Wireless Physical Layer Security with Imperfect Channel State Information: A Survey

Physical layer security is an emerging technique for improving wireless communication security, which is widely regarded as a complement to cryptographic technologies. To design physical layer security techniques for practical scenarios, uncertainty and imperfections in the channel knowledge need to be taken into account. This paper is a survey of recent research on physical layer security that considers imperfect channel state information （CSI） at communication nodes. We first give an overview of the main information-theoretic measures of secrecy performance with imperfect CSI. Then, we describe several signal processing enhancements in secure transmission designs. These enhancements include secure on-off transmission, beamforming with artificial noise, and secure communication assisted by relay nodes or in cognitive radio systems. Recent studies of physical layer security in large-scale decentralized wireless networks are also summarized. Finally, open problems for on-going and future research are discussed.

Robust MIMO Precoding for Cognitive Multiuser Relay Networks with Imperfect Channel State Information

In this paper, a novel robust precoder with imperfect channel state information(CSI)is proposed for multi-input multi-output(MIMO)cognitive multiuser networks equipped with relays. In the proposed model, the secondary users(SUs)are allowed to share the spectrum with the primary users(PUs)when the interference temperature(IT)is below a specific threshold. The transmitting strategy of relays is amplify-and-forward(AF), and the CSI error is characterized in terms of spherical uncertainty region. A minmax problem for the transmit power of the relays is considered when the mean square error(MSE)of SUs and the IT of PU meet their corresponding thresholds, and it is transformed into a semi-definite programming(SDP)problem to search for the solution. Numerical simulations demonstrate the effectiveness of the proposed precoder.

Adaptive Energy-Efficient Power Allocation for DAS with Imperfect Channel State Information and Antenna Selection

Considering that perfect channel state information(CSI) is difficult to obtain in practice,energy efficiency(EE) for distributed antenna systems(DAS) based on imperfect CSI and antennas selection is investigated in Rayleigh fading channel.A novel EE that is defined as the average transmission rate divided by the total consumed power is introduced.In accordance with this definition,an adaptive power allocation(PA) scheme for DAS is proposed to maximize the EE under the maximum transmit power constraint.The solution of PA in the constrained EE optimization does exist and is unique.A practical iterative algorithm with Newton method is presented to obtain the solution of PA.The proposed scheme includes the one under perfect CSI as a special case,and it only needs large scale and statistical information.As a result,the scheme has low overhead and good robustness.The theoretical EE is also derived for performance evaluation,and simulation result shows the validity of the theoretical analysis.Moreover,EE can be enhanced by decreasing the estimation error and/or path loss exponents.

Resource allocation algorithm in LTE uplink SC-FDMA system for time-varying channel with imperfect channel state information

In long term evolution （LTE） uplink single carrier frequency division multiple access （SC-FDMA） system, the restriction that multiple resource blocks （RBs） allocated to a user should be adjacent, makes the resource allocation problem hard to solve. Moreover, with the practical constraint that perfect channel state information （CSI） cannot be obtained in time-varying channel, the resource allocation problem will become more difficult. In this paper, an efficient resource allocation algorithm is proposed in LTE uplink SC-FDMA system with imperfect CSI assumption. Firstly, the resource allocation problem is formulated as a mixed integer programming problem. Then an efficient algorithm based on discrete stochastic optimization is proposed to solve the problem. Finally, simulation results show that the proposed algorithm has desirable system performance.

Forward Link Performance Analysis in CDMA Distributed Antenna Systems with Imperfect Channel Estimation

The impact of imperfect channel estimation on the forward-link performance inCDMA distributed antenna systems in multi-path fading environment is investigated. A detailedanalytical model based on a hybrid signal combining method is presented and exact outage probabilityexpression is derived. The investigation shows that the effect of imperfect channel estimatesvaries with system load. Furthermore, if simulcasting is employed, macro-diversity can decrease thesensitivity of forward-link to channel estimation errors and increase the forward-link outageperformance, which is contrary to the conclusion drawn based on the ideal channel estimationassumption.

