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IEEE Wireless Communications Letters

Achievable Secure Degrees of Freedom of ${K}$ -User MISO Broadcast Channel With Imperfect CSIT

Ye Fan, Xuewen Liao, Zhenzhen Gao, Victor C. M. Leung

Published Feb 20, 2019• 4 citations
Publisher

Abstract

In this letter, we derive the achievable secure degrees of freedom (SDoF) of K-user multiple-input single-output broadcast channel with imperfect channel state information (CSI) at the transmitter. With the help of an Nj -antenna external jammer, we propose a jamming rate splitting (J-RS) scheme to ensure the security of two wiretap models: 1) broadcast channel with confidential messages and 2) broadcast channel with an Ne-antenna external eavesdropper, where each legal node has no CSI of wiretap channels. Our converse is based on the degrees of freedom (DoF) of the network with secrecy constraints, and the achievability is based on J-RS. By numerical analysis, it indicates that the proposed scheme can achieve more SDoF than the traditional rate splitting scheme, zero forcing scheme, and jamming scheme, which can reach to the DoF of the network.

DOI
10.1109/lwc.2019.2900310

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Achievable Secure Degrees of Freedom of K{K}K -User MISO Broadcast Channel With Imperfect CSIT
In this letter, we derive the achievable secure degrees of freedom (SDoF) of K-user multiple-input single-output broadcast channel with imperfect channel state information (CSI) at the transmitter. With the help of an Nj -antenna external jammer, we propose a jamming rate splitting (J-RS) scheme to ensure the security of two wiretap models: 1) broadcast channel with confidential messages and 2) broadcast channel with an Ne-antenna external eavesdropper, where each legal node has no CSI of wiretap channels. Our converse is based on the degrees of freedom (DoF) of the network with secrecy constraints, and the achievability is based on J-RS. By numerical analysis, it indicates that the proposed scheme can achieve more SDoF than the traditional rate splitting scheme, zero forcing scheme, and jamming scheme, which can reach to the DoF of the network.
In this paper, we investigate the secure rate-splitting for the two-user multiple-input multiple-output (MIMO) broadcast channel with imperfect channel state information at the transmitter (CSIT) and a multiple-antenna jammer, where each receiver has an equal number of antennas and the jammer has perfect channel state information (CSI). Specifically, we design a secure rate-splitting multiple-access strategy, where the security of split private and common messages is ensured by precoder design with joint nulling and aligning the leakage information, regarding different antenna configurations. Moreover, we show that the sum-secure degrees-of-freedom (SDoF) achieved by secure rate-splitting is optimal and outperforms that by conventional zero-forcing. Therefore, we reveal the sum-SDoF of the two-user MIMO broadcast channel with imperfect CSIT and a jammer, and validate the superiority of rate-splitting for the security purpose in this scenario with emphasis of MIMO.
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.
We investigate the secure degrees of freedom (SDoF) of the wiretap and the K user Gaussian broadcast channels with multiple antennas at the transmitter, the legitimate receivers and an unknown number of eavesdroppers each with a number of antennas less than or equal to a known value NE. The channel matrices between the legitimate transmitter and the receivers are available everywhere, while the legitimate pair have no information about the eavesdroppers' channels. We provide the exact sum SDoF for the considered system. A new comprehensive upperbound is deduced and a new achievable scheme based on utilizing jamming is exploited. We prove that cooperative jamming is SDoF optimal even without the eavesdropper CSI available at the transmitters.
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.
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.
In this paper, the sum secure degrees of freedom (SDoF) of the K-user Multiple Input/Single Output (MISO) Broadcast Channel with Confidential Messages (BCCM) and alternating Channel State Information at the Transmitter (CSIT) is investigated. In the MISO BCCM, a K-antenna transmitter (TX) communicates toward K single-antenna receivers (RXs), so that message for RX k is kept secret from RX j with jsum= (2K − 1)/2. Interestingly, this SDoFsumis attained by a rather simple achievability in which the TX uses artificial noise to prevent the decoding of the message of the unintended receivers at RX 1. The proof for the case K = 3 is discussed in detail.