Elsevier

Physical Communication

Volume 54, October 2022, 101817
Physical Communication

Full length article
Two-level-enforced security with hybrid precoding for multicast massive MIMO wiretap systems

https://doi.org/10.1016/j.phycom.2022.101817Get rights and content

Abstract

Multicast hybrid precoding reaches a compromise among hardware complexity, transmission performance and wireless resource efficiency in massive MIMO systems. However, system security is extremely challenging with the appearance of eavesdroppers. Physical layer security (PLS) is a relatively effective approach to improve transmission and security performance for multicast massive MIMO wiretap systems. In this paper, we consider a transmitter with massive antennas transmits the secret signal to many legitimate users with multiple-antenna, while eavesdroppers attempt to eavesdrop the information. A fractional problem aims at maximizing sum secrecy rate is proposed to optimize secure hybrid precoding in multicast massive MIMO wiretap system. Because the proposed optimized model is an intractable non-convex problem, we equivalently transform the original problem into two suboptimal problems to separately optimize the secure analog precoding and secure digital precoding. Secure analog precoding is achieved by applying singular value decomposition (SVD) of secure channel. Then, employing semidefinite program (SDP), secure digital precoding with fixed secure analog precoding is obtained to ensure quality of service (QoS) of legitimate users and limit QoS of eavesdroppers. Complexity of the proposed SVD-SDP algorithm related to the number of transmitting antennas squared is lower compared with that of constant modulus precoding algorithm (CMPA) which is in connection with that number cubed. Simulation results illustrate that SVD-SDP algorithm brings higher sum secrecy rate than those of CMPA and SVD-SVD algorithm.

Introduction

The convenience of wireless communication attracts more and more users. The plentiful wireless devices demand more effective data transmission. Massive multiple-input–multiple-output (MIMO) is regarded as a promising technique. If infinite transmitting antennas are employed, the channels of different receivers are approximatively orthogonal [1]. It means that inter-user interference can be effectively eliminated to improve system capacity. Besides, massive MIMO not only brings tremendous multiplexing gain but also enhances the degree of freedom. Massive MIMO is also helpful to compensate propagation loss caused by high frequency. However, it is millimeter wave (mmWave) that makes massive MIMO practical [2], [3], [4].

The traditional full-digital precoding that needs the same number of transmitting antennas and radio frequency (RF) chains and pursues fast analog-to-digital converters leads to exorbitant cost in massive MIMO system. However, a notable performance gap exists between full-digital precoding and analog precoding which needs only one RF chain. RF chains which are more than one but far less than the number of transmitting antennas are required by hybrid precoding. Therefore, hybrid precoding embraces both greater achievable rate than analog precoding and smaller expense than full-digital precoding. The low-dimension digital precoding and the high-dimension analog precoding make up hybrid precoding in which the digital precoding consists of few RF chains to achieve multiplexing and the analog precoding is consisted by some phase shifters (PSs) which are energy-saving and economical to alleviate path loss caused by mmWave channels [5].

There are some existing studies for hybrid precoding of single user [6], [7] and multiple users [8], [9], [10] in massive MIMO systems with narrowband flat fading channels. Transforming wideband channels into narrowband channels by orthogonal frequency division multiplexing (OFDM) technology has been studied [11], [12], [13], [14]. Codebook-based schemes [15], [16], [17], [18], [19], [20], [21], [22] and codebook-free schemes [23], [24], [25], [26], [27], [28] have also been studied. Hybrid precoding is closely related to the premise of PSs’ resolution in both schemes. There is no doubt that PSs with infinite resolution bring great system performance. At the same time, they bring high power consumption and hardware complexity [29]. However, the above papers have no consideration of system security.

The signal transmission is dependent on electromagnetic wave, which makes illegal users have a chance to tap the secret information. The traditional security techniques require users to have strong computing power. The legitimate users spend much time on computing to avoid information leakage, which cannot satisfy the demand of low time delay. The system security can be effectively improved by combining massive MIMO and secure hybrid precoding as narrow beams and spatial degrees of freedom (DoF) can be supplied. Therefore, secure hybrid precoding in massive MIMO systems attains more and more attention. In order to make full use of wireless resource, we consider secure hybrid precoding in multicast massive MIMO system.

