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IEEE Transactions on Vehicular Technology

Ergodic Secrecy Rate of $K$-User MISO Broadcast Channel With Improved Random Beamforming

Ye Fan, Xuewen Liao, Zhenzhen Gao, Tong-Xing Zheng, Victor C. M. Leung

Published Oct 14, 2019• 6 citations
Publisher

Abstract

In this paper, we study the secrecy performance of a K-user multi-input single-output (MISO) broadcast channel with random beamforming (RB), where the transmitter is equipped with N antennas, and the eavesdropper has Ne antennas. We first propose a signal-splitting random beamforming (SSRB) scheme for a single-user MISO wiretap channel, and then improve the SSRB scheme with power-minimizing (PM), which is called a PM-SSRB scheme. To improve the spectral efficiency of a multiuser network, we combine PM with non-orthogonal multiple access (NOMA), and propose a hybrid NOMA (H-NOMA) scheme and a signal-splitting NOMA (SS-NOMA) scheme for the K-user MISO wiretap channel, respectively. The sum ergodic secrecy rate of the K-user scenario is analyzed comprehensively, and a closed-form expression for the lower bound on the ergodic secrecy rate is also derived for the single-user case. Simulation results show that, compared with the traditional hybrid artificial fast-fading scheme (AFF) and artificial noise (AN) scheme, the proposed SSRB scheme and PM-SSRB scheme perform much better in terms of the ergodic secrecy rate in all power regimes. More importantly, when the eavesdropper has more antennas than the transmitter, our schemes always outperform the AFF and AN schemes. The PM-SSRB scheme is also shown to be superior to the secret-key AFF scheme. For the multiuser case, the SS-NOMA scheme can achieve higher ergodic secrecy rate than the H-NOMA scheme.

