this topic [12]- [16]. In [12] the outage performance of user-aided cooperative NOMA was investigated where it was shown to be better than the noncooperative case. To improve the performance of cell-edge users in a cellular NOMA network, the cell-center users can act as relays in both half-duplex (HD) and full-duplex (FD) modes of operation to achieve a diversity gain [13]. Cooperative FD NOMA based user-aided relaying was proposed in [5], [14] to further save the resources and improve the spectral efficiency. Employing a user in cooperative relaying may consume its dedicated power and degrade its life time. Thus, energy harvesting (EH) techniques were exploited in cooperative NOMA which termed as simultaneous wireless information and power transfer (SWIPT) to compensate the user for the required power of relaying [15]. A joint power allocation and splitting factor design was proposed in [16] to enhance the system throughput and user fairness. On the other hand, relay-aided cooperative NOMA schemes have gained also a considerable attention in practical design of NOMA networks [17]- [19]. This can be implemented by deploying dedicated relays to increase the diversity. Coordinated direct and relayed transmission based cooperative NOMA was proposed in for both downlink and uplink communications [17], [18]. In [19] a multi-relay multi-antenna NOMA system was proposed to further increase the spectral efficiency.
The above contributions considered only one-way relaying (OWR) or unidirectional communication protocol which does not fulfill the dense mode of NOMA network operation. Twoway relaying (TWR) permits a simultaneous bidirectional communication to further improve the spectral efficiency. HD and FD TWR NOMA based networks were proposed in [20], [21] where the outage probability, diversity analysis and network throughput were derived and compared with OWR networks. A joint rate splitting and user grouping protocol for multi-pair TWR NOMA network was proposed in [22] for better utilization of resources and enhanced throughput. In [23] a joint antenna and relay selection scheme was proposed to enhance the transmission reliability for multiple access and time division broadcast relaying strategies in a TWR NOMA based networks where the optimal transmit power allocation was obtained.
However, due to the broadcast nature of wireless signals in a cooperative NOMA network, confidential information in this network is vulnerable to two main types of attack: 1) external eavesdropping: in which an illegitimate attacker that is not belonged to the network elements tries to overhear confidential signals and decode them for its own sake, 2) internal (untrusted) eavesdropping: in which a legitimate element in the network tries to decode confidential information of the other elements. There exist recent works that considered the external eavesdropping in NOMA networks. The secrecy performance and power allocation analysis was investigated in [24]- [28]. The beamforming design in multiple input single output (MISO) and multiple input multiple output (MIMO) NOMA networks to minimize information leakage was investigated in [29]- [35]. Exploiting relay selection and FD relaying techniques to confront external eavesdropping in cooperative NOMA networks was proposed in [5], [36]- [40]. Secure TWR NOMA based networks were also of a considerable interest. In [41], [42] the security issue of NOMA based TWR networks with artificial noise jamming (AN-jamming) were analyzed. However, the above works considered the external eavesdropping in NOMA networks while the impact of internal eavesdropping on the secrecy performance may be more dangerous as the network elements that share the same resource blocks may distrust each other. In the context of untrusted users, the authors of [43] investigated the case of untrusted far user that can decode confidential information of the near user via SIC where the secrecy outage probability of the near user and the outage probability of the far user were derived. The authors of [44] considered the case of multiple relay selection schemes to enhance the secrecy performance of a cooperative NOMA network of untrusted far user. The secrecy performance of a MISO NOMA system with untrusted far user was proposed in [30]. Unlike [30], [43], [44], two joint beamforming and power allocation schemes were proposed in [45] for a cooperative NOMA network with both untrusted near user and external eavesdroppers.
To enhance the secrecy performance in a HD untrusted OWR cooperative NOMA network, a novel NOMA-inspired jamming and relaying approach was proposed in [8] where the base station sends a superimposed mixture of destination and jamming signals and a positive secrecy sum rate can be always guaranteed. In [46], [47] the secrecy performance of cooperative NOMA networks with untrusted relay (UR) was studied in which a base station communicates with two users and one random user or the two users or the base station emit an AN-jamming signal to combat the UR. As the emitting of AN-jamming signal may degrade the eavesdropping capability of the UR, it may cause a simultaneous degradation in the reception quality of the other elements of the network. To overcome this issue, a novel secrecy-enhancing design for cooperative uplink/downlink NOMA with an UR was proposed in [48] where the near and far users send an adaptive jamming signal of a similar symbol structure. Thus, enabling legitimate users to cancel out the jamming signal while preventing the UR from eavesdropping.
However, in cooperative NOMA networks with multiple superimposed signals, the use of internal network interference can be a sufficient mean to degrade the eavesdropping capability and enhance the secrecy rate [49]. Thus, imposing an intended jamming signal may increase interference sources rather than combat eavesdropping which leads to inefficient information decoding at receivers, and this motivates our work as follows.

