On Security and Throughput for Energy Harvesting Untrusted Relays in IoT Systems Using NOMA

In this paper, we analyze the secrecy and throughput of multiple-input single-output (MISO) energy harvesting (EH) Internet of Things (IoT) systems, in which a multi-antenna base station (BS) transmits signals to IoT devices (IoTDs) with the help of relays. Specifically, the communication process is separated into two phases. In the first phase, the BS applies transmit antenna selection (TAS) to broadcast the signal to the relays and IoTDs by using non-orthogonal multiple access (NOMA). Here, the relays use power-splitting-based relaying (PSR) for EH and information processing. In the second phase, the selected relay employs the amplify-and-forward (AF) technique to forward the received signal to the IoTDs using NOMA. The information transmitted from the BS to the IoTD risks leakage by the relay, which is able to act as an eavesdropper (EAV) (i.e., an untrusted relay). To analyze the secrecy performance, we investigate three schemes: random-BS-best-relay (RBBR), best-BS-random-relay (BBRR), and best-BS-best-relay (BBBR). The physical layer secrecy (PLS) performance is characterized by deriving closed-form expressions of secrecy outage probability (SOP) for the IoTDs. A BS transmit power optimization algorithm is also proposed to achieve the best secrecy performance. Based on this, we then evaluate the system performance of the considered system, i.e., the outage probability and throughput. In addition, the impacts of the EH time, the power-splitting ratio, the numbers of BS antennas, and the numbers of untrusted relays on the SOP and throughput are investigated. The Monte Carlo approach is applied to verify our analytical results. Finally, the numerical examples indicate that the system performance of BBBR is greater than that of RBBR and BBRR.


