Proactive Eavesdropping via Jamming in NOMA Network

Recently, non-orthogonal multiple access (NOMA) has been considered as a promising technique in 5G network, and many investigations have addressed on the physical layer security to improve the security performance. In this paper, an alternative problem, where the eavesdropping process is considered as a legal activity, will be analyzed to track suspicious communications. More specifically, we study a wireless surveillance system in which the legitimate monitor is equipped with multi-antenna to overhear the messages between the suspicious receiver and the suspicious transmitter. Suspicious users are grouped into pairs and use the NOMA technique to transmit signals to a suspicious base station. Meanwhile, the legitimate monitor (LM) simultaneously transmits jamming signals, listens to suspicious links, decode-and-forward (DF) the eavesdropped information to the legitimate eavesdropper (LE). Based on the proposed mechanism, we investigate the power allocation policies for jamming signals of the legitimate monitor under deterministic and non-deterministic interference channel. Accordingly, we derive the closed-form expression of the successful eavesdropping probability for the best and the worst user to evaluate the system performance. Monte Carlo simulations are provided to verify our analytical results.


I. INTRODUCTION
Non-orthogonal multiple access (NOMA) has been proposed as a promising technique in the fifth generation (5G) networks [1]. This technique is based on the power-domain multiplexing at the transmitter(s) and utilizing successive interference cancellation (SIC) technique at the receiver(s) to serve multiple users in the same resource block (i.e., time/frequency/code) and massive connectivity can be realized efficiently [2]. However, due to the broadcast nature of wireless communication, NOMA is subject to some security problems at which attackers can exploit to extract confidential information [3]. Utilizing this approach of attackers, the physical layer security (PLS) approach named proactive eavesdropping has been adopted and attracted a lot of attention to not only improve the secure communication but also improve the system performance. [4]- [25].
Traditional works in the PLS have often treated eavesdroppers as unauthorized users and as a result, many of them focused on preventing information leaks [26]- [38]. More specifically, Lu. Lv et al. proposed a NOMA transmission scheme, which not only reduced the transmission outage probabilities but also decreased the secrecy outage significantly [26]. In [27], given the secrecy outage and transmit power constraints, authors proposed a NOMA scheme that is able to optimize the transmit power and then reduces the risk of eavesdropping. The authors of [28] investigated NOMA systems with untrusted near users, where joint beamforming and power allocation strategy was proposed to achieve a reliable and secure transmission.
Furthermore, the authors of [32] studied beamforming design to enhance PLS of NOMA with the aid of artificial noise. Unlike [32], a multiple-input single-output (MISO) system was investigated in [33], where a novel artificial noise aided secrecy beamforming was introduced to combat the eavesdroppers. Taking the advantages of relaying networks, works reported in [29]- [31] relied on a dedicated relay to make the communication between the base station (BS) and the paired users to improve ergodic secrecy rates and secrecy outage probability (SOP). Additionally, the secrecy issue of multiple-input multiple-output (MIMO) network with arbitrary number of antennas was studied in [37], where the random binary sequence was employed to achieve a secrecy communication.
In practice, the proactive legal eavesdropping is highly significant to monitor the information exchange between suspicious users such as criminals and terrorists who may use smartphones for illegal activities [5]- [7]. Thus, the eavesdroppers are considered as legitimate monitors for the purpose of wireless surveillance. In other words, the main objective of proactive eavesdropping is to exploit as much information as possible from the suspicious communication link [17], [39].
In [5], the authors proposed a legal eavesdropping system via the jamming approach to maximize the average eavesdropping rate, where the legitimate monitor emits jamming signals with optimized power control to moderate the suspicious communication rate. Subsequently, J. Xu et al. investigated a proactive eavesdropping scheme via the cognitive jamming and an optimal power allocation policy was proposed to maximize the eavesdropping non-outage probability and the relative eavesdropping rate in both delaysensitive and delay-insensitive cases for the suspicious communication [6]. As an extension of [5], [6], works reported in [16] addressed on a multi-antenna full-duplex (FD) monitor and maximized the eavesdropping non-outage probability by optimizing jamming power and transmit/receive beamforming vectors. D. Xu et al. considered a downlink suspicious NOMA network with multiple groups of suspicious users and proposed a heuristic iterative algorithm to maximize the number of successfully eavesdropped suspicious users [39]. In [40], under low detection probability condition at the suspicious receiver, the authors proposed an iterative search algorithm to maximize the surveillance performance.
