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IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM)

Secrecy for MIMO wiretap and MIMO broadcast channels with fading eavesdroppers: CSI does not increase the secure DoF

Mohamed Amir, Tamer M. Khattab, Tarek Elfouly, Amr Mahmoud Salem Mohamed

Published Aug 1, 2015• 6 citations
Publisher

Abstract

We investigate the secure degrees of freedom (SDoF) of the wiretap and the K user Gaussian broadcast channels with multiple antennas at the transmitter, the legitimate receivers and an unknown number of eavesdroppers each with a number of antennas less than or equal to a known value NE. The channel matrices between the legitimate transmitter and the receivers are available everywhere, while the legitimate pair have no information about the eavesdroppers' channels. We provide the exact sum SDoF for the considered system. A new comprehensive upperbound is deduced and a new achievable scheme based on utilizing jamming is exploited. We prove that cooperative jamming is SDoF optimal even without the eavesdropper CSI available at the transmitters.

DOI
10.1109/pacrim.2015.7334884

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We investigate the secure degrees of freedom (SDoF) of the wiretap and the K user Gaussian broadcast channels with multiple antennas at the transmitter, the legitimate receivers and an unknown number of eavesdroppers each with a number of antennas less than or equal to a known value NE. The channel matrices between the legitimate transmitter and the receivers are available everywhere, while the legitimate pair have no information about the eavesdroppers' channels. We provide the exact sum SDoF for the considered system. A new comprehensive upperbound is deduced and a new achievable scheme based on utilizing jamming is exploited. We prove that cooperative jamming is SDoF optimal even without the eavesdropper CSI available at the transmitters.
We investigate the secure degrees of freedom (SDoF) of a two-transmitter Gaussian multiple access channel with multiple antennas at the transmitters, a legitimate receiver and an unknown number of eavesdroppers each with a number of antennas less than or equal to a known value NE. The channel matrices between the legitimate transmitters and the receiver are available everywhere, while the legitimate pair have no information about the fading eavesdroppers’ channels. We provide the exact sum SDoF for the considered system. We show that it is equal to min(M1 + M2 − NE, 1/2(max(M1;N2 + max(M2;N) − NE,N). A new comprehensive upperbound is deduced and a new achievable scheme based on utilizing jamming is exploited. We prove that Cooperative Jamming is SDoF optimal even without the eavesdropper CSI available at the transmitters.
We determine the secure degrees of freedom region of the point to point and the two-transmitter Gaussian broadcast wiretap channels with multiple antennas at the legitimate receivers and the eavesdroppers with unknown eavesdroppers' CSI. The existence of unknown number of eavesdroppers is assumed but with maximum number of antennas at any eavesdropper is limited to a known value NEN_ENE​. The channel matrices between the transmitters and the receiver is available everywhere, while the legitimate pair have no information about the eavesdroppers channels. A new upperbound is established and The DoF region is characterized. It is important to note that the same problem was studied with arbitrarily varying eavesdropper channels, our region is larger than their upperbound. It is important to note that the same problem has been studied recently with arbitrarily varying eavesdropper channels and an upperbound has been derived. However, our achievable sum secure DoF exceeds their previously derived upperbound. Consequently, we revisited the uppperbound derivation and we re-derived a new mathematically robust upperbound.
We investigate the secure degrees of freedom (SDoF) of a two-transmitter Gaussian multiple access channel with multiple antennas at the transmitters, the legitimate receiver with the existence of an unknown number of eavesdroppers each with a number of antennas less than or equal to a known value NEN_ENE​. The channel matrices between the legitimate transmitters and the receiver are available everywhere, while the legitimate pair does not know the eavesdroppers' channels matrices. We provide the exact sum SDoF for the considered system. A new comprehensive upperbound is deduced and a new achievable scheme based on utilizing jamming is exploited. We prove that Cooperative Jamming is SDoF optimal even without the instantaneous eavesdropper CSI available at the transmitters.
We derive an upper bound for the sum secure Degrees of Freedom (sDoF) for the symmetric K-user MIMO Wiretap Multiple Access channel with full channel state information at transmitters (CSIT) but without the knowledge of eavesdroppers channel state information (CSI). We consider the symmetric case with K transmitters each equipped with M antennas, a base station with N antennas and an unknown number of eavesdroppers. Without assuming knowledge of the number (or location) of eavesdroppers, we assume that each eavesdropper has a maximum of Neantennas. The sum sDoF is shown to be upper bounded by Ds= min(max(M, N) - Ne/K, K M - Ne, N). Achievable schemes utilizing cooperative artificial noise transmission and zero-forcing decorrelators are shown to achieve the upper bound for a wide range of values of N/M.
The secrecy degrees of freedom (SDoF) of the Gaussian multiple-input and single-output (MISO) wiretap channel is studied under the assumption that delayed channel state information (CSI) is available at the transmitter and each receiver knows its own instantaneous channel. Such scenario is of practical interest since the legitimate receiver may send its channel states to the transmitter which is overheard by the eavesdropper. We first show that a strictly positive SDoF can be guaranteed whenever the transmitter has delayed CSI (either on the legitimate channel or/and the eavesdropper channel). In particular, in the case with delayed CSI on both channels, it is shown that the optimal SDoF is 2=3. We then generalize the result to the two-user Gaussian MISO broadcast channel with confidential messages and characterize the SDoF region when the transmitter has delayed CSI of both receivers. Interestingly, the artificial noise schemes are shown to provide the optimal SDoF region by masking the confidential message to the unintended receiver while aligning the interference at each receiver.
We investigate the secure degrees of freedom (SDoF) of the multiple-input multiple-output (MIMO) wiretap channel with intersymbol interference (ISI) in the presence of a multi-antenna cooperative jammer. We focus on the practically relevant setting with no channel state information at the transmitters (CSIT). More specifically, the legitimate transmitter and the cooperative jammer only have statistical knowledge of the channel in terms of the effective number of ISI channel taps, i.e., channel impulse response (CIR) lengths, toward the legitimate receiver and the eavesdropper. Our main contribution is to show that in the absence of CSIT, positive SDoF can be achieved by carefully exploiting: 1) the heterogeneity of the CIR lengths toward both receivers and 2) the relative number of antennas at the four terminals. To achieve secrecy, we propose a scheme in which the transmitter strategically sends a mixture of information and artificial noise symbols in a way that exploits the heterogeneity of CIR lengths. Additionally, the cooperative jammer transmits artificial noise symbols in a way that completely masks all the information symbols that are received at the eavesdropping node. Under the proposed scheme, positive SDoF can be achieved, even when the number of antennas at the legitimate receiver is less than the number of antennas at the eavesdropper.