In this paper, we consider a multi-cell massive MIMO system with matched-filter precoding and artificial noise (AN) generation at the base station (BS) for secure downlink transmission in the presence of multi-antenna passive eavesdroppers. We derive two tight lower bounds for the achievable ergodic secrecy rate and a tight upper bound on the secrecy outage probability of the considered system. The analytical results are used to optimize the amount of power allocated for AN generation. Our results reveal that AN generation is not required in massive MIMO systems as long as the number of BS antennas is much larger than the number of eavesdropper antennas. However, as the number of eavesdropper antennas increases relative to the number of BS antennas, AN becomes beneficial and the amount of power optimally allocated to AN generation increases with the number of eavesdropper antennas.
In this paper, we consider a multi-cell massive MIMO system with matched-filter precoding and artificial noise (AN) generation at the base station (BS) for secure downlink transmission in the presence of multi-antenna passive eavesdroppers. We derive two tight lower bounds for the achievable ergodic secrecy rate and a tight upper bound on the secrecy outage probability of the considered system. The analytical results are used to optimize the amount of power allocated for AN generation. Our results reveal that AN generation is not required in massive MIMO systems as long as the number of BS antennas is much larger than the number of eavesdropper antennas. However, as the number of eavesdropper antennas increases relative to the number of BS antennas, AN becomes beneficial and the amount of power optimally allocated to AN generation increases with the number of eavesdropper antennas.
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 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.
To reduce the number of radio-frequency chains of base station, the use of finite resolution analog beamforming is desirbale in massive multiple-input multiple-output system. This article investigates the secure downlink massive multiple-input multiple-output data transmission with artificial noise at base station in the presence of a multi-antenna passive eavesdropper. The achievable user’s ergodic information rate and ergodic capacity of the eavesdropper are analyzed in detail, respectively. With maximum ratio transmission or maximum ratio combining, we derive closed-form expressions for a tight lower bound on ergodic secrecy rate and tight upper bound for secrecy outage probability. Based on these analytical expressions, the effects of various system parameters on secrecy performance, such as power allocation factor, number of eavesdropper’s antennas, number of the user terminals, total transmission power, and finite resolution analog beamforming parameters, are investigated in detail. Also, the optimal power allocation scheme between data and artificial noise signals is achieved in closed form to maximize the ergodic secrecy rate. In addition, we derive the conditions that the secure massive multiple-input multiple-output system need to meet to obtain a positive secrecy rate. Finally, numerical simulation results validate the system’s secrecy performance and verify all the theoretical analytical results.
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 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.