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On the degrees of freedom of MIMO Multiple access channel with multiple eavesdroppers.

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

Published Apr 20, 2014• 0 citations
OpenAlex

Abstract

Abstract—Two-transmitter Gaussian multiple access wiretap channel with multiple antennas at the transmitters, legitimate receivers and eavesdroppers is studied. The existence of unknown number of eavesdroppers is assumed but with maximum number of antennas at any eavesdropper limited to a known value NE. The channel matrices between the transmitters and the receiver is available everywhere, while the legitimate pair have no infor-mation about the eavesdroppers channels. A new upperbound is established and A new achievable DoF region is provided and meets the upperbound for the majority of the region. It is important to the same problem was studied with arbitrarily varying eavesdropper channels. Our achievable region is larger than their upperbound. I.

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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.

IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM)•Aug 1, 2015•6 citations
Abstract—Two-transmitter Gaussian multiple access wiretap channel with multiple antennas at the transmitters, legitimate receivers and eavesdroppers is studied. The existence of unknown number of eavesdroppers is assumed but with maximum number of antennas at any eavesdropper limited to a known value NE. The channel matrices between the transmitters and the receiver is available everywhere, while the legitimate pair have no infor-mation about the eavesdroppers channels. A new upperbound is established and A new achievable DoF region is provided and meets the upperbound for the majority of the region. It is important to the same problem was studied with arbitrarily varying eavesdropper channels. Our achievable region is larger than their upperbound. I.
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 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.
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 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.
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.