Robust MSE precoder for imperfectly known MIMO wireless correlated channel

Aimed at that only one form of channel statistic information is utilized in traditional robust precoder schemes: either the channel mean or the transmit antenna correlation in multiple-input multiple-output (MIMO) wireless system, this paper proposes robust precoder designs which exploit both of statistic information to minimize the equalization mean-square error (MSE) with power constraint. Two different power constraints are studied. Besides the usual sum power constraint over all antennas, the per-antenna power constraint is imposed at transmitter in this paper. Since each antenna has its own amplifier, individual power constraint on each antenna is more realistic. Especially in MIMO-OFDM systems, the Peak-to-Average Ratio (PAR) is one of main practical problems. Simulations show that the proposed schemes have better performance than traditional normalized zero forcing schemes for imperfectly known correlated channel. Moreover, per-antenna power constraint can efficiently decrease the demand of dynamic range of power amplifier on each transmit antenna, especially in MIMO-OFDM systems.

Joint Optimization of Spectral and Energy Efficiency for Multi-Pair Full-Duplex Two-Way Relay Networks with Imperfect Channel State Information

An iterative algorithm is proposed for jointly optimizing spectral and energy efficiency in a multipair full-duplex (FD) two-way relaying (TWR) system with imperfect channel state information (CSI). Based on Dinkelbach method, a Taylor expansion based approximation method and the Generalized Lagrange Multiplier Method have been applied iteratively to obtain the near optimal relay amplified matrix and power allocation, respectively. And the simulation results illustrate the effectiveness of the proposed algorithm and the algorithm can converge quickly. © 2017, Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg.

Joint Energy-Efficient Power Allocation and Beamforming Design for mm Wave-NOMA System with Imperfect CSI

The joint power allocation(PA)and beamforming(BF)design problem is studied to maximize the energy efficiency of a two-user downlink millimeter-wave system with non-orthogonal multiple access under imperfect channel state information(CSI).By means of block coordinate descent,convex-concave procedure,and successive convex approximate,we propose a suboptimal joint PA and BF design scheme to address this non-convex problem.Simulation results verify that the proposed joint PA and BF design scheme is more effective when compared to some existing schemes.

Power control scheme for multiple antenna systems with space-time coding in Rayleigh fading channels

Two optimal power control （PC） schemes under the power constraint for space-time coded multiple input multiple output systems over the flat Rayleigh fading channel with the imperfect channel state information （CSI） are presented. One is based on the minimization of a bit error rate （BER）, and the other is based on the maximization of a fuzzy signal-to-noise ratio. In these schemes, different powers are allocated to individual transmit an- tennas rather than equal power in the conventional one. For the first scheme, the optimal PC procedure is developed. It is shown that the Lagrange multiplier for the constrained optimization in the power control does exist and is unique. A practical iterative algorithm based on Newton＇s method for finding the Lagrange multiplier is proposed. In the second scheme, some existing schemes are included, and a suboptimal PC procedure is developed by means of the asymptotic performance analysis. With this suboptimal scheme, a simple PC calculation formula is provided, and thus the calculation of the PC will be straightforward. Moreover, the suboptimal scheme has the BER performance close to the optimal scheme. Simulation results show that the two PC schemes can provide BER lower than the equal PC and antenna selection scheme under the imperfect CSI.

HIGH SNR SUM CAPACITY ANALYSIS OF BD MIMO BC SYSTEMS WITH IMPERFECT CSI

We investigate the sum capacity of Block Diagonalization precoding Multiple Input Mul-tiple Output Broadcast Channels(BD MIMO BC) with imperfect Channel State Information(CSI) at the base station.Since it is difficult to obtain the exact expression,a lower and an upper bounds of the sum capacity under Gaussian channel estimation errors are drived instead.Analyses show that the gap between two bounds is considerably tight at all Signal to Noise Ratio(SNR) region.From the lower bound of the sum capacity,we can see that the multiplexing gain tends to be zero at high SNR region,which indicates that the BD MIMO BC system with channel estimation errors is interference-limited at high SNR.

