An anti-eavesdropping scheme for hybrid multicast services with massive MIMO in 5G

Abstract

Physical layer security will play a critical role in the next generation of fifth-generation (5G) communication system, and assume that global channel state information can be obtained, a hybrid unicast/multicast transmission system for eavesdroppers in a Three-Dimensional Multi-Input Multi-Output (3D MIMO) channel scenario anti-eavesdropping program can be proposed. This system is analyzed and simulated under the cylindrical antenna array scenario with mutual coupling channel. Users (UEs) are divided into three groups, multicast group, unicast group and eavesdropping group. In order to eliminate the interference within each group, this system adopts multicast transmission beamforming in multicast group and linear transmission precoding in unicast group, then the interference among groups can be eliminated by zero-space method, and the confidential signal cannot be received by eavesdroppers with the anti-eavesdropping scheme. The simulation results indicate that under the anti-eavesdropping scheme of transmitting signals from transmitters, beamforming/precoding and interference cancellation, the secrecy rate has obvious improved.

Keywords

Multicast secrecy rate massive MIMO

1. Introduction

Traditionally, security issues have been considered at upper-layers and are usually based on cryptography methods that provides computationally-based security protocols. However, with the increasing computational power of eavesdroppers, the security of traditional encryption methods will gradually diminish. As the supplements to classical cryptographic security of higher layers, signal and code design are incorporated to suppress the information that can be extracted by an eavesdropper at the bit level. Hence, physical layer security has been widely recognized by the academic community in wireless networks [1]. Shannon’s landmark paper [2] on information theoretic security in 1949 paved the way for reinforce eavesdropper’s uncertainty about messages and followed by Wyner in 1975. Wyner proposed secure communications in a point-to-point wiretap channel [3] for characterizing the secrecy capacity of multiuser broadcast, interference, and multiple access channels with single antenna nodes, and Csiszar and Korner then jointly proposed the security capacity of broadcast channels, and laid a good foundation for the rapid development of wireless communication technology on security [4].

A dramatic increase in the number of Internet of Things (IoT) endpoints is expected. The emergence of IoT is one of the most important drivers of fifth-generation (5G) mobile networks. Therefore, 5G networks need to cater for an increase in the volume of data and the large increase of the number of service terminals. In addition, 5G networks also need to support services with new types of requirements, such as ultra-low latency and high reliability [5].

In order to cater the requirements mentioned before, new techniques that can improve both the operational reliability and spectral efficiency are required. Massive multiple-input multiple-output (MIMO) antenna technology is now highly introduced into substantial increase in throughput [6]. As the most popular and effective solution for 5G system, massive MIMO can increase the data rate and assist in the reliability fading links in wireless links without compromising the quality of base stations (BSs) and interactive mobile terminals (MTs). The admirable design of network can help to save a large amount of energy at the expense of slight lowering performance, resulting in the green communication and low computational complexity [7]. Therefore, 5G becomes an important candidate to provide mobile connectivity for the massive MIMO system [8]. In this paper, we are fascinated by 5G massive MIMO system.

It is worth mentioning that the multicast is an effective way to solve the problem of single-point transmission and multi-point reception, which can both save network bandwidth and reduce network load [9]. The broadcast nature of wireless medium makes massive MIMO networks vulnerable to eavesdropping by adversarial nodes. Therefore, the preprocessing of the transmitter is necessary, which can prevent users from receiving interference information, and eavesdroppers will not receive useful information. Most of the studies regard multicast bloom filters [10] as the best tools for compressing the status of multicast forwarding and overcoming the traffic leaks at the moment of receiving signals incorrectly. In addition, physical damage to the access points in 5G will result in a traffic burden for entire system. Therefore, multicast is considered a key solution for massive data communication as it can quickly propagate the same message to coverage areas without incurring further communication costs.

In this paper, we have developed a hybrid unicast/multicast transmission anti-eavesdropping scheme for the existing eavesdropper 3D massive MIMO channel. Assuming all channel state information can be obtained, then we investigate massive MIMO and the multicast in 5G system for secure communication, in a multiuser wiretap channel with a single transmitter, multiple legitimate users, and multiple illegal eavesdroppers, where access points are equipped with multiple antennas. Based on above research, we propose the anti-eavesdropping scheme, as null space exists in which from the wiretap channel to the channel of wiretapped subscriber. In 5G system, the massive MIMO based antenna array configuration allows the transmitting eNode B (eNB) to control the azimuth and elevation of wireless signal propagation, which is the reason that we call it 3D MIMO [11].

