鲁棒人工噪声辅助传输：MISO窃听通道的不确定性处理

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"这篇研究论文探讨了在具有通道不确定性的多输入单输出（MISO）窃听信道中，利用鲁棒人工噪声辅助传输设计来提高通信安全性的问题。作者Yanqun Tang、Jun Xiong、Dongtang Ma和Xiaoying Zhang针对主信道和窃听信道在发射机端的不完美信道状态信息（CSI）提出了两种不确定性模型，并通过优化策略来最大化秘密率，以抵抗潜在的窃听威胁。" 在无线通信领域，物理层安全（Physical Layer Security）是一个关键的研究方向，特别是在存在恶意监听者（eavesdropper）的情况下。本文关注的是多输入单输出（MISO）窃听信道，其中发射机拥有多个天线，而窃听者只有一个天线。在这种环境下，利用多径传播和波束赋形技术，发射机可以通过发送人工噪声（Artificial Noise, AN）来干扰窃听者，从而提高信息传输的安全性。文章首先考虑了确定性不确定性模型，即发射机对主信道和窃听信道的 CSI 存在精确但有限的不确定性。在这种情况下，作者通过半定规划（Semidefinite Programming, SDP）方法解决了最坏情况下的秘密率最大化问题（Worst-Case Secrecy Rate Maximization, WC-SRM）。SDP 是一种有效的优化工具，可以处理包含线性矩阵不等式的复杂优化问题。接着，研究转向了随机不确定性模型，这是指信道状态信息存在随机性。对于这种模型，作者提出了一种基于 WC-SRM 问题的次优解决方案，以解决约束了中断概率的秘密率最大化问题（Outage Probability Constrained Secrecy Rate Maximization, OP-SRM）。这种方法旨在保证在一定概率下，秘密率能超过预定阈值，即使在信道条件不利时也能提供一定的安全性。模拟结果表明，所提出的最坏情况鲁棒设计相比没有使用 AN 的最坏情况方法，能够显著提升系统的安全性性能。这验证了在存在信道不确定性时，结合人工噪声的传输策略的有效性。这篇论文对MISO窃听信道的鲁棒传输设计进行了深入研究，提供了在不完美信道信息环境下的安全通信策略，对于实际无线通信系统中的物理层安全有着重要的理论与实践价值。

2096 IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 11, NOVEMBER 2013

Robust Artiﬁcial Noise Aided Transmit Design for

MISO Wiretap Channels with Channel Uncertainty

Yanqun Tang, Jun Xiong, Dongtang Ma, and Xiaoying Zhang

Abstract—In this letter, we study the robust artiﬁcial noise

(AN) aided transmit design for a multiple-input single-output

(MISO) wiretap channel with a single-antenna eavesdropper. We

consider two uncertainty models for the imperfect channel state

information (CSI) on the main and eavesdropper’s channels at

the transmitter. For the deterministic uncertainty model, we solve

the worst-case secrecy rate maximization (WC-SRM) problem

via semideﬁnite program (SDP). For the stochastic uncertainty

model, we propose a suboptimal solution to the outage probability

constrained secrecy rate maximization (OP-SRM) problem based

on the robust design for the WC-SRM problem. The simulation

results demonstrate performance improvement of the proposed

worst case robust design as compared to that based on the worst

case method without usage of AN.

Index Terms—Physical layer security, wiretap channel, robust

design, artiﬁcial noise, channel uncertainty.

I. INTRODUCTION

ECENTLY, physical layer security has drawn much

attention, which exploits the randomness of wireless

propagation channels to enhance the security [1]–[3]. We study

the robust transmit design for multiple-input single-output

(MISO) wiretap channels in the presence of a single-antenna

eavesdropper. Assuming the channel state information (CSI)

at the transmitter is imperfect, we consider two uncertain ty

models for the errors on the main and eavesdropper’s channel,

i.e., the deterministic uncertainty model (DUM) [4]–[8] and

the stochastic uncertainty model (SUM) [6], [9], [10].