A. MOTIVATIONS AND CONTRIBUTIONS
The recent work of cooperative NOMA network with untrusted relaying focused on transmitting jamming signals simultaneously along with information signals to confuse eavesdropping against untrusted relaying. However, this may confuse the legitimate channels themselves and we have the following observations: • Exploiting inter-user interference (IUI) inherent in cooperative NOMA networks can deteriorate the eavesdropping capability more than confusing legitimate decoding of information signal. Therefore, IUI can play the role of cooperative jamming by performing a tradeoff design between the minimization of IUI at legitimate receivers and the maximization of IUI at the eavesdroppers to enhance the secrecy performance. This can be achieved by hindering SIC at the eavesdropper, particularly, by mixing a superimposed version of adaptive jamming and information signals, i.e., making a composite signal, at the UR. Consequently, the UR cannot be able to determine the decoding order of the mixed signal which can significantly degrade its ability to retrieve the confidential information signals coherently.
• Employing TWR in cooperative NOMA networks enables a bidirectional communication which leads to better utilization of the resources and recover the spectral efficiency loss inherent to OWR. In addition, combining TWR with NOMA forces the UR to exchange a dense information between nodes against the facility of its decoding process. Motivated by the previous observations, in this paper, we propose an enhanced secrecy performance of uplink/ downlink cooperative TWR NOMA network against untrusted relaying. In particular, the base station (Bs) communicates with the near (NU) and the far users (FU) where the communication with FU takes place by untrusted TWR. The main contributions can be summarized as follows: • An uplink/downlink cooperative TWR NOMA scheme against untrusted relaying is proposed in which Bs transmits a superimposed downlink signal for NU and FU where the communication to FU takes place via an UR. Meanwhile, FU transmits its uplink signal to the UR. The received signals at the UR incurs an IUI with unknown decoding order which impair the ability of the UR to separate and decode the composite signal and confuses its eavesdropping capability. Then, amplify and forward (AF) relaying is employed at the UR to forward the received signals to the destinations. To this end, an unavoidable level of IUI can be created at the UR when it tries to decode each user symbol coherently while the decoding quality at legitimate users is not affected.
• To evaluate the secrecy performance and investigate the benefits of the proposed scheme, an analytical expression of a lower bound on the uplink/downlink ergodic secrecy sum rate (ESSR) is derived. We demonstrate that a positive ESSR can be guaranteed by the proposed scheme with the least utilization of resources to complete an uplink/downlink communication. To gain more insights, an asymptotic scaling law of the ESSR is determined at high ρ where ρ is the transmit signal to noise ratio (SNR). It can be clarified that the proposed scheme can achieve an uplink/downlink scaling gain of ln ρ over two time slots of communication. Furthermore, the simulation results confirm the accuracy of the derived formulas and the superiority of the proposed scheme over the benchmark schemes.
• We obtain an optimal value of the uplink sharing power coefficient that maximizes the ESSR for an arbitrary constant value of downlink power coefficient to investigate the impact of IUI on the eavesdropping capability of the UR. First, we prove that the ESSR is a unimodal maximal function, then, the optimal value is obtained by carrying out an iterative algorithm based on the golden search method.

B. ORGANIZATION
The reminder of the paper is organized as follows.
In section II, we present the proposed cooperative TWR NOMA scheme with its design structure and channel modeling. The secrecy performance evaluation is investigated in section III and verified by simulation results in section IV. Then, the paper is concluded in section V.

