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arXiv:1507.00789 · IEEE Transactions on Information Theory

Secure Massive MIMO Transmission With an Active Eavesdropper

Yongpeng Wu, Robert Schober, Derrick Wing Kwan Ng, Chengshan Xiao, Giuseppe Caire

Published May 16, 2016• 297 citations
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Abstract

In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output systems with a multi-antenna active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform toward the eavesdropper, thus increasing its received signal power. Assuming matched filter precoding and artificial noise (AN) generation at the transmitter, we derive an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity. For the case of a single-antenna active eavesdropper, we obtain a closed-form expression for the optimal power allocation policy for the transmit signal and the AN, and find the minimum transmit power required to ensure reliable secure communication. Furthermore, we show that the transmit antenna correlation diversity of the intended users and the eavesdropper can be exploited in order to improve the secrecy rate. In fact, under certain orthogonality conditions of the channel covariance matrices, the secrecy rate loss introduced by the eavesdropper can be completely mitigated.

DOI
10.1109/tit.2016.2569118

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In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output systems with a multi-antenna active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform toward the eavesdropper, thus increasing its received signal power. Assuming matched filter precoding and artificial noise (AN) generation at the transmitter, we derive an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity. For the case of a single-antenna active eavesdropper, we obtain a closed-form expression for the optimal power allocation policy for the transmit signal and the AN, and find the minimum transmit power required to ensure reliable secure communication. Furthermore, we show that the transmit antenna correlation diversity of the intended users and the eavesdropper can be exploited in order to improve the secrecy rate. In fact, under certain orthogonality conditions of the channel covariance matrices, the secrecy rate loss introduced by the eavesdropper can be completely mitigated.
In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multipleinput multiple-output (MIMO) systems in the presence of an active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform towards the eavesdropper, thus increasing its received signal power. We derive an asymptotic achievable secrecy rate for matched filter precoding and artificial noise (AN) generation at the transmitter when the number of transmit antennas goes to infinity. For the achievability scheme at hand, we obtain the optimal power allocation policy for the transmit signal and the AN in closed form. For the case of correlated fading channels, we show that the impact of the active eavesdropper can be completely removed if the transmit correlation matrices of the users and the eavesdropper are orthogonal. Inspired by this result, we propose a precoder null space design exploiting the low rank property of the transmit correlation matrices of massive MIMO channels, which can significantly degrade the eavesdropping capabilities of the active eavesdropper.
In this paper, we study the design of secure communication for time-division duplex multi-cell multi-user massive multiple-input-multiple-output (MIMO) systems with active eavesdropping. We assume that the eavesdropper actively attacks the uplink pilot transmission and the uplink data transmission before eavesdropping the downlink data transmission of the users. We exploit both the received pilot's and the received data signals for uplink channel estimation. We show analytically that when both the number of transmit antennas and the length of the data vector tend to infinity, the signals of the desired user and the eavesdropper lie in different eigenspaces of the received signal matrix at the base station, provided their signal powers are different. This finding reveals that decreasing (instead of increasing) the desired user's signal power might be an effective approach to combat a strong active attack from an eavesdropper. Inspired by this observation, we propose a data-aided secure downlink transmission scheme and derive an asymptotic achievable secrecy sum-rate expression for the proposed design. For the special case of a single-cell single-user system with independent and identically distributed fading, the obtained expression reveals that the secrecy rate scales logarithmically with the number of transmit antennas. This is the same scaling law as for the achievable rate of a single-user massive MIMO system in the absence of eavesdroppers. The numerical results indicate that the proposed scheme achieves significant secrecy rate gains compared with alternative approaches based on matched filter precoding with artificial noise generation and null space transmission.
In this paper, we study the design of secure communication for time division duplexing multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with active eavesdropping. We assume that the eavesdropper actively attacks the uplink pilot transmission and the uplink data transmission before eavesdropping the downlink data transmission phase of the desired users. We exploit both the received pilots and data signals for uplink channel estimation. We show analytically that when the number of transmit antennas and the length of the data vector both tend to infinity, the signals of the desired user and the eavesdropper lie in different eigenspaces of the received signal matrix at the base station if their signal powers are different. This finding reveals that decreasing (instead of increasing) the desire user's signal power might be an effective approach to combat a strong active attack from an eavesdropper. Inspired by this result, we propose a data-aided secure downlink transmission scheme and derive an asymptotic achievable secrecy sum-rate expression for the proposed design. Numerical results indicate that under strong active attacks, the proposed design achieves significant secrecy rate gains compared to the conventional design employing matched filter precoding and artificial noise generation.
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.
The achievable secrecy rates for a cell-free massive multiple-input multiple-output (MIMO) in the presence of a single-antenna active eavesdropper are derived and compared with that of co-located massive MIMO. The active eavesdropper contaminates the uplink channel estimates at the access points (APs), and the downlink precoders at the APs are constructed based on this contaminated channel estimates. Hence, the APs inadvertently beamform confidential information towards the active eavesdropper during the downlink transmission. The achievable rates at the legitimate user nodes and the rates leaked into the active eavesdropper are derived for estimated/imperfect channel state information in the finite and infinite regimes of the number of APs. A transmit power allocation algorithm for maximizing the achievable secrecy rate is developed. Our analysis and numerical results reveal that the rate leaked into the eavesdropper can be of significance in the presence of active pilot attacks in cell-free massive MIMO.