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Abstract

Privacy and perspective are attracting more and more attention from worldwide users, so security in wireless communication system has become popular in recent researches, especially the physical layer security in 5G systems. In this article, we discuss the physical layer security in 5G downlink transmission systems; we propose the joint optimization of subcarrier, power, and artificial noise to achieve the higher security rate, our proposed method could approach to the upper bound of the security rate rather than the other methods, respectively. Then, in the simulation part, we present the theoretical and system-level simulation, and the results indicate that our proposed method could effectively increase the security rate without losing the system transmission speed.

Keywords

Physical layer security security rate joint optimization cooperative communication 5G

Introduction

Security and privacy in communication system refers to the information in the process of transmission, and interaction is not eavesdropping, destruction, and useable.¹ Wireless communication systems are able to receive the wireless signals; therefore, security and privacy in the wireless communication system is more severe. In addition, the wireless communication applications are becoming more and more popular, which involves personal privacy and interests of the business.² It also constantly appears to meet the needs of the public, such as mobile payment, online banking, and other business. Therefore, how to provide users with satisfaction and security as a wireless communication system to achieve sustainable and healthy development must face and solve the problem. Our research can provide more secure measures and techniques in some practical scenarios.

In the existing security and privacy studies in wireless network, the security measures are mostly about the traditional encryption system based on the key and encryption algorithm.³ This encryption system is working with the physical layer, which is independent to MAC layer, network layer, application layer, etc.,⁴ we call the upper security. In wireless communication systems, eavesdroppers are easy to receive the physical layer of the transmission signal,⁵ that is, the upper secure cipher text. When the eavesdropper intercepts a large number of cipher text,⁶ it is possible to find a simple way to obtain the key parameters that determine the security of the system. If the physical layer security can be achieved, so that the eavesdropper cannot receive or even if it cannot be properly decoded, then the system’s safety factor will be greatly improved. Our research is mainly focused on the use of channel-coding and signal-processing technologies, which makes eavesdroppers hard to receive or even received and cannot be correctly decoded, we will do this in the physical layer of security called physical layer security. As early as 1975, Wyner et al. had demonstrated the ability to use channel-coding techniques to provide security in the physical layer and to provide a safe transmission rate and a measure of safety. At present, multi-antenna and multi-carrier technology is widely used in wireless communication systems, and wireless LAN, wireless metropolitan area network, 4G, 5G, and other network standards are introduced in the multi-antenna multi-carrier systems.⁷ These technologies bring space and frequency through higher degrees of freedom for physical layer safe transmission. Nevertheless, the physical layer security in the multi-antenna multi-carrier system still exists with many unsolved problems. Therefore, it is necessary to study the physical layer security in the multi-antenna multi-carrier system, which will improve the security performance of the existing wireless communication system to a certain extent.

The rest of this article is organized as follows: In section “Related works,” related works about physical layer security in wireless communication systems have been listed, from which we point out the chances to propose our work. In section “Theoretical modeling and analysis,” we propose the theoretical analysis of resource allocation problems in 5G wireless communication systems. In section “Proposed algorithm,” we present our proposed novel joint resource allocation algorithm in 5G multi-carrier scenario based on the proof above. In section “Simulation and performance analysis,” simulation and analysis have been given to prove the above analysis. In section “Conclusion,” conclusion is given.

Related works

Wyner first proposes the theoretical analysis model of physical layer security in 1975. He mainly studies the degenerate discrete memoryless channeling model (Alice–Eve channel is the degraded channel of Alice–Bob channel). In his thesis, he gives the mathematical definition of safe transmission and the theoretical analysis of the eavesdropping channel.^8,9 It is concluded that the secure transmission rate of the degraded discrete memoryless channel is the difference between the mutual information of the Alice–Bob channel and the Alice–Eve channel.^10,11 Then, a variety of discrete or continuous single-input and single-output (SISO) eavesdropping channels has been studied extensively. In 1978, Cheong et al. studied the degraded Gaussian eavesdropping channel and demonstrated that the security capacity of the Gaussian eavesdropping channel is the difference between Alice–Bob channel capacity and Alice–Eve channel capacity. Then, Csizar et al. considered a more general channel model,^12,13 the system also has broadcast information and secret information for transmission, and the channel is no longer limited to the degraded channel; this article gives the broadcast information and secret information transmission rate capacity. There is also a corresponding study of the scheme of adding artificial noise (AN) to the SISO, but the SISO channel has no extra freedom to provide.^14–16 At this point, when the channels of Alice–Bob and Alice–Eve are both exact SISO channels, the channel capacity of the secure transmission has been comprehensively studied and shows that only when the Alice–Bob channel is stronger than the Alice–Eve channel to obtain a positive safe transfer rate. Furthermore, it is found that the use of reasonable power distribution, combined with opportunistic communication and AN design, can make the channel gain of Alice–Bob channel to be less than the average channel gain difference of Alice–Eve channel. There is a positive safe transmission rate at the statistical level.