II. SYSTEM MODEL AND DESIGN
Consider the security issue of a cooperative TWR NOMA wireless network that consists of one base station, Bs, the near user, NU and far user, FU, 1 that communicates with Bs via an AF-UR employing TWR and analog network coding (ANC) [50] techniques as shown in Fig.1. All these nodes are equipped with a single antenna and operate in HD mode of operation. It is assumed (as in [17]) that the link between Bs and FU is absent due to heavy shadowing loss and only the AF-UR is responsible for delivering information between Bs and FU. However, the UR is only trusted at the service level while it is not allowed to decode any confidential information at the data link processing level. This means that the UR is only permitted to perform AF protocol TWR that involves reliable channel state information (CSI) feedback and estimation as well as signal amplification and forwarding (e.g., it is assumed that full CSI is owned by the transmitting nodes via pilot estimation processes prior to information transmission [48] 2 ). To this end, the UR may try to intercept confidential information exchanged between nodes during 1 Two user NOMA model has been adopted by the third generation partnership project long-term evolution (3GPP-LTE) to minimize large inter-user interference and complex analysis inherent to multi-user NOMA model for practical implementation of cooperative NOMA networks, e.g., see [3]. 2 We will discuss a two-step CSI pilot estimation in subsection D. uplink/downlink communications for its own sake. Hence, it is necessary to minimize the information leakage at UR. 3 To do this, FU simultaneously exploits transmitting its NOMA uplink signal as a noise signal to increase IUI at the UR and impair its eavesdropping capability. From a practical perspective, the proposed scheme can be vastly founded in some applicable cellular networks. The intended network can consist of a Bs which is capable of exchanging information with a pair of two types of residential and roadway users. The Bs is directly linked to the residential user whereas it communicates with the roadway user via an UR located near the road signs. Each type of user has a hierarchical secrecy demand against the UR which can be curious to decode its received signals before forwarding them. Thus, the transmission rates are dynamically determined by the transmit nodes to maintain those secrecy demands.
The communications' channels are assumed to experience independent and identical distributed (i.i.d) quasi-static fading, i.e., channels' coefficients remain constants within a resource block of time but independently vary from block to another. Each uplink/downlink and relaying transmission is bounded by a transmit power budget of P while an additive white Gaussian noise (AWGN) is considered at each receiving node with mean equals to zero and variance equals to N 0 .
Considering channel reciprocity, let the channel coeffi- RF and h NF , respectively, follow circularly-symmetric complex Gaussian random variables with zero means and variances equal to . This means that = |h i | 2 follows an exponential distribution with normalized average channel gains λ i i.e., λ i , i ∈ {BN , BF, RN , RF, NF}.
Two communication phases (two time slots) are needed to complete information uplink/downlink transmission. This 3 Here, we consider the AF relaying protocol in the two-way scheme due to the following reasons: 1) AF relaying protocol is easy to implement where ANC can be applied efficiently to mix analog signals and reduce resource utilization; and 2) at low SNR, the AF relaying protocol can achieve better secrecy sum rate whatever the distance between Bs and UR is, e.g., see [46,50]. Furthermore, by exploiting the HD TWR, a positive secrecy capacity can be strictly achieved as we will see in the next section. can be described in the following two subsections where the system parameters used in this paper are summarized in Table 1.

A. FIRST PHASE
In this phase, Bs transmits simultaneously its downlink symbols x ND and x FD of NU and FU with power sharing coefficients of α and 1 − α, respectively, straightforwardly to NU and UR where E |x ND | 2 = E |x FD | 2 = 1. Meanwhile, FU transmits its uplink symbol which represents a background noise symbol at the UR, i.e., x FU , with a power sharing coefficient where E |x FU | 2 = 1. It is noted that NU shares the same uplink power budget, P, with FU with a power sharing coefficient of 1 − . Different from the cooperative AN-jamming schemes considered in the literature, e.g., see [46], where the AN relies on pseudo-random signals, FU generates its uplink signal as a noise background signal of deterministic waveform to the UR, e.g., x FU , which can easily decoded by NU relying on its captured characteristic during CSI estimation.
Following the NOMA principle, Bs transmits the signal P intended for its uplink communication as a background noisy signal at the UR. Thus, the received signal at UR and NU can be respectively expressed as where P is the transmit power,n R , n N ∼ CN (0, N 0 ), N 0 is the thermal noise variance of the receiving nodes. Without loss of generality, we assume that UR and NU are more close to Bs than FU in the sense that λ BN λ RF and λ BR λ RF . Thus, the SIC decoding order starts from x B towards x F . Particularly, the UR carries out a complex joint maximum likelihood (ML) detection 4 to decode its received composite signal and achieve better eavesdropping capability in a two-step decoding algorithm. In the first step, the UR tries to decode x FD by treating both x ND and x FU as interference then it subtracts x FD from its observation before the attempt of decoding x ND and x FU . In the second step, after a successful wiretapping of x FD , the UR performs SIC one more time to decode x ND by treating x FU as a noise before acquiring x FU . In the composite signal, x ND can indeed represent an additional interference when decoding x FU which can present an over-estimated capability of eavesdropping at the UR. Thus, the achievable rates for decoding x FD , x ND and x FU at the UR can be respectively expressed as where ρ P N 0 is the transmit signal to noise ratio (SNR) of the transmit power budget P. Recall that the uplink and downlink transmit power is bounded by P as P uplink ≤ P and P downlink ≤ P.
Depending on the previous knowledge of the CSI about x FU , NU can subtract x FU from its observation such that the achievable rates for decoding x FD and x ND at NU can be respectively expressed as 4 It is assumed that R can perform a complex joint ML detection to separate and remove IUI and decode the information signals correctly [8]. If the UR can perform more intelligent signal decoding techniques, such as the joint separation decoding technique, to indiviually separate the intended signals, the secure transmission may fail, and thus, the injection of a friendly jammer should be carried out to impair the decoding quality at the UR while the other nodes can decode their intended signals separately.
As such, we have considered in the first phase the overestimated capability of eavesdropping at the UR which provides a performance lower bound for the proposed system [8], [48].

