Performance analysis of secure communications over correlated slow‐fading additive white Gaussian noise channels

The broadcast nature of communications in wireless communication networks makes it vulnerable to some attacks, particularly eavesdrop attack. Hence, information security can have a key role to protect privacy and avoid identity theft in these networks, especially in distributed networks. In the wireless systems, the signal propagation is affected by path loss, slow fading (shadowing), and fast fading (multi‐path fading). As we know, there is a correlation between communication channels in the real radio environments. This correlation is defined by the correlation between their shadowing and/or multipath fading factors. So when there are several channels in the wireless systems, there is certainly a correlation between the channels. In this paper, we assume that the transmitter knows the full channel state information (CSI), it means the transmitter knows both the channel gains of the illegitimate (ie, eavesdropper) and the legitimate receivers and study the performance of secure communications of single‐input single‐output (SISO) systems consisting of single antenna devices, in the presence of a single antenna passive eavesdropper over correlated slow fading channels, where the main (transmitter to legitimate receiver) and eavesdropper (transmitter to illegitimate receiver) channels are correlated. Finally, we present numerical results and verify the accuracy of our analysis by Monte‐Carlo simulations.     

一种基于时空编码的物理层安全算法

针对多天线窃听系统的物理层安全问题,提出一种基于时空编码的预编码算法。首先,合法接收者发送训练序列用于发送者估计主信道状态信息,而窃听信道的状态信息合法用户均未知;其次,发送者利用均匀信道分解的方法提取主信道状态信息的特征参数,生成发射端预编码矩阵和合法接收端均衡矩阵,收发联合加密处理提高物理层安全;最后,利用 Monte Carlo方法进行仿真实验,数值分析表明,该算法在窃听者天线数目增多时能够实现非负的保密容量,即使窃听信道质量较好时,窃听者的接收性能仍维持在很差的水平,误码率高达0.5。     

Enhancing secrecy rates in a wiretap channel

Reliable communication imposes an upper limit on the achievable rate, namely the Shannon capacity. Wyner's wiretap coding ensures a security constraint and reliability, but results in a decrease of achievable rate. To mitigate the loss in secrecy rate, we propose a coding scheme in which we use sufficiently old messages as key and prove that multiple messages are secure with respect to all the information possessed by the eavesdropper. We also show that we can achieve security in the strong sense. Next, we study a fading wiretap channel with full channel state information of the eavesdropper's channel and use our coding/decoding scheme to achieve a secrecy capacity close to the Shannon capacity of the main channel (in the ergodic sense). Finally, we study a case where the transmitter does not have instantaneous information of the channel state of the eavesdropper, but only its distribution.     

On the error exponent for memoryless flat fading channels withchannel-state-information feedback

We derive the random coding error exponent for the time-independent flat fading channel with perfect knowledge of the channel state information (CSI) at both the receiver and the transmitter. That is, the CSI is feedback from the receiver to the transmitter. In such a situation, the transmitter is capable of optimizing the power allocation of the transmitted signal according to the fading state in order to obtain, for our case, the best error exponent. The power scheme obtained here is different from the water-pouring one, which is known to maximize the channel capacity     

Distributed QoS Based Robust Transmission Design for MISO Wiretap Channel with Cooperative Jamming

A communication network that consists of a transmitter, a legitimate receiver, an eavesdropper and several friendly helpers is considered. Both the transmitter and the helpers are equipped with multiple antennas while the legitimate receiver or the eavesdropper has one antenna. The transmitter and the helpers have the channel state information to the legitimate receiver. The channels to the eavesdropper are partially known and modeled with uncertainty ellipsoids. The transmitter applies maximum ratio transmission to the legitimate receiver. The helpers generate interference to degrade the receiving performance of the eavesdropper. The transmit power of the helpers is optimized with the worst-case secrecy rate requirement as the Quality of Service constraint. Based on robust convex optimization, a centralized optimization problem is developed for the helpers to generate interference efficiently with minimum total transmit power. A distributed algorithm is developed which scales well with a large number of helpers.     