I. INTRODUCTION
The Internet of Things (IoT) has attracted the attention of many researchers worldwide [1]- [3]; the main drive behind the future IoT relates to smart sensor technologies, including in farm monitoring, vehicular tracking, healthcare, and industrial environments [4]- [6]. Although the term IoT has been around for almost a decade, the corresponding technologies The associate editor coordinating the review of this manuscript and approving it for publication was Jun Wu . and protocols, such as massive connectivity, energy constraints, scalability and reliability limitations, and security, are still open research issues [7]- [9].
An important problem caused by the usage of massive IoT devices (IoTDs) is spectrum scarcity [5]. The nonorthogonal multiple access (NOMA) technique has been used as a promising solution to overcome this drawback. This is because NOMA can increase the connectivity and improve spectrum utilization in IoT systems [10]. For example, E. Hossain et al. investigated the system on a large scale using NOMA and concluded that NOMA not only improves spectral efficiency but also increases power efficiency [10]. I. Khan et al. proved that NOMA is a promising approach for future mobile Internet and IoT applications, which will require handling enormous increases in data traffic, massive connectivity, and low latency [9].
Furthermore, NOMA is able to simultaneously support users with good channel conditions as well as users with poor channel conditions by using the same bandwidth resources [11]. In addition, some works have compared the system performance of orthogonal multiple access (OMA) and NOMA [12]- [14]. For instance, Z. Chen et al. evaluated the system performance of NOMA and OMA by mathematical proof [12], while M. Zeng et al. compared NOMA and OMA for multiple-input multiple-output (MIMO) systems [13]. They concluded that the system performance of NOMA is better than that of OMA.
Energy consumption is actually another critical issue in IoT systems because of IoTDs' resource limitations [15]. Energy harvesting (EH) has emerged as a possible solution to meet the energy demands of IoT systems [7]. Thus, many works have focused on the perspective of EH usage in the IoT era [15]- [18]. For instance, N. Garg et al. introduced a survey on EH for IoTDs. They presented EH considering different energy sources and their comparisons. They then concluded that EH using solar or wind can obtain energy with very high efficiency; however, such harvesting is not available during night or in high-density building areas, respectively; in addition, EH from radio frequency (RF) is suitable for the IoTs due to its high availibility [15].
B. Alzahrani et al. introduced a resource management scheme for IoT systems with RF EH. The simulation results indicated that RF EH can increase the energy efficiency of IoT systems [16]. X. Song et al. investigated down-link NOMA networks and proposed a power allocation scheme to improve the energy efficiency with imperfect channel state information (CSI) [18]. Furthermore, D. D. Tran et al. investigated a multiple-input single-out (MISO) IoT system with simultaneous wireless information and power transfer, where the considered system consists of a multiantenna BS, multiple energy-limited relay clusters, and multiple IoTDs. Through Monte Carlo simulations, they showed that better system performance is obtained as the number of transmit antennas and relays increases [19].
To improve the scalability and reliability of IoT systems, cooperative relaying in which relays can be employed to support transmission from a base station (BS) to an IoTD, has been shown to be an effective method [20]. Note that relays can operate in two ways: to amplify and transmit the signal received from the source with a suitable power amplification coefficient by using amplify-and-forward (AF) techniques or to transmit the decoded signal using decode-and-forward (DF) techniques [19].
Unfortunately, the relays do not have the same security characteristics as the BS-IoTD pair since they belong to a heterogeneous network in certain scenarios [21], such as in a network consisting of networks used by a government or a financial institution whereby not all IoTD have the same level of security [20]. Thus, the relay can become an eavesdropper (EAV), i.e., an untrusted relay [22], [23]. This leads to confidential information possibly being monitored by the untrusted relay. Therefore, DF is not recommended since this technique requires that the untrusted relay decode the message before forwarding it to the IoTDs, i.e., AF is preferred [20], [21].
Due to the presence of untrusted relays, communication security is also a major challenge to IoT systems [20]. Traditional cryptographic encryption has been applied to overcome this reliability limitation. However, key distribution and management issues in IoT systems are difficult to control since these systems have massive numbers of resource-constrained IoTDs and different subsystems controlled by distinct operators [5].
As a result, physical layer secrecy (PLS) with high efficiency is an appealing approach for enhancing the secrecy performance in the IoT [5], [24]- [26]. The primary idea of PLS is exploiting the wireless channel characteristics to keep the confidential message from the EAV. For example, H. Hu et al. focused on the problem of secure communication between the IoTD and BS via the EH untrusted relay with the AF technique. The secrecy performances of the system were evaluated through the PLS in terms of the probability of successfully securing transmission [5]. L. Lv et al. introduced a novel NOMA-inspired relaying scheme using the AF technique to improve the PLS of untrusted relay networks. They then evaluated the PLS of their considered system by deriving an analytical expression for a lower bound on the ergodic secrecy sum rate [26].
To the best of our knowledge, RF EH untrusted relays in MISO IoT system using NOMA have not been studied extensively in recent works. Thus, in this paper, we consider PLS and throughput for a NOMA IoT system that consists of multi-antenna BS, multiple untrusted relays, multiple IoTDs with imperfect CSI. The primary contributions of this paper are summarized as follows: • We introduce a communication process in a MISO IoT system with multiple AF EH untrusted relays.
• We investigate three cooperative TAS and relay selection schemes, i.e., the best-BS-random-relay scheme (RBBR), random-BS-best-relay scheme (BBRR), and best-BS-best-relay scheme (BBBR), to analyze and compare the considered system securities.
• We derive closed-form expressions of the secrecy outage probability (SOP) with imperfect CSI by using statistical characteristics of end-to-end signal-tointerference-plus-noise ratio (SINR) for the three considered schemes. Based on the SOP, an optimal and convergent transmit power algorithm for the BS is proposed.
• We derive closed-form expressions of the outage probability and throughput for the three considered schemes. Accordingly, the system performance is evaluated by the outage probability and throughput metrics based on the optimal SOP. The remainder of this paper is organized as follows: In Section II, some related works on EH, NOMA, and the PLS of untrusted relays in IoT systems are presented. In Section III, a system model, a communication process, the end-to-end SINR, and the three communication schemes are introduced. In Section IV, the SOPs corresponding to the three considered schemes are analyzed. In Section V, the outage probability and throughput are derived. In Section VI, numerical results are shown and discussed. Finally, conclusions and directions for future research are presented in Section VII.