A typical massive MIMO wiretap system which consists of a transmitter, a legitimate receiver, and an eavesdropper has been considered [5], [30], [31], [32], [33], [34]. Secure hybrid beamforming has been considered in both codebook-based and codebook-free schemes [5]. Codebook-based hybrid beamforming has been considered to maximize secrecy rate in multi-input-single-output-multi-antenna eavesdropper (MISOME) system with Gaussian wiretap channel [35]. The hybrid beamforming algorithm that joints data and artificial noise (AN) precoding to maximize secrecy rate has been investigated in massive MIMO system [31]. Under the assumption of partial channel knowledge, a secure hybrid precoding algorithm has been proposed in multiple-input-single-output (MISO) system [36]. Hybrid precoding has been studied in MISO system with more than one eavesdroppers [37]. Two situations have been considered in that paper. The one aimed at maximizing the secrecy rate in MISO-OFDM systems with full channel knowledge at transmitter. The other was focus on minimizing the upper bound of secrecy outage probability with partial channel knowledge at transmitter. The framework for joint data and AN precoding to enhance system security has been discussed [38].

There were also many articles on robust and secure precoding [39], [40], [41], [42]. Secure precoding algorithm has been proposed to minimize transmission power in MISO scenarios, which solved the second-order cone programming problem by Bernstein-type inequalities and successful convex approximation [41]. Two secure precoding algorithms for multiple single-antenna legitimate receivers and multiple multi-antenna eavesdroppers in MIMO system have been proposed [39], [40]. [42] introduced AN to study secure precoding under the coexistence of multiple single-antenna legitimate users and a single multi-antenna eavesdropper. None of the above literature involves the research on secure hybrid precoding in Massive MIMO systems.

Unicast information transmission is not conducive to large-scale transmission of information. Compared with the unicast method, no matter how many receivers there are, there is at most one copy of the same multicast data stream on each link in multicast scenario. Using the multicast method to transmit information, the increase of users will not significantly increase the network load. Broadcasting is not conducive to data interaction for a specific user, and also consumes a lot of bandwidth. Compared with broadcast, multicast data flow will only be sent to the receivers that require data, which will not cause waste of network resources, and use bandwidth reasonably. Multicast also has many advantages, such as reducing network traffic, reducing server and CPU load, improving efficiency, reducing redundant traffic, optimizing performance and making multi-point applications possible. Multicast technology effectively solves the problem of single-point sending and multiple-point receiving, and realizes efficient point-to-multipoint data transmission in IP networks, which can save a lot of network bandwidth and reduce network load. The application of multicast is also very extensive, such as Internet TV, real-time audio and video conferencing, distance education and so on. Especially in the current prevention and control life of COVID-19, distance education is inevitable, and the multicast method is particularly important.

Though many secure hybrid precoding algorithms have been studied in the above papers, there is no consideration of the wiretap system which consists of multiple multi-antennas users and multiple multi-antennas eavesdroppers. In this paper, we investigate the problem of maximizing sum secrecy rate with a group of multiple-antenna legitimate users and multiple multiple-antenna eavesdroppers in multicast massive MIMO wiretap system.

Compared with other existing hybrid precoding studies, this paper has the following major contributions.

  • By comparing the different performance between the full-digital precoding with PLS and the full-digital precoding without PLS, this paper demonstrates the significance of PLS in multicast massive MIMO wiretap systems.

  • This paper considers the transmitter transmits a confidential data stream to a group of multiple-antenna legitimate users, while multiple multiple-antenna eavesdroppers attempt to overheard the information. The proposed SVD-SDP algorithm aims at maximizing sum secrecy rate. The secure analog precoding algorithm explores the connection of channels of Alice-to-Bobs and Alice-to-Eves to enhance the system security. The secure digital precoding algorithm further enhances sum secrecy rate through ensuring the QoS of legitimate users and limiting the QoS of eavesdroppers. The two parts achieve the two-level-security in multicast massive MIMO system.