联合发端天线选择和收端人工噪声的物理层安全传输方法

该文在同频全双工技术快速发展的背景下,针对物理层安全研究中波束成形技术的高复杂度和发端天线选择(TAS)技术的低性能,提出一种联合发端天线选择和收端人工噪声(AN)的物理层安全传输方法TAS-rAN。首先,有多根天线的发端,利用天线选择技术,选取能使合法接收方接收信噪比最大的天线发送保密消息;其次,有同频全双工能力的收端,在接收到消息的同时,发送人工噪声来扰乱窃听方对保密消息的窃听。在Nakagami-m信道下,推导了安全中断概率的闭合表达式,并基于此,得到非零安全容量的概率表达式;通过渐进安全中断概率的推导,得到TAS-rAN方法的安全分集度。仿真结果表明,与已有的TAS-single和TAS-Alamouti方法相比,TAS-rAN安全方法具有较强的稳定性,且能提供更优的安全性能。     

过时信道状态信息下的机会式中继选择系统的安全性能分析

在 Nakagami m衰落信道下,目的端和窃听者采用最大比合并策略,本文研究了在机会式自适应解码转发中继选择安全协作系统中的安全性能。由于实际信道中的反馈延迟,最优的合法中继选择基于合法信道反馈的过时信道状态信息。为了评价机会式中继选择在改善安全性能上的表现,分别推导了准确的正安全容量概率和准确的安全中断概率闭合表达式。此外,针对两种不同情况, 推导了形式简单的渐近表达式,并明确给出安全分集阶数和安全阵列增益。理论分析和数值仿真表明,增加中继个数和目的节点的天线数能够改善安全中断概率的性能表现,且在信道状态信息过时的条件下,系统的安全分集阶数与中继数无关。      

Secure Communication Over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.     

Secrecy Analysis of Cooperative Vehicular Relaying Networks over Double-Rayleigh Fading Channels

In this paper, we investigate physical-layer security performance of the cooperative vehicular relaying networks, wherein the communication from a source vehicle to the destination vehicle is assisted by an amplify-and-forward (AF) relay vehicle in the presence of a passive eavesdropper vehicle. We assume that the communication links between the vehicles experience double-Rayleigh fading. We also consider two AF relaying protocols: (1) fixed gain relaying which requires partial channel state information (CSI), and (2) variable gain relaying which requires full CSI. Specifically, we derive the novel intercept probability and ergodic secrecy capacity expressions for both fixed and variable gain relaying in the presence of double-Rayleigh fading channels. The numerical and simulation results verify our theoretical and analytical findings, and show the impacts of channel conditions and relay and eavesdropper locations on the system secrecy performance.

     

Capacity of Time-Varying Channels With Causal Channel Side Information

We derive the capacity of time-varying channels with memory that have causal channel side information (CSI) at the sender and receiver. We obtain capacity of block-memoryless and asymptotically block-memoryless channels with block-memoryless or weakly decorrelating side information. Our coding theorems rely on causal generation of the codewords relative to the causal transmitter CSI. The CSI need not be perfect, and we consider the case where the transmitter and receiver have the same causal CSI as well as the case where the transmitter CSI is a deterministic function of the receiver CSI. For block-memoryless and asymptotically block-memoryless channels, our coding strategy averages mutual information density over multiple transmission blocks to achieve the maximum average mutual information. We apply the coding theorem associated with the block-memoryless channel to determine the capacity and optimal input distribution of intersymbol interference (ISI) time-varying channels with causal perfect CSI about the time-varying channel. The capacity of this channel cannot be found through traditional decomposition methods     

Capacity of correlated MIMO Rayleigh channels

Abstract-This paper presents some exact results on the capacity of multiple-input-multiple-output (MIMO) channels subject to correlated Rayleigh fading when perfect channel state information (CSI) is known at the receiver. The authors focus on the semicorrelated scenario in which correlation exists either at the transmitter or at the receiver., They consider two cases: 1) the transmitter does not have any CSI and as such allocates power equally among transmitter antennas and 2) the transmitter only knows the statistical distribution of the channel. The first case derives the moment generating function (MGF) of the mutual information (MI) and then deduces from this MGF the mean MI. The authors also study the cumulative distribution function (CDF) of the MI, which can serve as an upper bound to the outage probability under the capacity versus outage formulation when the channel is nonergodic. The second case studies the capacity achieved by optimum power-loading and beamforming schemes based on covariance feedback. Numerical results illustrate that the full capacity of MIMO systems can be preserved even for relatively high values of correlation coefficients.     