B. SECOND PHASE
In this phase, the UR forwards an amplified version of its received signals to do its main function without analyzing the entire information contents. Meanwhile, NU transmits its uplink symbol x NU to Bs with a power allocation coefficient of 1 − . By exploiting the HD characteristic of the untrusted TWR, the transmission of the uplink signal containing x NU is completely secured so that x NU can not be eavesdropped by the UR as it is not able to transmit and receive at the same time. Thus, the received signal at Bs and FU can be respectively given by ANC and prior estimation cancellation term where g BR + g RF +1/ρ denotes the amplification factor of the UR and n B ∼ CN (0, N 0 ) and n F ∼ CN (0, N 0 ), where N 0 is the thermal noise variance of the receiving nodes, denote the AWGN at Bs and FU.
Since Bs has a prior knowledge of the self-amplified version of its transmitted signal, it can cancel out the term from its observation by using ANC and prior estimation cancellation techniques. Without loss of generality, it is assumed that the received uplink signal power of x NU is larger than that of x FU due to its close proximity to Bs. 5 Therefore, the decoding sequence at Bs is considered to start from After performing the NOMA SIC decoding technique, the achievable rates for decoding x FU and x NU at Bs can be respectively expressed as On the other hand, FU has a prior knowledge of its selfretransmitted signal, as well as, the interference signal from NU, so that it can easily cancel out the term h 2 P (1 − ) from its observation by using ANC technique. Recall that NU should be previously able to decode x FD according to (6) before decoding its own downlink signal which means that the achievable rate for decoding x FD at FU should be no more than C x FD N . From (6) and (9), the achievable rate for decoding x FD at FU can be expressed as where are the signal to interference noise ratio (SINR) for decoding x FD at NU and FU, respectively.

C. ERGODIC SECRECY SUM RATE (ESSR)
To characterize the statistical effectiveness of the proposed scheme, the ESSR is adopted as a secrecy performance metric. The ESSR is defined as the rate beyond which a secure communication rate can be available. The ESSR and a lower bound on the ESSR are mathematically given by where {A} + max (0, A), for arbitrary A and (a) is based on Jensen's inequality as in [8]. Remark 1: The proposed scheme can guarantee a positive secrecy sum rate. This is enabled by exploiting the HD characteristic of the TWR which reveals the term C x NU B is out of the eavesdropping capability. Different from [46], [48], the proposed scheme confirms achieving a secure performance mode to the premier uplink symbol, i.e., x NU , while completing an uplink/downlink communication in only two time slots.

D. CSI REQUIREMENTS
To obtain the required CSI prior to the uplink/downlink transmission process, a channel training mechanism is adopted at the transmitting nodes comprised of a two-step training mechanism with a transmission of six pilots.
Firstly, Bs needs to estimate g BN , g BR , g RN and g RF in order to adjust the achievable rates for x ND and x FD while FU needs to estimate g BN , g BR , g RF and g NF in order to adjust the achievable rate for x FU and the proper value of . Then, NU needs to estimate g BN in order to adjust the achievable rate for x NU according to the power budget, i.e., (1 − ) P. The training steps are described as follows:

III. ESSR PERFORMANCE ANALYSIS
In this section, we provide a detailed analysis on the secrecy performance of the proposed system in terms of the ESSR.
In particular, we derive analytical expressions for lower bound and asymptotic lower bound of the ESSR of the proposed scheme which represent a sufficient approach to determine the secrecy benefits of the proposed scheme. Furthermore, we obtain the optimal value of the power sharing coefficient of the uplink transmission, i.e., , to maximize the ESSR relying on the iterative golden search algorithm [51] given a fixed value of the power coefficient of the downlink transmission, i.e., α.

