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arXiv:0710.1325

The MIMOME Channel

Ashish J. Khisti, Gregory W. Wornell

Published Oct 5, 2007• 0 citations
arXivHTMLPDF

Abstract

The MIMOME channel is a Gaussian wiretap channel in which the sender, receiver, and eavesdropper all have multiple antennas. We characterize the secrecy capacity as the saddle-value of a minimax problem. Among other implications, our result establishes that a Gaussian distribution maximizes the secrecy capacity characterization of Csisz{á}r and K{ö}rner when applied to the MIMOME channel. We also determine a necessary and sufficient condition for the secrecy capacity to be zero. Large antenna array analysis of this condition reveals several useful insights into the conditions under which secure communication is possible.

DOI
10.48550/arxiv.0710.1325

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The MIMOME channel is a Gaussian wiretap channel in which the sender, receiver, and eavesdropper all have multiple antennas. We characterize the secrecy capacity as the saddle-value of a minimax problem. Among other implications, our result establishes that a Gaussian distribution maximizes the secrecy capacity characterization of Csisz{á}r and K{ö}rner when applied to the MIMOME channel. We also determine a necessary and sufficient condition for the secrecy capacity to be zero. Large antenna array analysis of this condition reveals several useful insights into the conditions under which secure communication is possible.
The MIMOME channel is a Gaussian wiretap channel in which the sender, receiver, and eavesdropper all have multiple antennas. We characterize the secrecy capacity as the saddle-value of a minimax problem. Among other implications, our result establishes that a Gaussian distribution maximizes the secrecy capacity characterization of Csisz{\'a}r and K{\o}rner when applied to the MIMOME channel. We also determine a necessary and sufficient condition for the secrecy capacity to be zero. Large antenna array analysis of this condition reveals several useful insights into the conditions under which secure communication is possible.
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.
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].
A Gaussian multiple input multiple output (MIMO) 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.
The role of multiple antennas for secure communication is investigated within the framework of Wyner's wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacity-achieving. In addition, we show that in the high signal-to-noise (SNR) ratio regime the penalty for not knowing eavesdropper's channel is small--a simple ``secure space-time code'' that can be thought of as masked beamforming and radiates power isotropically attains near-optimal performance. In the limit of large number of antennas, we obtain a realization-independent characterization of the secrecy capacity as a function of the number βββ: the number of eavesdropper antennas per sender antenna. We show that the eavesdropper is comparatively ineffective when β<1β<1β<1, but that for β≥2β\ge2β≥2 the eavesdropper can drive the secrecy capacity to zero, thereby blocking secure communication to the intended receiver. Extensions to ergodic fading channels are also provided.