Abstract
This paper exploits nonorthogonal multiple access (NOMA) to enhance the uplink secure transmission in Internet of Things (IoT) networks. Considering the different intercept ability of eavesdroppers (Eve), secrecy performances of both strong and weak Eve wiretap scenarios have been investigated. In strong Eve wiretap scenario (SWS), Eve is assumed to be powerful enough to decode message without interference and, in weak Eve wiretap scenario (WWS), Eve is assumed to have significant demodulation capability constraint. The new closed-form expressions of joint connection outage probability (JCOP), joint secrecy outage probability (JSOP), and sum secrecy throughput (SST) are derived in these two scenarios to indicate the impact of parameters, i.e., transmit power, codeword rate, and the placement of devices, on security performance. In order to demonstrate the superiority of NOMA, we also investigate the secrecy performance of orthogonal multiple access (OMA) system as a benchmark. Analysis results show that the performance in WWS is always better than that in SWS and, in low signal-to-noise ratio (SNR) or high codeword rate region, the performances of these two scenarios are close. In addition, we present the condition that NOMA outperforms OMA in terms of SST. Moreover, the placements of devices are significant to the SST performance of NOMA system. The suboptimal device placement scheme has been designed to maximize SST. Analysis results demonstrate that when Eve is far away from legal users, the suboptimal results tend to optimal.
1. Introduction
Internet of Things (IoT) offers a challenging notion of creating a world where all the things are connected via smart devices [1]. Various scenarios can be served by IoT networks, many of them concerning confidential or privacy information, such as Mobile Payment and Smart Healthcare. Due to the openness of the wireless medium, wireless communication networks are particularly susceptible to be eavesdropped [2]. The security of wireless IoT networks is a critical issue [3, 4]. Furthermore, the nodes in IoT networks are comprised of large number of machine-type communication (MTC) devices with power constraint and limited signal processing capability [5]. Consequently, traditional cryptography requiring high computing complexity is not practical for IoT systems when the devices’ communication resources are constrained.
Physical layer security (PLS) technology may be a promising solution for securing the IoT transmission. Compared with cryptography, it is a simple, lightweight, and efficient security scheme [6]. Various physical layer techniques have been proposed for improving security, such as relay selection transmission [7, 8] and artificial noise/jamming and beamforming [9, 10]. In particular, in resource-constrained system, [11] adopted energy harvesting to improve secrecy energy efficiency in physical layer. The study [12] improved secure spectrum efficiency and energy efficiency tradeoff by optimizing system parameters. The works [13] and [14] designed a lightweight secure modulation scheme and an on-off transmission scheme, respectively. And [15] introduced an opportunistic jamming scheme to enhance transmission security for low complexity devices. Recently, in IoT networks, PLS has become a popular technique for secure transmission. The study [5] provided some promising lightweight and low complexity PLS techniques for IoT. And [16] proposed a new compressed sensing security transmission model in IoT systems. Secrecy performance was analyzed in IoT networks under eavesdropper collusion [17]. The work [18] focused on designing a transmission scheme for securing relay communications in IoT networks.
On the other hand, nonorthogonal multiple access (NOMA) has been presented as a promising solution to increase connectivity in massive IoT applications [19–21]. The study [20] designed a new multiple-input multiple-output NOMA scheme severing two users with different quality of service (QoS) demand, which share the same nonorthogonal resources by adopting NOMA protocol. An uplink NOMA-based multiple access strategy for cellular massive IoT was proposed in [21], in which multiple devices share the same subband and base station performs successive interference cancellation (SIC) to distinguish the messages from different devices. By adopting NOMA concept, the strict limitations of the amount of resources can be broken and enabling more devices to be supported in IoT networks. Furthermore, NOMA can be introduced as a low complexity solution to enhance secure downlink transmission [22–29]. Specifically, [27] demonstrated that the secrecy rate of a multiple-input single-output (MISO) NOMA system is higher than that of orthogonal multiple access (OMA) system. In addition, in a NOMA assisted multicast-unicast scheme, security unicasting rate achieved by NOMA is larger than or equal to that of OMA [28]. Moreover, [29] studied the performance gain of NOMA over OMA and indicated that the NOMA scheme always outperforms OMA scheme. However, to the best of our knowledge, there is no published work that studies the PLS in NOMA-based IoT networks.