The organization of this paper is as follows: the architecture of proposed system and the importance of 5G multicast services are presented in Section 2. The null space based precoding strategy and user grouping scheme are described in detail in Section 3. In Section 4, the proposed scheme is validated through both simulations and experiments, and Section 5 concludes the paper.

Throughout this paper, we represent column vectors and matrices by lowercase and uppercase bold characters, respectively. Superscripts *, $H$ and $T$ denote the complex conjugate, Hermitian transpose and transpose of a matrix, respectively. The symbol $\otimes$ indicate the Kronecker product. $I_{N}$ is $N\times N$ identity matrix. $\mathbb{C}$ and $\mathbb{N}_{+}$ stand for the set of complex number and the set of positive integer, respectively.

2. System architecture

2.1 Architecture for massive MIMO system in the presence of eavesdroppers

In this paper, we model a hybrid unicast/multicast precoding scheme for 3D massive MIMO channel in the presence of eavesdroppers. As shown in Fig. 1. To facilitate the analysis, we only consider transmitter, users and eavesdroppers, and BS is the transmitter among them. Mobile phones are the hybrid unicast/multicast users, and these users are divided into unicast group and multicast group. Users in the red circle represent the eavesdropper group. Besides, the transmitter is equipped with multiple antennas, each user and each eavesdropper are equipped with single antenna respectively. In the proposed system, the BS sends legitimate signal to all hybrid users, which include users of unicast group and multicast group, and keeps the signal secret from all eavesdroppers. That means, the BS not only ensures green communication to the users, but also prevents the signal from being wiretapped by the eavesdroppers. To reach this goal, the worst user and the best eavesdropper can rule the secrecy rate, and null space can eliminate the redundancy which generated by the scheme of hybrid system.

Figure 1.

Massive MIMO system in the presence of eavesdroppers.

Next, the 3D massive MIMO channel model will be introduced in detail.

2.2 3D Massive MIMO channel model

A downlink massive MIMO system with $N$ antennas and $K$ single-antenna users is assumed ( $N,K\in\mathbb{N}_{+},N\geqslant K$ ) under the Non-Line-of-Sight (NLOS) condition, which can be given as [11]:

$\displaystyle\textbf{G}=\textbf{HD}$ (1)

where ${\bf G}=\left[{g_{1},g_{2},\ldots,g_{k}}\right]$ denotes the channel matrix, whose element $g_{k}\in\mathbb{C}^{1\times N}(k=1,2,\ldots,K)$ denotes the channel element between base station (BS) and the $k$ th user equipment (UE). ${\bf D}=\text{diag}\{\sqrt{\beta_{1}},\sqrt{\beta_{1}},\ldots,\sqrt{\beta_{K}}\}$ is the large scale channel matrix, where $\beta_{k}=\kappa d_{k}^{-\gamma}\zeta_{k}$ . $\zeta_{k}$ stands for the log-normal shadow fading factor, $\gamma$ represents the path loss exponent, and $d_{k}$ represents the distance between the $k$ th UE and BS; the constant value $\kappa$ is decided by the antenna characteristic and carrier frequency.

The channel matrix can be given by ${\bf H}=[{\bf H}_{1},{\bf H}_{2},\ldots,{\bf H}_{K}]$ in mutual coupling channel model, and the vector ${\bf H}_{k}\in\mathbb{C}^{1\times N}(k=1,2,\ldots,K)$ is described by [11]:

$\displaystyle{\bf H}_{k}^{H}={\bf ZR}_{k}{\bf v}_{k}$ (2)

where ${\bf Z}\in\mathbb{C}^{N\times N}$ represents the constant mutual coupling matrix decided by the antenna array configuration, and ${\bf R}_{k}$ and ${\bf v}_{k}$ represent the steering matrix and Gaussian stochastic factor, respectively. In addition, ${\bf Z}$ can be denoted by the following equation:

$\displaystyle{\bf Z}=(Z_{2}+Z_{1})({\bm{\Gamma}}+Z_{1}{\bf I})^{-1}$ (3)

where

$\displaystyle\Gamma=\left[\begin{array}[]{ccccc}{Z_{2}}&{Z_{3}}&0&\ldots&0\\ {Z_{3}}&{Z_{2}}&{Z_{3}}&\ldots&0\\ 0&{Z_{3}}&{Z_{2}}&\ldots&0\\ \vdots&\vdots&\ddots&\ddots&\vdots\\ 0&0&\ldots&{Z_{3}}&{Z_{2}}\\ \end{array}\right]$ (4)

The complex value of $Z_{1},Z_{2}$ and $Z_{3}$ denotes the load impedance, antenna impedance, and mutual impedance respectively.

The form of ${\bf R}_{k}$ and ${\bf v}_{k}$ depends on the antenna array configuration [11]. For convenience of description, a steering vector function can be defined as ${\bf a}(\theta)$ .

In the cylindrical antenna array scenario, $\theta_{k,i}$ and $\phi_{k,i}$ denote the azimuth of arrival (AoA) and elevation of arrival (EoA) of the $k$ th user, respectively. According to the steering matrix, the column steering vectors in ${\bf R}_{k}=[{\bf r}_{k,1},{\bf r}_{k,2},\ldots,{\bf r}_{k,A_{k}}]$ can be obtained as follows:

$\displaystyle R_{k}={\bf a}(\theta_{k,i},\phi_{k,i})=\text{vec}\left\{\left[e^% {\frac{-j2\pi r}{\lambda}\cos\left(2\pi\frac{0}{N}-\theta_{k,i}\right)},\ldots% ,e^{\frac{-j2\pi r}{\lambda}\cos(2\pi\frac{N-1}{N}-\theta_{k,i})}\right]\right% .\left.\otimes\left[1,e^{\frac{j2\pi d}{\lambda}\sin(\phi_{k,i})},\ldots,e^{% \frac{j2\pi(L-1)d}{\lambda}\sin(\phi_{k,i})}\right]\right\}$ (5)

where vec( $\cdot$ ) function denotes the vector of matrix, and $\lambda$ represents the wave length and $r$ is the radius of ring. $L$ stands for the number of circular antenna layer, and when $L=1$ , it means that the array is circular. $d$ denotes the distance between adjacent circular antenna, and $N$ represents the number of circular antenna elements,.

According to the 3D channel model we discussed above, the anti-eavesdropping scheme for hybrid unicast/multicast transmission system will be presented in the next section.

3. Anti-eavesdropping scheme for hybrid multicast transmission system in massive MIMO

3.1 Ideal secrecy rate of the system

Now, we can consider a user grouping scheme, the users can be divided into three groups, a unicast group, a multicast group, and an eavesdropping group. And we define $g_{m}=[g_{1},g_{2},\ldots,g_{k}]$ for the $m$ th group, where

$\displaystyle{g_{k}=\left\{{{\begin{array}[]{ll}1&\text{the $k$th user % subjects to the $m$th group,}\\ 0&{\text{otherwise.}}\\ \end{array}}}\right.}{\left({k=1,2,\ldots,K}\right)}$ (6)

and $K_{m}$ represents the number of users in $m$ th group, where $\sum{{}_{m}}K_{m}=K$ .

For the process of the hybrid multicast transmission system, system formula in Eq. (3.1) illustrates the interference cancellation of anti-eavesdropping scheme with the full view of entire system.

