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IEEE Wireless Communications Letters

Secrecy Degrees of Freedom of the 2 $\times$ 2 $\times$ 2 Interference Channel With Delayed CSIT

Zhao Wang, Ming Xiao, Mikael Skoglund

Published Apr 7, 2014• 10 citations
Publisher

Abstract

We consider the two-hop interference channel with confidential messages (ICC), where each transmitter sends one confidential message to its intended destination through two trusted relays. We study the secrecy degrees of freedom (SDoF) of the considered 2 × 2 × 2 ICC with delayed channel state information at transmitters (CSIT). We settle the optimal SDoF of the considered network to be (1/2, 1/2). Thus, the considered network has a strictly larger sum SDoF than a two-user one-hop ICC with even full CSIT. Moreover, we study the SDoF of the network with limited Shannon feedback, that only one relay can obtain the delayed CSIT and output feedback from the destinations. The optimal SDoF is also shown to be (1/2, 1/2), revealing that only limited feedback can also bring SDoF gain. Our proposed achievable schemes in both cases are integrated forms of the retrospective interference alignment and artificial noise transmission.

DOI
10.1109/lwc.2014.2315795

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Secrecy Degrees of Freedom of the 2 ×\times× 2 ×\times× 2 Interference Channel With Delayed CSIT
We consider the two-hop interference channel with confidential messages (ICC), where each transmitter sends one confidential message to its intended destination through two trusted relays. We study the secrecy degrees of freedom (SDoF) of the considered 2 × 2 × 2 ICC with delayed channel state information at transmitters (CSIT). We settle the optimal SDoF of the considered network to be (1/2, 1/2). Thus, the considered network has a strictly larger sum SDoF than a two-user one-hop ICC with even full CSIT. Moreover, we study the SDoF of the network with limited Shannon feedback, that only one relay can obtain the delayed CSIT and output feedback from the destinations. The optimal SDoF is also shown to be (1/2, 1/2), revealing that only limited feedback can also bring SDoF gain. Our proposed achievable schemes in both cases are integrated forms of the retrospective interference alignment and artificial noise transmission.
In this paper, the K-user interference channel with secrecy constraints is considered with delayed channel state information at transmitters (CSIT). We propose a novel secure retrospective interference alignment scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality. Achieving positive secure degrees of freedom (SDoF) 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 the 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 secrecy constraints. We present our achievable scheme for three models, namely: (1) K-user interference channel with confidential messages (IC-CM), and we show that 1 2 ( K − 6 ) SDoF is achievable; (2) K-user interference channel with an external eavesdropper (IC-EE); and (3) K-user IC with confidential messages and an external eavesdropper (IC-CM-EE). We show that for the K-user IC-EE, 1 2 ( K − 3 ) SDoF is achievable, and for the K-user IC-CM-EE, 1 2 ( K − 6 ) is achievable. To the best of our knowledge, this is the first result on the K-user interference channel with secrecy constrained models and delayed CSIT that achieves an SDoF which scales with K , square-root of number of users.
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 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.
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.
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.