A. A LOWER BOUND ON THE ESSR
To proceed forward, we use the definition of average rate (ergodic rate), i.e., E (C X ) E X (log (1 + x)), for a nonnegative random variable X as [52] where F X (x) and f X (x) are the cumulative density function (CDF) and the probability density function (PDF) of the random variable X, respectively. Theorem 1: A closed-form approximate expression for the lower bound of the ESSR, i.e., C lower ESSR , can be given by (17) at the bottom of the next page, where C BR = λ BR α, C RF = λ RF , C BN = λ BN α and λ k , k = 1, . . . , 5 are given in Appendix A.
Proof: See Appendix A. The above theorem provides an efficient approach to scale the secrecy performance of the proposed scheme in terms of some evaluations of simple functions. To give more insights about the impact of the system parameters and the feasibility of proposing TWR scenario upon the system to improve both reliability and security issues, we investigate the asymptotic scaling behavior of the ESSR of the proposed system when ρ grows to infinity.
To deal with, the approximations e 1/x ≈ 1 + 1/x and Ei (−1/x) ≈ − ln x can be used in (17) [48] with cooperative jamming and a scaling gain 1 2 ln ρ over the same system without cooperative jamming whereas it can offer the same uplink ESSR scaling gain of 1 4 ln ρ over the scheme proposed in [18]. This means that the proposed system can achieve an overall uplink/downlink ESSR scaling gain of 1 8 ln ρ over the adaptive uplink/downlink one-way relaying NOMA network proposed in [48] with the least utilization of resources.

B. THE OPTIMAL VALUE OF THE UPLINK/JAMMING COEFFICIENT *
In this subsection, we focus on finding out an optimal value of that maximizes the ESSR (e.g., C lower ESSR ) of the proposed system with arbitrary fixed values of Bs's power sharing coefficient, i.e., α, and uplink/downlink transmit power budget, i.e., P. 6 6 Unfortunately, a more general jointly optimal power allocation problem of ( ,α) can be considered to maximize the ESSR of the proposed scheme which is beyond this work.
In particular, it is desired to determine an optimal value * that satisfies the following optimization problem * = arg max C lower ESSR , such that { , α} ∈ [0, 1] , In fact it is very difficult to obtain * analytically due to a certain composite structure of C lower ESSR . Instead, we divide the main problem into a problem of a simple structure of C lower ESSR based on a desired secrecy performance mode. Then, we investigate that C lower ESSR has at most one maximal critical point under a certain condition on ∈ [0, 1]. Then, we find out the optimal value * by the utilization of the golden search algorithm for finding a maximum of a function.
First, we investigate that C lower ESSR combines an algebraic sum of monotonously increasing and decreasing functions of , then, we obtain * from the combined function as follows.
Based on the expression of C lower ESSR in (15), we consider the condition where a secrecy performance mode for all x ND , x FD , x NU and x FU symbols can be achieved, i.e., {A} + A. This leads to the following optimization problem * where C lower Theorem 2: Following the methodology of obtaining C lower ESSR in (15), C lower ESSR is a sum of two monotonically decreasing and increasing functions of and we have the following modified optimization problem * = arg max C lower ESSR , such that α ∈ [0, 1] , P constant, Proof: See Appendix C. Remark 3: It is noted that the determination of the maximum critical point inside [max (0, 1 ) , min (1, 2 )] depends basically on both the sum of the increasing rate of E (C I ) and the decreasing rate of E (C D ) with respect to . In other words, there exists only one maximum point * that can be found out within [max (0, 1 ) , min (1, 2 )] according to the rate of the sum of E (C I ) and E (C D ). Regarding (17), it is very difficult to obtain an analytical expression for * with respect to the parameters of C lower ESSR . Instead, we propose an iterative optimized algorithm based on the golden search method [51] to obtain a very convergent value of * .
The algorithm is summarized in the following steps as shown in Algorithm 1.

