CN111970653B - Anti-eavesdropping sparse signal detection method and system based on false censorship - Google Patents

Anti-eavesdropping sparse signal detection method and system based on false censorship Download PDF

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CN111970653B
CN111970653B CN202010504135.7A CN202010504135A CN111970653B CN 111970653 B CN111970653 B CN 111970653B CN 202010504135 A CN202010504135 A CN 202010504135A CN 111970653 B CN111970653 B CN 111970653B
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李刚
李成蹊
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Tsinghua University
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Abstract

本发明公开了一种基于虚伪审查手段的防窃听稀疏信号检测方法及系统，其中，该方法包括：将无线传感器网络设置为常规传感器和虚伪传感器两部分；根据无线传感器网络和被检测稀疏信号的参数设置计算出本地审查阈值；比较被检测稀疏信号和本地审查阈值，利用常规传感器将被检测稀疏函数中信息含量高的数据发送至融合中心，利用虚伪传感器将被检测稀疏函数中信息含量低的数据发送至融合中心；基于融合中心的自身信号模型，根据收到的压缩数据和每个传感器的身份构建局部最大势检测器，以作出相应的全局判决。该方法可以对稀疏度未知的稀疏信号实现低能耗的有效保密检测，具有更高的可实现性，且几乎可以达到其检测性能上限。

Figure 202010504135

The invention discloses an anti-eavesdropping sparse signal detection method and system based on a false examination method, wherein the method includes: setting a wireless sensor network into two parts: a conventional sensor and a false sensor; according to the wireless sensor network and the detected sparse signal The parameter setting calculates the local censorship threshold; compares the detected sparse signal with the local censorship threshold, uses the conventional sensor to send the data with high information content in the detected sparse function to the fusion center, and uses the fake sensor to send the detected sparse function with low information content. The data is sent to the fusion center; based on the fusion center's own signal model, a local maximum potential detector is constructed according to the received compressed data and the identity of each sensor to make a corresponding global decision. This method can realize effective and confidential detection with low energy consumption for sparse signals with unknown sparsity, which has higher achievability and can almost reach the upper limit of its detection performance.

Figure 202010504135

Description

基于虚伪审查的防窃听稀疏信号检测方法及系统Anti-eavesdropping sparse signal detection method and system based on false censorship

技术领域technical field

本发明涉及无线传感器网络的保密通信技术领域，特别涉及一种基于虚伪审查手段的防窃听稀疏信号检测方法及系统，具体可应用于存在窃听威胁且能量供应受限的无线传感器网络中的稀疏信号检测问题。The invention relates to the technical field of secure communication of wireless sensor networks, and in particular to a method and system for detecting sparse signals against eavesdropping based on false review means, which can be specifically applied to sparse signals in wireless sensor networks with eavesdropping threats and limited energy supply. Detect problems.

背景技术Background technique

由于实际应用中的多种信号都呈现内在的稀疏性，无线传感器网络中稀疏信号的分布式检测问题吸引了诸多关注。无线传感器网络通常由多个传感器和一个融合中心构成，其中，传感器负责对本地观测数据进行一定的初步处理并将其发送到融合中心，融合中心综合利用接收到的数据并做出稀疏信号是否存在的全局判决。由于无线传感器网络中能量和带宽常常极其受限，如何高效利用这些资源是稀疏信号的分布式检测中一个亟待解决的问题。压缩感知理论为解决这个问题提供了新的思路。基于该理论，在保证一定检测性能的前提下，本地传感器只需发送压缩后的数据到融合中心，从而大大减少了对带宽资源的占用和对能量的消耗。Due to the inherent sparseness of various signals in practical applications, the distributed detection of sparse signals in wireless sensor networks has attracted a lot of attention. A wireless sensor network is usually composed of multiple sensors and a fusion center. The sensor is responsible for performing some preliminary processing on the local observation data and sending it to the fusion center. The fusion center comprehensively utilizes the received data and determines whether a sparse signal exists. global judgment. Since energy and bandwidth are often extremely limited in wireless sensor networks, how to efficiently utilize these resources is an urgent problem to be solved in the distributed detection of sparse signals. Compressed sensing theory provides a new idea to solve this problem. Based on this theory, under the premise of ensuring a certain detection performance, the local sensor only needs to send the compressed data to the fusion center, thus greatly reducing the occupation of bandwidth resources and energy consumption.

