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arXiv:1002.4548

Interference Alignment for the Multi-Antenna Compound Wiretap Channel

Ashish J. Khisti

Published Feb 24, 2010• 4 citations
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Abstract

We study a wiretap channel model where the sender has $M$ transmit antennas and there are two groups consisting of $J_1$ and $J_2$ receivers respectively. Each receiver has a single antenna. We consider two scenarios. First we consider the compound wiretap model -- group 1 constitutes the set of legitimate receivers, all interested in a common message, whereas group 2 is the set of eavesdroppers. We establish new lower and upper bounds on the secure degrees of freedom. Our lower bound is based on the recently proposed \emph{real interference alignment} scheme. The upper bound provides the first known example which illustrates that the \emph{pairwise upper bound} used in earlier works is not tight. The second scenario we study is the compound private broadcast channel. Each group is interested in a message that must be protected from the other group. Upper and lower bounds on the degrees of freedom are developed by extending the results on the compound wiretap channel.

DOI
10.48550/arxiv.1002.4548

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We study a wiretap channel model where the sender has$M transmitantennasandtherearetwogroupsconsistingoftransmit antennas and there are two groups consisting oftransmitantennasandtherearetwogroupsconsistingofJ_{1}andandandJ_{2}$receivers respectively. Each receiver has a single antenna. We consider two scenarios. First we consider the compound wiretap model — group 1 constitutes the set of legitimate receivers, all interested in a common message, whereas group 2 is the set of eavesdroppers. We establish new lower and upper bounds on the secure degrees of freedom (d.o.f.). Our lower bound is based on the recently proposed real interference alignment scheme. The upper bound provides the first known example which illustrates that the pairwise upper bound used in earlier works is not tight. The second scenario we study is the compound private broadcast channel. Each group is interested in a message that must be protected from the other group. Upper and lower bounds on the d.o.f. are developed by extending the results on the compound wiretap channel.
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We study the K-user Gaussian interference wiretap channel with N external eavesdroppers. All the transmitters, receivers and eavesdroppers have a single antenna each. We propose an achievable scheme to lower bound the secure degrees of freedom (d.o.f.) for each transmitter-receiver pair. Our approach is based on the (real) interference alignment technique. Our achievable scheme not only aligns the interference at each receiver to prevent the d.o.f. from vanishing, but also aligns the signals observed by the eavesdroppers to reduce the secrecy penalty. The achievable secure d.o.f. of each transmitter-receiver pair is shown to be equations for almost all channel gains.
In this paper, we study the information-theoretical security of the K-user MIMO Y wiretap Gaaussian channels and deduce the lower bounds of the secure degrees of freedom (SDOF). Due to the different receiving links of the eavesdropper, we propose two MIMO Y wiretap models which are called Broadcast Wiretap Channel (BWC) and Multi-access Broadcast Wiretap Channel (MBWC), respectively. Each legitimate user equipped with M antennas intends to transmit independent signals via an intermediate amplify-and-forward (AF) relay with N antennas. Besides, there exists an eavesdropper with Ne antennas close to the K users (K ≥ 3). Based on the asymptotic real interference alignment and the structured cooperative jamming, the security of the MIMO Y wiretap channels can be guaranteed. From the asymptotic analysis, we can find that a lower bound of the sum SDOF in BWC is K/4. While in the MBWC model, since the relay working in the full duplex mode broadcasts cooperative jamming signals to all the other nodes especially to the eavesdropper, the lower bound of sum SDOF is K2-3K/4(K-1), which is altered along with the number of users.