Enhancing secrecy capacity of multi‐relay wiretap systems with partial channel state information

Distributed precoding has provento be capable of enhancing the secrecy capacity of the multi‐relay wiretap system. An iterative distributed precoding and channel state information (CSI) sharing scheme can be used to reduce the CSI overhead at each relay node. However, in practical applications, the CSI of each relay node cannot be perfectly known to themselves, especially that of the relay‐eavesdropper channels. Thus, partial CSI for the relay‐eavesdropper links is assumed, and the corresponding distributed precoding and CSI sharing schemes are investigated. Under the assumption that the average value of the relay‐eavesdropper channel is known at each relay node, an extended iterative distributed precoding and CSI sharing scheme is proposed. Simulation results demonstrate that with the increase of the power ratio of the constant part to the random part of the relay‐eavesdropper channels, the proposed scheme with partial CSI performs increasingly close to the one with perfect CSI in secrecy capacity. Copyright © 2014 John Wiley & Sons, Ltd.     

Capacity Analysis for Continuous Alphabet Channels With Side Information, Part II: MIMO Channels

In this second part of our two-part paper, we consider the capacity analysis for wireless mobile systems with multiple-antenna architectures. We apply the results of the first part to a commonly known baseband, discrete-time multiple-antenna system where both the transmitter and receiver know the channel's statistical law. We analyze the capacity for additive white Gaussian noise (AWGN) channels, fading channels with full channel state information (CSI) at the receiver, fading channels with no CSI, and fading channels with partial CSI at the receiver. For each type of channels, we study the capacity value as well as issues such as the existence, uniqueness, and characterization of the capacity-achieving measures for different types of moment constraints. The results are applicable to both Rayleigh and Rician fading channels in the presence of arbitrary line-of-sight and correlation profiles.     

Preventing Eavesdropper by Artificial Noise in MIMO-OFDM Systems

The PHY security has been the focus of the researchers since the day it was proposed. The researchers have mentioned many kinds of methods to prevent the eavesdropper from overhearing the confidential signal in different types of networks and environments. However, none of them have proposed a method which can be used in MIMO-OFDM. In this paper, we propose a new method to protect the confidential signal from the eavesdropper. We present a new antennas allocation scheme to make a full use of the CSI of the transmitter and helpers, and propose a double check scheme to distinguish the eavesdropper from helpers. At last, we use GA solve the optimization equation and gain the maximum of the secrecy capacity within limited power consumption. To the best of our knowledge, this is the first method of dealing with the eavesdropper in MIMO-OFDM, and both the schemes, including the antennas allocation scheme and the double check scheme, are the first of its kinds in this type of network environment.     

Secure Broadcasting Over Fading Channels

We study a problem of broadcasting confidential messages to multiple receivers under an information-theoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are considered: parallel channels and fast-fading channels. For the case of reversely degraded parallel channels, one eavesdropper, and an arbitrary number of legitimate receivers, we determine the secrecy capacity for transmitting a common message, and the secrecy sum-capacity for transmitting independent messages. For the case of fast-fading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while that of the eavesdropper is known only to itself. We show that, using a suitable binning strategy, a common message can be reliably and securely transmitted at a rate independent of the number of receivers. We also show that a simple opportunistic transmission strategy is optimal for the reliable and secure transmission of independent messages in the limit of large number of receivers.     

