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International Conference on Communications

Non-asymptotic analysis of secrecy capacity in massive MIMO system

Yin Long, Zhi Chen, Lingxiang Li, Jun Fang

Published Jun 1, 2015• 3 citations
Publisher

Abstract

In this paper, we consider a massive MIMO wiretap system where the transmitter, the receiver and the eavesdropper are equipped with a large number of antennas. Being different from the previous works using asymptotic random matrix theory, our analysis relies on the concentration measure of non-asymptotic random matrix theory which allows us to obtain tight bounds for secrecy capacity of massive MIMO system with finite antenna number. The analytical and simulation results reveal the following, in the massive MIMO system employing equal power allocation at each transmit antenna: 1) the secrecy capacity falls within a bounds with a probability growing exponentially with the number of transmit antenna, while the ergodic secrecy capacity falls within a deterministic bounds; 2) the gap between the upper and the lower bound on secrecy rate is proportional to the square root of the SNR at legitimate receiver and the SNR at eavesdropper, respectively; 3) when the entry of legitimate channel matrix and eavesdropping channel matrix satisfies Gaussian distribution, the gap between the upper and the lower bound on secrecy rate is a linear reciprocal function of the number of transmit antennas.

DOI
10.1109/icc.2015.7249046

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In this paper, we consider a massive MIMO wiretap system where the transmitter, the receiver and the eavesdropper are equipped with a large number of antennas. Being different from the previous works using asymptotic random matrix theory, our analysis relies on the concentration measure of non-asymptotic random matrix theory which allows us to obtain tight bounds for secrecy capacity of massive MIMO system with finite antenna number. The analytical and simulation results reveal the following, in the massive MIMO system employing equal power allocation at each transmit antenna: 1) the secrecy capacity falls within a bounds with a probability growing exponentially with the number of transmit antenna, while the ergodic secrecy capacity falls within a deterministic bounds; 2) the gap between the upper and the lower bound on secrecy rate is proportional to the square root of the SNR at legitimate receiver and the SNR at eavesdropper, respectively; 3) when the entry of legitimate channel matrix and eavesdropping channel matrix satisfies Gaussian distribution, the gap between the upper and the lower bound on secrecy rate is a linear reciprocal function of the number of transmit antennas.
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.
Wireless security has become an important issue for modern wireless networks. Due to the broadcast nature of wireless channels possibility of eavesdropping the transmission is provided for non-legitimate receivers. In the present paper, we consider a multi-antenna wiretap channel in a fast-fading environment with only statistical channel state information available at the receiver. The overall performance of such channel is characterized by the ergodic secrecy capacity, which, in general, cannot be characterized explicitly. Nevertheless, based on the assumption that the numbers of antennas at legitimate terminals and the number of eavesdroppers grow large without bound, we derive a deterministic approximation for the achievable ergodic secrecy rate under arbitrary channel inputs. The obtained large-system approximation matches well with the actual simulated secrecy rates, revealing some interesting behavior of the secrecy rates in the given scenario.
Security issues in wireless networks have become a subject of growing interest in recent years due to the broadcast nature of wireless channels. In this paper, we investigate secure communication over a multi-antenna wiretap channel in the presence of randomly distributed eavesdroppers. In the fast fading environment, the overall performance of this channel is traditionally characterized by the ergodic secrecy capacity, which, in general, cannot be derived explicitly. Nevertheless, based on the assumption that the numbers of antennas at legitimate terminals and the number of eavesdroppers grow large without bound, we derive a deterministic approximation of an achievable ergodic secrecy rate for arbitrary inputs. In addition, we characterize the secrecy rates for practically relevant separate-decoding scheme at the receiver. We validate the proposed large-system approximation through numerical simulations and observe a good match with the actual secrecy rates. Finally, we also analyze some interesting behavior of the secrecy rates in the given scenario depending on the geometry of the nodes.
This paper studies the impact of transmit antenna selection on the secrecy performance of massive MIMO wiretap channels. We consider a scenario in which a multi-antenna transmitter selects a subset of transmit antennas with the strongest channel gains. Confidential messages are then transmitted to a multi-antenna legitimate receiver while the channel is being overheard by a multi-antenna eavesdropper. For this setup, we approximate the distribution of the instantaneous secrecy rate in the large-system limit. The approximation enables us to investigate the optimal number of selected antennas which maximizes the asymptotic secrecy throughput of the system. We show that increasing the number of selected antennas enhances the secrecy performance of the system up to some optimal value, and that further growth in the number of selected antennas has a destructive effect. Using the large-system approximation, we obtain the optimal number of selected antennas analytically for various scenarios. Our numerical investigations show an accurate match between simulations and the analytic results even for not so large dimensions.
We consider the problem of secure communication in wireless fading channels in the presence of quantized version of the receivers channel sate information at transmit side. The transmitter has multiple antennas and is able to simultaneously transmits an information bearing signal and artificial noise. For general values of signal to noise ratio (SNR), we obtain the exact closed-form expression for the distribution function of output signal to interference plus noise ratio at the legitimate receiver and a lower bound of the ergodic secrecy capacity can be obtain by using simple numerical integration. For the interference-limited case, we obtained a closed-form expression for a lower bound of secrecy capacity. Our results apply to arbitrary number of antennas and number of feedback bits. The analytical and numerical results show that the ergodic secrecy capacity lower bound approaches to a constant as the SNR of system grows large. In addition, we find that, for system with reasonable number of feedback bits, the optimal power allocation strategy should allocate most of the available power to the information signal.
We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers. Our technique involves a careful study of a Sato-like upper bound via the solution of a certain algebraic Riccati equation.