II. RELATED WORK
In this section, the summary of recent work on PLS and EH untrusted relay in IoT with NOMA transmission is introduced.
To enhance the reliability and secrecy performance, the PLS in IoT systems using untrusted relays has been considered [5], [21], [27], [28]. For example, D. Chen et al. focused on the secrecy performance of uplink transmission in an IoT system, where multiple IoTDs communicate with a BS with the help of an untrusted relay. Based on the maximum end-to-end signal-to-noise ratio (SNR), they proposed the optimal scheduling scheme to improve the secrecy throughput [21]. Nevertheless, this work focused on a simple system with one untrusted relay, and the authors did not investigate the impact of EH on the secrecy performance of the considered system. Therefore, to investigate the impact of EH on secrecy performance, H. Hu et al. considered a cognitive IoT system, where the problem of secure communication between the IoTD and a BS via an EH untrusted relay was analyzed. They derived the closed-form expressions of the probability of successful secure transmission to evaluate the secrecy performances [5]. Furthermore, to extend the system, V. N. Vo et al. considered an IoT system whereby multiple IoTD and untrusted relays harvested energy from multiple power transfer stations (PTSs), and the IoTDs then transmited the signal to the BS with the help of untrusted relays. The authors then studied the secrecy performance of three relay selection schemes based on the SOP and throughput metrics [27]. However, the spectrum scarcity in the case of a large number of IoTDs was not investigated in those works.
To increase the connectivity and ensure effective spectrum utilization, the application of NOMA to an IoT system has been considered. For example, L. Lv et al. introduced a novel NOMA relaying scheme to improve the PLS of untrusted relay networks. Analytical expressions of an ergodic secrecy sum rate (ESSR) are derived to evaluate the secrecy performance, and the numerical results show that the significant ESSR improvement of the NOMA scheme is better than that of conventional orthogonal multiple access [26].
D.-T. Do et al. investigated a system in a scenario consisting of an untrusted relay required by users at far distances, where the NOMA is used to serve a large number of users. The SOP is derived to evaluate the secrecy performance [29]. Note that the above works assume that the CSIs of the communication links are perfectly known to the receiver; nevertheless, the perfect CSI is difficult to obtain because of the channel estimation errors, feedback, and quantization errors [18]. Thus, considering imperfect CSI in wireless communication systems is essential to investigating a system that well models a real-world application.
T. A. Le et al. studied a NOMA system with imperfect successive interference cancellation (SIC) using EH untrusted relays. In this context, the relays use a power-switching architecture to harvest energy and AF to forward signals. The closed-form expressions of the SOP are derived to analyze the secrecy performance. The numerical results indicated that NOMA offers better secrecy performance with multiple users [30]. However, cooperation between direct links and the relay as well as the multi-antenna BS to improve the secrecy performance and throughput was not considered. Likewise, the trade-off between the secrecy performance and throughput was also not investigated in that work.
Based on the above survey, no publication has investigated the SOP optimization with imperfect CSI; thus, we focus on this issue to evaluate the throughput performance of a secure IoT system consisting of a BS with multiple antennas, multiple untrusted relays, and multiple IoTDs.

III. SYSTEM MODEL
In this section, we introduce the system model, channel assumptions, communication protocol, and scheduling schemes.

A. SYSTEM MODEL AND CHANNEL ASSUMPTIONS
We consider the IoT architecture as in Fig. 1, where the system consists of a BS (e.g., controller), multiple EH relays, and multiple IoTDs (e.g., sensors). The BS transmits signals to the IoTDs by using NOMA and utilizes the relays for forwarding the signal to the IoTDs to improve the throughput. The relays then use the AF technique to send the collected information to the IoTDs by using NOMA. Here, we investigate the case in which the relays are not authenticated by a legitimate BS and IoTDs, i.e., an untrusted relay. This means that the reliable communication of the considered IoT system can be improved significantly by utilizing multiple relays; however, the end-to-end information should not be revealed to untrusted relays.
Note that the BS is equipped with multiple antennas, and the IoTDs and untrusted relays have a single antenna due to their size and capability limitations. Without loss of generality, all channels are assumed to be mutually independent [34] and are described in Table 1. We also assume that channels in each block of time (from the BS to the untrusted relays, from the untrusted relays to the IoTDs, and from the BS to the IoTDs) are independent and modeled as block flat Rayleigh fading channels, i.e., the channel gains are random variables (RVs) distributed following an exponential distribution [35]- [37]. Accordingly, the probability density function (PDF) and cumulative distribution function (CDF) are expressed as follows [31]- [33]:

