We investigate a two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes. The channel transfer matrices at the legitimate terminals are fixed and revealed to all the terminals, whereas the channel transfer matrix of the eavesdropper is arbitrarily varying and only revealed to the eavesdropper. We characterize the secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver and uses a single-user wiretap code is sufficient to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using an induction procedure, where at each step we combine the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.
We investigate a two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes. The channel transfer matrices at the legitimate terminals are fixed and revealed to all the terminals, whereas the channel transfer matrix of the eavesdropper is arbitrarily varying and only revealed to the eavesdropper. We characterize the secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver and uses a single-user wiretap code is sufficient to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using an induction procedure, where at each step we combine the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.
A two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices of the legitimate users are fixed and revealed to all the terminals, whereas the channel matrices of the eavesdropper are arbitrarily varying and only known to the eavesdropper. The secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint is characterized. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver, and uses a single-user wiretap code for each user, is shown to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using induction, where at each step one combines the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.
In this work we considered the Gaussian two-user interference channel where the eavesdropper channel is arbitrarily varying, all channel matrices have rank less than or equal to 2, and the eavesdropper has 1 antenna. We identify a class of these channel models for which the secrecy degrees of freedom (s.d.o.f.) region is achieved by letting only one user transmit a time. We also provided a non-trivial example for which such a transmission strategy is sub-optimal in terms of s.d.o.f. region. The achievable scheme for this example introduces a new technique to achieve secrecy for MIMO wiretap channels, in which the transmitter-receiver pair uses linear precoding so that effectively the signals are beam-formed toward a direction that can not be attained by the eavesdropper and is at the same time orthogonal to interference from the other user.
In this work, a class of information theoretic secrecy problems is addressed where the eavesdropper channel states are completely unknown to the legitimate parties. In particular, MIMO wiretap channel models are considered where the channel of the eavesdropper is arbitrarily varying over time. Assuming that the number of antennas of the eavesdropper is limited, the secrecy rate of the MIMO wiretap channel in the sense of strong secrecy is derived, and shown to match with the converse in secure degrees of freedom. It is proved that there exists a universal coding scheme that secures the confidential message against any sequence of channel states experienced by the eavesdropper. This yields the conclusion that secure communication is possible regardless of the location or channel states of (potentially infinite number of) eavesdroppers. Additionally, it is observed that, the present setting renders the secrecy capacity problems for multi-terminal wiretap-type channels more tractable as compared the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access wiretap channel (MIMO MAC-WT) and the Gaussian MIMO broadcast wiretap channel (MIMO BC-WT) where the transmitter(s) and the intended receiver(s) have the same number of antennas.
A two-receiver MIMO broadcast-wiretap channel is considered where the channel state of the eavesdropper is arbitrarily varying. It is assumed that the eavesdropper knows this channel state perfectly whereas the legitimate nodes have no knowledge of it. It is further assumed that the eavesdropper experiences no additive noise. The channel between the transmitter and the two legitimate receivers is a constant MIMO Gaussian broadcast channel. This paper establishes the secrecy degrees of freedom region for transmitting a common-confidential message as well as a private- confidential message to each receiver. It is observed that a straightforward extension of single user random binning does not achieve the optimal secrecy degrees of freedom (s.d.o.f.) region. The proposed coding scheme that achieves the s.d.o.f. region involves simultaneous diagonalization of the channel matrices of the two legitimate receivers using the generalized singular value decomposition (GSVD) as well as a particular \emph{structured binning} across codebooks that minimizes the rate of the fictitious message. While the focus is on achieving weak secrecy for ease of exposition, an outline is provided on how the results can be extended for achieving strong secrecy.
In this paper, a class of information theoretic secrecy problems is addressed where the eavesdropper channel state is completely unknown to the legitimate parties. In particular, a Gaussian MIMO wiretap channel is considered, where the eavesdropper channel state can vary from one channel use to the next, and the overall channel state sequence is known only to the eavesdropper. When the eavesdropper has fewer antennas than the transmitter and its intended receiver, a positive secrecy rate in the sense of strong secrecy is proved to be achievable and shown to match with the converse in secure degrees of freedom. This yields the conclusion that secure communication is possible regardless of the location or channel states of the eavesdropper. Additionally, it is observed that, the present setting renders the secrecy capacity problems for some multiterminal wiretap-type channels more tractable as compared to the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access (MAC) wiretap channel and the two-user Gaussian MIMO broadcast (BC) wiretap channel, where the transmitter(s) and intended receiver(s) have the same number of antennas.
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].