NOMA can be applied in both uplink and downlink [30]. By using SIC, the receiver can detect the intended information from superposition signals [24, 28]. However, the process of SIC increases the signal processing complexity and imposes a high demand of detection capability at receiver. Notably, [24–29] all assumed that the SIC is performed ideally. It is overoptimistic, especially when the receivers have significant communication resources constraint. When adopting NOMA concept at uplink, the devices do not need to use SIC, which reduces its signal processing complexity. In addition, it becomes reasonable to assume that the SIC is applied perfectly, because the receiver is usually a base station or an access point with powerful detection capability in IoT networks. Significantly, it is a multiuser communication scenario which makes the analysis of PLS different from that in downlink NOMA systems. As far as we know, the PLS performance of uplink NOMA in IoT networks has not been investigated. The secure communication of uplink NOMA in IoT networks is worthy of our attention. Then, a fundamental question arises to be addressed: Can NOMA enhance the secrecy performance in IoT networks?
Because various scenarios are served by IoT networks, the wiretapping scenario also can be in variety. In this paper, two scenarios, i.e., strong eavesdropper (Eve) wiretap scenario (SWS) and weak Eve wiretap scenario (WWS), are considered according to the detection capability of Eve. In addition, we introduce uplink NOMA to enhance secure transmission of IoT networks in these two scenarios. Moreover, a low complexity device placement scheme is proposed to further enhance the security of uplink NOMA-based IoT networks. Our principal contributions are summarized as follows:(i)We first exploit uplink NOMA to improve security performance in IoT networks. The new closed-form expressions of joint connection outage probability (JCOP), joint secrecy outage probability (JSOP), and sum secrecy throughput (SST) are derived both in SWS and WWS. The impact of different detection capability of Eve on secrecy performance is investigated. Analysis results show that the transmission in WWS is always securer than that in SWS and, in low signal-to-noise ratio (SNR) or high codeword rate region, secrecy performances in WWS and SWS are close.(ii)The performance of OMA-based benchmark system is analyzed. We present the condition that NOMA outperforms OMA in terms of SST, which shows that in high SNR or low codeword rate region NOMA is likely outperforming OMA and when channel states (CS) of devices are very different, NOMA tends to get a high performance gain on OMA.(iii)We introduce a device placement method and formulate it as an optimization problem for further improving SST. However, it is a multiparameter and nonconvex optimization problem which is challenging for results derivation. A practical scheme is provided and we propose an upper bound of the SST. In SWS, we can only obtain the suboptimal results. However, in WWS, optimal results are available in some cases. Analysis results show that when Eve is far away from legal users, SST obtained from our device placement scheme becomes close to its upper bound tightly, which indicates that the suboptimal results tend to be optimal.(iv)By simulation, we confirm the accuracy of our analysis including security performance and device placement method. In addition, simulation results show that there is an optimal desired transmission SNR or codeword rate which maximizes the SST both in WWS and in SWS. Moreover, in low SNR region or high codeword rate region, results from our device placement scheme are also close to their upper bound tightly.
The rest of the paper is organized as follows. The uplink NOMA-based IoT networks and channel model are introduced in Section 2. In Section 3, we derive a set of closed-form expressions of secrecy performance in three scenarios. Section 4 introduces a security enhancing methods. We formulate the optimization problem of this method and give the suboptimal solutions. The security performance and optimal solutions are verified by numerical and simulation results in Section 5. Finally, Section 6 concludes the paper.
