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IEEE Wireless Communications and Networking Conference

Secure Degrees of Freedom of User Rank-Deficient Multiple Access Wiretap Channel

Hongtao Luo, Qiang Wang, Jingyi Chen

Published Mar 24, 2025• 1 citation
Publisher

Abstract

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 with$M$and$N$antennas, respectively, while the eavesdropper has$K$antennas. 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.

DOI
10.1109/wcnc61545.2025.10978274

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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.
This letter investigates the secure degrees of freedom (SDoF) for a 2-user rank-deficient (M, D) interference channel with confidential messages (ICCM) in which each node is equipped with M antennas. In this model, each transmitter intends to send a confidential message to the corresponding receiver while ensuring that the messages are kept secret against the unintended receiver. Unlike the existing studies on 2-user multiple-input multiple-output (MIMO) interference channel models, channel matrices in this letter do not need to be full rank, and they can take arbitrary rank, D ≤ M. According to different configurations of ranks and number of antennas, the problem is divided into two regimes, and the exact SDoF is given by min(2D, 4M - 2D/3). Then, we propose a converse proof, in which the outer bound is proved by using information theoretic methods. Finally, we propose different achievable schemes for the corresponding regimes by utilizing the spatial alignment, symbol extension, and zero-forcing techniques. It can be obviously seen that the full rank situation on ICCM can be regarded as a special case when D = M.
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.
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.
This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel with a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. We first study the rank of the optimal input covariance matrix that achieves the secrecy capacity of the MIMO Gaussian wiretap channel under an average power constraint. The rank and other properties of the optimal solution are derived based on certain relationships between the channel matrices for the legitimate receiver and eavesdropper. Next, by obtaining necessary and sufficient conditions on the MIMO wiretap channel parameters, we determine the conditions under which the optimal input covariance matrix is full-rank or rank-deficient. For the case that the optimal input covariance is full-rank, we fully characterize the solution. When the optimal input covariance is rank-deficient, we show that the given MIMO wiretap channel can be modeled by an equivalent wiretap channel whose optimal input covariance is full rank and achieves the same secrecy capacity as the original system. Numerical results are presented to illustrate the proposed theoretical findings.