Considering the relaying networks, the works in [8], [14], [15] considered the eavesdropping of the two-hop suspicious communication link. In particular, G. Ma et al. studied the wireless surveillance of a two-hop suspicious communication link by a half-duplex legitimate monitor. They concluded that the eavesdropping rate at the legitimate monitor can be significantly improved by jointly optimizing the eavesdropping mode selection as well as the transmit power [15]. X. Jiang et al. considered legitimate surveillance in a dual-hop DF relaying system. They proposed two strategies to maximize the eavesdropping rate, the corresponding optimal beamformer, and the power allocation scheme has been derived. The numerical results showed that the system performance is better compared with intuitive benchmark schemes [14]. Meanwhile, authors in [8] proposed extract and approximate optimal jamming scheme for the proactive eavesdropping over an amplify-and-forward (AF) relay network. The results indicated that the optimal jamming scheme outperforms passive monitoring and proactive monitoring via constant-power jamming. H. Wu at et al. investigated a proactive eavesdropping scheme with a decode-and-forward relay and optimized the transmit power and location deployment at the relay to maximize the average eavesdropping rate [41].
To investigate relay-aimed proactive eavesdropping systems, J. Moon et al. considered a proactive eavesdropping system where a central monitor eavesdrops the information exchanged between a pair of suspicious entities through AF, FD relays and a cooperative jammer. They proposed an effective two-layer optimization method to obtain a globally optimal power allocation at both the relay and the jammer for maximizing the eavesdropping rate. The numerical results indicated that the proposed solution improves the system performance compared to the conventional scheme [11]. Additionally, J. Moon et al. investigated a novel proactive eavesdropping method via spoofing relay manner to further improve the information surveillance capability of the legitimate monitor, and three possible spoofing relay strategies were presented to maximize the eavesdropping performance [10].
B. Li et al. considered the proactive eavesdropping for multiple suspicious communication links [9], [25]. In [9], B. Li proposed a cooperative eavesdropping scheme, where a primary legitimate monitor and an assistant legitimate monitor cooperatively interfere the suspicious links between an illegal transmitter and receiver to maximize the eavesdropping energy efficiency. The numerical results showed that a cooperative scheme can improve the legitimate eavesdropping performance significantly. Furthermore, B. Li et al. presented a novel intervention strategy selection and power allocation solution based on jamming/relay features. They concluded that the proposed approach can effectively improve the eavesdropping rate compared to the conventional eavesdropping approach [25]. However, to the best of the author's knowledge, there are few existing works to address the proactive eavesdropping on the NOMA network which is considered as a potential technique applying for the 5G network.
Thus, we investigate legitimate proactive eavesdropping for a NOMA system where a LM transmits jamming signals to suspicious users to make the eavesdropping channel capacity higher than the data rate of the suspicious users. Taking this opportunity, the LM listens to the message and then forwards the intercepted data from the suspicious users to the LE. Besides, the LE can legitimately eavesdrop through the direct links. The main contributions of this work are summarized as follows: • The communication protocol for the proactive eavesdropping system in the NOMA network is proposed. Accordingly, power allocation policies for deterministic and non-deterministic interference links of jamming signals of the LM are obtained. • The closed-form expression of the successful eavesdropping probability for the best and the worst user are derived to evaluate the legitimate eavesdropping performance.
• Numerical results show that the number of user-pair, the number of antennas at the legitimate monitor, and power allocation are important factors to enhance legal eavesdropping performance for the best user. In this paper, we consider a scenario with a multiple antennas legitimate monitor, multiple antennas suspicious base station and suspicious users employ the NOMA technique to transmit signals to a suspicious base station.
The rest of this paper is organized as follows. In Section II, the system and channel model are introduced. In Section III, the power allocation policies for the jamming signal of the LM under deterministic and non-deterministic interference channel is calculated. Furthermore, the closedform expressions of the successful eavesdropping probability for the best user and the worst user are derived. In Section IV, numerical results are provided to verify the analytical expressions. Finally, Section V summarizes the paper.