$\displaystyle\textbf{ Y}=\sqrt{P}\textbf{ GJ}{\bm{\omega}}{\bf S}+{\textbf{ z}% },\textit{and }$ $\displaystyle\textbf{ z}=\left[{{\textbf{ z}}_{0},{\textbf{ z}}_{1},\ldots,{% \textbf{ z}}_{M},{\textbf{ z}}_{N}}\right]^{T},$ $\displaystyle\textbf{ S}=\left[{{\textbf{ s}}_{0},{\textbf{ s}}_{1},\ldots,{% \textbf{ s}}_{M},{\textbf{ 0}}}\right]^{T},$ $\displaystyle{\bm{\omega}}=\textit{diag}\left({\bm{\Omega}}_{0},\textbf{ w}_{1% },\ldots,\textbf{ w}_{M},\textbf{ w}_{N}\right),$ (7) $\displaystyle\textbf{ J}=\left[{{\textbf{ J}}_{0},{\textbf{ J}}_{1},\ldots,{% \textbf{ J}}_{M},{\textbf{ J}}_{N}}\right],$ $\displaystyle\textbf{ G}=\left[{{\textbf{ G}}_{0},{\textbf{ G}}_{1},\ldots,{% \textbf{ G}}_{M},{\textbf{ G}}_{N}}\right]^{T},$ $\displaystyle\textbf{ Y}=\left[{{\textbf{ y}}_{0},{\textbf{ y}}_{1},\ldots,{% \textbf{ y}}_{M},{\textbf{ y}}_{N}}\right]^{T}.$

In Eq. (3.1), index 0 represents the unicast group, index from 1 to $M$ denote the multicast, and index $N$ is the eavesdropping group, and eavesdroppers act as unicast or multicast UEs. In addition, $P$ denotes the signal power in BS, and $Y$ is the received signal of the transmitted signal $S$ , which already been processed by the precoding matrix $\omega$ and projection matrix $J$ . $z$ denotes the White Gaussian noise. The matrix ${{\bf w}}_{m}$ is represented by

$\textbf{ w}_{m}=\frac{1}{\lambda}\left[\hat{\bf g}_{m,1}^{\ast},\hat{\bf g}_{m% ,2}^{\ast},\ldots,\hat{\bf g}_{m,K_{m}}^{\ast}\right],$

where $\lambda$ denotes the normalization factor, and it can ensure $\omega_{m}=\frac{1}{\lambda}\sum_{j=1}^{K_{m}}\hat{\bf g}_{m,1}^{\ast}$ . ${\bm{\Omega}}_{0}$ represents the precoding matrix of unicast group users.

According to [12], the secrecy rate of the system is as follows:

$\displaystyle R_{S}=\max\{I_{D}-I_{E},0\}$ (8) $\displaystyle I_{D}=\log\{1+\textit{SINR}_{m,j}\}$ (9) $\displaystyle I_{E}=\log\{1+\textit{SINR}_{N,j}\}$ (10)

where $I_{D}$ represents the mutual information between the legitimate transmitter and the legitimate user. $I_{E}$ denotes the mutual information between them. The ideal goal is to reach the maximization of the $R_{S}$ , so $I_{D}$ should be as maximum as possible, and $I_{E}$ is as minimum as possible. The calculations of these two parameters and SINR are described in detail in the following subsections.

3.2 Anti-eavesdropping scheme

The null-space method based interference cancellation algorithm is implemented in this anti-eavesdropping scheme. To eliminate the interferences between all $M$ unicast group and multicast groups as well as eavesdropper group, a projection matrix for group $m$ is proposed. It is worth noting that the projection matrix of eavesdropper is orthogonal to the wiretap channel, because the purpose is to suppress the received signal in the eavesdropper group. The projection matrix of hybrid multicast group must satisfy that it spans a subspace of the null-space for the channel vectors in all hybrid multicast other groups. For group $m$ , the joint channel matrix of users in all groups can be denoted by ${\textbf{ G}}=\left[{{\textbf{ G}}_{0},{\textbf{ G}}_{1},\ldots,{\textbf{ G}}_{M},{\textbf{ G}}_{N}}\right]$ , where channel grouping matrix ${\textbf{ G}}_{m}=\left[{{\textbf{ g}}_{m,1},{\textbf{ g}}_{m,2},\ldots,{\textbf{ g}}_{m,K_{m}}}\right]$ .