DOI
10.1109/tvt.2019.2947375

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Ergodic Secrecy Rate of KKK-User MISO Broadcast Channel With Improved Random Beamforming
In this paper, we study the secrecy performance of a K-user multi-input single-output (MISO) broadcast channel with random beamforming (RB), where the transmitter is equipped with N antennas, and the eavesdropper has Ne antennas. We first propose a signal-splitting random beamforming (SSRB) scheme for a single-user MISO wiretap channel, and then improve the SSRB scheme with power-minimizing (PM), which is called a PM-SSRB scheme. To improve the spectral efficiency of a multiuser network, we combine PM with non-orthogonal multiple access (NOMA), and propose a hybrid NOMA (H-NOMA) scheme and a signal-splitting NOMA (SS-NOMA) scheme for the K-user MISO wiretap channel, respectively. The sum ergodic secrecy rate of the K-user scenario is analyzed comprehensively, and a closed-form expression for the lower bound on the ergodic secrecy rate is also derived for the single-user case. Simulation results show that, compared with the traditional hybrid artificial fast-fading scheme (AFF) and artificial noise (AN) scheme, the proposed SSRB scheme and PM-SSRB scheme perform much better in terms of the ergodic secrecy rate in all power regimes. More importantly, when the eavesdropper has more antennas than the transmitter, our schemes always outperform the AFF and AN schemes. The PM-SSRB scheme is also shown to be superior to the secret-key AFF scheme. For the multiuser case, the SS-NOMA scheme can achieve higher ergodic secrecy rate than the H-NOMA scheme.
In this paper, we study the secrecy performance of multiple-input single-output (MISO) wiretap channel with random beamforming (RB), where the eavesdropper is equipped with multiple antennas. In traditional RB schemes, the transmitter utilizes only one antenna to emit information signal and adopts the rest antennas to produce a random beamforming vector for security. To make full use of the power resource and improve the secrecy performance, we propose a power-minimizing and signal-splitting random beamforming (PM-SSRB) scheme, where the random beamforming vector is generalized with arbitrary number of transmit antennas based on power-minimizing. To evaluate the secrecy performance of the proposed scheme, we analyze the ergodic secrecy rate and derive the closed-form expression of the ergodic rate of the MISO wiretap channel. Simulation results show that, compared with the traditional hybrid artificial fast-fading scheme (AFF) and artificial noise (AN) scheme, the proposed SSRB scheme and PM-SSRB scheme perform much better in terms of the ergodic secrecy rate in all power regimes. More importantly, when the eavesdropper has more antennas than the transmitter, our schemes always outperform the AFF and AN schemes. The PM-SSRB scheme is also shown to be superior to the secret-key AFF scheme.
In this paper, we consider max-min fairness for a downlink two-user multi-input single-output (MISO) system with imperfect channel state information available at transmitter (CSIT) taking into account the total power constraint and the physical layer security. Considering the worst-case channel uncertainty for a potential eavesdropper (PE), we study the robust secure beamforming algorithm design which maximizes the minimum achieved worst-case secrecy rate among single-antenna legitimate users. In contrast to existing schemes adopted in the literatures, we propose a rather unorthodox rate splitting (RS) scheme which advocates the dual use of a common message serving both as a desired message and artificial noise (AN) for legitimate users and the PE, respectively. The algorithm design is formulated as a non-convex optimization problem which is generally intractable. As a compromise approach, we apply the successive convex approximation (SCA) method which facilitates the design of a low-complexity suboptimal iterative algorithm. In each iteration, a rank-constrained semi-definite program (SDP) is solved optimally by SDP relaxation (SDR). Simulation results demonstrate that our proposed robust secure beamforming scheme in the MISO-RS secure transmission system outperforms that of the non-robust counterpart. Moreover, our results also unveil that the proposed RS scheme can achieve a superior performance compared to the existing non-orthogonal multiple access (NOMA) schemes and the traditional scheme.
The artificial noise (AN) scheme is an efficient strategy for enhancing the secrecy rate of a multiple-input-single-output channel in the presence of a passive eavesdropper, whose channel state information is unavailable. Recently, a randomized beamforming scheme has been proposed for deteriorating the eavesdropper's bit-error-rate performance via corrupting its receiving signal by time-varying multiplicative noise. However, the secrecy rate of such a scheme has not been well addressed yet. In this paper, we name it the artificial fast fading (AFF) scheme and provide a comprehensive secrecy rate analysis for it. We show that with this scheme, the eavesdropper will face a noncoherent Ricean fading single-input-multiple-output channel. Although the closed-form secrecy rate is difficult to obtain, we derive an exact expression for the single-antenna-eavesdropper case and a lower bound for the multiantenna-eavesdropper case, both of which can be numerically calculated conveniently. Furthermore, we compare the AFF scheme with the AN scheme and show that their respective superiorities to each other depend on the number of antennas that the transmitter and the eavesdropper possessed, i.e., when the eavesdropper has more antennas than the transmitter does, the AFF scheme achieves a larger secrecy rate; otherwise, the AN scheme outperforms. Motivated by this observation, we propose a hybrid AN-AFF scheme and investigate the power allocation problem, which achieves better secrecy performance further.
In this paper, we employ Cooperative Rate-Splitting (CRS) technique to enhance the Secrecy Sum Rate (SSR) for the Multiple Input Single Output (MISO) Broadcast Channel (BC), consisting of two legitimate users and one eavesdropper, with perfect Channel State Information (CSI) available at all nodes. For CRS based on the three-node relay channel, the transmitter splits and encodes the messages of legitimate users into common and private streams based on Rate-Splitting (RS). With the goal of maximizing SSR, the proposed CRS strategy opportunistically asks the relaying legitimate user to forward its decoded common message. During the transmission, the eavesdropper keeps wiretapping silently. To ensure secure transmission, the common message is used for the dual purpose, serving both as a desired message and Artificial Noise (AN) without consuming extra transmit power comparing to the conventional AN design. Taking into account the total power constraint and the Physical Layer (PHY) security, the precoders and timeslot allocation are jointly optimized by solving the nonconvex SSR maximization problem based on Sequential Convex Approximation (SCA) algorithm. Numerical results show that the proposed CRS secure transmission scheme outperforms existing Multi-User Linear Precoding (MU-LP) and Cooperative Non-Orthogonal Multiple Access (C-NOMA) strategies. Therefore, CRS is a promising strategy to enhance the PHY security in Multi-antenna BC systems.
In this paper, we consider the problem of secure communication in multiuser downlink wiretap networks where there exist a base-station (BS) equipped with multiple antennas, multiple legitimate receivers and a passive eavesdropper. The transmitter simultaneously transmits an information signal and artificial noise (AN) separately to the intended receivers and the eavesdropper, in which way, the secrecy rate at the eavesdropper can be seriously degraded without thinking about it location. Different schemes are studied about the power allocation of the multiple antennas in the BS, namely the average power allocation scheme and the Water-filling scheme. And in the average power allocation scheme, Zero-forcing (ZF) pre-coding scheme is used at the BS to eliminate the internal interference of all the security users. We obtain an analytical closed form expression of an achievable ergodic secrecy rate and use it as the objective function to optimize the power allocation rate between the information signal and the AN in the two schemes.
In this letter, we study on-off opportunistic beamforming for the multiuser downlink channel with a passive eavesdropper. Two opportunistic scheduling schemes exploiting multiuser diversity are investigated which require limited feedback of the effective signal-to-noise ratio (SNR) from the legitimate users. For the two scheduling schemes, we derive new closed-form expressions for the ergodic secrecy rate with on-off beamforming over Rayleigh fading channels. Numerical results are provided to verify our analytical results and illustrate the impact of multiuser diversity on the secrecy performance.