II. SYSTEM MODEL
In this section, we introduce the system model and communication protocol.

A. PROTOCOL DESCRIPTION
We consider an uplink NOMA system as shown in Fig. 1. The system consists one suspicious base station B with N antennas, 2K suspicious users denoted by U = {U (1) , ..., U (2K) }, one legitimate monitor E are equipped M +1 antennas, whereas the legitimate eavesdropper D is deployed with a single antenna. The each suspicious user is equipped with a single antenna. We assume that the suspicious users are grouped into pairs randomly U l →E. It is noted that E immediately forwards the decoded message to D once E decodes the eavesdropped message successfully. Moreover, we assume that D is in the coverage range of U (k) l , i.e., D also eavesdrops signals from U (k) l . In the considered context, the suspicious users and B may be devices of criminals or terrorists while E and D may be drones, unmanned aerial vehicle (UAV), or smartphones which are equipped for soldiers in the battle field. The base station E The legitimate monitor D The legitimate eavesdropper N The number of antennas installed at the suspicious base station M + 1 The number of antennas installed at the legitimate monitor 2K The number of suspicious users U (k) l The k−th suspicious user-pair, where l ∈ {1,2} and 1 The channel gain between U The power allocation coefficient of user-pair U The power allocation coefficient of the LE f X The probability density function of X  l →D link, respectively (n ∈ {1, 2, . . . , N }, m ∈ {1, 2, . . . , M }), g n is the channel gain between the n-th antenna of B and E, β m denotes the channel gains between the m-th antenna of E and D. Furthermore, we assume the channel state information (CSI) of all links are perfectly known at the LM and LE by the method given in [25], [42]. We also assume that users are operating in the indoor environment and there is none-line-of sight among users [43]. Accordingly, all channels are modeled as Rayleigh fading, and the respective channel gains X (X ∈ {h l , g n , β m }) are random variables (RV) distributed following exponential distribution with channel mean gain Ω X . Figure 1: System model of proactive eavesdropping in NOMA networks.
Thus, the probability density function (PDF) and cumulative distribution function (CDF) are formulated, respectively, as follows [44]:

B. SIGNAL MODEL
For communication, the user-pair U (k) l broadcasts a superimposed signal to B which is a mixture signal of U (k) 1 and U (k) 2 . Meanwhile, the legitimate monitor E broadcasts jamming signal s J with the transmit power P J . Then the received signal at the n-th branch antenna of B could be expressed as where P s is the total transmit power of the user-pair U has better quality of channel than that one of U (k) 2 . It means that a higher power level is allocated to U (k) 2 , while a lower power level will be assigned to U as an interference. After that, the B subtracts the signal of U by SIC and then decodes the signal of U (k) 2 [45]. As a result, the instantaneous signal-to-interference-plus-noise ratio (SINR) of U at the n-th branch antenna of B subject to the interference induced by E can be respectively formulated, as where P J is the power of jamming signal generated by E.
Since B uses the selective combining technique to process the signal, the SINR of the user-pair U (k) l at B can be expressed as follows: With (6) and (7), the achievable data rate of U (k) l →B suspicious link under the effect of a jamming signal from E can be given respectively as where W denotes the system bandwidth.
On the other hand, due to the broadcast nature of wireless transmission, E also eavesdrops the signals which transmitted from the user-pair U (k) l . Accordingly, the received signal at the m-th antenna of E is given by where σ E ∼ N (0, N 0 ) denotes the AWGN at E. Similarly, we assume that SIC can also be successfully implemented at E, i.e, in the first phase, E first decodes U As a consequence, the instantaneous SINR of the user-pair U (k) l at the m-th branch antenna can be expressed as, respectively E also applies the selection combining (SC) technique to enhance the quality of received signal. Accordingly, SINR of the user-pair U (k) l at E can be expressed, respectively, as follows: In the second phase, E forwards the signal to D over the antenna which has the best channel gain. E operates as jammer to emit the jamming signal, which is known to D while remains unknown to the illegal users. Thus, the jamming signal can be canceled out at D and confuse only the illegal users. The received signal at D can be expressed as where P e ∈ [0, P max J ] is the transmit power of E used to forward the eavesdropping message to D, δ from the received signals by considering the signal of U (k) 1 as interference. Accordingly, the instantaneous SINR at D can be written, respectively, as D also applies the SC technique to improve the quality of received signal. Thus, SINR of the user-pair U (k) l at D can be expressed, respectively, as follows: Based on (13) and (18), the achievable data rate of U (k) 1 at E and D can be expressed, respectively, as follows Next, combining (14) and (19), the achievable rate of U (k) 2 at E and D can be formulated, respectively, as follows In direct link, D also can overhear signal from the userpair U (k) l . Thus, the SINR of U (k) l →D links are expressed, respectively, as follows Based on (24) and (25), the achievable data rate of the U (k) l →D links are given, respectively, as follows R (k,SD) 1 With (20), (21), (26), (27), (22) and (23), the end-to-end data rate of U (k) l at D over the relaying links and direct links is given by

