Security-Reliability Analysis of Noma-Based Multi-Hop Relay Networks in Presence of an Active Eavesdropper with Imperfect Eavesdropping CSI

In this paper, we evaluate system performances of a multi-hop relay protocol with presence of an active eavesdropper. In the proposed protocol, a source attempts to transmit its data to a destination with assistance of multiple intermediate relays. From the eavesdropping Channel State Information (CSI) estimated, the source and relays adjust their transmit power so that the eavesdropper cannot overhear the transmitted data. Moreover, to enhance throughput for the proposed system, Non-Orthogonal Multiple Access (NOMA) technique with a simple power allocation is also proposed. We derive exact closed-form expressions of the Outage Probability (OP) and throughput for the data transmission over Rayleigh fading channel. In addition, when the CSI estimation is imperfect, Intercept Probability (IP) at the eavesdropper is derived. Finally, Monte Carlo simulations are presented to verify the theoretical derivations.


Introduction
Recently, Non-Orthogonal Multiple Access (NOMA) technique [1], [2], [3] and [4] has gain much attention as an efficient method to significantly improve the data rate for wireless communication systems.Different from the conventional orthogonal multiple access, a transmitter can simultaneously send multiple data at the same time, code and frequency to one/multiple receivers by allocating different transmit power levels to the transmitted data.At the receivers, a Successive Interference Cancellation (SIC) technique is used to extract the intended data.
Secured communication techniques at the physical layer [5], [6], [7] and [8] have become an efficient method to obtain the data security without using complex cryptographic methods.In the physical-layer security, the physical properties of the wireless channel such as Channel State Information (CSI) and distances of the connection links can be used to protect the transmitted data.To the best of our knowledge, there are several published papers related to physical-layer security issue in NOMA-based relay networks.Particularly, the authors in [9] optimized secrecy sum rate of a NOMAbased downlink system including a transmitter, multiple legitimate users and a passive eavesdropper.Similar to [9], the authors in [10] proposed a secured down-link communication scenario where one multiple antenna base station communicates with multiple single antenna users using NOMA.
Different from the previous published works [9] and [10], this paper considers a multi-hop relay network, in which a source uses NOMA to transmit its data to a destination via multiple intermediate relays, in presence of an active eavesdropper.To avoid the eavesdropper from overhearing the transmitted data, the transmitters including the source and relays attempt to estimate the Channel State Information (CSI) between themselves and the eavesdropper, and then adjust their transmit power appropriately.For performance evaluation, we derive exact closed-form expressions of Outage Probability (OP) and throughput for the proposed scheme over Rayleigh fading channel.Moreover, when the eavesdropping CSI estimation is imperfect, Intercept Probability (IP) at the eavesdropper is also derived.We then perform Monte Carlo simulations to verify our theoretical derivations.
The rest of the paper is organized as follows.The system model and the proposed scheme are described in Sec. 2. In Sec. 3. , the performance evaluation of the protocol is described.The simulation results are presented in Sec. 4. Finally, the paper is concluded in Sec. 5.

System Model
Figure 1 shows system model of a NOMA-based multihop transmission protocol, where the source (N 0 ) communicates with the destination (N K ) via the via the multi-hop fashion with the help of K−1 relay nodes, respectively denoted by N 1 , N 2 ,. . .and N K−1 .In the considered network, the Eavesdropper (E) appears and tries to overhear the data transmitted by the source and the relays.Assume that all of the terminals have Data Links Eavesdropping Links a single half-duplex radio and a single antenna, and hence a Time-Division Multiple Access (TDMA) is occupied.To avoid the eavesdropper from combining the transmitted data with Maximal Ratio Combining (MRC), the transmitters including source and relays use Randomize-and-Forward (RF) to randomly generate codebook [11] and [12].We also assume that all of the channels between two arbitrary terminals are Rayleigh fading.Moreover, because the eavesdropper is an active node, the source and relay nodes attempt to estimate Channel State Information (CSI) between themself and the node E.
Considering the communication at the kth hop (k = 1, 2, ..., K) where N k−1 sends the source data to N k while E overhears the data.Let h k and g k denote the channel coefficients of the N k−1 → N k and N k−1 → E links.We also denote g e k as the CSI estimated by N k−1 .The correlation between g k and g e k can be formulated as in [13] and [14]: where ρ is channel correlation factor and ε is estimation error.
Moreover, channel gains exponential Random Variables (RVs) whose parameters [15] and [16] are λ D,k and λ E,k , respectively.It is worth noting that γ e E,k = |g e k | 2 also follows an exponential distribution with the parameter λ E,k .To take path-loss into account, these parameters can be modeled by where respectively, and β is path-loss exponent.
Using NOMA, the transmitter N k−1 combines two source data, i.e., x 1 and x 2 , to create a superimposed data x c as follows: where P k−1 is transmit power of N k−1 , α 1 and α 2 are power allocation coefficients with α 1 +α 2 = 1 and Then, u c is sent to N k , and the received data at N k can be expressed as where n k is Gaussian noise at N k whose mean and variance are 0 and σ 2 0 , respectively.Following the principle of NOMA, by treating u 2 as noise, N k first decodes u 1 and then removes this data from the received data (z k ).As a result, the instantaneous Signal-to-Interference-plus-Noise Ratio (SINR), with respect to u 1 , can be obtained as After completely removing the interference component α 1 P k−1 h k u 1 , the received data z k can be rewritten by From Eq. ( 6), the instantaneous SINR obtained to decode u 2 is formulated by From Eq. ( 5) and Eq. ( 7), the channel capacity, with respect to u 1 and u 2 , can be given, respectively by where the factor 1 K indicates that the data transmission is split into K orthogonal time slots.
Due to the broadcast nature of wireless channel, the eavesdropper E can receive the data u c from the node N k−1 and decodes u 1 and u 2 with SIC, similarly as the receiver N k does.Similar to Eq. ( 8) and Eq. ( 9), the instantaneous channel capacity received at E, with respect to u 1 and u 2 , can be expressed, respectively by Let us consider the probability that N k can decode both u 1 and u 2 correctly.This event can be formulated by where R th is a predetermined target rate, and τ = 2 KR th − 1.
Then, we can give Eq.( 11) by the following formula: where From Eq. ( 13), we observe that the value α 2 must satisfy the condition by Next, it is worth noting that if ∆ 1 ≥ ∆ 2 , when N k decodes u 1 successfully then it also decodes u 2 successfully.Therefore, we propose a simple power allocation as Combining Eq. ( 14) and Eq. ( 15), we obtain Moreover, from Eq. ( 16), we can easily observe that to maximize J k , the optimal values α 1 and α 2 can be given, respectively as Considering the decoding probability at the eavesdropper; also, once this node can decode u 1 correctly, then it can decode the data u 2 successfully.As mentioned above, the transmitter N k−1 attempts to estimate the eavesdropping CSI for adapting its transmit power using the following strategy: P k−1 γ e E,k ≤ γ th , where γ th is a predetermined value.Hence, the maximum transmit power of N k−1 is obtained by Substituting Eq. ( 17) and Eq. ( 19) into Eq.( 5) and Eq. ( 10), respectively, yields Then, the end-to-end channel capacity of the data link can be obtained by Moreover, the channel capacity of the eavesdropping links is dominated by the highest link, which means From Eq. ( 21) and Eq. ( 22), we can formulate the Outage Probability (OP) and the Intercept Probability (IP), respectively as Finally, throughput of the N 0 → N K connection can be defined by where the factor 2 implies that the destination can receive two data u 1 and u 2 at the same time.

