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IEEE Transactions on Vehicular Technology

Artificial-Noise-Aided Coordinated Secure Transmission Design in Multi-Cell Multi-Antenna Networks With Limited Feedback

Zhiyao Tang, Liang Sun, Xinyu Tian, Dusit Tao Niyato, Yang Zhang

Published Dec 13, 2021• 13 citations
Publisher

Abstract

In this paper, we consider secure communications in a multi-cell downlink multi-antenna system, where each multi-antenna base station (BS) sends confidential messages to one intended legitimate user (LU) with a passive multi-antenna eavesdropper trying to intercept the messages in this cell. To enhance the secure communications of the cell-edge users, the multiple BSs employ coordinated beamforming with the aid of artificial-noise (AN) beamforming. We conduct a mathematically rigorous secrecy performance analysis of the considered system and obtain new accurate closed-form expressions of a lower bound on the ergodic rate of each LU and an upper bound of the ergodic rate of each eavesdropper without assuming asymptotes for any system parameter (except for the “worst-case” scenario with zero noise power). Then, a lower bound on the ergodic secrecy rate (ESR) of each LU follows. Based on the derived analytical results, we propose a low-complexity algorithm to optimize the channel sate information (CSI) feedback bits allocation for the channels of target signal link and inter-cell interference links. Furthermore, we develop explicit sufficient conditions on the set of system parameters under which there are at least two BSs to coordinated secure transmission. Through both theoretical analysis and numerical results, we can verify that the obtained analytical lower bound on ESR of each LU as a function of the set of power allocation coefficients is generallyneither convex nor concave. Thus, we propose to employ some numerical method to find a sub-optimal power allocation solution. Finally, numerical results are also provided to validate our theoretical results and the proposed feedback bits and power allocation methods.

