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IEEE International Conference on Acoustics Speech and Signal Processing

Secure MIMO Interference Channel with Confidential Messages and Delayed CSIT

Tong Zhang, P.C. Ching

Published Apr 16, 2019• 6 citations
Publisher

Abstract

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.

DOI
10.1109/icassp.2019.8683897

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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.
In this letter, we study the secure degrees-of-freedom (SDoF) characterization for the multiple-input multiple-output (MIMO) X channel with confidential messages and delayed channel state information at the transmitter (CSIT). In particular, we propose a transmission scheme, which can be regarded as a generalization of the state-of-the-art scheme without security and with delayed CSIT. The key of this generalization is performing the security analysis, by which we derive the optimal duration of the artificial noise transmission phase. As a result, we derive the sum-SDoF lower bound. Furthermore, we reveal that if the number of receive antennas, denoted byN{N}N, is fixed, the minimum number of transmit antennas achieving the maximum of the lower bound is7+338N\frac {7+\sqrt {33}}{8}N87+33​​N.
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 -.
The secrecy degrees of freedom (SDoF) of the Gaussian multiple-input and single-output (MISO) wiretap channel is studied under the assumption that delayed channel state information (CSI) is available at the transmitter and each receiver knows its own instantaneous channel. Such scenario is of practical interest since the legitimate receiver may send its channel states to the transmitter which is overheard by the eavesdropper. We first show that a strictly positive SDoF can be guaranteed whenever the transmitter has delayed CSI (either on the legitimate channel or/and the eavesdropper channel). In particular, in the case with delayed CSI on both channels, it is shown that the optimal SDoF is 2=3. We then generalize the result to the two-user Gaussian MISO broadcast channel with confidential messages and characterize the SDoF region when the transmitter has delayed CSI of both receivers. Interestingly, the artificial noise schemes are shown to provide the optimal SDoF region by masking the confidential message to the unintended receiver while aligning the interference at each receiver.
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.
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.
The multiple-input single-output (MISO) wiretap channel with K legitimate single-antenna receivers, one single-antenna eavesdropper in presence of delayed channel state information at the transmitter (CSIT) is considered. The transmitter is equipped with (K+1) antennas and has independent messages intended for each one of the K legitimate receivers. While for the case of a single receiver wiretap channel, i.e., K = 1, the optimal secure degrees of freedom (SDoF) with delayed CSIT was recently characterized in [1] and shown to be 2/3, the extension to the multi-receiver case (K > 1) is far from straightforward. We present new results and insights for the simplest non-trivial extension of this problem, i.e., for the case of K = 2 receiver MISO wiretap channel with delayed CSIT. The contribution of this paper is two fold: a) an asymptotic achievable scheme is presented for the case of two legitimate receivers which achieves a sum-SDoF of 36/37 and b) a novel converse proof is presented which shows that the sum-SDoF is upper bounded by 16/15.