2. Network Model
In this paper, we consider an uplink NOMA-based IoT network. Considering a passive wiretap scenario, the detection capability of Eve is unknown. In addition, various scenarios served by IoT networks result in the variety kinds of Eve. For simplifying the analysis, we consider two extreme wiretap scenarios, i.e., strong Eve wiretap scenario and weak Eve wiretap scenario, according to the detection capability of Eve. Uplink NOMA scheme enables one receiver to serve multiple devices simultaneously. It is worth noticing that two users’ scheme was selected for performing NOMA in 3GPP LTE Advanced [31]. We also consider a two users’ uplink power-domain NOMA scheme in IoT networks. These two users denoted as device and device are grouped as a device pair. As shown in Figure 1, the pair devices transmit confidential message to a base station under the malicious attempt of the Eve. The received signal at base station (BS) and Eve can be expressed asrespectively, where and denote the transmit power of device and device and are the normalized message for device and device , respectively. denote the zero-mean additive white Gaussian noise (AWGN) at base station and Eve, which are assumed to have the same variance . are the distance between devices and BS, respectively, and are the distance between devices and Eve. is the path loss with fading exponent . are small-scale fading coefficients, which are supposed to obey independent and identical complex Gaussian distribution with zero mean and variance is [24]. We assume that transmit power of devices is fixed and equal; i.e., .
2.1. Channel Capacity of Base Station
According to the protocol of NOMA, device and device transmit message to the BS at the same time and frequency. The nonorthogonal messages are overlapped and interfered by each other. In order to distinguish the mixing messages, SIC is widely adopted. Based on the principle of SIC, the message with stronger power is demodulated first under the interference from another device. And, then, remodulate the demodulated message and deduct it from the overlapping signal. In an ideal situation, the remained message is pure for another device [24]. The impact of the path loss is generally more dominant than small scaling fading effects. In addition, transmit powers of the two devices are assumed to be the same. Hence, the decoding order is dependent on the distances between the devices and BS. Without loss of generality, we assume that the location of device is closer to BS and demodulated first. According to the Shannon channel capacity formula, the channel capacity of device and device at BS can be expressed asrespectively, where denotes transmit SNR. Because device is interfered by device , when tends to infinite, tends to a finite value, however with tending to infinite.
2.2. Channel Capacity of Strong Eve
We consider a strong Eve which has equal or superior capability of BS. By applying powerful multiuser detection techniques, the overlapping messages from devices can be distinguished by the Eve perfectly [24]. In SWS, the channel capacity of devices and can be written asrespectively. For an infinite transmission SNR , both the channel capacities of device and device at Eve are infinite value for SWS. Based on (3), when tends to be infinite, the capacity of device in legal channel is a finite value. It demonstrates that SWS is really a detrimental scenario for secure transmission.
2.3. Channel Capacity of Weak Eve
In WWS, the Eve has significant demodulation capability constraint, which can also be seen as a malignant device [28]. Because of limited demodulation capability, the interference from each other cannot be eliminated. Consequently, in WWS, the channel capacity of devices and at Eve can be expressed asrespectively. Both the capacities of device and device at Eve are limited by the interference from each other. Comparing with (3) and (4), the interference in WWS deteriorates the illegal channel more seriously than that in SWS. It shows that WWS is a relative secure wiretap scenario.
3. Secrecy Performance Analysis
In this section, we will study the secrecy performance in SWS, WWS, and OMA-based benchmark system. Considering the limitation of devices’ ability, we assume a fix transmission rate situation. Based on the well-known Wyner wiretap code theorem [32], codeword rates and confidential information rates are fixed. We suppose that the statistic channel state information (CSI) of legal and illegal channel is available by legal devices. By the way, this assumption is adopted by many literatures [24, 28, 29]. Under these assumptions, we first analyze the reliability performance in NOMA system. And, then, the secrecy performance is studied in WWS, SWS, and OMA-based benchmark system. Finally, we compare the security performance between NOMA and OMA in terms of SST.
3.1. Reliability Performance of NOMA
Connection outage probability (COP) is a popular metric for reliability performance, which denotes the probability of legal channel capacity dropping below to the codeword rate [11]. We define the joint connection outage probability for the device pair as that of either the device or device outage. JCOP can be expressed in the following equation:where and are codeword rate of device and deice , respectively. The closed-form expression of JCOP is written aswhere , , and which denotes the path loss ratio of device to device at BS.