To calculate ${\textbf{ J}}_{m}\left({m=0,1,\ldots,M,N}\right)$ by singular value decomposition (SVD), the projection matrix for group $m$ represented by ${\textbf{ J}}_{m}\in{\rm C}^{N\times N}$ is obtained by equations as follows:

$\displaystyle\textbf{ G}_{\bar{m}}=\textbf{ U}_{\bar{m}}{\bm{\Lambda}}_{\bar{m% }}\textbf{ V}_{\bar{m}}$ (11) $\displaystyle{\textbf{ J}}_{m}={\textbf{ V}}_{\bar{m}}^{0}\left({{\textbf{ V}}% _{\bar{m}}^{0}}\right)^{H}$ (12) $\displaystyle{\textbf{ U}}_{\bar{m}}\in\mathbb{C}^{N\times N},{\textbf{ V}}_{% \bar{m}}\in\mathbb{C}^{\left({K-K_{m}}\right)\times\left({K-K_{m}}\right)},{% \bm{\Lambda}}_{\bar{m}}\in\mathbb{C}^{N\times\left({K-K_{m}}\right)}$ (13)

where $\textbf{ G}_{\bar{m}}$ is the joint channel matrix of UEs in all other groups. ${\textbf{ U}}_{\bar{m}}$ , ${\textbf{V}}_{\bar{m}}$ and ${\bm{\Lambda}}_{\bar{m}}$ denote SVD factor matrices. ${\textbf{ V}}_{\bar{m}}^{0}\in\mathbb{C}^{\left({K-K_{m}}\right)\times N}$ represents a subspace of column vector space of ${\textbf{ V}}_{\bar{m}}$ . Through the operation, the signal leakage from each group will be eliminated, thereby ensuring the efficiency of transmission.

In this paper, the local cell multicast is considered, and $\omega_{m}\in\mathbb{C}^{N\times 1}$ represents the multicast beamforming vector with $||\omega_{m}||^{2}=1$ in the $m$ th multicast group. Besides, in $m$ th group, the stochastic information with unit power multicasted can be represented by $s_{m}$ . Therefore, the signal vector ${\textbf{ x}}_{m}$ can be described by

$\displaystyle{\textbf{ x}}_{m}=\sqrt{p_{m}}\omega_{m}s_{m}$ (14)

where $p_{m}$ is the transmission power of $m$ th group. We can assume that the same spectrum is shared by all groups, and the signal received by the $j$ th user can be expressed as:

$\displaystyle y_{m,j}=\hat{\bf g}_{m,j}^{H}{\textbf{ x}}_{m}+\sum\limits_{n% \neq m}^{M}\hat{\bf g}_{m,j}^{H}{\textbf{ x}}_{n}+z_{m,j}=\sqrt{p_{m}}\hat{\bf g% }_{m,j}^{H}\omega_{m}s_{m}+\sum\limits_{n\neq m}^{M}\sqrt{p_{n}}\hat{\bf g}_{m% ,j}^{H}\omega_{n}s_{n}+z_{m,j}$ (15)

where $z_{m,j}$ is the additive zero-mean Gaussian noise, and variance is expressed as $\sigma^{2}$ . In addition, SINR received by $j$ th user in $m$ th group can be denoted as

$\displaystyle\textit{SINR}_{m,j}=\frac{p_{m}|\hat{\bf g}_{m,j}^{H}\omega_{m}s_% {m}|^{2}}{\sum_{n\neq m}^{M}p_{n}t|\hat{\bf g}_{m,j}^{H}\omega_{n}s_{n}|^{2}}+% \sigma^{2}$ (16)

In massive MIMO system, the transmit power of each antenna is inversely proportional to the number of antennas [13], $p_{m}=\rho_{m}\frac{E}{N}$ , where $E$ is the total transmit power of BS and $\rho_{m}\in\left[{0,1}\right]$ represents the power ratio of $m$ th group. Taking into account the perfect CSI (Channel State Information) scenario, it is feasible to use the mathematical form of max-min fairness (MMF) to solve the multicast problem in literature [14].

By multiplying ${\bm{\Omega}}_{0}$ and the transmit vector, multi-user MIMO (MU-MIMO) linear precoding can be achieved, where ${\bm{\Omega}}_{0}\in\mathbb{C}^{N\times K_{0}}$ denotes the precoding matrix and $K_{0}$ represents the users’ number in group 0.

The block diagonalization (BD) precoding algorithm aims to remove the inter-user interference and this process makes sure that the interferences from other users can located in the null space.

A Theorem of multicast beamforming scheme is formed in reference [15] and the MU-MIMO linear precoding of BD scheme is implemented in unicast group and multicast groups, respectively.