B. COMMUNICATION PROCESS
Adopting the PSR protocol [5], [38], the communication process is shown in Fig. 2, which is divided into 2 phases as follows: • Phase 1: In a block time τ T : The BS selects one of I antennas to broadcast superimposed mixed signals, i.e., x B = √ α m x m + √ α n x n , to the IoTDs and untrusted relays using TAS [19], where x m and x n are the signals received by S m (far IoTD) and S n (near IoTD), and α m and α n are the power allocation coefficients that satisfy the condition α m + α n = 1 and α m > α n [39]. Note that we adopt the assumption given in [40], [41] that the destination node pairs are selected arbitrarily but that they must satisfy the characteristics of NOMA, i.e., the near sensors having good channel condition are allocated a lower power level than the far sensors (which have bad channel conditions). Thus, the received signals in the first phase at S π are expressed as where n (1) S π ∼ CN (0, N 0 ), N 0 is additive white Gaussian noise (AWGN), and P B is the transmit power of the BS. Note that imperfect CSI of the communication link between the BS and the IoTD is considered, i.e., the channel coefficient of the BS-IoTD link is estimated by using MMSE estimation error as follows [42]- [45]: where is the channel estimation error, and e is defined as the correctness of the channel estimation. According to the NOMA technique, S m decodes the message x m by treating S n 's message as noise. Therefore, the instantaneous SINR at the m-th IoTD from the BS is written as follows: where ρ B = P B /N 0 . Furthermore, at the n-th IoTD, S n first decodes the message x m and then removes this element to obtain its message by using SIC. Here, we assume that S n can decode x m successfully by adopting the method proposed in [43], [46]. Thus, the SINR at S n necessary to detect x n from the BS is expressed as At untrusted relay R k , power-splitting-based relaying (PSR) is deployed by dividing the transmit power of the BS into two streams: µP B for EH and (1 − µ)P B for information processing, where 0 < µ < 1 is the powersplitting ratio [38]. Thus, the harvested energy at R k can be formulated as where τ is the fraction of the block time T for EH, η is the energy conversion efficiency of the k-th untrusted relay, and P B is the transmit power of the BS. Here, due to the short distance, the untrusted relays apply a constant gain to the received signal from the BS [47]- [49], i.e., the fixed-gain between BS and the untrusted relay is known. This reduces the amount of mathematical computation (in practical scenarios, the fixed-gain is known, as the channel is less variable and can be calculated by statistical information collected by the operator). Thus, we apply the fixed-gain EH and relay at the untrusted , [50]- [52]. Accordingly, the harvested energy at R k can be rewritten as Furthermore, the received signal at the k-th untrusted relay is expressed as where n R k ∼ CN (0, N 0 ). Therefore, the received SINRs at the k-th untrusted relay for detecting x m and x n are expressed as follows: • Phase 2: In the remaining time of (1 − τ ) T , the selected untrusted relay uses the harvested energy in the first phase for relaying the signal to the IoTDs by applying AF with NOMA. Here, the transmit power and the variable amplifying coefficient at R k are expressed as follows: Consequently, the received signal at S π in the second phase is formulated as where n (2) S π ∼ CN (0, N 0 ). Note that we consider the imperfect CSI of the communication link between the selected untrusted relay and S π , i.e., where h R k S π is the channel coefficient estimated using MMSE for h R k S π and e R k S π ∼ CN (0, e ) is the channel estimation error. Thus, the SINRs for detecting x m and x n transmitted from R k at S m and S n are expressed as (16) and (17), as shown at the bottom of this page, where ρ R k = P R k /N 0 .