无线传感器网络中，很多传感器被布置在无人看管的位置，对这些传感器的电池更换十分困难。如果全部传感器节点都只发送压缩后的数据，数据传输仍耗能巨大，所以应当选择更高效的信息发送方法。现有的低能耗分布式稀疏信号检测方法有基于审查策略的检测器，如C.Li,G.Li,and P.K.Varshney,“Distributed Detection of Sparse SignalsWith Censoring Sensors Via Locally Most Powerful Test,”IEEE SignalProcess.Lett.,vol.27,pp.346-350,2020.在该方法中，传感器在发送本地压缩数据前会对其进行一定的审查，目的是只发送信息含量高的数据。具体地，各个传感器会基于压缩后的数据计算本地的似然比，并且只发送大于某个阈值的似然比到融合中心，融合中心利用接收到的数据并考虑信号内在的稀疏特征，应用局部最大势检测器对稀疏度未知的稀疏信号进行检测。但是，这种方法适用的是理想安全的无线传感器网络，即网络中不存在任何窃听者带来的威胁。In wireless sensor networks, many sensors are placed in unattended locations, and it is very difficult to replace the batteries of these sensors. If all sensor nodes only send compressed data, the data transmission still consumes a lot of energy, so a more efficient information transmission method should be selected. Existing low-energy distributed sparse signal detection methods include detectors based on censorship strategies, such as C.Li, G.Li, and P.K. Varshney, "Distributed Detection of Sparse SignalsWith Censoring Sensors Via Locally Most Powerful Test," IEEE SignalProcess. Lett., vol. 27, pp. 346-350, 2020. In this method, the sensor will censor local compressed data before sending it, in order to send only data with high information content. Specifically, each sensor will calculate the local likelihood ratio based on the compressed data, and only send the likelihood ratio greater than a certain threshold to the fusion center. The maximum potential detector detects sparse signals whose sparsity is unknown. However, this method is suitable for ideally secure wireless sensor networks, that is, there is no threat from any eavesdropper in the network.

在一些实际应用场景如分布式雷达网络和认知无线电网络中，由于无线传感器网络自身具有分布式特性和广播特性，其中传输的信息容易遭到窃听，窃听者也想窃取关于信号和目标是否存在的相关信息。现有的针对传统分布式检测问题的低能耗防窃听方法有设计审查区间法，如S.Marano,V.Matta,and P.K.Willett,“Distributed Detection WithCensoring Sensors Under Physical Layer Secrecy,”IEEE Trans.Signal Process.,vol.57,no.5,pp.1976-1986,May.2009.在该方法中，本地传感器节点在发送数据前对数据进行一定的审查，从而达到降低发送数据引起的能耗的目的。系统中存在的窃听者可以观测各个本地传感器和融合中心间有无数据发送活动，并据此推断目标是否存在。为了保证系统的绝对保密性(即保证窃听者无法窃取到任何有用信息)，该方法通过合理设计审查区间使得两种假设下传感器节点的两个发送概率相等，从而达到完全蒙蔽窃听者的目的。但是该方法的缺点在于它要求传感器节点掌握两种假设下数据的准确概率分布，在实际应用中是很难实现的，尤其是在稀疏度未知的稀疏信号检测问题中。因此，亟待一种低能耗分布式防窃听稀疏信号检测方法。In some practical application scenarios such as distributed radar networks and cognitive radio networks, due to the distributed and broadcast characteristics of wireless sensor networks, the transmitted information is vulnerable to eavesdropping, and eavesdroppers also want to steal information about the existence of signals and targets. related information. Existing low-energy eavesdropping methods for traditional distributed detection problems include design review interval methods, such as S.Marano, V.Matta, and P.K. Willett, "Distributed Detection With Censoring Sensors Under Physical Layer Secrecy," IEEE Trans.Signal Process ., vol.57, no.5, pp.1976-1986, May.2009. In this method, the local sensor node conducts a certain review of the data before sending the data, so as to reduce the energy consumption caused by sending the data. . The eavesdropper in the system can observe whether there is data transmission activity between each local sensor and the fusion center, and infer whether the target exists or not. In order to ensure the absolute confidentiality of the system (that is, to ensure that the eavesdropper cannot steal any useful information), this method makes the two transmission probabilities of the sensor nodes equal under the two assumptions by reasonably designing the review interval, so as to completely blind the eavesdropper. However, the disadvantage of this method is that it requires sensor nodes to master the accurate probability distribution of the data under two assumptions, which is difficult to achieve in practical applications, especially in the problem of sparse signal detection with unknown sparsity. Therefore, a low-energy distributed anti-eavesdropping sparse signal detection method is urgently needed.