DOI
10.1109/tvt.2021.3134758

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In this paper, we consider secure communications in a multi-cell downlink multi-antenna system, where each multi-antenna base station (BS) sends confidential messages to one intended legitimate user (LU) with a passive multi-antenna eavesdropper trying to intercept the messages in this cell. To enhance the secure communications of the cell-edge users, the multiple BSs employ coordinated beamforming with the aid of artificial-noise (AN) beamforming. We conduct a mathematically rigorous secrecy performance analysis of the considered system and obtain new accurate closed-form expressions of a lower bound on the ergodic rate of each LU and an upper bound of the ergodic rate of each eavesdropper without assuming asymptotes for any system parameter (except for the “worst-case” scenario with zero noise power). Then, a lower bound on the ergodic secrecy rate (ESR) of each LU follows. Based on the derived analytical results, we propose a low-complexity algorithm to optimize the channel sate information (CSI) feedback bits allocation for the channels of target signal link and inter-cell interference links. Furthermore, we develop explicit sufficient conditions on the set of system parameters under which there are at least two BSs to coordinated secure transmission. Through both theoretical analysis and numerical results, we can verify that the obtained analytical lower bound on ESR of each LU as a function of the set of power allocation coefficients is generallyneither convex nor concave. Thus, we propose to employ some numerical method to find a sub-optimal power allocation solution. Finally, numerical results are also provided to validate our theoretical results and the proposed feedback bits and power allocation methods.
This paper comprehensively studies the physical layer security in frequency division duplex multi-antenna cellular systems, where the multi-antenna base stations (BSs), legitimate users (LUs), and eavesdroppers are all randomly located. Each BS employs artificial-noise (AN)-aided multi-user linear beamforming with limited channel state information feedback. Based on the stochastic geometry theory, we first derive an analytical expression of a lower bound on the ergodic secrecy rate (ESR) of the typical LU without assuming asymptotes for any system parameter. We then develop a tight closed-form approximation on the optimal number of feedback bits to maximize a lower bound on the per-user net ESR, which takes into consideration the cost of uplink spectral efficiency for limited feedback. Moreover, the power allocation coefficient between message-bearing signals and AN can be optimized by using a bisection search method. Our main finding is that, the optimum number of feedback bits scales linearly with the path-loss exponent and the number of antennas, and scales logarithmically with the channel coherence time. The derived analytical results can also provide system-level insights into the ESR performance of the multi-antenna random cellular networks with limited feedback and the optimal system design. Numerical results are also presented to verify the obtained results.
We present a secure multi-user multi-antenna transmission framework based on artificial-noise-aided linear zero-forcing beamforming, with limited channel state information feedback from multiple distributed legitimate users (LUs). The secrecy performance of the proposed scheme is analytically investigated and optimized. We develop a new accurate closed-form expression of a lower bound on the ergodic secrecy rate (ESR) of each LU without assuming asymptotes for any system parameter. To make system design tractable, we develop another lower bound on ESR which is so analytically amenable that it enables one to not only extend the results of the previous related works but also explore some untouched aspects of the well known artificial-noise-aided scheme. We derive the optimized power allocation coefficient to message-bearing signals which maximizes the latter ESR lower bound. Furthermore, we theoretically study respectively the impacts of the two main parameters, i.e., transmit power P and the number of feedback bits of each LU B, on the power allocation coefficient, and show the asymptotic results for the high-power and high-quantization-resolution systems. We also develop a sufficient condition on P and B under which a positive ESR of each LU can be achieved. We study some important parameters called the minimum required transmit power (MRTP) and the minimum required number of feedback bits (MRFBs) for each LU to achieve a positive ESR or to achieve a target ESR, which have rarely been touched before. Besides, we propose the algorithms to obtain the MRTP and MRFBs. Numerical results are also provided to verify our theoretical results.
In this letter, we consider the problem of secure communication in the downlink of a multi-cell multiple-input multiple-output (MIMO) system under imperfect channel state information (CSI) at the base stations (BSs). The passive eavesdroppers are considered, whose CSI are unavailable at the BSs. Coordinated Beamforming (CBf) and artificial noise (AN) are employed for secrecy enhancement. Based on regularized channel inversion (RCI) precoding, we derive a novel closed-form expression of secrecy sum-rate in the large-system regime. Based on the result, the regularization parameter and the power allocation ratio between the information signal and AN are optimized. Compared to the perfect CSI case, it shows that the channel estimation error can drastically reduce the secrecy sum-rate, and more power needs to be allocated for AN when the channel estimation error grows larger. The analytical results are validated with the finite-size system by simulation.
We consider a low-complexity transceiver design for secure communications of a multiuser multi-antenna system with an external multi-antenna eavesdropper. We propose to employ Tomlinson–Harashima precoder (THP) to simultaneously transmit message-bearing signals and artificial noise (AN) according to the quantized channel state information (CSI). Based on random vector quantization of the channel vectors, we obtain analytical approximations of the ergodic secrecy rate (ESR) of each legitimate receiver (LR) and the ergodic secrecy sum rate of the system with arbitrary system parameters. Based on the obtained analytical results, the near-optimal power allocation to the information signals and AN can be obtained using a numerical method. We show using an information-theoretical method that, besides the advantage in the ESR over the linear precoding scheme, THP can reduce the supported rate of the eavesdropper’s channel by preventing the eavesdropper from obtaining the legitimate channels’ (quantized) CSI. The ESR loss of each LR compared with the perfect CSI case will increase without bound for a fixed number of feedback bits. We also derive a feedback bit scaling law to solve this problem. Finally, numerical results are provided to verify our analytical results and also the advantage of the proposed secure nonlinear transceiver over the corresponding linear scheme.
We study secure multi-antenna transmission with limited feedback from the intended receiver and no feedback from the malicious eavesdropper. Our system uses the artificial-noise-aided beamforming approach to enhance secrecy, considering slow fading channels with outage constraints on the reliability performance of legitimate communication and the secrecy performance against eavesdropping. Our analytical results provide conditions on the minimum number of feedback bits and the minimum strength of the intended channel for making secure transmission possible. We observe that strengthening the secrecy outage constraint puts higher requirements on the number of feedback bits and the strength of the intended channel. To maximize the achievable secrecy rate, the optimal transmit power allocation between the information signal and the artificial noise is also derived in closed form.
We consider nonlinear transceiver design for downlink multiuser multi-antenna secure communications with an external multi-antenna eavesdropper. The multi-antenna transmitter simultaneously transmits confidential-message-bearing signals and artificial noise (AN) using nonlinear Tomlinson Harashima precoding based on the limited channel state information feedback. For the proposed nonlinear secure transceiver, we reveal the mechanism behind which makes this nonlinear precoding superior than the linear precoding methods in guaranteeing secrecy of wireless multiuser multi-antenna systems. We also obtain analytical bounds of the ergodic secrecy rate of each legitimate receiver and the ergodic secrecy sum rate of the system. Based on the analytical result, the near optimal power allocation to the information signals and AN can be obtained using numerical method. Numerical results are shown to verify the advantage of the proposed nonlinear method over the linear zero-forcing precoding.