C. THE END-TO-END SINR AND CHANNEL CAPACITY
At the IoTDs, selection combining (SC) are utilized to process the received signals [38], [53]. Thus, the end-to-end SINRs at S m and S n for decoding x m and x n are formulated as follows: where 1 , 2 , 3 , 4 , and 5 are defined as follows: Note that we consider the case in which the relays are not authenticated by legitimate BS or IoTDs, i.e., the relays may become EAVs. This means that confidential information may be revealed to untrusted relays. Thus, to measure the secrecy performance under the threat of an untrusted relay, VOLUME 7, 2019 we employ the secrecy capacity concept given in [5], [21], i.e., the secrecy capacity at S m and S n can be formulated, respectively, as follows: Substituting (10) and (18) into (25) and substituting (11) and (19) into (26), we have the SINRs for decoding x m and x n at S m and S n as (27) and (28), as shown at the bottom of this page, respectively, where 6 and 7 are defined as D. SCHEDULE SCHEME • The RBBR: A transmit antenna at the BS is randomly Furthermore, the condition of the channel R k →S m is worse than that of R k →S n . Thus, to improve the secrecy performance and throughput, this scheme intends to select the best untrusted relay R * among the K intermediate nodes to maximize the channel gain of the link from R * to the m-th IoTD. Mathematically, the selected untrusted relay in RBBR is written as • The BBRR: An untrusted relay is randomly chosen among {R k } K k=1 . Furthermore, the condition of the channel B→S m is worse than that of B→S n . Thus, to improve the secrecy performance and throughput, this scheme intends to select a transmit antenna of the BS to maximize the channel gain of the direct link from the BS to the m-th IoTD, i.e., the BS with the selected transmit antenna is given by • The BBBR: To improve the system performance, an antenna is chosen among I antennas of the BS such that the channel gain from that antenna to the m-th IoTD is the best. Similarly, an untrusted relay is chosen among K intermediate nodes such that the channel gain from that relay to the m-th IoTD is the best, i.e., the selected antenna and the selected untrusted relay are chosen as (31) and (32), respectively.

IV. OPTIMAL POWER ALLOCATION IN THE PRESENCE OF UNTRUSTED RELAYS BASED ON THE SOP
In this section, the SOP will be analyzed over Rayleigh fading channels [35], and the optimal power allocation algorithm will be introduced.

A. SECRECY OUTAGE PROBABILITY
Following [29], [39], the SOP for decoding x m and x n of an IoT system in the presence of an EH untrusted relay is defined as either the channel secrecy capacity probability of transmission links for decoding x m or that for decoding x n must be lower than predefined thresholds, λ sec Sm or λ sec Sn , respectively, i.e., where ∈ {RBBR, BBRR, BBBR} and Pr{.} is a probability function. In accordance with the definition of conditional probabilities, the SOP of the considered system can be rewritten as Next, we introduce the closed-form for the SOP of the three considered schemes.
Remark 1: Assume that V j (j ∈ {1, · · · , J }) is an exponentially distributed independent RV with mean values V j . The CDF of U = aV j /(bV j + c) is formulated as where a 1 , b 1 , and c 1 are constants. For the proof, see Appendix A. Using Remark 1 with a 1 = α m ρ B , b 1 = α n ρ B , c 1 = 5 , and u = m 6 , the expression P
For the proof, see Appendix A.

2) DERIVATION FOR THE BBRR
Similar to the RBBR, the SOP for the BBRR is derived as follows: where P (1) sec Sn and P (2) sec Sn are defined as (41) and (42)

3) DERIVATION FOR THE BBBR
Following the definition of BBBR, the best antenna of the BS and the best untrusted relay are selected; thus, the SOP for the BBBR is obtained as where P (1) sec Sn and P (2) sec Sn are defined as (41) and (42) where P BBRR (2) asym Sm is defined as in (51) asym Sn , and P (2) asym Sn are defined as (58)

C. OPTIMAL SOP IN THE PRESENCE OF UNTRUSTED RELAYS
Based on the communication process, we predict that when the transmit power is small, the channel capacities at the untrusted relay and IoTD are also small, i.e., the probability that the IoTDs receive the messages without eavesdropping is low. This leads to a low secrecy capacity, i.e., the secrecy performance is improved as the transmit power is increased. Nevertheless, the secrecy capacity will decrease if the transmit power of the BS is high since the untrusted relay can become an EAV and steal the confidential communications between the BS and the IoTDs. Thus, the SOP will increase again. Therefore, an optimal transmit power exists such that the considered system can achieve the best secrecy performance. Accordingly, we propose the algorithm illustrated in Algorithm 1 to determine the optimal transmit power at the BS such that the SOP is the lowest and that the transmit power at the BS is such that the SOP converges. In particular, the values of ρ B are split into an array (δ b , δ e ) with I elements, where δ 1 < δ 2 are the smallest and largest values of ρ B , and the starting point of the SOP O sec is set to 1. Next, we update O sec ( 1 ) with respect to ρ B ( 1 ), where 1 ∈ (1, I). The iteration loop process will be stopped when O sec ( 1 + 1) > O sec ( 1 ) with ρ * B , and the optimized transmit power is found using the formula P * B = ρ * B N 0 . Similarly, to determine the transmit power convergence, we update O sec ( 2 ) with respect to ρ B ( 2 ), where 2 ∈ (1, I). The iteration loop process will be stopped when O sec ( 1 ) − O asym = ε (ε → 0) with ρ B conv , and the converged transmit power is P B conv = ρ B conv N 0 . Note that the aforementioned iteration process (lines 4-9 and 11-14) attempts to improve the accuracy of the approximations to a particular minimum in the original feasible region by using the element I and ε, i.e., the accuracy of the algorithm convergence is higher for larger I and smaller ε.