发明内容SUMMARY OF THE INVENTION

本发明旨在至少在一定程度上解决相关技术中的技术问题之一。The present invention aims to solve one of the technical problems in the related art at least to a certain extent.

为此，本发明的一个目的在于提出一种基于虚伪审查手段的防窃听稀疏信号检测方法，该方法可以对稀疏度未知的稀疏信号实现低能耗的有效保密检测。Therefore, an object of the present invention is to propose a detection method for anti-eavesdropping sparse signals based on false censorship means, which can realize effective security detection with low energy consumption for sparse signals with unknown sparsity.

本发明的另一个目的在于提出一种基于虚伪审查手段的防窃听稀疏信号检测系统。为达到上述目的，本发明一方面实施例提出了基于虚伪审查手段的防窃听稀疏信号检测方法，包括以下步骤：将无线传感器网络设置为常规传感器和虚伪传感器两部分；根据所述无线传感器网络和被检测稀疏信号的参数设置计算出本地审查阈值；比较所述被检测稀疏信号和所述本地审查阈值，利用所述常规传感器将所述被检测稀疏函数中信息含量高的数据发送至融合中心，利用所述虚伪传感器将所述被检测稀疏函数中信息含量低的数据发送至融合中心；基于所述融合中心的自身信号模型，根据收到的数据和每个传感器的身份构建局部最大势检测器，以作出相应的全局判决。Another object of the present invention is to propose an anti-eavesdropping sparse signal detection system based on a false examination method. In order to achieve the above object, an embodiment of the present invention proposes an anti-eavesdropping sparse signal detection method based on a false review method, which includes the following steps: setting the wireless sensor network into two parts: a conventional sensor and a false sensor; according to the wireless sensor network and The parameter setting of the detected sparse signal calculates a local censorship threshold; compares the detected sparse signal and the local censorship threshold, and uses the conventional sensor to send the data with high information content in the detected sparse function to the fusion center, Use the fake sensor to send data with low information content in the detected sparse function to the fusion center; build a local maximum potential detector based on the received data and the identity of each sensor based on the fusion center's own signal model , in order to make the corresponding global judgment.

本发明实施例的基于虚伪审查手段的防窃听稀疏信号检测方法，利用虚伪审查策略增强系统的保密性，可以对稀疏度未知的稀疏信号实现低能耗的有效保密检测，同时，还提供了策略中最佳系统参数的计算方法，在绝对保密即窃听者无法获取任何有用信息的条件下，融合中心可以达到最佳的检测性能，与相关技术相比，本发明实施例具有更高的可实现性，并且几乎可以达到其检测性能的上限。The anti-eavesdropping sparse signal detection method based on the false inspection method according to the embodiment of the present invention utilizes the false inspection strategy to enhance the confidentiality of the system, and can realize low-energy and effective confidential detection of sparse signals with unknown sparsity. The calculation method of the optimal system parameters, the fusion center can achieve the best detection performance under the condition of absolute confidentiality, that is, the eavesdropper cannot obtain any useful information. Compared with the related art, the embodiment of the present invention has higher achievability , and can almost reach the upper limit of its detection performance.

