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IEEE Transactions on Wireless Communications

Achieving Full Secure Degrees-of-Freedom for the MISO Wiretap Channel With an Unknown Eavesdropper

Mohaned Chraiti, Ali Ghrayeb, Chadi M. Assi

Published Aug 17, 2017• 5 citations
Publisher

Abstract

In this paper, we study the achievable secure degrees-of-freedom (sdof) for the multiple-input singleoutput (MISO) wiretap channel with an unknown eavesdropper. It is assumed that the eavesdropper's (Eve's) channel state information (CSI) is unknown to the transmitter (Alice) and legitimate receiver (Bob). Recent studies have shown that the achievable sdof in the sense of strong secrecy is zero when Eve's number of antennas is equal to or more than Bob's number of antennas, which is the scenario considered in this paper. To this end, we propose a novel precoding technique and a coding strategy that together achieve full sdof in the sense of strong secrecy without knowing Eve's CSI and without using artificial noise. The proposed precoding method uses the CSI of the Alice-Bob channel in a nonlinear fashion, which makes the transmitted symbols undecodable at Eve. The proposed coding scheme is based on the channel resolvability concept and ensures strong secrecy. Achieving full sdof with an unknown Eve's CSI is significant, because it is contrary to what is believed about the achievable sdof for the MISO wiretap channel in the sense of strong secrecy. We also show that the proposed scheme achieves near Alice-Bob's channel capacity in the sense of strong secrecy with a probability approaching one at finite signal-to-noise ratio.

DOI
10.1109/twc.2017.2738638

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In this paper, we study the achievable secure degrees-of-freedom (sdof) for the multiple-input singleoutput (MISO) wiretap channel with an unknown eavesdropper. It is assumed that the eavesdropper's (Eve's) channel state information (CSI) is unknown to the transmitter (Alice) and legitimate receiver (Bob). Recent studies have shown that the achievable sdof in the sense of strong secrecy is zero when Eve's number of antennas is equal to or more than Bob's number of antennas, which is the scenario considered in this paper. To this end, we propose a novel precoding technique and a coding strategy that together achieve full sdof in the sense of strong secrecy without knowing Eve's CSI and without using artificial noise. The proposed precoding method uses the CSI of the Alice-Bob channel in a nonlinear fashion, which makes the transmitted symbols undecodable at Eve. The proposed coding scheme is based on the channel resolvability concept and ensures strong secrecy. Achieving full sdof with an unknown Eve's CSI is significant, because it is contrary to what is believed about the achievable sdof for the MISO wiretap channel in the sense of strong secrecy. We also show that the proposed scheme achieves near Alice-Bob's channel capacity in the sense of strong secrecy with a probability approaching one at finite signal-to-noise ratio.
In this paper, we consider the achievable secure degrees-of-freedom (sdof) for the multiple-input single-output (MISO) wiretap channel with an unknown Eavesdropper's channel state information (CSI). The underlying system model comprises three nodes: a multi-antenna transmitter (Alice), a single-antenna receiver (Bob) and a single-antenna eavesdropper (Eve). Recent studies have shown that the achievable sdof in the sense of strong secrecy is zero when Eve's number of antennas is equal or more than Bob's number of antennas, which applies to the scenario considered in this paper. Moreover, using artificial noise, which deemed to be the only possible strategy to degrade Alice-Eve's channel when Eve's CSI is unknown, may no longer be efficient due to the recently introduced methods for managing interference in a one-dimensional space (e.g., real interference alignment). In this paper, we propose a novel precoding technique and a coding strategy that together achieve full sdof in the sense of strong secrecy without knowing Eve's CSI and without using artificial noise. The proposed precoding method uses the CSI of the Alice-Bob channel in a nonlinear fashion, which makes it difficult for Eve to decode even when Eve has the CSI of all channels, whereas the proposed coding scheme ensures strong secrecy.
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.
Physical layer security in wireless networks has received increasing attention in recent years. In this paper, we consider multiple-input single-output (MISO) fading wiretap channels, where the transmitter utilizes artificial noise-aided precoding (ANaP) transmission strategy to maximize the secrecy capacity of the channel. When the channel state information (CSI) of Eavesdropper's (Eve's) channel is known at Alice, we prove that the optimal ANaP strategy reduces to the conventional precoding strategy, i.e., all the transmit power should be allocated to the precoding of information signal. When the CSI of Eve's channel is unknown at Alice, we find that there exists an optimal power allocation ratio between the information signal and the artificial noise and that this power ratio depends on the number of antennas as well as the available transmit power at Alice. In particular, when the available transmit power at Alice increases or the number of antennas at Alice decreases, more power should be allocated to the artificial noise.
We consider the time-correlated multiple-input single-output (MISO) wiretap channel where a multi-antenna transmitter wishes to convey a confidential message to its receiver in the presence of an eavesdropper. Assuming that the transmitter with delayed channel state information acquires some knowledge on current channel state due to the temporal correlation, the secrecy degrees of freedom (SDoF), capturing the behavior of the secrecy capacity in high signal-to-noise ratio regime, is studied. We characterize the optimal SDoF and provide the achievable scheme that takes advantage of both spatial precoding and digitalized artificial noise alignment.
We consider the multiple-input multiple-output (MIMO) wiretap channel with intersymbol interference (ISI) in which a transmitter (Alice) wishes to securely communicate with a receiver (Bob) in presence of an eavesdropper (Eve). We focus on the practically relevant setting in which there is no channel state information (CSI) at Alice about either of the channels to Bob or Eve, except statistical information about the ISI channels (i.e., Alice only knows the effective number of ISI taps). The key contribution of this work is to show that even with no CSI at Alice, positive secure degrees of freedom (SDoF) are achievable by carefully exploiting a) the heterogeneity of the ISI links to Bob and Eve, and b) the relative number of antennas at all the three terminals. To this end, we propose a novel achievable scheme that carefully mixes information and artificial noise symbols in order to exploit ISI heterogeneity to achieve positive SDoF. To the best of our knowledge, this is the first work to explore the idea of exploiting ISI channel length heterogeneity to achieve positive SDoF for the MIMO wiretap channel with no CSI at the legitimate transmitter.
This article considers a two-way multiple-input multiple-output (MIMO) Rayleigh block fading wiretap channel with two full-duplex nodes (Alice and Bob) exchanging messages simultaneously and wiretapped by a $ {N}_{ {e}}$ -antennas eavesdropper (Eve). The channel state remains unchanged over a coherence interval T and is unknown to all terminals, including Alice, Bob, and Eve, at the beginning of the coherence interval. We first show the expression of the optimal signal waveform for Alice and Bob, which maximizes the sum secrecy rate, should be the products of independent random diagonal matrices and isotropically distributed unitary matrices. Then, conditioned on large T and small $ {N}_{ {e}}$ , the upper-bound for the secure degree of freedom (s.d.o.f.) of the two-way wiretap channel is derived, and a constant-norm-signaling (CNS) scheme is presented to achieve this theoretical bound. Finally, we formulate an optimization problem of the s.d.o.f. achieved by the CNS scheme for general cases with arbitrary T and $ {N}_{ {e}}$ , and solve this problem by exploring the monotonicity of the achievable s.d.o.f.. Our result shows that the optimal s.d.o.f. can be independent of coherence time T and becomes the product of the numbers of legitimate nodes's transmitter antennas (NLNTA) for large $ {N}_{ {e}}$ and small NLNTA.