V. SYSTEM PERFORMANCE ANALYSIS A. OUTAGE PROBABILITY
The IoTDs combine the signals from the BS and the selected untrusted relay by using SC at the second phase in the communication process. Therefore, an outage event for the pair IoTDs, i.e., m-th IoTD S m and n-th IoTD S n , can be interpreted as either S m or S n cannot decode its own message [41]. Based on the above explanation, the outage probability of the considered IoT system is expressed as follows: where λ op Sm and λ op Sn are the target rates at S m and S n , respectively. Here, without loss of generality, we set τ = 1/2, which is the similar to conventional relay systems [5], [38]; thus, C op Sm and C op Sn are defined as Similar to (43), (44), and (47), the outage probabilities of S m and S n pair for RBBR, BBRR, and BBBR are obtained as follows: where P BBBR(1) op Sn , and P (2) op Sn are respectively defined as follows: if α n 1 − 4 9 > 0 0, if α n 1 − 4 9 ≤ 0. (71)

B. THROUGHPUT ANALYSIS
In this subsection, we study the throughput to estimate how fast the system can be achieved under the optimal SOP. The BS and untrusted relays transmit signals at a constant rate, and the system throughput is subjective to the impact of outage probability. To consider the delay-limited mode for practical implementations, the system throughput is investigated, and this important metric is formulated as [41]