Multi-antenna technology (e.g. large scale antenna system (LSAS) or distributed antenna system (DAS) in 5G) has been widely used because of its diversity and reuse effects, bringing significant progress toward physical layer security. In a multi-antenna system, the secure transmission rate is still the difference between the Alice–Bob and Alice–Eve channels. Unlike the SISO channel, a multi-antenna system can achieve a greater secure transmission rate by designing a transmit beamforming or precoding so that the transmit signal better matches Bob’s objective physical channel.¹⁷ In addition, Alice can intentionally interfere with the Eve channel by sending AN, thereby reducing the Eve channel quality to improve the safe transmission rate. In the SISO channel, as long as the Bob channel gain is worse than the Eve channel, the sender cannot do anything; security transmission rate can only be zero.¹⁸ Thus, how to design the autocorrelation matrix of the transmitted signal in the multi-antenna system to increase the system to obtain a secure transmission rate is a matter of concern. When Alice has multiple antennas, Bob and Eve have only one antenna, which is called multiple-input and single-output (MISO) eavesdropping channel.¹⁹ Shafiee and Li et al. have given the optimal beamforming of the MISO system when the channel input is a Gaussian signal. When Alice, Bob, and Eve are equipped with multiple antennas, they are called MIMO Multiple-Eavesdropping (MIMOME) eavesdropping channels.²⁰ When Alice and Eve are equipped with multiple antennas, and Bob has only one antenna, it is called MISO Multiple-Eavesdropping (MISOME) eavesdropping channel. Khisti et al. have studied the MIMOME channel and MISOME channel and pointed out that when the signal-to-noise ratio (SNR) of the system is very high, the multi-antenna system approximation to the optimal precoding matrix is based on the Alice–Bob channel Generalized Singular Value Decomposition (GSVD) of Alice–Eve channel.²¹ At the same time, Oggier et al. also studied the safe transmission capacity of the multiple-input and multiple-output (MIMO) eavesdropping channel. There are many scholars from the signal processing level to optimize the multi-antenna system to send the waveform, which can effectively improve the safe transmission rate of the system. AN means that Alice adds AN to the sending signal, and the purpose is that through reasonable design, this noise has no effect on Bob and can interfere with Eve.

Orthogonal frequency-division multiplexing (OFDM) technology, which is of much concern to multi-antenna technology, is widely used because it can effectively overcome frequency selective fading. OFDM-based physical layer security transmission has also attracted many scholars to study. When the OFDM channel is input as a Gaussian signal, Li et al. studied the optimal subcarrier power allocation to maximize the secure transmission rate of the OFDM system.^22–24 In addition, given the good effect of AN in multi-antenna system, how to add AN in OFDM to improve the security performance of the system is also worthy of study. In addition to the signal processing point of view, there are many scholars on the eavesdropping channel–coding research, which is the physical layer of security applications in the real system. At the same time, how to use the random characteristics of the wireless channel to generate the key has also been widely concerned. Alice–Bob channel for Alice and Bob’s common observation of the random signal,²⁵ and Eve does not know this random signal. Alice and Bob are both using the two-way communication, so both sides obtain Alice–Bob’s wireless channel, through the wireless channel common extraction to produce a consistent key, and Eve obtains the key. In previous studies,^26–28 physical layer security in MIMO systems is introduced, but the optimization is only based on single parameter.

Theoretical modeling and analysis

The capacity of wiretap channel is defined by Shannon formula. In the well-known Alice–Bob model, the security capacity is defined by: $C = max Rs = [\log_{2} (1 + ({| h |}^{2} P_{s} / σ_{bob})) - \log_{2} (1 + ({| g |}^{2} P_{s} / σ_{eve}))]^{+}$ .From this equation, we can infer that the capacity is limited by transmission power, channel, and noise; this is the reason we choose the three parameters to perform the joint allocation to achieve higher security capacity.