3.3 Secrecy rate of the system

According to the Eq. (8), we can evaluate the secrecy rate of $j$ th user in $m$ th group. The received signal by each group is shown in Eq. (3.1), the SINR received by the $j$ th user in the $m$ th group denotes in Eq. (16), and the null space scheme is applied between the groups, thus the $I_{D}$ is derived by Eq. (9):

$\displaystyle I_{D}=\sum\limits_{m=0}^{M}{\sum\limits_{j=1}^{K}{\log(1+\textit% {SINR}_{m,j})}}=\sum\limits_{m=0}^{M}\sum\limits_{J=1}^{K}\log\left(1+\frac{p_% {m}|\hat{\bm{g}}_{m,j}^{H}\omega_{m}s_{m}|^{2}}{\sum_{n\neq m}^{M}p_{n}|\hat{% \bm{g}}_{m,j}^{H}\omega_{n}s_{n}|^{2}+\sigma^{2}}\right)=\sum\limits_{m=0}^{M}% {\sum\limits_{j=0}^{K}{\log\left(1+\frac{p_{m}\left|{{{\hat{\bm{g}}}}_{m,j}^{H% }\omega_{m}s_{m}}\right|^{2}}{\sigma^{2}}\right)}}$ (17)

Since there is null space in the wiretap channel where the secret information is located, the eavesdroppers cannot receive the legitimate signal. Our proposed anti-eavesdropping scheme sets the transmitted signal $S_{N}=0$ , thus we can get the following information:

$\displaystyle{\textbf{ x}}_{N}=\sqrt{P_{N}}\omega_{N}s_{N}=0$ (18)

As the eavesdropper group spans the subspace of the null-space of the channel vectors of multicast and unicast UEs, thus, in the eavesdropper group $N$ , the signal received of $j$ th user is transformed by Eq. (15):

$\displaystyle y_{N,j}={{\hat{\bm{g}}}}_{N,j}^{H}{\textbf{ x}}_{N}+\sum_{n\neq N% }^{M}{{{\hat{\bm{g}}}}_{N,j}^{H}}{\textbf{ x}}_{n}+z_{N,j}=\sqrt{p_{N}}\hat{% \bm{g}}_{N,j}^{H}w_{N}s_{N}+\sum_{n\neq N}^{M+1}\sqrt{p_{n}}\hat{\bm{g}}_{N,j}% ^{H}\omega_{n}s_{n}+z_{N,j}=z_{N,j}$ (19)

where $z_{N,j}$ is the additive zero-mean Gaussian noise and $o^{2}$ denotes variance. The SINR detrived by the $j$ th user in eavesdropping group is transformed by Eq. (15):

$\displaystyle\textit{SINR}_{N,j}=\frac{p_{N}\left|{{{\hat{\bm{g}}}}_{N,j}^{H}w% _{N}s_{N}}\right|^{2}}{\sum\nolimits_{n\neq N}^{M}{p_{n}\left|{{{\hat{\bm{g}}}% }_{N,j}^{H}\omega_{n}s_{n}}\right|^{2}}+\sigma^{2}}=0$ (20)

To sum up, the mutual information between the transmitter and the eavesdropper is derived by Eq. (10):

$\displaystyle\text{I}_{E}=\sum\limits_{j=1}^{K}\text{log(1 $+$ SINR}_{N,j})=0$ (21)

After simplification, the secrecy rate of the system can be obtained:

$\displaystyle R_{S}=\max\{I_{D},0\}$ (22)

The high-speed transmission can be provided for unicast users by the hybrid system we proposed. At the same time, multicast services can be provided for multicast users, thereby greatly improve the system spectrum utilization.

4. Simulation results

Simulations and experiments are conducted to evaluate the performance of our proposed hybrid system, and the secrecy rate is a major concern in the system, we choose the cylindrical antenna array for analysis, and simulations are implemented with and without the mutual coupling channel model. For all the eavesdropping multicast service groups, all simulations run 200 times, the illustrated performance metrics are calculated as the average metrics. The beamformer is calculated by Theorem 1 [14], while the BD precoding is performed in unicast group. The precoding of the eavesdropper group depends on the group which the eavesdroppers will wiretap. Some necessary parameters are listed in Table 1.