另外，根据本发明上述实施例的基于虚伪审查手段的防窃听稀疏信号检测方法还可以具有以下附加的技术特征：In addition, the anti-eavesdropping sparse signal detection method based on the false review method according to the above-mentioned embodiment of the present invention may also have the following additional technical features:

进一步地，在本发明的一个实施例中，所述无线传感器网络由一个融合中心和多个传感器构成。Further, in an embodiment of the present invention, the wireless sensor network consists of a fusion center and a plurality of sensors.

进一步地，在本发明的一个实施例中，所述信息含量高的数据为所述被检测稀疏信号压缩后的观测数据的绝对值大于所述本地审查阈值的数据，采用所述常规传感器将所述被检测稀疏信号压缩后发送至融合中心；所述信息含量低的数据为所述被检测稀疏信号压缩后的观测数据的绝对值小于所述本地审查阈值的数据，采用所述虚伪传感器将所述被检测稀疏信号压缩后发送至所述融合中心。Further, in an embodiment of the present invention, the data with high information content is the data in which the absolute value of the compressed observation data of the detected sparse signal is greater than the local censorship threshold, and the conventional sensor is used to The detected sparse signal is compressed and sent to the fusion center; the data with low information content is the data whose absolute value of the compressed observation data of the detected sparse signal is less than the local review threshold, and the false sensor is used to The detected sparse signal is compressed and sent to the fusion center.

进一步地，在本发明的一个实施例中，所述信息含量高的数据为所述被检测稀疏信号压缩后的观测数据的绝对值大于所述本地审查阈值的数据，采用所述常规传感器将所述被检测稀疏信号压缩后发送至融合中心；所述信息含量低的数据为所述被检测稀疏信号压缩后的观测数据的绝对值小于所述本地审查阈值的数据，采用所述虚伪传感器将所述被检测稀疏信号压缩后发送至所述融合中心。Further, in an embodiment of the present invention, the data with high information content is the data in which the absolute value of the compressed observation data of the detected sparse signal is greater than the local censorship threshold, and the conventional sensor is used to The detected sparse signal is compressed and sent to the fusion center; the data with low information content is the data whose absolute value of the compressed observation data of the detected sparse signal is less than the local review threshold, and the false sensor is used to The detected sparse signal is compressed and sent to the fusion center.

进一步地，在本发明的一个实施例中，所述常规传感器的审查发送方式为：Further, in an embodiment of the present invention, the examination sending method of the conventional sensor is:

Figure GDA0003215297400000031
Figure GDA0003215297400000031

其中，yq为被检测稀疏信号被压缩后的观测数据，β为本地审查阈值，q为第q个传感器节点，Th为包含所有常规传感器的索引集合。Among them, y q is the compressed observation data of the detected sparse signal, β is the local censorship threshold, q is the qth sensor node, and Th is the index set containing all regular sensors.

进一步地，在本发明的一个实施例中，所述虚伪传感器的审查发送方式为：Further, in an embodiment of the present invention, the examination and sending method of the fake sensor is:

Figure GDA0003215297400000032
Figure GDA0003215297400000032

其中，yq为被检测稀疏信号被压缩后的观测数据，β为本地审查阈值，q为第q个传感器节点，Td为包含所有虚伪传感器的索引集合。Among them, y q is the compressed observation data of the detected sparse signal, β is the local censorship threshold, q is the qth sensor node, and T d is the index set containing all false sensors.

