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Performance Analysis of Linear Precoding for Secure Multiuser MIMO Systems with a Multiple-Antenna Eavesdropper

Hao Deng, Hui‐Ming Wang, Chaowen Liu, Wenjie Wang

Published Dec 1, 2014• 0 citations
Publisher

Abstract

In this paper, we investigate the secrecy performance of matched-filter (MF) and zero-forcing (ZF) precoding in a multiuser massive multiple-input multiple-output (MIMO) system with a multi-antenna passive eavesdropper. For the two precoding schemes, we find that the equivalent wiretap channels are similar and thus the eavesdropper achieves the approximate same sum-rate. Closed-form expressions of ergodic secrecy sum-rate (ESSR) are derived for the both schemes in the low and high signal-to-noise ratio (SNR) regimes. We show that a positive ESSR of MF scheme may be not achieved when the BS simultaneously serves more than two users with high transmit power, while the ESSR of ZF scheme always grows with the number of the served users. On the contrast, MF scheme is better than ZF scheme in the low SNR regime. Simulation results corroborate the analytic results.

DOI
10.1109/glocom.2014.7417657

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In this paper, we investigate the secrecy performance of matched-filter (MF) and zero-forcing (ZF) precoding in a multiuser massive multiple-input multiple-output (MIMO) system with a multi-antenna passive eavesdropper. For the two precoding schemes, we find that the equivalent wiretap channels are similar and thus the eavesdropper achieves the approximate same sum-rate. Closed-form expressions of ergodic secrecy sum-rate (ESSR) are derived for the both schemes in the low and high signal-to-noise ratio (SNR) regimes. We show that a positive ESSR of MF scheme may be not achieved when the BS simultaneously serves more than two users with high transmit power, while the ESSR of ZF scheme always grows with the number of the served users. On the contrast, MF scheme is better than ZF scheme in the low SNR regime. Simulation results corroborate the analytic results.
In this paper, we investigate the secrecy performance of matched-filter (MF) and zero-forcing (ZF) precoding in a multiuser massive multiple-input multiple-output (MIMO) system with a multi-antenna passive eavesdropper. For the two precoding schemes, we find that the equivalent wiretap channels are similar and thus the eavesdropper achieves the approximate same sum-rate. Closed-form expressions of ergodic secrecy sum-rate (ESSR) are derived for the both schemes in the low and high signal-to-noise ratio (SNR) regimes. We show that a positive ESSR of MF scheme may be not achieved when the BS simultaneously serves more than two users with high transmit power, while the ESSR of ZF scheme always grows with the number of the served users. On the contrast, MF scheme is better than ZF scheme in the low SNR regime. Simulation results corroborate the analytic results.
Massive Multiple Input Multiple Output (MIMO) has been considered as an emerging technology to enhance the spectral and energy efficiency for the upcoming wireless communication systems. This paper derives a closed-form approximation for the Ergodic Achievable Secrecy Sum-Rate (EASSR) by considering the joint impact of eavesdroppers and jammers. Two widely used linear precoding techniques, Zero-Forcing (ZF) and Maximum Ratio Transmission (MRT), were used in conjunction with matrix and vector normalization to analyze the secrecy performance. Closed-form expressions are used to explain how the secrecy performance is affected when using the ZF and MRT precoding in the eavesdropping and jamming attack models. We also analyze and compare the performances of different combinations of normalization method and precoding technique in various scenarios. From the analytical expressions and simulation results, we observe that the vector and matrix normalization perform better for the ZF precoding than for the MRT precoding in high Signal-to-Noise Ratio (SNR) scenarios. However, in low SNR, the MRT with matrix normalization outperforms the ZF with vector normalization regardless of the number of users in the system. Further, we observe that the MRT fails to serve more than two users in high SNR scenario. Numerical results obtained from Monte Carlo simulation are used to corroborate the accuracy of the asymptotic secrecy analysis.
The secrecy performance of forward link multi-user massive multiple-input multiple-output (MIMO) system is investigated in this paper. The base station (BS) equipped with a large number of transmit antennas sends mutually independent datas to multiple single-antenna legitimate users simultaneously. A passive multi-antenna eavesdropper is placed in the scenario to intercept the signals. We consider the case that the number of legitimate users and eavesdropper antennas increases proportionally with the number of BS antennas. Maximum ratio transmission (MRT) is used as linear precoder at the BS. Lower bounds on the ergodic achievable rate of legitimate users and upper bounds of the eavesdropper are derived. By minimizing the upper bounds on the achievable rates of the eavesdropper while satisfying the rate constraints of legitimate users, we present the corresponding optimal radiated power scaling (RPS) factor. In the limit of an infinite number of BS antennas, we prove that the optimal RPS factor converge to a different constant limit with that of the case in which the number of legitimate users and eavesdropper antennas is finite. We show that when the number of BS antennas grows large, the secrecy performance is mainly determined by the ratios between the number of BS antennas, legitimate users and eavesdropper antennas. A number of simulation results are presented to visualize the analysis.
In this paper, we consider physical layer security provisioning in multi-cell massive multiple-input multiple-output (MIMO) systems. Specifically, we consider secure downlink transmission in a multi-cell massive MIMO system with matched-filter precoding and artificial noise (AN) generation at the base station (BS) in the presence of a passive multi-antenna eavesdropper. We investigate the resulting achievable ergodic secrecy rate and the secrecy outage probability for the cases of perfect training and pilot contamination. Thereby, we consider two different AN shaping matrices, namely, the conventional AN shaping matrix, where the AN is transmitted in the null space of the matrix formed by all user channels, and a random AN shaping matrix, which avoids the complexity associated with finding the null space of a large matrix. Our analytical and numerical results reveal that in multi-cell massive MIMO systems employing matched-filter precoding (1) AN generation is required to achieve a positive ergodic secrecy rate if the user and the eavesdropper experience the same path-loss, (2) even with AN generation secure transmission may not be possible if the number of eavesdropper antennas is too large and not enough power is allocated to channel estimation, (3) for a given fraction of power allocated to AN and a given number of users, in case of pilot contamination, the ergodic secrecy rate is not a monotonically increasing function of the number of BS antennas, and (4) random AN shaping matrices provide a favourable performance/complexity tradeoff and are an attractive alternative to conventional AN shaping matrices.
In this paper, we consider physical layer security provisioning in multicell massive multiple-input-multiple-output (MIMO) systems. Specifically, we consider secure downlink transmission in a multicell massive MIMO system with matched-filter precoding and artificial noise (AN) generation at the base station (BS) in the presence of a passive multiantenna eavesdropper. We investigate the resulting achievable ergodic secrecy rate and the secrecy outage probability for the cases of perfect training and pilot contamination. Thereby, we consider two different AN shaping matrices, namely, the conventional AN shaping matrix, where the AN is transmitted in the null space of the matrix formed by all user channels, and a random AN shaping matrix, which avoids the complexity associated with finding the null space of a large matrix. Our analytical and numerical results reveal the following, in multicell massive MIMO systems employing matched-filter precoding: 1) AN generation is required to achieve a positive ergodic secrecy rate if the user and the eavesdropper experience the same path loss; 2) even with AN generation, secure transmission may not be possible if the number of eavesdropper antennas is too large and not enough power is allocated to channel estimation; 3) for a given fraction of power allocated to AN and a given number of users, in case of pilot contamination, the ergodic secrecy rate is not a monotonically increasing function of the number of BS antennas; and 4) random AN shaping matrices provide a favorable performance/complexity tradeoff and are an attractive alternative to conventional AN shaping matrices.
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.