Proof. Substituting (3) and (4) into (9), we can obtainAfter some mathematical manipulations, the desired result can be easily derived.
From (10) we can find that when tends to be infinite, tends to instead of zero. It demonstrates that the effect of is limited for improving reliability performance. In addition, when tends to zero, i.e., device far away from BS, JCOP tends to 1, because COP of device is always one. Due to the fact that (10) is not a monotonic function with , there may exist an optimal for maximizing the reliability performance.
3.2. Secrecy Performance in SWS
Secrecy outage probability (SOP) is widely used to evaluate the secrecy performance, which denotes the probability of illegal channel capacity growing up to the redundancy rate [11]. We define the joint secrecy outage probability for the device pair as that of either the device or device outage, which is similar to the definition in [24]. Based on Wyner wiretap code theorem, the JSOP of device pair in SWS can be written as follows:where are secrecy rate of device and device , respectively. and are redundancy rate. The closed-form expression of can be written aswhere , , , and . denotes the average receiving SNR of device at Eve and represents the path loss ratio of device to device at Eve.
Proof. Substituting (5) and (6) into (12), we can obtainBecause of the independence between and , can be written asAfter some mathematical manipulations, (13) is obtained.
Obviously, (13) shows that is a monotonic increasing function with and when tends to be infinite, tends to unity. It indicates that high average receiving SNR at Eve is detrimental for secure transmitting. When tends to zero, i.e., device far away from Eve, JSOP tends to which is SOP of device . It demonstrates that the transmit security of device is guaranteed and JSOP is only determined by the SOP of device .
JCOP denotes the reliability performance and JSOP represents the secrecy performance, which are inadequate to evaluate the efficiency performance of NOMA. However, in our definition, we consider these two devices as an entirety and investigate the joint secrecy performance. Nonzero SST can not be obtained when any one of devices undergo outage. Joint secrecy performance is more interesting when these two devices are related and sum secrecy throughput is adopted as the metric for device pair, which represents sum transmission rate of device pair under the constraints of joint reliability and security. SST can be expressed asFrom the analysis above, we can find that and are independent. The product of and represents the reliable and secure connection probability. is sum secrecy rate. Under the above definition, nonzero SST can not be obtained when any one of the devices undergo outage.
After substituting (10) and (13) into (16), the closed-form expression of can be written asEquation (17) shows that SST is jointly determined by JCOP and JSOP. JCOP is a decrease function about transmit power. However, JSOP is an increase function about transmit power. Thus, SST may not be a monotonous function about transmit power, which means an optimal transmit power existed for maximizing SST. In addition, SST is also not a monotonous function about or and the secrecy rate can be optimized can be optimized for achieving better performance. Furthermore, due to the interference between devices, the location of device which is determined by and has significant impact on network performance which will be further studied in the next section.
3.3. Secrecy Performance in WWS
Similarly, the JSOP in WWS can be written asThe closed-form expression of is
Proof. See Appendix A.
Based on (19), there are two different results when transmit power tends to be infinite. When JSOP tends to 1 and when JSOP tends to . This is because higher codeword redundancy rates can increase secrecy performance. Furthermore, when tends to zero, i.e., device far away from Eve, JSOP tends to . It demonstrates that when tends to zero, SOP of device is the only parameter affecting JSOP.
Similar to (16), the SST in WWS can be expressed as By substituting (10) and (19) into (20), the closed-form expression of can be directly derived as
Similar to SWS, SST in WWS also is jointly determined by JCOP and JSOP and an optimal transmit power , or location of device may be found to maximize SST. The expression of SST is rather complicated and the further insights will be investigated by numerical results and simulations.
Remark 1. Comparing (5) with (7) and (6) with (8), we can find that the capacity of illegal channel in SWS is always bigger than that in WWS. It demonstrates that the message in WWS is securer than that in SWS. In (17) and (21), we can also find the impacts of parameters, i.e., transmit power, codeword rate, and the placements of devices, on SST performance. Among them, the placements of devices are special for NOMA system, determined by and . SST can be enhanced by optimizing and and we propose a further researching in Section 4.