III. SYSTEM PERFORMANCE ANALYSIS
In this section, we first derive the power allocation policies for the jamming signal in cases deterministic and nondeterministic channel between LM and SBS is available and is not available. Subsequently, we analyze the successful legitimate eavesdropping probability at D.

A. POWER ALLOCATION POLICY FOR JAMMING SIGNAL
E transmits a proactive jamming signal with power P J to degrade the achievable data rate of U (k) l at the suspicious base station, U (k) l responds by immediately increasing its transmit power P s to maintain the outage performance of system. Thus, if E causes serious interference to the suspicious base station so that U (k) l cannot adjust its transmit power to maintain communication rate, U (k) l will stop communicating and the legitimate eavesdropping process fails.
The transmit power P s of the user-pair U (k) l and jamming power P J of the LM in practice subject to a maximum power constraint as follows: Further, in order not to cause harmful interference to the suspicious base station, E needs to adjust the jamming power to guarantee the decoding outage probability at the suspicious base station which can be expressed in terms of the outage probability constraint as follows: where O 1 , O 2 are outage probability of U Pr α (k) where φ 0 = 2 γ th W − 1. Depending on the CSI of the E→B interference link, we consider the power allocation for jamming signal in two cases as follows 1) Deterministic Interference Link from the LE to the SBS In this case, the CSI of the interference link is available at LE. It means that g n is deterministic.
Using Equation (1), (2), the f h (k) 2,n and F h (k) 1,n are given by Substituting (36) and (37) into (35), we have We assume that the antennas of suspicious base station close to each other. Thus, all branches of antenna have the same channel mean gain, i.e., Ω h (k) [46]. Finally, O 1 is obtained as By substituting (39) into (31) and after some mathematical manipulations, we obtain an expression for the power of the jamming signal as follows: where and {x} + = max{x, 0}. Whenever U (k) l can adjust its transmit power to adapt to the jamming signal and to guarantee its outage performance, E can further increase P J . However, E must stop increasing transmit power of the jamming signal where U should satisfy the following constraint: Next, we calculate the expression for jamming power of E which satisfies U (k) 2 's outage probability constraint. By applying exponential distribution, (34) can be derived as Combining (32) and (44), we obtain an expression for the jamming power as follows: where P J is the power of jamming signal for a given P s . Although U (k) l can adapt its transmit power P s according to the channel condition and interference, it can not increase the power higher than the value P max s . Further, the right hand side of (45) is a monotonically increasing function with respect to P s . Thus, the range for the P J under the outage probability constraint of U (k) 2 and peak jamming power constraint of E is obtained as Combining (29), (43) and (47), the range for the transmit power of the jamming signal in deterministic interference link case is formulated as follows: In this subsection, channel gain g n is a random variable (RV) distributed following exponential distribution with channel mean gain Ω g . To archive the analytical expression of O 1 in (33), we have the following lemma. Lemma 1. Let a,b, and c are positive constants. Further, let X, Y, and Z are independent and exponentially distributed RVs with mean values Ω X , Ω Y , and Ω Z , respectively. Then CDF of T is obtained by (50) where T is defined as (49) By applying (50), outage probability of U (k) 1 can be derived as follows: By substituting (51) into (31) and after some mathematical manipulations, we obtain an expression for the jamming power of E under the outage probability constraint of U (k) 1 as follows: where π 1 is defined as To maintain quality of service (QoS) of U (k) 1 at SBS, E must control the jamming power to satisfy the following constraint: Next, we calculate the outage probability of U (k) 2 . Applying (16) in [47], the OP 2 can be derived as follows: Combining (29) and (55), we obtain an expression for the jamming power under the outage probability constraint of U (k) 2 as follows where π 2 is defined as The right hand side of (56) is a monotonically increasing function with respect to P s . Thus, the range for the P J under the outage probability constraint of U (k) 2 and peak jamming power constraint of E is formulated as Combining (29), (54) and (56), the range for the jamming power of E in non-deterministic interference link case is formulated as follows: (59)