Table 1
Simulation parameters

Parameters	Values
Scenario	NLOS
Frequency	38 GHz
Tx/Rx antenna height	36/1.5 m
Number of BS antenna	1 to 1024/128
User number	$K=$ 74
Antenna interval for	$d=$ 0.5 wave length $r=$ 1
Cylindrical antenna array	wave length $M=$ 10
SNR	$-$ 10 dB to 30 dB/10 dB
$Z$ 1/ $Z$ 2/ $Z$ 3	50/50/50 $\Omega$
Tx/Rx antenna gain	25/13.3 dB

Figure 2.

Secrecy rate of the system in cylindrical antenna array with null space.

4.1 Secrecy rate of users in cylindrical antenna array

Figure 2 shows the correctness of the hybrid multicast precoding system proposed in this paper, and the wiretap channel exists in cylindrical antenna array. In massive MIMO, the secrecy rate of the whole system is illustrated. The number of the antennas is 128, and the number of unicast users is 32. Besides, the BD precoding is used for the system. In addition, the number of users in the multicast group is also 32, and the multicast beamforming is used here. What is different here is that the number of users in eavesdropper group is 10, and the eavesdropper wiretaps the unicast users, thus the BD precoding is used in eavesdropper group. Among these three groups, the secrecy rate of the unicast group is the highest. The secrecy rate of the eavesdropper group is 0, which is consistent with the theoretical analysis. Since Mutual Coupling (MC) produces an additional correlation between the antennas, the channel becomes spatially dependent, and the value of MC secrecy rate is generally low. It can be found that the reduction of secrecy rate for unicast group is more than that of multicast group. The full secrecy rate of the system represents the transmission performance of all users. As a result, the performance of the proposed hybrid system is much better than that of the traditional unicast system.

The effect of the number of antennas at the transmitter on the secrecy rate of the system under the cylindrical antenna arrays is presented in Fig. 3. Among them, Nt represents the number of antennas. The SNR is 10 dB, and the number of unicast group users is 32. Besides, the BD precoding is used here. In addition, the number of users in the multicast group is 32, and the number of users in the eavesdropper group is 10. The influence of MC on the antenna array is also considered. With the increase of the number of antennas at the transmitter, it can be seen from the figure that the average secrecy rate of the system has increased, thus the proposed system in this paper can be applied to the massive MIMO 5G scenario, and the scheme can meet the requirements of massive MIMO.

Figure 3.

The effect of the number of antennas in cylindrical antenna arrays on the secrecy rate.

Figure 4.

The effect of the number of eavesdropper with null space on the secrecy rate.

Figure 5.

The effect of the number of eavesdropper without null space on the secrecy rate.

4.2 Analysis of the anti-eavesdropping scheme

The comparison of Figs 4 and 5 shows the high performance of the anti-eavesdropping scheme proposed in this paper. Under the same condition, since the eavesdropper group has not received any legitimate signals, the capacity of this group is the minimum in Fig. 4, while in Fig. 5, the capacity of this group has increased gradually because of the simulation without null space, and the eavesdropper can be regarded as a normal user, which is illegal. On the other hand, the secrecy rate of all groups in Fig. 4 is much higher than that in Fig. 5, which illustrates that our disable scheme is effective to system security and suppresses the user to receive legitimate information.

5. Conclusion

This paper investigates the multicast service of massive MIMO technology in physical layer in 5G communication system, and security plays an essential role in the system. This paper proposes a hybrid unicast/multicast precoding security system model in the presence of eavesdroppers. In order to ensure the security of the system, the anti-eavesdropping scheme of interference cancellation based on the null space is used to eliminate the leakage signal between the two groups, and can prevent users from receiving useful information in the eavesdropper group. To eliminate the interference of the users in each group, BD precoding and multicast beamforming are used to different groups. The simulation results demonstrate that the anti-eavesdropping scheme can effectively suppress the spectrum efficiency of the eavesdropper group. Under the mutual coupling, the performance of the system is reduced, and the performance of the unicast group is lower than that of the multicast group. At the same time, the performance of the proposed system is better than that of the traditional unicast model, and it can be used in the future 5G wireless communication network. In the future work, we will consider the impact of interference and noise on our proposed system.

Footnotes

Acknowledgments

This work is supported by the National Key R&D Program of China under Grant 2017YFB0802300.

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