3.4. Secrecy Performance in OMA-Based Benchmark System
In OMA system, different orthogonal resources are allocated to different devices. In order to get a fairness and reasonable comparison, we consider a two users’ situation and they are also named as device and device . The sum secrecy rate can be expressed as where and are resource allocation coefficients and . For time-division multiple access (TDMA) system, the resource is transmission time. However, for frequency-division multiple access (FDMA), the resource is bandwidth. Without loss of generality, we consider a TDMA system as OMA-based benchmark system. Specifically, the conventional TDMA scheme with equal time sharing is adopted by many studies [29]. In this paper, we also adopt equal time sharing scheme for convenience; i.e., . The other system parameters are the same as NOMA system.
In OMA system, there is no interference between devices. The channel capacity of device and device at BS can be written asrespectively. In an equal time sharing scheme, half of transmitting time is used by every device. Consequently, the average channel capacity is half of that in NOMA. Similar to NOMA system, JCOP in OMA system can be expressed asBecause the resources are equal and orthogonally used by devices, the codeword rate is half of that in NOMA system. The expression of can be easily derived as follows:Because of no interference between devices, when tends to be infinite, tends to zero. It demonstrates that the effect of is not limited for improving reliability performance in OMA system.
In illegal channel, derivation of JSOP in OMA system is the same as the derivation of . The expression of JSOP in OMA can be directly written asObviously, when tends to be infinite, tends to unity, which is the same as one-user OMA system.
According to the definition of SST in NOMA system, the SST in OMA can be expressed asBecause resources are equally shared by devices in OMA system, the SST is half when compared with NOMA system. After substituting (26) and (27) into (28), can be finally expressed asIn two users’ OMA system, and are also important parameters for SST. In (29), is a decrease function about and increase function about , which show that being far away from Eve and close to BS can enhance performance. This conclusion is also the same as that in traditional one-user OMA system.
3.5. Secrecy Performance Comparison Between NOMA and OMA System
NOMA allows two devices to transmit message with nonorthogonal resources, which increases connectivity and also gives more chances to Eve for wiretapping. The performance comparison between NOMA and OMA is not straightforward. According to the analysis of Remark 1, the message in WWS is securer than that in SWS. Thus, it is reasonable to take the performance in SWS as benchmark to compare it with that in OMA scheme. Moreover, due to NOMA enabling massive connectivity supported in network, more devices can transmit credential message at the same time. Therefore, SST may be an appropriate comparison metric. Based on (17) and (29), the condition of NOMA outperforming OMA is directly given as follows:In (30), the expression in the left part of the inequality is a decrease function about and . It shows that lower codeword rate makes NOMA more likely to outperform OMA. In addition, it is an increase function about and . It indicates that increasing average receiving SNR makes NOMA tend to be superior than OMA. Especially, when is small, i.e., the channel conditions of pair devices are very different, NOMA will likely obtain better performance than OMA.
4. Enhancing Security by Device Placement
In this section, a low complexity device placement method is proposed for uplink NOMA to enhance security performance in IoT networks. It is wort pointing out that this secrecy enhancement method does not increase the signal processing complexity and power consumption, which is suitable for the low cost IoT applications [5]. We have assumed that the statistic CSI of legal and illegal channel are available by legal devices. Because multiple devices are served in uplink NOMA system, the statistic CSI of Eve is available by more than one device. Consequently, the location of Eve is also available. We assume a scenario where the locations of Eve and device are fixed but the placement of device which is determined by path loss ratios and is chosen under security constraint. Therefore, the optimal placement of device can be obtained by optimizing and .
4.1. Optimization Problem of Device Placement
As it is analyzed in Section 3, optimization problem can be formulated as follows:where is the distance between BS and Eve and . Because the location of device is determined by and , they have to satisfy the constraint of triangle inequality which is described in the shade area of Figure 2. Equation (31) is a two parameters’ optimization problem. In addition, because of the constraint, it is a nonconvex problem in nature. For these reasons, solving the optimization problem is challenging. Naturally, it is more practicable when optimizing and separately. However, because of the triangle inequality constraint between and , the optimal results may not be obtained.