  • A series of simulations illustrate that the SVD-SDP algorithm can effectively enhance system security.

Looking ahead, AN is useful to further elevate system security and robust hybrid precoding is worth investigating.

The remainder of this paper is arranged as follows. The system model and problem formulation are given in Section 2 The proposed secure hybrid precoding algorithm are demonstrated in Section 3. The simulation results and analysis are shown in Section 4 The conclusion for this paper is provided in Section 5.

Boldface lower cases and upper cases indicate column vectors and matrices, respectively. AH denotes the conjugate-transpose operations of A. E{} represents statistical expectation. IN indicates an identity matrix of dimension N. Ca×b denotes the set of complex matrixes of dimension a×b. A0 means that A is Hermitian positive semidefinite. Tr(.) indicates a trace operation. CN(a,D) denotes a complex Gaussian distribution with mean a and covariance matrix D. AF denotes the Frobenius norm of the matrix A. A(i,j) represents the element of the ith row and the jth column of the matrix A. |a| and a are the magnitude and norm of a scalar a and vector a, respectively.

Section snippets

System model and problem formulation

In this section, system model and secure hybrid precoding problem are provided.

The proposed SVD-SDP algorithm

In this section, in order to solve secure hybrid precoding problem, objective function is transformed in some equivalent ways. Furthermore, the problem is transformed into two suboptimal problems, including secure analog precoding problem and secure digital precoding problem. Secure analog precoding problem is based on secure channel to improve system security and channel gain by SVD, which can assure the signal reception of legitimate users but inhibit the eavesdroppers’ access to information

Simulation results and analysis

In this section, simulation results averaged over 1000 random channel realizations are provided to demonstrate that the proposed secure hybrid precoding algorithm can bring well system performance. The parameter settings in the simulation are shown in Table 2, the channel model adopts the millimeter wave channel mentioned in Section 2, there are 10 clusters in the channel, each cluster contains only one propagation path, the channel gain obeys the complex Gaussian distribution of the unit

Conclusion

The importance of PLS in multicast massive MIMO wiretap system is proved by comparing secrecy rate of the full-digital precoding with PLS to the full-digital precoding without PLS in this paper. The proposed SVD-SDP algorithm aims at enhancing two-level-enforced security in multicast massive MIMO wiretap system based on widely used geometric-based multipath channel model. The proposed secure analog precoding algorithm is based on secure channel to improve channel gain and system security. The

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by 2020 Industrial Technology Foundation Public Service Platform Project, China (2020-0105-2-1) and Science and Technology Innovation Fund Project of Shunde Graduate School,University of Science and Technology Beijing, China (BK20AF004).

Xiangping Qi received the B.Sc. degree in Electronic Information Engineering from Hebei University of Economics and Business, Hebei, China in 2019. She is currently pursuing the M.Sc. degree in information and communication engineering from the School of University of Science and Technology Beijing. Her current research interests include hybrid precoding and physical layer security.

References (47)

  • ChenW. et al.

    Artificial noise aided hybrid precoding design for secure mmwave MIMO system

  • D.M.

    Research on pilot contamination of massive MIMO system

    (2017)
  • RappaportT.S. et al.

    Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design

    IEEE Trans. Commun.

    (2015)
  • PiZ. et al.

    An introduction to millimeter-wave mobile broadband systems

    IEEE Commun. Mag.

    (2011)
  • RappaportT.S. et al.

    Millimeter wave mobile communications for 5G cellular: It will work!

    IEEE Access

    (2013)
  • TianX. et al.

    Secure hybrid beamformers design in mmwave MIMO wiretap systems

    IEEE Syst. J.

    (2019)
  • HuangW. et al.

    Alternating optimization based low complexity hybrid precoding in millimeter wave mimo systems

    IEEE Commun. Lett.

    (2019)
  • RenT. et al.