Algorithm 1 Iterative Algorithm for Determining * Based on the Golden Search Method
Input: α, ρ, g BR , g RF , g BN , u 1 = 10 −3 , N iter. = 0 and a maximum tolerance ε = 10 −4 . 1: Calculate: 1 , 2 , In this section, we provide numerical results to validate the analytical results of our enhanced secrecy performance scheme for TWR based cooperative NOMA network with UR via Monte Carlo simulations with 10 4 iterations. In particular, we discuss the secrecy performance point of view of the proposed scheme in terms of the state of art schemes that concern the untrusted relaying based NOMA and OMA networks.
In terms of the uplink/downlink ESSR performance, we compare our proposed scheme with three benchmark schemes described as follows: 1) The adaptive uplink/downlink cooperative jamming NOMA based network proposed in [48]: In this scheme, Bs uses the NOMA principle to send a downlink superimposed signal, i.e., x ND √ Pα + x FD √ P (1 − α), to communicate with NU directly and FU by the aid of a one-way HD UR. Meanwhile, FU emits an adaptive structured jamming signal during its idle state to overcome information leakage at the UR. This adaptive jamming signal has the same symbol structure as the NOMA symbol structure and it is well-known to the corresponding receivers. Then, the UR uses the AF technique to forward its received signal. 7 Meanwhile, Bs sends another information signal to NU. In the uplink communication, both NU and FU sends their information signals to Bs and the UR, respectively. Meanwhile, NU emits in parallel a superimposed adaptive jamming signal with its information signal. Then, the UR amplifies and forward its received signal. Meanwhile, NU sends another information signal to Bs. It has been verified that the proposed system in [48] outperform the proposed system in [17,18] without adaptive jamming signals.
2) The uplink/downlink NOMA based network with destination aided AN-jamming proposed in [53]: Different from the previous proposed scheme [48] Fig. 2 the detection capability of the TWR system under PAR1 by discussing the probability of miss detection (PMD) of the symbol x FU when the UR employs the joint complex ML detection algorithm. In Fig. 2, the PMD of Bs and the UR are plotted versus ρ when the joint complex ML detection is employed for a predetermined values of g BR and g RF . It is evident that the PMD of Bs decreases rapidly and faster than the UR when the analytical i.e., or equivalently the condition αρ 2 g BR −ρ (g BR + g RF )−1 > 0 is met and the PMD gap increases with ρ. This means that and α should be carefully designed in order to achieve a positive secrecy rate for x FU .
To start a comparative study on the secrecy performance between the proposed and the benchmark schemes. The lower bound of the ESSR (i.e., C lower ESSR ) of the proposed and the benchmark schemes are computed firstly by summing up the uplink and downlink secrecy rates. In Fig. 3, the analytical and simulation results C lower ESSR for the proposed and benchmark schemes are plotted under PAR1 versus ρ. It is evident that C lower ESSR of proposed scheme converges to the scale of lnρ in high ρ regime whereas benchmark 1 scheme converges to the scale of 7 8 ln ρ in high ρ per two time slots of an uplink/downlink communication. Furthermore, it is evident that benchmark 2 reaches a floor value at high ρ. This is because the transmitted AN-jamming signal x z an unknown structure at the receiving nodes, degrades the reception quality regardless of confusing the eavesdropping capability of the UR. Benchmark 3 scores the worst C lower ESSR performance among the comparative schemes. This is because it needs at least six time slot resources to complete an uplink/downlink communication. This emphasize that the proposed scheme yields the highest C lower ESSR with the least number of resources of a completed uplink/downlink communication.
To illustrate the impact of variation of the system parameters on the C lower ESSR of the proposed scheme, the derived formula in (17) and the simulation analysis of C lower ESSR are plotted in Fig. 4 for two different channel gain settings, i.e., namely, the previous PAR1 settings, when λ i = 0.5 (i.e., denoted as PAR2), i ∈ {BN , BF, RN , RF, NF}) and when λ RF = 0.3 and all λ i = 0.5, (i.e., denoted as PAR3), i ∈ {BN , BF, RN , NF}). It is observed that the slope of the C lower ESSR curve in both scenarios converges the scale of lnρ in medium to high range of ρ. This emphasizes that the proposed scheme can achieve ESSR scaling gain of lnρ. Moreover, it is  evident that the derived formula of C lower ESSR in (17) agrees well with its corresponding simulation result which verifies the asymptotic convergence of this analytical formula. Fig. 5 depicts the optimal value of the uplink/jamming sharing coefficient ( * ) of the proposed C lower ESSR by using the method of golden search algorithm with ρ = 10. It is evident that there exists one and only one maximum value of within ∈ [ 1 , min (1, 2 )] when the secrecy performance of x ND , x FD , x NU and x FU symbols can be achieved as C lower ESSR is a unimodal maximum of . Considering the impact of g RF on the performance, Fig. 5 is plotted for two different λ RF settings, i.e., λ RF = 1 shown in Fig. 5a and λ RF = 0.5 shown in Fig. 5b, while λ i = 0.5 for i ∈ {BN , BF, RF, NF}) where we consider that 1 > 0, 2 > 1. Although the increasing of g RF makes the symbol x FU vulnerable to be eavesdropped by the UR, it can greatly increase the IUI within the composite signal received by the UR, and therefore, it can impair the eavesdropping capability of the UR and improve the overall lower bound of the ESSR, e.g., C lower ESSR . VOLUME 8, 2020