为达到上述目的，本发明另一方面实施例提出了基于虚伪审查手段的防窃听稀疏信号检测系统，包括：设置模块，用于将无线传感器网络设置为常规传感器和虚伪传感器两部分；计算模块，用于根据所述无线传感器网络和被检测稀疏信号的参数设置计算出本地审查阈值；比较模块，用于比较所述被检测稀疏信号和所述本地审查阈值，利用所述常规传感器将所述被检测稀疏函数中信息含量高的数据发送至融合中心，利用所述虚伪传感器将所述被检测稀疏函数中信息含量低的数据发送至融合中心；构建模块，用于基于所述融合中心的自身信号模型，根据收到的数据和每个传感器的身份构建局部最大势检测器，以作出相应的全局判决。In order to achieve the above object, another embodiment of the present invention proposes an anti-eavesdropping sparse signal detection system based on a false review method, including: a setting module for setting the wireless sensor network into two parts: a conventional sensor and a false sensor; a computing module, for calculating a local censorship threshold according to the parameter settings of the wireless sensor network and the detected sparse signal; a comparison module for comparing the detected sparse signal and the local censorship threshold, and using the conventional sensor to compare the detected sparse signal with the local censorship threshold. The data with high information content in the detected sparse function is sent to the fusion center, and the fake sensor is used to send the data with low information content in the detected sparse function to the fusion center; a building block is used to build a module based on the fusion center's own signal model, which builds a local maximum potential detector based on the received data and the identity of each sensor to make the corresponding global decision.

本发明实施例的基于虚伪审查手段的防窃听稀疏信号检测系统，利用虚伪审查策略增强系统的保密性，可以对稀疏度未知的稀疏信号实现低能耗的有效保密检测，同时，还提供了策略中最佳系统参数的计算方法，在绝对保密即窃听者无法获取任何有用信息的条件下，融合中心可以达到最佳的检测性能，与相关技术相比，本发明实施例具有更高的可实现性，并且几乎可以达到其检测性能的上限。The anti-eavesdropping sparse signal detection system based on the false censorship method according to the embodiment of the present invention utilizes the false censorship strategy to enhance the confidentiality of the system, and can realize low-energy and effective confidentiality detection for sparse signals with unknown sparsity. The calculation method of the optimal system parameters, the fusion center can achieve the best detection performance under the condition of absolute confidentiality, that is, the eavesdropper cannot obtain any useful information. Compared with the related art, the embodiment of the present invention has higher achievability , and can almost reach the upper limit of its detection performance.

另外，根据本发明上述实施例的基于虚伪审查手段的防窃听稀疏信号检测系统还可以具有以下附加的技术特征：In addition, the anti-eavesdropping sparse signal detection system based on the false review method according to the above-mentioned embodiment of the present invention may also have the following additional technical features:

进一步地，在本发明的一个实施例中，所述无线传感器网络由一个融合中心和多个传感器构成。Further, in an embodiment of the present invention, the wireless sensor network consists of a fusion center and a plurality of sensors.

进一步地，在本发明的一个实施例中，所述信息含量高的数据为所述被检测稀疏信号压缩后的观测数据的绝对值大于所述本地审查阈值的数据，采用所述常规传感器将所述被检测稀疏信号压缩后发送至融合中心；所述信息含量低的数据为所述被检测稀疏信号压缩后的观测数据的绝对值小于所述本地审查阈值的数据，采用所述虚伪传感器将所述被检测稀疏信号压缩后发送至所述融合中心。Further, in an embodiment of the present invention, the data with high information content is the data in which the absolute value of the compressed observation data of the detected sparse signal is greater than the local censorship threshold, and the conventional sensor is used to The detected sparse signal is compressed and sent to the fusion center; the data with low information content is the data whose absolute value of the compressed observation data of the detected sparse signal is less than the local review threshold, and the false sensor is used to The detected sparse signal is compressed and sent to the fusion center.