    Hybrid precoding design for energy efficient millimeter-wave massive MIMO systems

    IEEE Commun. Lett.

    (2019)
  • DongF. et al.

    Low-complexity hybrid precoding for multi-user mmwave systems with low-resolution phase shifters

    IEEE Trans. Veh. Technol.

    (2019)
  • DuttaB. et al.

    Low-complexity subspace-based multi-user hybrid precoding

    IEEE Commun. Lett.

    (2018)
  • DilliR.

    Performance analysis of multi user massive MIMO hybrid beamforming systems at millimeter wave frequency bands

    Wirel. Netw.

    (2021)
  • YuanH. et al.

    Low complexity hybrid precoding for multiuser millimeter wave systems over frequency selective channels

    IEEE Trans. Veh. Technol.

    (2018)
  • LiuY. et al.

    Low-complexity OFDM-based hybrid precoding for multiuser massive MIMO systems

    IEEE Wirel. Commun. Lett.

    (2019)
  • ChenY. et al.

    Channel-covariance and angle-of-departure aided hybrid precoding for wideband multiuser millimeter wave MIMO systems

    IEEE Trans. Commun.

    (2019)
  • SunX. et al.

    Codeword selection and hybrid precoding for multiuser millimeter-wave massive MIMO systems

    IEEE Commun. Lett.

    (2018)
  • El AyachO. et al.

    Spatially sparse precoding in millimeter wave MIMO systems

    IEEE Trans. Wireless Commun.

    (2014)
  • AlkhateebA. et al.

    Frequency selective hybrid precoding for limited feedback millimeter wave systems

    IEEE Trans. Commun.

    (2016)
  • ChenJ.-C.

    Efficient codebook-based beamforming algorithm for millimeter-wave massive MIMO systems

    IEEE Trans. Veh. Technol.

    (2017)
  • AlkhateebA. et al.

    Limited feedback hybrid precoding for multi-user millimeter wave systems

    IEEE Trans. Wireless Commun.

    (2015)
  • NguyenD.H. et al.

    Hybrid MMSE precoding for mmwave multiuser MIMO systems

  • GaoX. et al.

    Turbo-like beamforming based on tabu search algorithm for millimeter-wave massive MIMO systems

    IEEE Trans. Veh. Technol.

    (2015)
  • WangJ. et al.

    Beamforming codebook design and performance evaluation for 60GHz wideband WPANs

  • WangZ. et al.

    Iterative hybrid precoder and combiner design for mmwave multiuser MIMO systems

    IEEE Commun. Lett.

    (2017)
  • Xiangping Qi received the B.Sc. degree in Electronic Information Engineering from Hebei University of Economics and Business, Hebei, China in 2019. She is currently pursuing the M.Sc. degree in information and communication engineering from the School of University of Science and Technology Beijing. Her current research interests include hybrid precoding and physical layer security.

    Yueyun Chen is a Professor of information and communication engineering at University of Science and Technology Beijing. She graduated with a B.S. degree in Radio Technology from South China University of Technology, and M.S. and Ph.D. degrees in Communication and Information System from Beijing Jiaotong University, respectively. She is a senior member of the China Institute of Electronic (CIE), a member of the academic committee and the academic degree committee of the information and communication engineering in the school of Computer and Communication Engineering of USTB. She won the second class price of Science and Technology Progress Award of Beijing, and Outstanding Scientists and Technicians in Electronic Field of Beijing. Her research interesting includes wireless mobile communication theory and system, broadband wireless communication technology, radio signal processing, wireless networks, space information and communication technology, etc.

    Rongling Jian received his M.Sc. and Ph.D. degrees in information and communication engineering from the School of University of Science and Technology Beijing in 2021. Now he works in vivo Communication Research Institute department of vivo Mobile Communication Co., Ltd.

    Jintao Wang received her the B.Sc. degree in communication engineering from the School of University of Science and Technology Beijing in 2019. She is currently pursuing the M.Sc. degree in information and communication engineering from the School of University of Science and Technology Beijing. Her current research interests include antenna selection and physical layer security.

    View full text