Considering there are $N$ subcarriers in the 5G OFDM systems, each user in the system is equipped with single antenna. In OFDM system, while the transmitter is equipped with single antenna, the AN is designed using the degree of freedom (DOF) provided by the cyclic prefix (CP), this means, the noise is added in frequency domain in the zero space of Bob. Therefore, the signal will only affect the receivers without using the channel environment of Bob. We establish the scenario with one Alice, one Eve, and $K$ Bob located at the base station cell, where Alice is the base station, Bob is the registered user, and Eve is the illegal user that may monitor the system. In Figure 1, we illustrate the principle of the physical layer security in wireless systems. The target is to minimize the information received by Eve, so the possible operation to reduce the mutual information is to add some noise or use the transmission beamforming.

Figure 1.

Principle of physical layer security in wireless systems.

In Figure 2, we propose the system model of the physical layer security in 5G systems. The base station is working as Alice, the registered users are Bobs, and the illegal user located outside the base station is called Eve. Eve may obtain information through the information leakage of wireless signals. The base station side could not control the direction and range of the wireless signals, so the wiretap user Eve could receive the same signal with the reduced power, but the content is the same as that of the registered users. To minimize the information obtained by the illegal user, the system could adopt many operations, such as power control, AN, and resource allocation.

Figure 2.

System model of the Alice–Eve–Bob. The wiretap user Eve is trying to obtain information from the wireless leakage.

Define $H_{k, i} \in C$ the $k th$ channel gain on the $i th$ subcarriers, define $π_{k, i} \in N (0, 1)$ the assignment factor, where $π_{k, i} = 1$ means Alice arranges the $i th$ subcarrier to Bob $k$ . To make the arrangement fair, we restrict that every subcarrier could only be assigned to one registered user, this means we have the limitation that $\sum_{k = 1}^{K} π_{k, i} = 1$ . Using the same definition of parameters $i$ and $k$ , define $p_{k, i}$ the transmission power, and $s_{k, i}$ is the input signal that follows the complex Gaussian distribution. So, the information that Alice sends to Bob $k$ in the $i th$ subcarrier could form a vector ${\vec{x}}_{k} = [x_{k, 1}, x_{k, 2}, \dots, x_{k, N}]^{T}$ , and the transmission signal could be expressed using the following equation

$x_{k, i} = π_{k, i} \sqrt{p_{k, i}} s_{k, i}$ (1)

After the channel, the received signal could be expressed as

$y_{k, i} = h_{k, i} x_{k, i} + n$ (2)

The expression in frequency domain of equation (2) could be formed using the Fourier transform

$y_{k} = F R^{cp} H_{k, 0} (T^{cp} F^{H} x_{k} + a) + w_{k}$ (3)

Define $F$ the Fourier transform and $F^{H}$ the inverse-Fourier transform. $T = [{\tilde{E}}_{N_{cp} \times N}^{T} I_{N}]^{T}$ means the additional matrix of the CP, and ${\tilde{E}}_{N_{cp} \times N}^{T}$ means the last $N_{cp}$ line of the unit matrix $I_{N}$ . $R = [0_{N_{cp} \times N}^{T} I_{N}]^{T}$ means the matrix without CP. For wiretap user Eve, the received information could be expressed using

$z = F R^{cp} G_{0} (T^{cp} F^{H} x_{k} + a) + v$ (4)

In the above equations, $a$ means the additional AN, and $H_{k, 0}$ means the channel response of Alice–Bob channel in the time domain, which is a cyclic matrix. So, the received signal of Bob $k$ at the subcarrier $i$ could be expressed as follows

$y_{k, i} = π_{k, i} H_{k, i} \sqrt{p_{k, i}} s_{k, i} + f_{i}^{H} R^{cp} H_{k, 0} a + w_{k, i}$ (5)

Similarly, the received signal of Eve is given in equation (6)

$z_{i} = G_{i} \sum π_{k, i} \sqrt{p_{k, i}} s_{k, i} + f_{i}^{H} R^{cp} G_{0} a + v_{i}$ (6)

