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IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

Time-correlated MISO wiretap channel with delayed CSIT

Mari Kobayashi, Sheng Yang, Giovanni Geraci

Published Jun 1, 2013• 4 citations
Publisher

Abstract

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.

DOI
10.1109/spawc.2013.6612040

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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.
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 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.
We study the Gaussian multiple-input multiple-output multiple-eavesdropper wiretap channel where a transmitter wishes to communicate a confidential message to a legitimate receiver in the presence of eavesdroppers. Each node in the network is equipped with an arbitrary number of antennas. Furthermore, channels are time varying, and there is no channel state information available at the transmitter (CSIT) with respect to eavesdroppers' channels; and transmitter only has access to delayed CSIT of the channel to the legitimate receiver. The secure degrees of freedom (SDoF) for such a network has only been characterized for special cases, and is unknown in general. We completely characterize the SDoF of this network for all antenna configurations. In particular, we strictly improve the state-of-the-art achievable scheme for this network by proposing more efficient artificial noise alignment at the receivers. Furthermore, we develop a tight upper bound by utilizing three important inequalities that provide lower bounds on the received signal dimensions at receivers which supply delayed CSIT or no CSIT. These inequalities together allow for analysis of signal dimensions in networks with heterogeneous CSIT; and as a result, we present a converse proof that leads to characterization of SDoF for all possible antenna configurations.
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 study the Gaussian MIMOME wiretap channel where a transmitter wishes to communicate a confidential message to a legitimate receiver in the presence of eavesdroppers, while the eavesdroppers should not be able to decode the confidential message. Each node in the network is equipped with arbitrary number of antennas. Furthermore, channels are time varying, and there is no channel state information available at the transmitter (CSIT) with respect to eavesdroppers' channels; and transmitter only has access to delayed CSIT of the channel to the legitimate receiver. The secure degrees of freedom (SDoF) for such network has only been characterized for special cases, and is unknown in general. We completely characterize the SDoF of this network for all antenna configurations. In particular, we strictly improve the state-of-the-art achievable scheme for this network by proposing more efficient artificial noise alignment at the receivers. Furthermore, we develop a tight upper bound by utilizing 4 important inequalities that provide lower bounds on the received signal dimensions at receivers which supply delayed CSIT or no CSIT, or at a collection of receivers where some supply no CSIT. These inequalities together allow for analysis of signal dimensions in networks with asymmetric CSIT; and as a result, we present a converse proof that leads to characterization of SDoF for all possible antenna configurations.
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.