Underlay协同频谱共享系统中基于SDF-DZFB的物理层安全传输

协同中继传输不仅能改善认知用户的传输可靠性,而且也能增强认知用户物理层安全性。针对Underlay模式下多中继协同频谱共享认知无线网络,本文设计了基于选择译码转发和分布式迫零波束成形（SDF-DZFB）的物理层安全传输方案,其中,假设存在单个被动窃听节点窃听中继节点的发送信号,在认知用户发送端同时考虑峰值干扰温度约束和最大发射功率约束,中继和认知用户目的端都受到主用户干扰。在此情况下,分析了认知用户发送端分别到目的端（称为主链路）和到窃听节点（称为窃听链路）的等效信干噪比的统计特性,进而推导出系统安全中断概率性能的闭式表达式。为了揭示所提物理层安全传输方案的安全分集度性能,本文进一步分析了高信噪比条件下安全中断概率的渐近表达式。计算机仿真验证了本文的理论分析结果。      

恶意导频干扰对采用人工噪声方案系统的安全性能影响分析

针对窃听方发送恶意导频干扰破坏系统安全性能的问题,本文将研究场景扩展到三节点MIMO(Multple-Input Multiple-Output)网络,首先分析存在恶意导频干扰时最小二乘和最小均方误差准则下的信道估计结果,并推导基于人工噪声的系统安全速率公式,得出当窃听方到达发送方的导频干扰功率大于合法接收方达到的功率时,安全速率值只能为零.然后,进一步分别研究半双工窃听方和全双工窃听方场景下的最优功率分配方案.最后,通过数值仿真分析窃听者位置、窃听者类型和干扰功率等因素对安全性能的影响.     

增强物理层安全的联合发射天线选择和人工噪声技术

针对未来多天线通信系统的安全问题,提出了一种增强无线物理层安全的传输策略。该策略基于发射天线的选择以及人工噪声,并采用Alamouti编码。它可以使发射机和接收机以较低的复杂度代价提高合法信道的分集增益,同时有效干扰窃听信道,使通信系统获得更高的安全容量。对系统安全容量、天线数量、以及信息信号与人工噪声之间的功率分配等问题进行了研究,仿真结果表明,该传输策略能够有效地增强物理层安全。      

Capacities of time-varying multiple-access channels with sideinformation

We determine the capacity regions for a class of time-varying multiple-access channels (TVMACs), when the underlying channel state evolves in time according to a probability law which is known to the transmitters and the receiver. Additionally, the transmitters and the receiver have access to varying degrees of channel state information (CSI) concerning the condition of the channel. Discrete-time channels with finite input, output, and state alphabets are considered first. The special case of a TVMAC, with the channel state process being a time-invariant, indecomposable, aperiodic Markov chain, shows a surprising anomaly in that imperfect transmitter CSI can cause the capacity under some distributions for the initial state to be strictly larger than that under a stationary distribution for the initial state. We also study a time-varying multiple-access fading channel with additive Gaussian noise, when various amounts of CSI are provided to the transmitters and perfect CSI is available to the receiver, and the fades are assumed to be stationary and ergodic. Implications for transmitter power control are discussed     

Joint channel estimation and resource allocation for MIMO systems-part I: single-user analysis

Multiple antenna systems are known to provide very large data rates, when the perfect channel state information (CSI) is available at the receiver. However, this requires the receiver to perform a noise-free, multi-dimensional channel estimation, without using communication resources. In practice, any channel estimation is noisy and uses system resources. We shall examine the trade-off between improving channel estimation and increasing the achievable data rate. We consider transmitside correlated multi-input multi-output (MIMO) channels with block fading, where each block is divided into training and data transmission phases. The receiver has a noisy CSI that it obtains through a channel estimation process, while the transmitter has partial CSI in the form of covariance feedback. In Part I of this two-part paper, we consider the single-user case, and optimize the achievable rate jointly over parameters associated with the training phase and data transmission phase. In particular, we first choose the training signal to minimize the channel estimation error, and then, develop an iterative algorithm to solve for the optimum system resources such as time, power and spatial dimensions. Specifically, the algorithm finds the optimum training duration, the optimum allocation of power between training and data transmission phases, the optimum allocation of power over the antennas during the data transmission phase.