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Electronics Letters

Secrecy capacity and optimal time allocation for MISO wiretap channel with a multiple‐antennas jammer

Xiaoming Liu, Bin Li, Feng Zhao

Published Apr 27, 2020• 1 citation
Publisher

Abstract

A closed‐form expression of the achievable secrecy rate is derived in this study, which is used as the objective function to find the optimal time allocation of channel estimation and transmission. Theory analysis and numerical results demonstrate that the maximum secrecy capacity depends on the total time budget as well as the power at the transmitter.

DOI
10.1049/el.2020.0678

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A closed‐form expression of the achievable secrecy rate is derived in this study, which is used as the objective function to find the optimal time allocation of channel estimation and transmission. Theory analysis and numerical results demonstrate that the maximum secrecy capacity depends on the total time budget as well as the power at the transmitter.
In this letter, we consider physical layer security in multiple-input single-output (MISO) fading wiretap channels, where the transmitter utilizes a jamming-aided precoding transmission strategy to maximize the achievable secrecy rate of the channel. The instantaneous channel state information of the eavesdropper's channel is considered unavailable at the transmitter. We derive the closed-form expression of the ergodic secrecy rate, based on which we find that there exists an optimal power allocation ratio between the information signal and the jamming signal. Asymptotic analysis shows that the optimal power ratio depends on the number of antennas as well as the available transmit power at Alice.
This paper studies the optimal tradeoff between secrecy and non-secrecy rates of the MISO wiretap channels for different power constraint settings: sum power constraint only, per-antenna power constraints only, and joint sum and per-antenna power constraints. The problem is motivated by the fact that channel capacity and secrecy capacity are generally achieved by different transmit strategies. First, a necessary and sufficient condition to ensure a positive secrecy capacity is shown. The optimal tradeoff between secrecy rate and transmission rate is characterized by a weighted rate sum maximization problem. Since this problem is not necessarily convex, equivalent problem formulations are introduced to derive the optimal transmit strategies. Under sum power constraint only, a closed-form solution is provided. Under per-antenna power constraints, necessary conditions to find the optimal power allocation are derived. Sufficient conditions are provided for the special case of two transmit antennas. For the special case of aligned channels, the optimal transmit strategies can deduced from an equivalent point-to-point channel problem. Last, the theoretical results are illustrated by numerical simulations.
In this letter, we aim to achieve secure communication for a multiple-input single-output (MISO) wiretap channel in the presence of multiple non-colluding eavesdroppers. It is assumed that the eavesdroppers' channels are unavailable to the transmitter, and artificial noise (AN) is used to provide masked beamforming for degrading the eavesdroppers' channels. First, we derive the secrecy rate outage probability for the masked beamforming system and then the optimal power allocation between data and AN is obtained in closed form for minimizing the secrecy rate outage probability under a total power constraint. The effects of the number of transmit antennas, the transmit power, and the target secrecy rate on the optimal power allocation parameter are characterized. Numerical results are presented to show the performance of our proposed power allocation scheme.
In this paper, we study the achievable secrecy rate of the multiple input single output (MISO) wiretap channel, which consists of a transmitter, a legitimate receiver and multiple eavesdroppers. The transmitter is equipped with multiple antennas, while the receiver and all the eavesdroppers each have a single antenna. We assume that the transmitter has perfect channel state information (CSI) for their links to legitimate receiver, but it has only imperfect CSI for their channels to eavesdroppers. Optimal transmit covariance matrix is obtained based on worst-case secrecy rate maximization, under power constraints. The maximum secrecy rate computation can be formulated as a non-convex optimal problem, which cannot be solved directly. In this paper, we transform non-convex optimal problem into a quasi-convex optimal problem which can be efficiently solved with the bisection method. The simulation result and analysis demonstrate the effectiveness of our methods.
The future wireless networks require both high data transmission rates and secure communications. However, there exists a trade-off between secure and non-secure rates since only a fraction of the maximal achievable reliable rate in a wiretap channel can be considered as secure. This paper studies the optimal transmit strategies that achieve the optimal trade-off between the communication rate and secrecy rate for the MISO wiretap channels with different power constraint settings including sum power constraint only, per-antenna power constraints only, and joint sum and per-antenna power constraints. First, a necessary and sufficient condition to ensure a positive secrecy capacity is shown. After that, closed-form solutions to find an optimal transmit strategy of related problems are derived. This provides a parametrization of the boundary of the maximal achievable rate and secrecy rate without additional time-sharing. The optimal trade-off is characterized by the convex hull of the region. Lastly, the results are illustrated by numerical examples.
We consider transmission of confidential data over multiple-input single-output multiple-eavesdropper (MISOME) Rayleigh-fading wiretap channels. The transmitter has access to full channel state information (CSI) of a legitimate link but only partial CSI of an eavesdropper link in forms of the average received signal-to-noise power ratio (SNR). In this location-aware scenario, we develop the optimal power allocation strategy that maximizes the secrecy rate achievable by beamforming. The optimal power control is regulated in an on-off fashion with the threshold depending only on the numbers of antennas and the average SNRs. By rescuing the vanishing high-SNR degree of freedom for secure communication from this optimal on-off beamforming with the artificial noise scheme, we further derive the achievable ergodic secrecy rate of MISOME wiretap channels in closed form.