4.2. Suboptimal Scheme of Device Placement
We introduce an easy-to-accomplish scheme to simplify problem (31). From (16) and (20), we can find that and have independent expression in . Inspired by this, we separate (31) into two parts and each part is a single-parameter optimization problem. The scheme is expressed as follows:where . In this scheme, is priority optimized without triangle inequality constraint, and is optimized with triangle inequality constraint. Therefore, and can determine the location of device . However, this scheme is a suboptimal method. It should be pointed out that this scheme is appropriate for the scenario where legal channels are stronger than wiretap channels and we will prove that the results obtained from this scheme tend to be optimal when Eve stays far away from legal channel.
Problem (32) can be solved directly and the following lemma gives a preliminary result of problem (33).
Lemma 2. If has at most one stationary point, is formulated asWhere is the result of the following problem:If locates in feasible region 1 showed in Figure 2, the results from this scheme are optimal. However, the results are suboptimal when locating in other regions, i.e., regions 2, 3, and 4.
Proof. See Appendix B.
Remark 3. When Eve is far away from legal channel, i.e., , we can find that . Based on (13) and (19), tends to be zero. Consequently, problem (31) degrades to problem (32) which is optimized in our scheme. It demonstrates that the suboptimal results from our device placement scheme tend to be optimal. Significantly, the results from the proposed method are lower bound of SST and this is useful for robust secrecy design.
4.2.1. Optimization of
The following lemma provides the closed-form expression of .
Lemma 4. According to the scheme, is given by
Proof. The first-order partial derivative of with respect to can be written asBy setting , we can obtain only one result in feasible region which is showed in (36). Furthermore, when , and when , . Therefore, is the minimum of . The proof is completed.
The result of (32) is applicable for both SWS and WWS, because they have the identical expression of . However, the results of problem (33) are different in SWS and WWS.
4.2.2. Optimization of in SWS
The optimal result of in SWS is given in following lemma.
Lemma 5. The result of problem (33) in SWS is expressed as
Proof. The first-order partial derivative of with respect to can be written asWe can find that for all . It shows that is an increase function, and . According to Lemma 2, Lemma 5 can be obtained and the results are always suboptimal.
4.2.3. Optimization of in WWS
To derive the result of problem (33) in WWS, we first give the result of a special case in the following lemma.
Lemma 6. Assuming a specific situation where and , the result of problem (33) in WWS is given bywhere is the result of the following equation:
Proof. See Appendix C.
The key to problem (33) is the derivation of . When or , solving problem (35) in WWS is quite challenging. Instead, we investigate by detailed simulations and numerical calculations repeatedly in different parameters and find that can be obtained by solving the following equation:Although it does not formally identify the globally optimal solution, it identifies a locally optimal solution [33]. Combining with (40), we can get a suboptimal result.
4.3. Upper Bound of Optimization Problem
To show the performance of our scheme, the benchmark is required. However, getting the result of problem (31) needs a two-dimension searching method, which is complicated and time-consuming. We introduce an easy-to-implement upper bound of problem (31), which is formulated as follows:It is the form of problem (31) without triangle constraint. Thus, the feasible region of and is the sum area of regions 1 to 4 showed in Figure 2. It demonstrates that the SST achieved by (43) is always equal to or bigger than that achieved by (31).
Problem (43) can be equally separated into two parts. They are formulated as follows:We can find that (44) is equal to (32) and they have the same result expressed in (36). For (45), in SWS, according to Lemma 5, . Besides, in WWS, based on Lemma 6, . Because and are obtained without triangle constraint, the location of device can not be determined by and . Although it is not practical, we can regard the SST obtained from (43) as a benchmark to show the performance of our suboptimal device placement scheme.
According to the definition, and represent the path loss ratio, which denotes the distance relationship of devices to BS and devices to Eve, respectively. The locations of device and Eve are assumed to be known by BS. According to and , the location of device can be determined. If the result is optimal, there may be one or two optimal locations for device . However, there only exists one location for device when the result is suboptimal.