We ﬁrst optimize the worst-case secrecy rate maximization

(WC-SRM) problem for the DUM. In [4], the authors ex-

ploited the saddle-point property to transform the WC-SRM

problem into a convex problem. In [5], the authors studied

the r obust design with the artiﬁcial noise (AN) for a MISO

wiretap channel with multiple single-antenna eavesdroppers.

The WC-SRM problem was solved by performing a one-

dimensional lin e search in which a series of semideﬁnite

programs (SDP) are involved. The work was later extended to

the multi-antenna case for the eavesdroppers in [6]. However,

in the aforementioned works, the CSI on the main channel

was all assumed to be perfect at the transmitter. Furthermore,

in [7] and [8], the authors studied the robust transmit designs

for the DUM on the main and eavesdropper’s channels. The

authors of [7] provided an explicit solution, and the authors of

Manuscript received July 22, 2013. The associate editor coordinating the

re view of this paper and approving it for publication was A. Rabbachin.

The authors are with the College of Electronic Science and

Engineering, National University of Defense Technology, Changsha,

410073, China (e-mail: {tangyanqun, xj8765, dongtangma}@nudt.edu.cn,

zxy

nudt@163.com).

This work was supported in part by the NSFC under Grants 61372099,

61101096 and 61302140.

Digital Object Identiﬁer 10.1109/LCOMM.2013.100713.131673

[8] solved the WC-SRM problem by a SDP solution. However,

the usage of AN has not been considered in [7] and [8]. Thus,

we will ﬁll up the gap in this letter and propose a robust AN

aided transmit design in terms of the input covariance matrices

for information-bearing signal and AN. Similar to [5], [6], [8],

we also solve the WC-SRM problem via SDP. The simulation

results show that our proposed design provides better secrecy

performance than the method in [7].

Then, we optimize the outage probability constrained se-

crecy rate maximization (OP-SRM) problem for the SUM. For

a MISO wiretap channel with multiple single-antenna eaves-

droppers, assuming that the transmitter knows perfect CSI

on the m ain channel and statistical information of the eaves-

dropper’s channel, the authors in [11] derived a closed-form

power allocation for m inimizing secrecy outage probability.

Considering the case o f imperfect CSI on the eavesdropper’s

channel, the authors of [9] presented the projection methods

to optimize the b eamforming schemes without/with usage of

AN, and the authors of [10] provided a safe approximation

method based on the Bernstein-type inequality. Later in [6],

the work was extended to the multi-antenna case for the

eavesdroppers. The mathematical relationship between the

SUM and the DUM derived in [12] was exploited to solve

the OP-SRM problem. However, all the works in [6], [9]–

[11] did not consider the case of imperfect CSI on the main

channel. Thus, we consider the SUM for the CSI errors on the

main and eavesdropper’s channels. Similar to [6], we adopt

the relationship to provide an approximation to the OP-SRM

problem and solve it based on the developed robust design for

the WC-SRM problem.

II. S

YSTEM MODEL

We consider a multiple-input single-output single-antenna

eavesdropper (MISOSE) system where a N

-antenna transmit-

ter (Alice) sends conﬁdential messages to a legitimate receiver

(Bob) in the presence of an eavesdropper (Eve). The signals

received at Bob and Eve, respectively, are deﬁned as

= h

x + n

= g

x + n

, (1)

where h ∈ C

and g ∈ C

denote the channel vectors

for the main channel between Alice and Bob and the eaves-

dropper’s channel between Alice and Eve, respectively. The

scalars n

and n

denote the zero-mean unit-variance additive

white complex Gaussian noises at Bob and Eve, respectively.

The vector x ∈ C

denotes the signal transmitted at Alice

with x = s + z,wheres is the conﬁdential message intended

for Bob with covariance matrix Q

∈ C

×N

,andz is the

AN created by Alice to confuse Eve with covariance matrix

∈ C

×N

1089-7798/13$31.00

 2013 IEEE

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