According to previous studies,^4,6,24 the AN must satisfy

$f_{i}^{H} R^{cp} H_{k, 0} a = 0, if π_{k, i} = 1, \forall k$ (7)

Let $a = Ud$ , $U$ is the semidefinite matrix and $d ~ CN (0, (σ^{2} / N_{cp}) I)$ , and by applying the AN, the received signal could be expressed as

$y_{k, i} = π_{k, i} H_{k, i} \sqrt{p_{k, i}} s_{k, i} + w_{k, i}$ (8)

$z_{i} = G_{i} \sum π_{k, i} \sqrt{p_{k, i}} s_{k, i} + f_{i}^{H} R^{cp} G_{0} Ud + v_{i}$ (9)

Proposed algorithm

To maximize the security rate, we propose the joint optimization of power, AN, and subcarrier to enhance the sum capacity rate. According to Munisankaraiah and Kumar,²⁴ we could form the optimization problem as follows

$\begin{matrix} max_{p_{k, i}, π_{k, i}, σ^{2}} \sum_{k = 1}^{K} R_{k} (p_{k, i}, π_{k, i}, σ^{2}) \\ s . t . \sum_{i = 1}^{N} \sum_{k = 1}^{K} p_{k, i} π_{k, i} + σ^{2} \leq P \\ π_{k, i} \in {0, 1}, p_{k, i} \geq 0, σ^{2} \geq 0 \\ \sum_{k = 1}^{K} π_{k, i} = 1 \end{matrix}$ (10)

For problem 10, the sub-problem to optimize the allocation of subcarriers has the optimal solution proposed in Moosavi and Bui,¹¹ and the optimal solution is given below. The physical meaning of this optimization means the subcarriers are assigned to Bob with the maximum channel gain, so the security rate could be maximized according to the definition of security rate

$π_{k, i}^{*} = {\begin{matrix} 1, & if k = argmax {| H_{k^{'}, i} |^{2}, k' = 1, 2, \dots, K} \\ 0, & otherwise \end{matrix}$ (11)

By applying the optimal solution of subcarrier allocation, the optimization problem could be reduced to two-dimensional

$\begin{matrix} max_{p_{k, i}, σ^{2}} \sum_{k = 1}^{K} R_{k} (p_{k, i}, {π^{*}}_{k, i}, σ^{2}) \\ s . t . \sum_{i = 1}^{N} \sum_{k = 1}^{K} p_{k, i} π_{k, i} + σ^{2} \leq P \\ p_{k, i} \geq 0, σ^{2} \geq 0 \end{matrix}$ (12)

The optimal allocation of subcarriers could be obtained through equation (11). So, the solution for the nonconvex problem expressed in equation (12) could be tackled using the dual function to transform the optimization problem to convex.

The Lagrange function expressed in equation (12) could be obtained through the following equation

$\begin{matrix} L (p_{k, i}, σ^{2}, λ) \\ = \begin{matrix} \sum_{i = 1}^{N} \sum_{k = 1}^{K} {\log_{2} (1 + π_{k, i}^{*} | H_{k, i} |^{2} p_{k, i}) - \log_{2} (1 + \frac{π_{k, i}^{*} | G_{i} |^{2} p_{k, i}}{σ^{2} b_{i}^{H} b_{i} + 1})}^{+} \end{matrix} \\ + λ (p - \sum_{i = 1}^{N} \sum_{k = 1}^{K} π_{k, i}^{*} p_{k, i} - σ^{2}) \end{matrix}$ (13)

For any fixed $λ$ , the solution for Dual Lagrange function is given using the following equation

$D (λ) \overset{Δ}{=} \max_{p_{k, i} \geq 0} L (p_{k, i}, σ^{2}, λ)$ (14)

It is clear that $D (λ)$ is convex about $λ$ , and the partial derivation is explicit, and ${p^{*}}_{k, i} and {σ^{2}}^{*}$ are the optimal solution when $λ$ is given

$\nabla D (λ) \overset{Δ}{=} P - \sum_{i = 1}^{N} \sum_{k = 1}^{K} {p^{*}}_{k, i} - {σ^{2}}^{*}$ (15)

The method to obtain the two optimal variables is using the dichotomy, and the optimal solution of the two variables is given in the following equations