Corollary 1
Without using NOMA, OP can be rewritten by Proof: In this case, N k−1 only sends u 1 to N k at the kth time slot.In particular, the fractions of transmit power are set by α 1 = 1 and α 2 = 0.With the same manner as Proof of Proposition 3.1.We can obtain Eq. ( 29).Remark 1: From Eq. (26), Eq. ( 28) and Eq. ( 29), because θ ≥ τ σ 2 0 /γ th , it is obvious that OP wo ≤ OP.

Corollary 3
Without using NOMA, throughput of the data link is calculated by Proof: Since the destination only receives one data from source, the system throughput is formulated by Substituting Eq. (30) into Eq.(32), we obtain Eq. (31).

Simulation Results
In this section, we present Monte Carlo simulation results to verify the theoretical results and to compare the performances of the protocols discussed in the previous sections.In simulation environment, we consider a two-dimensional plane in which the co-ordinates of the nodes the relay N k , k = 0, 1, ..., K, and the eavesdropper are (k/K, 0) and (0.5, 1), respectively.In all of the simulations, we fix the path-loss exponent (β), the target rate (R th ) , the variance of noise σ 2 0 by 3, 0.5 and 1, respectively.In Fig. 2, we present the outage performance of the proposed protocol as a function of γ th .In this figure, the correlation coefficient ρ is set by 0.99.It can be observed from Fig. 2 that the value OP decreases with the increasing of γ th .Moreover, the outage performance is better with higher number of hops.It is also seen that OP of the proposed system without using NOMA is always lower than that of the NOMA-based system.It is worth noting that the theoretical and simulation results are in good agreement, which validates our theoretical analysis.In Fig. 3, we show the ThroughPut (TP) of the N 0 → N K as a function of γ th .In this figure, the theoretical results are obtained from Corollary, Subsec.3.3.and Corollary, Subsec.3.4., ρ is also set by 0.99.We can be observed that the value TP increases slowly with the increasing of γ th .Besides, the throughput is higher when number of hops decreases and when the number of hops increases in which value TP seems to be saturated with the increasing of γ th .It is also seen that TP of the proposed system without using NOMA is always lower than the NOMA-based system.This again demonstrates the effectiveness of the NOMA-based system as in our proposal.
Figure 4 presents Intercept Probability (IP) as a function of γ th when ρ = 0.99.As illustrated in this figure, IP increases with higher value of γ th .It is due to the fact that when γ th is high, the transmit power of N k−1 is high, which increases the channel capacity of the eavesdropping links.As expected, this figure shows that when number of hops is lower, value IP is higher.Figure 5 shows value IP as a function of γ th when K = 8.Similar to Fig. 4, intercept probability at the eavesdropper increases with higher value of γ th .However, we can see that the value IP will be lower with the higher channel correlation factor ρ.

Conclusion
In this paper, we proposed and analyzed system performances of a multi-hop relay protocol with presence of an active eavesdropper.By employing different combining techniques at relays and destination, the diversity order of the proposed protocols equals to the number of hops.In addition, to improve throughput for the multi-hop relay system, we proposed Non-Orthogonal Multiple Access (NOMA) technique with a simple power allocation.We derived the asymptotic closed-form expressions of the outage probability, intercept probability and throughput over Rayleigh fading channel.Finally, Monte Carlo simulations were presented to validate our derivations.

Fig. 1 :
Fig. 1: System model of NOMA-based multi-hop transmission protocol in presence of one eavesdropper.

Fig. 3 :
Fig. 3: Throughput of the N 0 → N K as a function of γ th when ρ = 0.99.
Figure5shows value IP as a function of γ th when K = 8.Similar to Fig.4, intercept probability at the eavesdropper increases with higher value of γ th .However, we can see that the value IP will be lower with the higher channel correlation factor ρ. Figure4 and