5. Numerical Results
In this section, we present the numerical results for verifying our analysis. Unless otherwise stated, some of the simulation parameters are in Table 1. We introduce bit per channel use (BPCU) as the unit of transmitting rate. The distances between each other are set to be small values, which do not lose the generality, and also adopted in [24, 30].
Figure 3 plots and versus with , , , and . The analysis curves of are calculated from (10) and (26) and theoretic results of are calculated from (13), (19), and (27). In this figure, we first observe that the simulations precisely match the theoretic curves, which validates our analysis. And, then, we observe that the curves of decrease and the curves of increase as the increasing of . In addition, the curve of in SWS is the same as that in WWS and of strong Eve and OMA system are also the same, which correspond to our analysis. Moreover, due to no interference in OMA system, it has lower COP than NOMA and as, with the increasing of , COP of OMA tends to zero. In particular, in WWS is always lower than that in SWS and OMA system because ability limited Eve is interfered by devices in WWS.
Figure 4 plots the SST of NOMA and OMA system versus transmit SNR with , , and for . The analysis curves are obtained from (17), (21), and (29). Significantly, we find that the Monte Carlo simulation points match precisely with the analytical curves, which certifies to the accuracy of our analysis. We first observe that for both NOMA and OMA system the curves of SST first increase and then decrease as the increasing of . can be optimized for maximizing SST, however, which is beyond the scope of this work. Secondly, we can find that NOMA system is outperforming OMA system in high SNR region, which is correspond to the analysis of (30). In addition, SST is always bigger in WWS than that in SWS, which confirms the analysis in Section 4. We also find that at low region the SST is nearly equal in SWS and WWS. This is because, at low SNR region, the effect of interference at Eve is negligible, so the security performance in SWS is close to that in WWS.
Figure 5 plots the SST versus with , , and for and . Firstly, we observe that the curves of SST first increase and then decrease with the increasing of for different . There may also exist an optimal which makes the system achieve maximum SST. There are many literatures about finding the optimal [33] and this work is beyond the scope of this paper. In addition, when is bigger enough, the gap of SST between WWS and SWS tends to be zero. This is due to the fact that increasing enhances the ability of resisting wiretapping. When is bigger enough, is negligible; the key restriction of SST is which is the same in WWS and SWS. Moreover, we give a performance comparison between and , which shows the similar trends as the increasing of . By the way, we can get the similar characteristics when SST is versus or . Ultimately, we can find that when is high enough, the security performance of OMA system outperforms that in NOMA system, which is proved by (30).
Figure 6 plots versus with BPCU, for and . Firstly, we can observe that of NOMA system first decrease and then increase as the increasing of for different . However, in OMA system is a decrease function about . This is because in NOMA system when device becomes close to device , the CS of device is improved but deteriorating the CS of device ; however, it only improves the CS of device in OMA system. Besides, , obtained from (36), always stand for the minimum point of in NOMA system precisely which verifies Lemma 4. Moreover, as the increasing of , is decreasing, which corresponds to Figure 3. In addition, as the increasing of , also decreases, because far away from device can reduce its interference. Ultimately, When is small, of OMA and that of NOMA system are close. It verifies that pairing users whose CS are very different achieves high transmission efficiency gain on OMA.
Figure 7 plots SST versus with , dB, and BPCU for different in their feasible region. We first observe that always stand for the maximum point of SST in NOMA system in their feasible region, which verifies Lemma 2. In addition, are always standing for the suboptimal results in SWS for different , which is proved by Lemma 5. In WWS, when , is located in region 2, is suboptimal result; when , is located in region 1, we can observe that is optimal result.