B. DISCUSSION AND FUTURE WORK
In this subsection, further discussion is added to clarify the impact of different system parameters on the secrecy performance and investigate how the proposed scheme can be extended to more general systems of practical considerations. It is worthy noting that the proposed scheme relies basically on imposing unordered composite signal to increase IUI and impair the decoding quality at the UR. Thus, system parameters should be carefully designed to unleash the benefits of deploying TWR technique into the UR to achieve the desirable level of secrecy performance in the end to end uplink/downlink communication process.
On one side, it can be observed that g RN has no impact on the secrecy performance (i.e., or equivalently the ESSR) of the proposed scheme as NU has a prior knowledge about both x B and x F signals to extract its downlink signal, i.e., x ND , whereas its uplink signal, i.e., x N , cannot be eavesdropped by the UR due to its HD limitation.
On the other side, g RF has a crucial impact on the ESSR of the proposed scheme. It is cleared that large value of g RF makes the uplink signal x F more vulnerable to be eavesdropped by the UR whereas small value of g RF sacrifices the interference level at the UR when it tries to decode the superimposed x B signal for its own sake.
Furthermore, g BR (i.e., λ BR ) is an important parameter of determining 1 and 2 which should be carefully designed to maintain the desired secrecy performance of x ND , x FD , x NU and x FU . In particular, for a specific α, should be designed within the range of max (0, 1 ) < < min (1, 2 ). Additionally, λ BN should be also designed in the sense that the spatial location of NU is closer to Bs than the others in order to increase the ESSR.
However, if those certain parameters cannot be controlled, an external injection of a friendly jamming signal should be devised or even switching the UR to perform OWR technique [48] with cooperative jamming.
The proposed scheme can be extended to multi-user multiantenna systems. In particular, the multi-user system can provide higher degrees of freedom and diversity gain to enhance the ESSR by a joint user and jamming scheduling design [55]. In multi-antenna systems, joint beamforming and power optimization with cooperative jamming can be applied to further achieve better ESSR in delay-tolerant secrecysensitive scenarios.
Considering global CSI availability at Bs, the proposed scheme can serve to schedule random users according to their current locations from Bs. In particular, a circular zone centered at Bs with a coverage radius equals to the distance between Bs and the UR can be invoked in the scheduling process. Thereafter, the user located within this zone can be scheduled as NU, otherwise, the user is scheduled as FU. And therefore, mobile users can decide to switch back and forth to the UR according to their current location inside and outside the zone.
Another direction of practical implementation can be extensively applied to the proposed scheme with imperfect CSI where novel multi-pair, multi-user and multi-antenna joint selection strategies can be performed to maintain different secrecy targets for users of different secrecy performance levels [56]. In general, integrating those strategies into the proposed scheme can significantly enhance the ESSR.

V. CONCLUSION
In this paper, we proposed an enhanced secrecy performance scheme of cooperative uplink/downlink NOMA networks against untrusted relaying. To save resources and prevent eavesdropping, TWR and IUI techniques were exploited at the UR to intensify the exchange of information signals and confuse the eavesdropping capability at the UR, respectively.
To reveal the merits of the proposed scheme, we derived an analytical expression for the lower bound of the uplink/downlink ESSR and verified it by simulation results. The results demonstrated that the proposed scheme can achieve an improvement in the uplink/downlink ESSR than the benchmark schemes with the least utilization of resources. Furthermore, we obtained an optimal value for the uplink power sharing coefficient by holding an iterative algorithm based on the golden search method.

APPENDIX A PROOF OF THEOREM 1
To find out a closed form expression for C lower ESSR , we firstly have to derive mathematical formulas for αρg BR +1 , then, we can obtain the desired formulas as follows.
By substituting by β (g BR + g RF + 1/ρ) − 1 2 , X FU and X NU can be rewritten respectively as Based on the above, the CDF of X ND can be expressed as where P(.) is the probability function. Hence, E C x ND R can be obtained as Consequently, E C x FU R can be simply obtained as E C x ND R by interchanging λ BR by λ RF and ρ by . Furthermore, the CDF of Y FD can be expressed as and E C x FD R can be obtained as After applying some algebraic manipulations, the method of undetermined coefficients as used in [57]- [59] and using [ [54], 3.352. [2][3][4][5], we arrive at In this regard, the CDF of X FU ρ g BR g RF (2g BR + g RF +1/ρ) can be accordingly expressed as x, ρ, )) , is the modified Bessel's function of the second kind. It is noted that we use VOLUME 8, 2020 [[54], 3.324.1] and the substitution ρy − 2x = t in (A. 7) where the condition y > 2x/ ρ should be satisfied.
Recall that we focus on the lower bound of the ESSR, then, K 1 (x) can be upper-bounded by K 1 can be simply obtained as and γ x FD F , whereas the lower bound for the minimum tends to a lower bound. Thus, the CDF of X FD can be expressed by the following probability According to (12), P 1 can be obtained as e whereas P 2 can be obtained after substituting for β in (12) as Substituting into (A.10), we can get the CDF of X FD as x, ρ, )) . (A.12) Recall that we search for a lower bound of the ESSR in the sense that we can making the use of the relation K 1 (x) ≤ 1/x when ρ → ∞ to simplify the analysis. Then, E C x FD F can be expressed as where step (d) follows by letting (1 − α − αx) = 1/u and Finally, the CDF of X NU ρg BR g RF +2g BR + g RF +1/ρ can be evaluated as where we can making the use of the relation can be simply obtained as 16) where in step (g) follows after performing some algebraic manipulations, λ 4 ( ) = (1 − ) λ BN and λ 5 ( ) = 1 λ BR − 1 λ RF . This completes the proof.

