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International Conference on Communications

The Two-Way MIMO Wire-Tap Channel

Oussama Souihli, Tomoaki Otsuki Ohtsuki

Published Jun 1, 2009• 6 citations
Publisher

Abstract

We introduce the two-way MIMO wire-tap channel and convey its potential to provide information-theoretic secure communications. We mainly address two challenges, namely the channel estimation and the single-user decodability issues. For the former, as the channel estimation becomes trickier owing to self-interference, we propose that users project their training signals on orthogonal subspaces to ensure their separability upon reception. For the latter, we suggest that each user uses, among the available antennas only the antenna subset that ensures both peers are not single-user decodable while maximizing their achievable secrecy sum-rate. Thus, unlike the result reported in literature about the two-way single-antenna wire-tap channel, we demonstrate that it is possible to achieve a positive secrecy rate even when a user is single-user decodable, provided that a sufficient number of transmit antennas be available. Finally, we observe that the proposed scheme, unlike secrecy schemes based on Wyner's degraded wire-tap channel, provides positive secrecy sum-rate even when the eavesdropper's channels incur as little noise as the legitimate users', and maintains the secrecy rate's growth in the high SNR regime, a fact we demonstrate by computer simulations. This makes the proposed scheme a better candidate for high-throughput secrecy applications.

DOI
10.1109/icc.2009.5199519

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We introduce the two-way MIMO wire-tap channel and convey its potential to provide information-theoretic secure communications. We mainly address two challenges, namely the channel estimation and the single-user decodability issues. For the former, as the channel estimation becomes trickier owing to self-interference, we propose that users project their training signals on orthogonal subspaces to ensure their separability upon reception. For the latter, we suggest that each user uses, among the available antennas only the antenna subset that ensures both peers are not single-user decodable while maximizing their achievable secrecy sum-rate. Thus, unlike the result reported in literature about the two-way single-antenna wire-tap channel, we demonstrate that it is possible to achieve a positive secrecy rate even when a user is single-user decodable, provided that a sufficient number of transmit antennas be available. Finally, we observe that the proposed scheme, unlike secrecy schemes based on Wyner's degraded wire-tap channel, provides positive secrecy sum-rate even when the eavesdropper's channels incur as little noise as the legitimate users', and maintains the secrecy rate's growth in the high SNR regime, a fact we demonstrate by computer simulations. This makes the proposed scheme a better candidate for high-throughput secrecy applications.
The compound wire-tap channel is studied, which is based on the classical wire-tap channel with the channel from the source to the destination and the channel from the source to the wire-tapper taking a number of states, respectively. This channel can also be viewed as the wire-tap channel with mul-tiple destinations and multiple wire-tappers, i.e., multicast with multiple wire-tappers. The source wishes to transmit information to all destinations and wants to keep the information secret from all wire-tappers. For the discrete memoryless compound wire-tap channel, lower and upper bounds on the secrecy capacity are derived and are shown to match for the degraded channel. The parallel Gaussian compound wire-tap channel is further studied, for which the secrecy capacity and the characterization of an optimal power allocation are obtained. The secrecy degree of freedom (s.d.o.f.) is also derived, which connects the secure communication rate in the high SNR regime to secure networking coding for deterministic networks. Finally, the multi-antenna (i.e., MIMO) compound wire-tap channel is studied. The secrecy capacity is established for the degraded MIMO compound wire-tap channel and an achievable s.d.o.f. is given for the general MIMO compound wire-tap channel.
We find the secrecy capacity of the 2-2-1 Gaussian MIMO wire-tap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.
Abstract—We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary. Index Terms—Information-theoretic security, multiple-input multiple-output (MIMO), multiple antennas, 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].
We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.
We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.