Figures 8 and 9 plot SST versus and , respectively, with and . In these figures, and are adaptively changed due to the increasing of or according to Lemmas 2 and 4, respectively. In Figure 8, we find that, in low SNR region, our results are very close to the upper bound. In Figure 9, we observe that, in high region, our results are also close to their upper bounds tightly. As both in low SNR region and in high region, the security outage performance can be ensured and SST is restricted by principally which is optimized in our method. Consequently, the results from our method tend to be optimal. Both Figures 8 and 9 show that the curves of WWS are closer to their upper bounds than that of SWS since by our scheme only suboptimal result can be obtained in SWS. In particular, when Eve is away from legal channel, i.e., increasing and , our results approach their upper bounds closer in both Figures 8 and 9. It certificates our analysis in Remark 3.
6. Conclusion
In this paper, we have first exploited uplink NOMA to enhance PLS in IoT networks. The closed-form expressions of JCOP, JSOP, and SST are derived in SWS and WWS. Analysis results show that the secrecy performance in WWS is always better than that in SWS and the two scenarios have similar performance in low SNR region or high region. In addition, we also have studied the security performance of TDMA system as a benchmark to show superiority of NOMA. The condition that NOMA outperforms OMA in terms of SST is provided. Moreover, we formulate an easy-to-implement scheme of device placement. Although the scheme obtains optimal results only in some cases, when Eve is far away from legal users, the suboptimal results tend to be optimal. In addition, simulation results show that, in low SNR region and high region, our results also tend to be optimal. Besides, by simulation, we find that there exists an optimal desired transmission power or codeword rate, which maximizes the SST both in SWS and in WWS. The optimization of those parameters may be a future research direction. Furthermore, we assume that statistic CSI of Eve is available by legal users. In reality, it is impractical especially for a totally passive Eve. Moreover, the massive devices are randomly distributed in IoT networks. Using stochastic geometry approach for modeling the positions of devices and Eve may be another promising research direction.
Appendix
A. The Proof of (19)
To derive , based on (18), we can formulatewhere . For obtaining a practical value, we letAfter some simplification manipulations, we can obtainWhen , we can formulatewhere . After some mathematical manipulations, we can obtainWhen , we can formulateAfter some mathematical manipulations, we can obtainAbove all, (19) is derived.
B. The Proof of Lemma 2
In order to find the optimal , the general idea is investigating the monotonicity of target function in its feasible region which is determined by its extreme point. When the considered target function has at most one stationary point, the problem becomes explicit. If the extreme point is located in the feasible region, the optimal point is the extreme point. If the extreme point is located in the sides of the feasible region, the target function is a monotonic function and the optimal point locates at the boundary of the feasible region. According to Figure 2 and the value of , four cases based on the location of extreme point should be considered to discuss the result of optimal .
We first obtain and , where and . Thus, is the extreme point of . In addition, we assume that has at most one stationary point. Thus, when , is monotonic decrease function about and when , is monotonic increase function about . The four cases are discussed as follows.
If locates in region 1, i.e.,and satisfies the triangle inequality constraint. and the result is optimal. However, when does not locate in region 1, i.e., does not satisfy the triangle inequality constraint, and the results are suboptimal.
If is located in region 2, i.e.,and is monotonic increase function about and the feasible region is expressed asTherefore .
If is located in region 3, i.e.,and is monotonic decrease function about and the feasible region can be written asTherefore, .
If is located in region 4, i.e.,and is monotonic decrease function about and the feasible region is expressed asTherefore, .
Combining the above four cases, we obtain Lemma 2.
C. The Proof of Lemma 6
When , and , based on (19), can be expressed asThe first-order partial derivative of with respect to can be written asFrom (C.2), we can find that when tends to be zero, ; when , . So at least existing one make . If there is only one indicated as , it is the optimal result of (35). We will prove that only one makes below.
The second-order partial derivative of with respect to can be expressed asWhen tends to zero, . It shows that, with the increasing of , first increases. When begins to decrease, i.e., , which can be further expressed asAfter some calculations, we can obtainWe investigate the result of , i.e.,Introducing a functionwe find thatThus, we can obtainSo,
The result shows that when , . Based on the above two results, first increases and when it begins to decrease it always stays positive value. It further demonstrates that have only one result which is expressed in (41).
Based on (34), Lemma 6 is obtained.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (no. 61771487, no. 61471393, and no. 61371122).