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IEEE Conference on Communications and Network Security

On the secure Degrees of Freedom for the K-user symmetric MIMO Wiretap MAC channel

Ahmed Bendary, Yahya Z. Mohasseb, Hisham Dahshan

Published Oct 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1109/cns.2016.7860554

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We investigate the secure degrees of freedom (SDoF) of the K-user MIMO multiple access (MAC) and the two user MIMO interference channel. An unknown number of eavesdroppers are trying to decode the messages sent by the transmitters. Each eavesdropper is equipped with a number of antennas less than or equal to a known value NE. The legitimate transmitters and receivers are assumed to have global channel knowledge. We present the sum SDoF of the two user MIMO interference channel. We derive an upperbound on the sum SDoF of the K-user MAC channel and present an achievable scheme that partially meets the derived upperbound.
We investigate the secure degrees of freedom (SDoF) of the -user MIMO multiple access channel (MAC) in the vicinity of an eavesdropper which is trying to decode the messages sent by the transmitters. The eavesdropper is equipped with antennas and has fading channels. The transmitters and the legitimate receiver are assumed to be oblivious of the eavesdropper channels values. We derive an upperbound on the sum SDoF of such -user MAC channel and present an achievable scheme that partially meets the derived upperbound.
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 consider two fundamental multi-user channel models: the multiple-input multiple-output (MIMO) wiretap channel with one helper (WTH) and the MIMO multiple access wiretap (MAC-WT) channel. In each case, the eavesdropper has K antennas while the remaining terminals have N antennas each. We consider a fast fading channel where the channel state information (CSI) of the legitimate receiver is available at the transmitters but no CSI at the transmitters (CSIT) is available for the eavesdropper's channel. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for each channel model for the regime K ≤ N, and show that in this regime, the MAC-WT channel reduces to the WTH in the absence of eavesdropper CSIT. For the regime N ≤ K ≤ 2N, we obtain the optimal linear s.d.o.f., and show that the MAC-WT channel and the WTH have the same optimal s.d.o.f. when restricted to linear encoding strategies. In the absence of any such restrictions, we provide an upper bound for the sum s.d.o.f. of the MAC-WT channel in the regime N ≤ K ≤ 2N. Our results show that unlike in the single-input single-output case, there is loss of s.d.o.f. for even the WTH due to lack of eavesdropper CSIT when K ≥ N.
We investigate the secure degrees of freedom (SDoF) of the two-transmitter multiple access channel (MAC) with multiple antennas transmitters and multiple antennas legitimate receiver in the vicinity of an eavesdropper that has NE antennas. The SDoF is derived for two cases of the legitimate nodes knowledge about eavesdroppers' channels, instantaneous CSI and statistical CSI. Comparing the SDoF of the two cases, the effect of eavesdropper CSI knowledge on the SDoF is developed. We derive the exact sum SDoF for both cases and provide matching respective upperbounds. We show that obtaining statistical CSI can achieve even more SDoF in some cases than obtaining the instantaneous eavesdropper's channels coefficients if some time slots were dedicated to channel estimation.