VI. NUMERICAL RESULTS
In this section, we provide insightful numerical results for evaluating the secrecy performance and throughput of the EH untrusted relay IoT system. In particular, we investigate the impacts of ρ B , the EH time, the number of BS antennas, the number of untrusted relays, and the predefined threshold on the SOP, the outage probability, and the throughput of the pairs of IoTDs S m and S n . Unless otherwise stated, we investigate the considered system in a square of unit area. The coordinates of the gateway and π-th IoTD are B (0.0, 0.0) and S π (A π , B π ), respectively. The selected untrusted relay is collocated at R k (A k , B k ). The path-loss exponent of the considered system that is placed in free space is equal to 2 [33]. The following system parameters are used for both the analysis and simulation [31], [43], [54]: }; the EH efficiency coefficients η ∈ (0, 1); the fractions of the EH time τ ∈ (0, 1); the powersplitting ratio µ ∈ (0, 1); ρ B ∈ [−20, 40] (dB); the secrecy thresholds for decoding x m and x n are λ sec Sm = 0.01 (kbps) and λ sec Sn = 0.02 (kbps), respectively; the predefined thresholds of IoTDs for successfully decoding x m and x n are λ op Sm ∈ (0.01, 0.5) (kbps) and λ op Sn ∈ (0.01, 0.5) (kbps), respectively; the number of BS antennas I ∈ {2, 5, 8}; and the number of untrusted relays K ∈ {2, 5, 8}. Note that we evaluated and compared the three schemes as follows: • RBBR: A random antenna and the best untrusted relay from I antennas of the BS and from K untrusted relays, respectively, are selected to transfer information to the IoTDs.
• BBRR: The best antenna and a random untrusted relay from I antennas of the BS and from K untrusted relays, respectively, are selected to transfer information to the IoTDs.
• BBBR: The best antenna and the best untrusted relay from I antennas of the BS and from K untrusted relays,  respectively, are selected to transfer information to the IoTDs. Fig. 3 plots the SOP curves for different ρ B of the RBBR, BBRR, and BBBR. The SOP of the BBBR is better than that of the BBRR and RBBR. This is because the BBBR chooses the best antenna of the BS and the best untrusted relay to send signals to the IoTDs, i.e., this scheme obtains the best diversity gain among the three schemes. Furthermore, the secrecy performance of BBRR outperforms that of RBBR. This is because the untrusted relays can steal the confidential communications from the BS-to-IoTD links; hence, the BS's antenna selection is more effective than untrusted relay selection. This trend applies to all SOP simulations.  In addition, the SOP of ρ B tends to 40 (dB), and the SOPs of the three schemes all decrease to the optimal point (ρ B = −5(dB)) and then increase to close to the convergence point (ρ B = 20(dB) for RBBR and BBRR and ρ B = 25(dB) for BBBR), which is consistent with Algorithm 1. Fig. 4 investigates the impact of the EH time on the SOP of RBBR, BBRR, and BBBR. It is obvious that the secrecy performance is improved as the EH time is increased. This is because the untrusted relays will harvest more energy when the EH time is higher. Furthermore, when the numbers of antennas of the BS and untrusted relays increases, the SOP is improved. It is easy to understand that the diversity gain will increase at the BS with the higher numbers of antennas and untrusted relays. In addition, to investigate the effects of both ρ B and τ , we plot the 3-D figure in Fig. 5. Again, we can  see that the SOP obtains the optimal point of ρ B = −5(dB), and this point will decrease with increasing EH time. We can see that the SOP of case 1 is higher than that of case 2. This is because although the untrusted relays in case 1 harvest energy better than do those in case 2, the untrusted relays in case 1 also capture the confidential signal more easily than do those in case 2.
Furthermore, the SOPs of the three considered schemes decrease with increasing µ. This result occurs because the EH VOLUME 7, 2019 power increases while the power for information processing decreases. This leads to a reduction in the received signal strength at the untrusted relays, and hence, the SOP decreases.
To illustrate this more clearly, we show the impact of µ and τ on the SOP in the 3-D figure in Fig. 7. We can see that the SOP is improved as either µ or τ increases. Furthermore, the SOP of the BBRR decreases to close to that of the BBBR as µ increases. When µ tends nearly to 1, the untrused relays do not have power for information process, i.e., the received signal at the IoTDs is only affected by the BS's antenna selection. Fig. 8 depicts the outage probability variation with respect to the power-splitting ratio and the channel estimation error under three schemes, in which the optimal transmit power for ensuring satisfactory secrecy performance is fixed. It is observed that the outage probabilities of BBRR and BBBR are the same and better than that of RBBR. Furthermore, the outage probability decreases as the channel estimation error improves. The secrecy performance is better when the CSI is predicted to be more accurate. Fig. 9 shows the impact of ρ B on the throughput for the three considered schemes. Similar to the SOP, we can see that the throughput of the BBBR is better than that of the remaining schemes. Furthermore, in contrast to the SOP, the throughputs are improved with increasing ρ B and unchanged when ρ B is sufficiently large. This is because the IoTDs more easily obtain the signal given the higher power of the BS. From Figs. 3 and 9, we can observe that the SOP is improved under the small transmit power, while this leads to low throughput. This is the trade-off between secrecy performance and throughput.

VII. CONCLUSION
In this work, the secrecy and throughput of a cooperative EH untrusted relays IoT system using NOMA with imperfect CSI were analyzed. Three cooperative schemes (i.e., RBBR, BBRR, and BBBR) were introduced to analyze the secrecy and throughput of the considered IoT system. The closedform expressions for the exact and asymptotic SOP were derived. Based on that, an algorithm for determining the transmit power optimization and convergence was proposed. The closed-form expressions for the throughput of the three considered schemes were also obtained and verified by Monte Carlo simulation results. The numerical examples show that the BBBR outperforms RBBR and BBRR when the secrecy performance and throughput metrics are investigated. In addition, the SOP and the throughput for the three schemes improves as the number of BS antennas and untrusted relays increase. For future work, we are currently considering the issue of adaptive power allocation for NOMA in IoT systems that consist of multiple relay clusters to improve the SOP and throughput for IoT application systems.

APPENDIX A PROOF THE REMARK 1
Following the definition of conditional probability, the CDF of U can be written as Substituting (2) into (73), the proof is complete.

APPENDIX B PROOF THE REMARK 2
Similar to Remark 1, the CDF of U * can be written as Adopting the definition of conditional probability, we have Substituting (2) into (75), the proof is complete.