APPENDIX B PROOF OF COROLLARY 1
At high transmit SNR, based on (15) and (17) can be regarded to scale as a constant with the ever increase of ρ as Y FD , Y ND , Y FU and X NU approach a constant value with ρ → ∞, respectively.
Furthermore, by utilizing the approximations e 1/x ≈ 1 + This completes the proof.

APPENDIX C PROOF OF THEOREM 2
Recall that the secrecy performance of x ND , x FD , x NU and x FU can be achieved. It is evident from (4) and (8)  αρg BR +f 2 ( ) , where f 1 ( ) = g BR g RF + 1 + + 1/g RF ρ and f 2 ( ) = ρg RF + 1. Since we consider the condition where a secrecy performance mode is achieved, i.e., when {A} + A, the term E C x FD F − E C x FD R is a monotonically increasing function of when f 1 ( ) increases slower than f 2 ( ). Otherwise, the term E C x FD F − E C x FD R 0, e.g., no secrecy performance for x FD can be achieved. In other words, the condition f 1 ( ) − f 2 ( ) = g BR g RF + (1 − ρg RF ) + 1 g RF ρ < 0 must be hold to guarantee that a secrecy performance for x FD can be achieved. Furthermore, the condition (1 − ρg RF ) < 0, i.e., or equivalently g RF > 1/ρ, can guarantee that the term E C x FD F − E C x FD R is a monotonically increasing function of . Consequently, the term E C x FD F − E C x FD R is a monotonically increasing function of with positive secrecy performance when both g RF > 1/ρ and > ρg BR +1 g RF ρ(ρg RF −1) are satisfied.
Next, we discuss the monotonicity of the term . It is evident from (5) and (12)  Finally, it is evident from (11) that the term E C x NU B 1 2 log 1 + (1− )ρg BN (g BR + g RF +1/ρ) ρg BR g RF +2g BR + g RF +1/ρ is a monotonically decreasing function of . Combining the above discussion and using the fact that the sum of monotonically increasing (or decreasing) functions is also an increasing (or decreasing) function, it is evident that C lower ESSR is a sum of two monotonically decreasing and increasing functions of and the first part of the proof is completed. Let Recall that E C x NU B is a monotonically decreasing function of which can be rewritten after some algebraic manipulations as E (C D ) ≡ log 2 −D 1 + D 2 + D 3 , where D 1 , D 2 and D 3 are arbitrary coefficients independent of . Thus, E (C D ) is a strictly decreasing function of ∈ [0, 1]. Furthermore, E (C I ) can be further rewritten after some algebraic manipulations as E (C I ) ≡ log 2 I 1 3 +I 2 2 +I 3 +I 4 I 5 4 +I 6 3 +I 7 2 +I 8 +I 9 , where I 1 to I 9 are arbitrary positive coefficients independent of , then, E (C I ) has negative roots and it comprises a sum of monotonically increasing functions of with positive secrecy performance of x ND , x FD and x FU if and only if > ρg BR +1 g RF ρ(ρg RF −1) and < g BR (αρg BR −1)−1/ρ g RF . Thus, E (C I ) is a strictly increasing function of ∈ [max (0, 1 ) , min (1, 2 )], where 1 = ρg BR +1 g RF ρ(ρg RF −1) and 2 = g BR (αρg BR −1)−1/ρ g RF . Consequently, C lower ESSR ≈ E (C D ) + E (C I ) has at most one maximal critical point of , ∈ [max (0, 1 ) , min (1, 2 )] and the second part of the proof is completed.