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IEEE International Conference on Consumer Electronics - Berlin (ICCE-Berlin)

Secrecy capacity for MIMO fading channel with size-limited eavesdropper

Fan Wei, Hou Xiaoyun, Yan Mei Zhu, Huang Tingjin, Wei Hao

Published Sep 1, 2014• 0 citations
Publisher

Abstract

In the multiple input multiple output (MIMO) wiretap channel model which contains path loss, shadow fading and small-scale fading, we consider the effect of both spatial correlation and antenna mutual coupling, with limited size of eavesdropper which has Multi-antenna. Via Monte Carlo simulation, we analyze the effect on secrecy capacity when the location of the transmitter and the eavesdropper changes relatively, under the situation that the number of antennas of the eavesdropper is greater than the legitimate receiver's. The simulation results show that, based on different status of the wiretap channels, a corresponding safety distance between the transmitter and the eavesdropper should be calculated to ensure the system security.

DOI
10.1109/icce-berlin.2014.7034259

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In the multiple input multiple output (MIMO) wiretap channel model which contains path loss, shadow fading and small-scale fading, we consider the effect of both spatial correlation and antenna mutual coupling, with limited size of eavesdropper which has Multi-antenna. Via Monte Carlo simulation, we analyze the effect on secrecy capacity when the location of the transmitter and the eavesdropper changes relatively, under the situation that the number of antennas of the eavesdropper is greater than the legitimate receiver's. The simulation results show that, based on different status of the wiretap channels, a corresponding safety distance between the transmitter and the eavesdropper should be calculated to ensure the system security.
Although conventional cryptographic security mechanisms are essential to the overall problem of security, the openness of wireless medium poses both threats and opportunities for securing transmission. Information theoretic security is attracting researchers for its robust nature. In this paper, a Gaussian multiple input multiple output multiple eavesdropper (MIMOME) channel is considered where a transmitter is communicating to a receiver in the presence of an eavesdropper. The transmitter is equipped with multiple antennas, while the receiver and the eavesdropper also contains multiple antennas. We present a technique for determining the secrecy capacity of the MIMO channel under Gaussian noise. To do so, we transform the channel into multiple single input multiple output (SIMO) Gaussian wiretap channel and then use scalar approach using standard techniques of communications theory. Then we consider the effect of fading and found out the limiting values of the secrecy capacity.
In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the antennas at the legitimate receiver are more than (or equal to) those at the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to be the same as the eavesdropper's channel matrix. Next, under the total power constraint over all transmit antennas, we analytically solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, thanks to the proposed degraded channel, we can transform the stochastic MIMOME optimization problem to be a Schur-concave one and then find its solution. Besides total power constraint, we also investigate the secrecy capacity when the transmitter is subject to the practical per-antenna power constraint. The corresponding optimization problem is even more difficult since it is not Schur-concave. Under the two power constraints considered, the corresponding MIMOME secrecy capacities can both scale with the signal-to-noise ratios (SNR) when the difference between numbers of antennas at legitimate receiver and eavesdropper are large enough. However, when the legitimate receiver and eavesdropper have a single antenna each, such SNR scalings do not exist for both cases.
This chapter considers securing wireless communications at the physical layer using multiple antennas. In particular, the multiple antenna (MIMO) wiretap channel is presented and its secrecy capacity is provided. Further investigation of the high-SNR characterization of the secrecy capacity, i.e., secure degrees of freedom, reveals that the secrecy capacity of the MIMO wiretap channel does not scale with the transmit power when the eavesdropper has an advantage over the legitimate transmitter in the number of antennas. An external multi-antenna cooperative jammer terminal is introduced to the channel model in order to improve its secrecy capacity scaling with power. The secure degrees of freedom for this new multi-terminal multi-antenna channel is characterized. While for these models the eavesdropper channel state information is known at the legitimate terminals, the chapter next removes this assumption and presents results that utilize multiple antennas in order to provide secure communications irrespective of the eavesdropper channel state. An achievable strong secrecy rate and the secure degrees of freedom characterization for the MIMO wiretap channel when the eavesdropper channel is arbitrary, varying, and unknown at the legitimate terminals are presented. Finally, the extension of this model to the two-user multiple access MIMO wiretap channel is considered and its secure degrees of freedom region is characterized. Introduction The wiretap channel and the notion of secrecy capacity, introduced in [1] and generalized by [2], have provided the framework for physical layer design for wireless channels with information theoretic guarantees against eavesdropping. A natural model in wireless communications is one which utilizes multiple antennas for transmission and reception at each node. The improvement in secrecy rate that can be obtained using multiple antennas in a point-to-point channel with an eavesdropper has been studied extensively in several references, including [3, 4]. Specifically, the secrecy capacity of the Gaussian model consisting of a multiple antenna legitimate transmitter, a multiple antenna legitimate receiver, and a multiple antenna eavesdropper, termed the multiple-input multiple-output (MIMO) wiretap channel, has been identified in full generality in [5, 6].
In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the antennas at the legitimate receiver are more than (or equal to) those at the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to be the same as the eavesdropper's channel matrix. Next, under the total power constraint over all transmit antennas, we analytically solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, thanks to the proposed degraded channel, we can transform the stochastic MIMOME optimization problem to be a Schur-concave one and then find its solution. Besides total power constraint, we also investigate the secrecy capacity when the transmitter is subject to the practical per-antenna power constraint. The corresponding optimization problem is even more difficult since it is not Schur-concave. Under the two power constraints considered, the corresponding MIMOME secrecy capacities can both scale with the signal-to-noise ratios (SNR) when the difference between numbers of antennas at legitimate receiver and eavesdropper are large enough. However, when the legitimate receiver and eavesdropper have a single antenna each, such SNR scalings do not exist for both cases.
In this paper, we consider the secure transmission in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When legitimate receiver has more (or equal) antennas than the eavesdropper, we prove the first MIMOME secrecy capacity result with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is forming an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of which the same as the eavesdropper's channel matrix. Next, subject to the total power constraint overall transmit antennas, we solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, with aids of the proposed degraded channel, we show that the stochastic MIMOME optimization problem can be transformed to be a Schur-concave problem to find its optimal solution. Finally, we find that the MIMOME secrecy capacities scale with the signal-to-noise ratios with large enough numbers of antennas at legitimate receiver. However, as shown in previous works, such a scaling does not exist for wiretap channels with single antenna at legitimate receiver and eavesdropper each.