$p_{k, i}^{*} = {\begin{matrix} \frac{\sqrt{C_{i}^{2} - \frac{4 π_{k, i}^{*} | H_{k, i} |^{2} | G_{i} |^{2} (λ + π_{k, i}^{*} | H_{k, i} |^{2} - | G_{i} |^{2}}{λ}} - C_{i}}{2 π_{k, i}^{*} | H_{k, i} |^{2}} \\ 0 \end{matrix}$ (16)

$\frac{\partial L (p_{k, i}^{*}, σ^{2}, λ)}{\partial σ^{2}} = 0$ (17)

Note that the explicit solution of $σ^{2}$ is not available, so only using the dichotomy, we could find the solution to equation (17).

The joint optimization of our proposed method to allocate subcarriers, power, and AN is given in the following algorithm, where joint optimization result could be obtained to obtain the optimized security rate without losing system performance significantly.

Proposed algorithm:
1. Initialize: $λ_{h} = λ_{l} = 0, p_{k, i} \|_{i = 1}^{N}$ 2. $λ = λ_{h} / λ_{l}$ , let $t = 0$ .3. Repeat:4. $t = t + 1$ ;5. Get $p_{k, i}$ by solving equation (16);6. Compute $σ^{2}$ using (17)7. Stop when $L_{t} (p_{k, i}, σ^{2}, λ) - L_{t - 1} (p_{k, i}, σ^{2}, λ) \leq 0.001$ 8. If $\sum_{i = 1}^{N} \sum_{k = 1}^{K} p_{k, i} + σ^{2} \leq P$ 9. $λ = λ_{h}$ 10. Otherwise $λ = λ_{l}$ 11. Go to step 2 until condition 7 is obtained

Proposed algorithm:

1. Initialize:

λ_{h} = λ_{l} = 0, p_{k, i} |_{i = 1}^{N}

λ = λ_{h} / λ_{l}

, let

t = 0

.3. Repeat:4.

t = t + 1

;5. Get

p_{k, i}

by solving equation (16);6. Compute

σ^{2}

using (17)7. Stop when

L_{t} (p_{k, i}, σ^{2}, λ) - L_{t - 1} (p_{k, i}, σ^{2}, λ) \leq 0.001

8. If

\sum_{i = 1}^{N} \sum_{k = 1}^{K} p_{k, i} + σ^{2} \leq P

λ = λ_{h}

10. Otherwise

λ = λ_{l}

11. Go to step 2 until condition 7 is obtained

In the proposed algorithm, we first initialize the parameters $λ_{h} = λ_{l} = 0 and p_{k, i} |_{i = 1}^{N}$ , which means the initial status of Lagrange function is established. Then, the algorithm comes to the loop, where the initial counter is $t = 0$ . In every loop, we will calculate the transmission power $p_{k, i}$ and the AN $σ^{2}$ . The condition that stops the loop is given in step 7, this means the Lagrange function has discovered the proper solution that the gap is less than 0.001. If the loop does not meet the stop condition, we will refresh the parameter $λ$ using steps 8–10.

Simulation and performance analysis

In the simulation part, we propose the simulation result of the proposed joint allocation of power, subcarrier, and AN; both system level and theoretical results are given in this part.

First, we propose the simulation result of theoretical analysis. In Figure 3, the position information of the system is given. We deploy 1 base station as Alice, 10 registered users as Bob, and 1 illegal user as Eve. The x- and y-axes represent the position in meter, and the Alice is located at (10, 10), Eve is located at (120, 100), and Bobs are randomly located between Alice and Eve as shown in Figure 3. Note that both system level and theoretical analysis are using the same position information.

Figure 3.

System position in the simulation platform.

In Figure 4, we present the simulation result of the theoretical analysis. The x-axis means the normalized SNR and the y-axis means the normalized security rate. The normalized SNR is defined by $SN R_{normalized} = SN R_{k} / \sum_{k} SN R_{k}$ , which means the SNR value normalized by the sum of all the SNRs. The normalized security has the similar definition: $C_{norm} = C_{k} / \sum_{k} C_{k}$ .

Figure 4.

Theoretical analysis of our proposed method versus upper and lower bounds.