ROBUST OPTIMIZATION OF TRANSMIT/RECEIVE BEAMFORMER FOR MIMO DOWNLINK WITH IMPERFECT CSI AT BASE STATION

A robust scheme is proposed to jointly optimize transmit/receive beamformers for Mul-tiple Input Multiple Output(MIMO) downlinks where the available Channel State Information(CSI) at Base Station(BS)(CSIBS) is imperfect.The criterion is to minimize the sum Mean Square Error(sum-MSE) over all users under a constraint on the total transmit power,which is a non-convex and non-linear problem.Observing from the first order optimization condition that the optimal trans-mit/receive beamformers are mutually dependent,the transmit/receive beamformers for each user are updated iteratively until the sum-MSE is minimized.Simulation results indicate that the proposed scheme can effectively mitigate the system performance loss induced by imperfect CSIBS.

NOMA增强型D2D组的鲁棒资源分配算法

为提高非正交多址接入(non-orthogonal multiple access,NOMA)增强型设备到设备(device-to-device,D2D)组链路的鲁棒性和能效,考虑非理想信道状态信息(channel station information,CSI),提出一种能效优化的鲁棒资源分配算法.首先,在保证子信道分配、蜂窝用户和D2D组最小速率以及D2D组最大传输功率约束下,建立最大最小鲁棒能效模型;其次,考虑最坏情况法将信道不确定性建模为有界信道估计误差,并用泰勒级数展开式、凸松弛、变量转换法将原多变量耦合问题转化为凸优化问题;最后,用拉格朗日对偶理论求解.仿真结果表明,所提出的算法将传输速率控制在最低速率阈值以上,具有良好的鲁棒性,与其他算法相比能效提高了8.3%.

Cross-layer design of combining AMC with HARQ in cooperative relay system with perfect and imperfect CSI

A cross-layer design which combines adaptive modulation and coding (AMC) at the physical layer with a hybrid automatic repeat request (HARQ) protocol at the data link layer (LL) is presented, in cooperative relay system over Nakagami-m fading channels with perfect and imperfect channel state information (CSI). In order to maximize spectral efficiency (SE) under delay and packet error rate (PER) performance constraints, a state transition model and an optimization framework with perfect CSI are presented. Then the framework is extended to cooperative relay system with imperfect CSI. The numerical results show that the scheme can achieve maximum SE while satisfying transmitting delay requirements. Compared with the imperfect CSI, the average PER with perfect CSI is much lower and the spectral efficiency is much higher.

可重构智能表面辅助多用户NOMA网络鲁棒资源分配

在不完美信道状态信息(Channel State Information,CSI)和不完美串行干扰消除(Successive Interference Cancellation,SIC)的场景下,研究了可重构智能表面(Reconfigurable Intelligent Surface,RIS)辅助多用户非正交多址接入(Non-Orthogonal Multiple Access,NOMA)网络的鲁棒资源分配问题.在考虑两类用户(信息用户和能量用户)服务质量(Quality of Service,QoS)和信息用户SIC约束下,建立了基站发射功率最小化的优化问题.该问题是一个多变量耦合的非凸优化问题.为了求解该问题,本文使用松弛变量、线性近似、S-程序、符号定性法转化该问题的非凸约束.然后将优化问题分解为两个子问题,最后使用交替优化方法迭代求解两个子问题,直到发送功率收敛.仿真结果表明:该文算法具有较好的收敛性,实现了资源的鲁棒分配,同时有效地降低基站发射功率.

智能反射面辅助的多入单出共生无线电鲁棒安全资源分配算法

针对信道不确定性影响、无线信息泄露和障碍物阻挡导致通信质量下降等问题,该文提出一种基于智能反射面(RIS)辅助的多输入单输出(MISO)共生无线电(SR)鲁棒安全资源分配算法。考虑主用户的安全速率约束、次用户的最小速率约束、RIS最小能量收集约束,基于有界信道不确定性,建立了一个联合主被动波束赋形优化的资源分配问题。利用半正定松弛、S-procedure和变量替换法将含参数摄动的非凸问题转化为确定性的凸优化问题,并提出一种基于半正定松弛的鲁棒资源分配算法。仿真结果表明,与现有算法相比,该文算法具有较好的收敛性和鲁棒性。

