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IEEE Communications Letters

Ergodic Secrecy Sum-Rate for Downlink Multiuser MIMO Systems With Limited CSI Feedback

Na Li, Xiaofeng Tao, Jin Xu

Published Apr 24, 2014• 37 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2014.2319821

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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.
To date, the achievable ergodic secrecy sum rate has been studied for multiuser MIMO downlink systems with single-antenna receivers only. In this paper, we study multiuser MIMO downlink systems with multiple-antenna receivers and an external single-antenna eavesdropper to be kept ignorant of the transmitted messages. We adopt the block diagonalization technique at the transmitter to remove inter-user interference, and derive closed-form expressions of the achievable rate for the intended users and the information leakage rate for the eavesdropper. Furthermore, we analyze asymptotic characteristics of the ergodic secrecy sum rate for the system in the high and low SNR regime, and obtain a tight lower bound in the regime of large transmit and receive antennas. Finally, numerical results validate the accuracy of the theoretical analysis.
Channel state information (CSI) at the transmitter is of importance to the performance of physical layer security based on multi-antenna networks. Specifically, CSI is not only beneficial to improve the capacity of the legitimate channel, but also can be used to degrade the performance of the eavesdropper channel. Thus, the secrecy rate increases accordingly. This letter focuses on the quantitative analysis of the ergodic secrecy sum-rate in terms of feedback amount of the CSI from the legitimate users in multiuser multi-antenna downlink networks. Furthermore, the asymptotic characteristics of the ergodic secrecy sum-rate in two extreme cases is investigated in some detail. Finally, our theoretical claims are confirmed by the numerical results.
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.
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.
Security and privacy have become increasingly critical demands in wireless networks, which, however, are particularly susceptible to eavesdropping attacks due to the broadcast nature of radio signals. This paper considers the problem of secure communication in the multiuser downlink with a passive eavesdropper (Eve), whose channel state information (CSI) is unavailable. The transmitter simultaneously transmits concurrent information signals to the users and artificial noise (AN) to Eve. We first assume that all users' CSI is perfectly known by the transmitter and derive a closed-form expression for the ergodic secrecy sum rate (SSR) in the large-system limit. We then use it as an objective function to optimize the power allocation between information signals and the AN. It shows that more power needs to be used for AN when Eve has more antennas and when the system serves fewer users. We also extend the analysis to the imperfect-CSI scenario, where the SSR saturates at high transmit power, and it is better to create more AN than to increase the signal strength when the channel estimation error is large. We derive a scale law of feedback bits (for frequency-division duplexing (FDD) systems) to maintain a constant rate offset compared with the perfect-CSI case and the optimal length of training sequence (for time-division duplexing (TDD) systems) to maximize the effective SSR. It shows that more feedback bits and longer training sequences are required to deal with the eavesdropping problem. Closed-form expressions derived in this paper can reduce the complexity of system analysis and design.
In this paper, we consider the downlink transmission over a single-cell massive multiple-input-multiple-output (MIMO) system in the presence of multiple single-antenna eavesdroppers (massive MIMOME). We concentrate on the practical scenario where partial channel state information (CSI) of legitimate users and no CSI of eavesdroppers are available at the base station and consider both types of eavesdroppers including the non-colluding and colluding eavesdroppers. Random unitary beamforming (RUB) based scheme is used to describe the partial CSI of legitimate users. We derive the closed-form expression of ergodic secrecy rate for RUB based massive MIMOME transmission, and its single legitimate user particular case. We also present numerical results to illustrate the performance-complexity tradeoff among different massive MIMO transmission schemes. We show that RUB based scheme can enhance secrecy performance of massive MIMO transmission with lower implementation complexity.