B. SUCCESSFUL LEGITIMATE EAVESDROPPING PROBABILITY ANALYSIS
In this section, we characterize successful legitimate eavesdropping probability at D. The legitimate eavesdropping process is successful, only if the eavesdropping message is decoded successfully at D with the help of E. Here, E acts as a relay and active jamming station to help the eavesdropping process of D.
It is worth noting that U (k) 1 has better channel gain than U (k) 2 , therefore its SINR is better than that one of U (k) 2 . Accordingly, we consider two cases, namely, the best and the worst user. VOLUME 4, xxxx 1) Successful legitimate eavesdropping probability for the best user In this subsection, we evaluate the successful legitimate eavesdropping probability for U (k) 1 which has the best endto-end data rate among K user-pairs and the successful legitimate eavesdropping probability for the best user is accordingly expressed as where R (k) 1,E2E is defined in (28). Next, EP 1 can be derived as where R min . P 1 and P 2 are presented, respectively, as The closed-form expression of P 1 and P 2 are obtained, respectively, as (64) Finally, EP 1 can formulate the successful eavesdropping probability as follows where P 1 and P 2 are given by in (64) and (65), respectively.
2) Successful legitimate eavesdropping probability for the worst user In this subsection, we calculate successful legitimate eavesdropping probability for U (k) 2 which has the worst endto-end data rate among K user-pairs. And the successful legitimate eavesdropping probability for the worst user is accordingly expressed as where R (k) 2,E2E is defined in (28). Further, EP 2 can be derived as where R min . F 1 and F 2 are presented, respectively, as The closed-form expression of F 1 and F 2 are obtained, respectively, as Proof. See Appendix C.
Finally, EP 2 can be obtained as where F 1 and F 2 are given in (71) and (72), respectively.

