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Secrecy Performance Analysis for An-Aided Linear ZFBF in MU-MIMO Systems with Limited Feedback

Lu Cao, Zhiyao Tang, Liang Sun, Zhenni Pan, Shigeru Shimamoto, Yong Feng

Published Dec 1, 2019• 0 citations
Publisher

Abstract

Although there have been extensive works on artificial-noise-aided (AN-aided) secure transmission schemes for multi-antenna systems, there is still lack of study on the AN-aided scheme employing the widely used linear zero-forcing beamforming (ZFBF) for systems with multiple distributed users. Particularly, there is no analytical secrecy performance for general system settings with neither perfect nor imperfect channel state information of the legitimate users at the transmitter (CSIT). This paper considers the AN-aided ZFBF based on the quantized CSIT for secure communication in the downlink multiuser multi-antenna systems with an external multi-antenna eavesdropper. We develop an approximated closed-form lower bound on the ergodic rate of each legitimate user (LU), and also a closed-form upper bound on the maximum achievable ergodic rate for each LU's messages over the eavesdropper's channel without assuming any asymptotes for system parameters. Then, an approximated closed-form lower bound on the ergodic secrecy rate of each LU follows. Simulation results validate our analytical secrecy performance results and also the effectiveness of AN in enhancing the secrecy performance of linear ZFBF.

DOI
10.1109/globecom38437.2019.9014215

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Although there have been extensive works on artificial-noise-aided (AN-aided) secure transmission schemes for multi-antenna systems, there is still lack of study on the AN-aided scheme employing the widely used linear zero-forcing beamforming (ZFBF) for systems with multiple distributed users. Particularly, there is no analytical secrecy performance for general system settings with neither perfect nor imperfect channel state information of the legitimate users at the transmitter (CSIT). This paper considers the AN-aided ZFBF based on the quantized CSIT for secure communication in the downlink multiuser multi-antenna systems with an external multi-antenna eavesdropper. We develop an approximated closed-form lower bound on the ergodic rate of each legitimate user (LU), and also a closed-form upper bound on the maximum achievable ergodic rate for each LU's messages over the eavesdropper's channel without assuming any asymptotes for system parameters. Then, an approximated closed-form lower bound on the ergodic secrecy rate of each LU follows. Simulation results validate our analytical secrecy performance results and also the effectiveness of AN in enhancing the secrecy performance of linear ZFBF.
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 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.
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.
We study transceiver design for secure communication of multiuser multi-antenna systems with assistant of a cooperative helper. There is an external multiple-antenna eavesdropper trying to obtain the confidential messages. Due to the finite-rate constraint of feedback channels, only quantized channel state information of the legitimate users is available at the transmitter and the helper. A nonlinear precoding strategy using Tomlinson Harashima precoding at the legitimate transmitter and a null-space beamforming scheme at the helper are proposed based on the quantized channel state information. Assuming a genie-aided perfect successive interference cancelation at Eve, we obtain closed-form expressions of the performance bounds for the achievable ergodic rate of each legitimate user and the ergodic secrecy sum rate. Numerical results illustrate that our proposed nonlinear-precoded strategy outperforms linear precoding scheme.
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.
This paper investigates the ergodic secrecy sum-rate for the downlink multiuser MIMO system with independent confidential messages, each of which is intended for one of the users and should keep secret from others. We adopt zero-forcing beamforming with limited channel state information (CSI) feedback at the transmitter, and derive the closed-form expression for the ergodic secrecy sum-rate. Moreover, we analyze some of its asymptotic characteristics, which provide guidance on secure transmission design. Finally, all theoretical results are validated by numerical simulations.