The black curve means the upper bound calculated by Shannon formula, and the pink one is the lower bound that represent the random allocation of power, noise, and the subcarriers. The red dotted line means the proposed method, and the blue one means the method without adding the AN. We assume the Poisson arrival process of the data packet, and the normalized security rate may increase along with the transmission speed, sometimes a burst in transmission. Therefore, in the simulation part, we only calculated the normalized security rate using the real-time computational method. From this figure, we can infer the following:

Our proposed method is very close to the upper bound, because the original optimization problem has been divided into two convex problems, and each of them is proved to be independent, so the only gap is caused by the nonconvex allocation caused by subcarriers using the dichotomy.

AN nearly plays the minimum role in the security rate, because the noise is orthogonal to the effective user, but noise to the illegal user and the illegal user may not be affected due to the limited power of the noise.

At the beginning of the simulation, the proposed method exceeds the upper bound of the security rate, this is because we set the initial value of the minimum capacity, otherwise the simulation may not reach the convergence.

In Figure 5, we plot the performance of illegal user compared to the successful decoded rate. The success rate is defined using the SNR bound of the lowest 5% users among the 10 registered users. This means if the illegal user receives the SNR higher than the worst 5%, we consider it a success. In this figure, the x-axis means the normalized SNR of Eve received, and the y-axis means the success rate given in log coordinate. The red curve means the performance using our proposed method, the blue one means the method without using the subcarrier allocation (random allocation instead), and the green one means the method without AN. From this result, we can infer that using our proposed method, the success rate for illegal user will greatly decrease when the SNR goes high; the effect of subcarrier allocation is not serious when the normalized SNR is higher than 0.4, where AN becomes the primary effective factor to restrict the illegal user from the information.

Figure 5.

Success rate for Eve under different assumptions.

In Figure 6, we present the result of system-level simulation using the proposed method.²⁹ The iteration means the iteration time using our proposed method (iteration of variable t). It is clear that using the proposed method, the convergence value could be obtained within 12 times, and the joint optimized value could be obtained using only two iterations. The simulation parameters and assumptions are the same in our previous work in Zhang and Lin.³⁰ In this figure, the x-axis means the iteration time, where the system-level simulation platform needs to perform to obtain the better performance, the y-axis means the information bit that the illegal user obtained in bit. This means the successful decoded information bit obtained during the whole simulation process, including the necessary signaling or control information.^31–32 The blue curve means the proposed method using the joint optimization of AN, subcarrier, and power; the pink one means the method without global channel information (blind resource allocation); the green one means the method of power allocation; and the red one means the method of beamforming. From this figure, we can infer the following:

Our proposed method is quite effective to reduce the possibility that Eve may obtain useful information.

Beamforming is not the effective method to control the leakage of the information, because the power is the key factor to decide the success rate to decode, and only the electrical beamforming could not greatly affect the wiretap user, especially when the user is close to the registered one.

Power control is the effective method to reduce the leakage of the information, and it is suitable to be placed in the real system for its implementation, and the complexity is low.

Figure 6.

System-level result of our proposed method.

Conclusion

In this article, considering the necessity of the security and privacy in the wireless network, we discuss the physical layer security problem in 5G network. We propose the mathematical model of the wiretap users and successfully tackled the joint optimization problem of AN, power, and subcarrier allocation, and we divided the complex and nonconvex problem into three sub-problems and solved them through the convex optimization, dual optimization, and derivation. In the simulation part, we present the theoretical and system-level results of our proposed method; it is clear that our proposed method works significantly well and reduces about 34% of the information leakage compared to power control and beamforming method.

Footnotes

We would like to thank all the reviewers for their kind suggestions to this work.

Handling Editor: Anton Kos

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This work was funded by China’s 973 project under grant of 2012CB316002 and China’s 863 project under grant of 2013AA013603,Qualcomm Innovation Fellowship. The work of Su Hu was jointly supported by the MOST Program of International S&T Cooperation (grant no. 2016YFE0123200),National Natural Science Foundation of China (grant no. 61701503/61471100/61101090/61571082),Science and Technology on Electronic Information Control Laboratory (grant no. 162105003),and Fundamental Research Funds for the Central Universities (grant no. ZYGX2015J012/ZYGX2014Z005).

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A novel joint optimization of downlink transmission using physical layer security in cooperative 5G wireless networks

Abstract

Keywords

Introduction

Related works

Theoretical modeling and analysis

Proposed algorithm

Simulation and performance analysis

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References