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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Secure degrees of freedom of the MIMO multiple access wiretap channel

Pritam Mukherjee, Şennur Ulukuş

Published Nov 1, 2015• 8 citations
Publisher

Abstract

We consider a two-user multiple-input multiple- output (MIMO) multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide alignment based achievable schemes and matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.

DOI
10.1109/acssc.2015.7421190

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IEEE Conference on Communications and Network Security•Oct 1, 2016•2 citations
We consider a two-user multiple-input multiple- output (MIMO) multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide alignment based achievable schemes and matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.
We consider a two-user multiple-input multiple-output multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide achievable schemes based on vector space alignment and real alignment techniques for fixed and fading channel gains. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.
In this study, we investigate a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel, in which the channel matrices of users exhibit rank deficiency. In this model, the legitimate transmitters and receiver are equipped withMMMandNNNantennas, respectively, while the eavesdropper hasKKKantennas. The channel matrices of legitimate users are rank-deficient, whereas those between transmitters and the eavesdropper are full-rank, representing a worst-case scenario. We derive the optimal secure degrees of freedom (SDoF) for this model by combining two separate outer bounds. Considering the variations in the number of antennas at each node and the rank of user channels, we categorize our analysis into several regimes. We then present achievable schemes for each regime, grounded in spatial interference alignment, symbol extension and zero-forcing techniques.
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 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 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.