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IEEE International Symposium on Information Theory (ISIT)

Secrecy degrees of freedom of wireless X networks using artificial noise alignment

Zhao Wang, Ming Xiao, Mikael Skoglund, H. Vincent Poor

Published Jun 1, 2015• 3 citations
Publisher

Abstract

The problem of transmitting confidential messages in the M × K wireless X network is considered, in which each transmitter intends to send one confidential message to every receiver. In particular, the secrecy degrees of freedom (SDOF) of the considered network are studied by an artificial noise alignment (ANA) approach, which integrates interference alignment and artificial noise transmission. At first, an SDOF upper bound is derived for the M × K X network with confidential messages (XNCM) K(M-1)/K+M-2 to be equation. By proposing an ANA approach, it is shown that the SDOF upper bound is tight when either K = 2 or M = 2 for the considered XNCM with time/frequency varying channels. For K, M ≥ 3, it is shown that an SDOF of K(M-1)/K+M1 equation can be achieved, even when an external eavesdropper appears. The key idea of the proposed scheme is to inject artificial noise into the network, which can be aligned in the interference space at receivers for confidentiality. The proposed method provides a linear approach for secure interference alignment.

DOI
10.1109/isit.2015.7282528

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The problem of transmitting confidential messages in the M × K wireless X network is considered, in which each transmitter intends to send one confidential message to every receiver. In particular, the secrecy degrees of freedom (SDOF) of the considered network are studied by an artificial noise alignment (ANA) approach, which integrates interference alignment and artificial noise transmission. At first, an SDOF upper bound is derived for the M × K X network with confidential messages (XNCM) K(M-1)/K+M-2 to be equation. By proposing an ANA approach, it is shown that the SDOF upper bound is tight when either K = 2 or M = 2 for the considered XNCM with time/frequency varying channels. For K, M ≥ 3, it is shown that an SDOF of K(M-1)/K+M1 equation can be achieved, even when an external eavesdropper appears. The key idea of the proposed scheme is to inject artificial noise into the network, which can be aligned in the interference space at receivers for confidentiality. The proposed method provides a linear approach for secure interference alignment.
The problem of transmitting confidential messages in M x K wireless X networks is considered in which each transmitter intends to send one confidential message to every receiver. In particular, the secure degrees of freedom (SDOF) of the considered network are studied based on an artificial noise alignment (ANA) approach, which integrates interference alignment and artificial noise transmission. At first, an SDOF upper bound is derived for the M x K X network with confidential messages (XNCM) to be K(M-1)/K+M-2. By proposing an ANA approach, it is shown that the SDOF upper bound is tight when K = 2 for the considered XNCM with time-/frequency-varying channels. For K ≥ 3, it is shown that SDOF of K(M-1)/K+M-1 can be achieved, even when an external eavesdropper is present. The key idea of the proposed scheme is to inject artificial noise into the network, which can be aligned in the interference space at receivers for confidentiality. Moreover, for the network with no channel state information at transmitters, a blind ANA scheme is proposed to achieve SDOF of K(M-1)/K+M-1 for K, M ≥ 2, with reconfigurable antennas at receivers. The proposed method provides a linear approach to secrecy coding and interference alignment.
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.
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 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.
We consider the K-user interference channel with confidential messages (IC-CM) with intersymbol interference (ISI). The main contribution of this paper is to show that sum-secure degrees of freedom (SDoF) can be made to linearly increase with the number of users K with no channel state information at the transmitters (CSIT). We demonstrate that this is true whenever the channel impulse response (CIR) lengths from the legitimate transmitters towards their respectively intended receivers are larger than those from the interfering transmitters towards the unintended receivers. To design this scheme, we use: a) the simple channel matrix structures of the received signal space to eliminate interference and allow decodability at the intended receivers. b) an injection of artificial noise into the transmitted signal from a strategically chosen small number of transmitters that act as cooperative jammers in order to preserve confidentiality of messages at unintended receivers. This is the first work showing that the SDoF of the K-user IC-CM with ISI can linearly increase with K, the number of users.
Previous work showed that the X network with M transmitters, N receivers has MN/M+N−1 degrees of freedom. In this work we study the degrees of freedom of the X network with secrecy constraints, i.e. the X network where some/all messages are confidential. We consider the M × N network where all messages are secured and show that N(M−1)/M+N−1 degrees of freedom can be achieved. Secondly, we show that if messages from only M − 1 transmitters are confidential, then MN/M+N−1 degrees of freedom can be achieved meaning that there is no loss of degrees of freedom because of secrecy constraints. We also consider the achievable secure degrees of freedom under a more conservative secrecy constraint. We require that messages from any subset of transmitters are secure even if other transmitters are compromised, i.e., messages from the compromised transmitter are revealed to the unintended receivers. We also study the achievable secure degrees of freedom of the K user Gaussian interference channel under two different secrecy constraints where 1/2 secure degrees of freedom per message can be achieved. The achievable scheme in all cases is based on random binning combined with interference alignment.