IV. NUMERICAL RESULTS
In this section, we provide numerical examples for the power allocation policies of the jamming signal, and evaluate the successfully legitimate eavesdropping probability at the legitimate eavesdropper of the considered system. We use Monte Carlo simulations by averaging results for independent loops. We consider the system which consists three user-pairs (K = 3) with channel mean gains respectively as Ω     γ J = P J /N 0 and the transmit SNR γ s = P s /N 0 of U (k) l for deterministic and non-deterministic interference link, respectively. We observe that to force U (k) l to increase its transmit SNR γ s , the legitimate monitor must increases the transmit SNR γ e of jamming signal.
However, for the same region of the U (k) l transmit SNR [-5, 10] dB, the demand for the transmit SNR of the jamming signal for the non-deterministic interference link is always higher than the one of the deterministic interference link. To make this statement more clear, we observe the case Ω gn = 1 in both Fig. 2 and 3. Clearly, the transmit SNR of the jamming signal only needs to increase from -10 dB to 12 dB to keep the transmit SNR of the U (k) 1 in the range of [-2, 10] dB (see Fig. 2). However, the transmit SNR of the jamming signal must increase from 2 dB to 15 dB to keep the transmit SNR of the U (k) 1 in the range of [-2, 10] dB (see Fig. 3). In other words, the LM only needs a low power level for the jamming signal when the LM knows exactly the CSI of the E→B interference link.
Furthermore, the result shown in these figures shows that when channel mean gain of U (k) l →B link increases, e.g., Ω h1 = {2, 4, 5}, the LM needs more transmit SNR for jamming signal to keep the transmit SNR of U (k) l at the same level, e.g., γ s = -2 (dB). This can be explained by the fact that the user U (k) l only needs to use a small amount of power to maintain its QoS when U (k) l →B link in a good condition. Thus, LM requires a high power level for the jamming signal to generate sufficient interference to the B.
Figs. 4 shows the impact of the number of user-pair on the successful eavesdropping probability for the best user. It is clear that the successful eavesdropping probability is improved significantly as the number of user-pair increases, i.e,. K = 1, 2, 3. As K increases, this probability increase to 1. This means that as the number of user-pair increases, the ability to select the best user is more diverse and efficient. As result, successful eavesdropping probability of system is VOLUME 4, xxxx  improved. Figs. 5 shows the impact of the number of user-pair on the successful eavesdropping probability for the worst user. In contrast to the best user, the successful eavesdropping probability will be reduced quickly as the number of userpair increases, i.e., K = 1, 2, 3. In case K = 3, we see that the successful eavesdropping probability is zero when the transmit SNR γ s is smaller than 5 dB. This is because as the number of user-pair increases, the ability to select the worst user is more diverse and efficient. Thus, the successful eavesdropping probability of the system is degraded. Fig. 6 and 7 show the impact of the number of eavesdropping antennas M at LM on the successful legitimate eavesdropping probability for the best and the worst user. It is observed that the successful legitimate eavesdropping probability increases as the number of eavesdropping antennas increase for both the best and the worst user. This result occurs because the diversity gain at LM increases as M increases. This indicates that increasing the transmit antenna M is an effective yet simple way to improve eavesdropping probability, which is easily achieved in 5G networks with a large antenna array.
Finally, Fig. 8 shows the impact of the power allocation coefficient δ (k) 1 and the transmit power P s of U (k) l on the successful legitimate eavesdropping probability for the best user which has the best end-to-end data rate among K users U (k) 1 . Note that the power allocation coefficient must be between 0 and 0.5. As is shown from this figure, the successful legitimate eavesdropping probability increases significantly as the power allocation coefficient and transmit power increases. This result can be explained by the fact that the legitimate eavesdropper D can more easily capture the signals from the suspicious users as these sources increase 10 VOLUME 4, xxxx their transmit power.

V. CONCLUSIONS
In this work, we have investigated a proactive eavesdropping scheme in the NOMA networks where the legitimate monitor is proactive to jam the suspicious receivers to improve the eavesdropping performance. The power allocation policies which maintain the outage performance of the suspicious link under deterministic and non-deterministic interference channels were considered. The closed-form expression of the successful eavesdropping probability for the best user and the worst user were derived to evaluate the system performance. The numerical results show that when the interference channel between the LM and SBS is deterministic, the required power level of the jamming signal is smaller than in the case of non-deterministic interference link between LM and SBS. It was shown that the successful eavesdropping probability for best user is higher with increasing the number of user-pair and the number of antennas of the legitimate monitor. Furthermore, the successful eavesdropping probability for the best user was impacted by the power allocation between NOMA users. .

APPENDIX A PROOF LEMMA 1
The CDF of T is defined as follows: After some mathematical manipulations, F T (t) can be derived as The proof is completed.

APPENDIX B
P 1 is calculated as where φ 1 = 2 r 1 W − 1. Applying exponential distribution, P 1 can be derived as After some mathematical manipulations, P 1 is obtained as Further, P 2 is calculated as where Next, P 21 is calculated as where φ 2 = 2 where f f (k) . We also assume that all branches of antenna of E have the same channel mean gain, i.e., Ω f (k) , Ω β (k) m = Ω β . After some mathematical manipulations, P 21 can be expressed as Applying exponential distribution, P 22 can be derived as Substituting (84) and (87), we obtain P 2 as The proof is completed.