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IEEE Transactions on Vehicular Technology

Secure Degrees of Freedom of the Three-User MIMO Broadcast Channel With Delayed CSIT

Tong Zhang, Gaojie Chen, Rui Wang

Published Sep 2, 2022• 5 citations
Publisher

Abstract

This paper investigates the sum-secure degrees-of-freedom (SDoF) of three-user multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). Specifically, we obtain non-trivial sum-SDoF upper and lower bounds. Firstly, we derive the sum-SDoF upper bound by means of statistical equivalence property, security constraints, and permutations. Then, for the sum-SDoF lower bound, we leverage the artificial noise transmission and interference re-transmission to design two transmission schemes, which have holistic and sequential higher-order symbol generation, respectively. For these two schemes, we propose the redundancy reduction approach for security analysis, by which the minimal duration of artificial noise transmission phase of the scheme is obtained. To eliminate the redundant equations in security analysis, this approach first identifies the constituent equations, and then analyzes the rank of assemble of them. As a result, both the proposed sum-SDoF upper and lower bounds are tighter than the existing sum-SDoF upper and lower bounds, respectively. Furthermore, the proposed lower bound showcases a three-user coding gain.

DOI
10.1109/tvt.2022.3203804

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The degrees of freedom (DoF) of the two-user Gaussian multiple-input and multiple-output (MIMO) broadcast channel with confidential messages is studied under the assumption that delayed channel state information (CSI) is available at the transmitter. We characterize the optimal secrecy DoF (SDoF) region and show that it can be achieved by a simple artificial noise alignment scheme. The proposed scheme sends the confidential messages superposed with the artificial noise over several time slots. Exploiting delayed CSI, the transmitter aligns the transmit signal in such a way that the useful message can be extracted at the intended receiver but is completely drowned by the artificial noise at the unintended receiver. The proposed scheme can be regarded as a nontrivial extension of Maddah-Ali Tse scheme and enables us to quantify the resource overhead, or equivalently the DoF loss, to be paid for the secure communications.
Secure degrees-of-freedom (SDoF) for multiple-input multiple-output (MIMO) interference channel with confidential messages and delayed channel state information at transmitter (CSIT) remains unclear, even for single-input single-output (SISO) case. In this paper, we propose an achievable SDoF for MIMO interference channel with confidential messages and delayed CSIT by designing a multi-phase achievable scheme. For the proposed scheme, we first establish a multi-phase transmission procedure with undetermined phase durations. In the next, the security and decoding conditions on feasible phase durations are derived. Finally, an achievable SDoF maximization problem with respect to phase durations is solved under security and decoding conditions. Due to effective coordination of interference, the proposed achievable SDoF can be 20% greater than the SDoF of MIMO wiretap channel with delayed CSIT, which removes one transmitter from the MIMO interference channel.
The secrecy degrees of freedom (SDOF) of the multiple-input single-output (MISO) broadcast channel with confidential messages (BCC) is studied. The network consists of a two-antenna transmitter and two single-antenna receivers, each demanding a confidential message from the transmitter. The problem is investigated with mixed channel state information at transmitter (CSIT), which is a combination of perfect delayed CSIT and inaccurate current CSIT. When the variance of the estimation error for the current CSIT scales with O(P-α), with α ∈ [0, 1], it is shown that the optimal sum SDOF of the considered BCC is 1+α. Furthermore, the optimal SDOF region of the considered MISO BCC is shown to be a polygon scaling with α. The proposed scheme is based on an artificial noise alignment that can combine the benefits of both types of delayed and current CSIT. These results can be seen as an extension of results of Yang et al. and Gou-Jafar to multiuser networks with secrecy constraints.
In this paper, the K-user interference channel with confidential messages is considered with delayed channel state information at transmitters (CSIT). We propose a novel secure transmission scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality. Achieving confidentiality is challenging due to the delayed nature of CSIT, and the distributed nature of the transmitters. Our scheme works over two phases: phase one in which each transmitter sends information symbols mixed with artificial noises, and repeats such transmission over multiple rounds. In the next phase, each transmitter uses delayed CSIT of the previous phase and sends a function of the net interference and artificial noises (generated in previous phase), which is simultaneously useful for all receivers. These phases are designed to ensure the decodability of the desired messages while satisfying the confidentiality constraints. The proposed scheme achieves a sum secure degrees of freedom (SDoF) of at least [1/2](√K-6). To the best of our knowledge, this is the first result on the K-user interference channel with confidential messages and delayed CSIT that achieves a SDoF which scales with K -.