非完美CSI下的全双工中继网络的能效谱效均衡

为优化非完美信道状态信息下的解码转发全双工中继网络的能效和谱效,提出了一种基于该网络模型的能效谱效均衡策略。通过构建能量效率和频谱效率的折中优化函数,将一个非凸的多目标优化问题转换为一个凸的单目标优化问题,利用求导法和拉格朗日乘子法求解在不同折中因子下的最优中继发射功率。仿真结果表明,可以通过改变折中因子来优化系统的能效和谱效值,获得最优能效和谱效的性能折中。

基于队列稳定性的卫星安全波束成形算法

针对频谱共享且存在受窃听风险的空天地一体化网络,提出了一种基于窃听者非完美信道状态信息的鲁棒安全波束成形方法。首先,在卫星、无人机和基站均采用多播技术服务地球站和地面用户,且实现频谱资源共享的情况下,建立长期平均功耗的最小化为目标,用户服务质量、窃听概率、发送功率预算和数据队列稳定性为约束条件的联合优化问题;其次,为了解决长期平均约束,利用李雅普诺夫优化技术将随机优化问题转化为每个时隙的惩罚发送功率最小化问题,并提出了一种迭代算法,结合伯恩斯坦不等式和连续凸逼近算法,以获取波束成形权向量以实现空天地一体化网络的安全可靠传输。最后,仿真结果证实了提出的方案可以显著提高保密性能,同时在功耗和队列稳定性之间取得良好的折中。

基于非理想测量基选择的水下连续变量量子密钥分发方案

在基于零差探测的水下连续变量量子密钥分发系统中,测量基选择是必不可少的步骤.然而在实际中,接收端数模转换器的带宽有限,这会导致测量基选择出现缺陷,即接收方无法在相位调制器上精确地调制出相应的相位角来进行测量基选择以实施零差探测.非理想测量基选择会引入额外的过噪声,影响水下连续变量量子密钥分发方案的安全性.针对这个问题,本文提出基于非理想测量基选择的水下连续变量量子密钥分发方案,详细分析非理想测量基选择对水下连续变量量子密钥分发系统性能的影响.研究结果表明,由非理想测量基选择所引入的过噪声能够降低水下高斯调制量子密钥分发的密钥率与最大传输距离,因而降低系统的安全性.为了实现可靠的水下连续变量量子密钥分发,本文对非理想测量基选择所引入的额外过噪声进行定量分析并获得其安全界限,并且考虑不同海水深度对所提出方案安全界限的影响,有效地解决由非理想测量基选择所带来的安全隐患.此外,对所提出的方案,本文不仅考虑了其渐近安全性,也考虑了其组合安全性,后者能够获得比前者更紧的性能曲线.本文所提出的方案旨在推动水下连续变量量子密钥分发系统的实用化进程,为全球量子通信网络的水下通信中水信道参数的准确评估提供理论指导.

面向窃听用户的RIS-MISO系统鲁棒资源分配算法

针对信道不确定性影响、用户信息泄露和能效提升等问题,该文提出一种基于不完美信道状态信息的可重构智能反射面(RIS)多输入单输出系统鲁棒资源分配算法。首先,考虑能量收集最小接收功率约束、合法用户最小保密速率约束、基站最大发射功率约束及RIS相移约束,基于有界信道不确定性,建立一个联合优化基站主动波束、能量波束、RIS相移矩阵的多变量耦合非线性资源分配问题。然后,利用Dinkelbach,S-procedure和交替优化方法,将原非凸问题转换成确定性凸优化问题,并提出一种基于连续凸近似的交替优化算法。仿真结果表明,与传统非鲁棒算法对比,所提算法具有较低的中断概率。

基于非理想信道状态信息的鲁棒安全发送方法

针对协方差信道状态信息(Channel State Information,CSI)不理想导致的通信系统安全性能恶化问题,该文提出一种鲁棒的人工噪声辅助的物理层安全发送方法。该方法基于非理想的协方差信道信息,对发送者的波束成形向量及人工噪声协方差进行联合优化设计,从而最大化系统的最差情况安全速率(Worst-Case Secrecy Rate,WCSR)。该功率受限的安全速率最大化问题是非凸的,采用半定松弛(Semi Definite Relaxation,SDR)技术和Lagrange对偶理论将其转化为一系列的半定规划(Semi Definite Program,SDP)问题进行求解。仿真结果表明,与现有方案相比,所提方法的安全性能有了明显的提升。