进一步地，在本发明的一个实施例中，所述常规传感器的审查发送方式为：Further, in an embodiment of the present invention, the examination sending method of the conventional sensor is:

Figure GDA0003215297400000041
Figure GDA0003215297400000041

其中，yq为被检测稀疏信号被压缩后的观测数据，β为本地审查阈值，q为第q个传感器节点，Th为包含所有常规传感器的索引集合。Among them, y q is the compressed observation data of the detected sparse signal, β is the local censorship threshold, q is the qth sensor node, and Th is the index set containing all regular sensors.

进一步地，在本发明的一个实施例中，所述虚伪传感器的审查发送方式为：Further, in an embodiment of the present invention, the examination and sending method of the fake sensor is:

Figure GDA0003215297400000042
Figure GDA0003215297400000042

其中，yq为被检测稀疏信号被压缩后的观测数据，β为本地审查阈值，q为第q个传感器节点，Td为包含所有虚伪传感器的索引集合。Among them, y q is the compressed observation data of the detected sparse signal, β is the local censorship threshold, q is the qth sensor node, and T d is the index set containing all false sensors.

本发明附加的方面和优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本发明的实践了解到。Additional aspects and advantages of the present invention will be set forth, in part, from the following description, and in part will be apparent from the following description, or may be learned by practice of the invention.

附图说明Description of drawings

本发明上述的和/或附加的方面和优点从下面结合附图对实施例的描述中将变得明显和容易理解，其中：The above and/or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of embodiments taken in conjunction with the accompanying drawings, wherein:

图1为本发明一个实施例的基于虚伪审查手段的防窃听稀疏信号检测方法的流程图；FIG. 1 is a flowchart of a method for detecting sparse signals against eavesdropping based on false censorship means according to an embodiment of the present invention;

图2为本发明一个实施例的基于虚伪审查手段的防窃听稀疏信号检测方法下的无线传感器系统模型示意图；FIG. 2 is a schematic diagram of a wireless sensor system model under an anti-eavesdropping sparse signal detection method based on false censorship means according to an embodiment of the present invention;

图3为本发明一个实施例的常规传感器本地的审查发送策略示意图；3 is a schematic diagram of a local censorship sending strategy of a conventional sensor according to an embodiment of the present invention;

图4为本发明一个实施例的虚伪传感器本地的审查发送策略示意图；FIG. 4 is a schematic diagram of a local censorship sending policy of a fake sensor according to an embodiment of the present invention;

图5为本发明一个实施例的基于虚伪审查的防窃听稀疏信号检测方法的具体流程图；5 is a specific flowchart of a method for detecting sparse signals against eavesdropping based on false review according to an embodiment of the present invention;

图6为虚伪审查法在绝对保密条件和不同信号强度下的检测性能与检测性能上限的对比图；Figure 6 is a comparison chart of the detection performance and the upper limit of detection performance of the false review method under absolute confidentiality conditions and different signal strengths;

图7为本发明一个实施例的基于虚伪审查手段的防窃听稀疏信号检测系统结构示意图。FIG. 7 is a schematic structural diagram of an anti-eavesdropping sparse signal detection system based on a false censorship method according to an embodiment of the present invention.

具体实施方式Detailed ways

下面详细描述本发明的实施例，所述实施例的示例在附图中示出，其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的，旨在用于解释本发明，而不能理解为对本发明的限制。The following describes in detail the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary, and are intended to explain the present invention and should not be construed as limiting the present invention.

需要说明是，在由一个融合中心和Q个传感器构成的无线传感器网络中，对稀疏信号的检测问题可以建模为如下的二元假设检验问题：It should be noted that in a wireless sensor network composed of a fusion center and Q sensors, the detection problem of sparse signals can be modeled as the following binary hypothesis testing problem:

Figure GDA0003215297400000051
Figure GDA0003215297400000051

其中，H0和H1分别表示目标不存在的情况和目标存在的情况。sq是第q个传感器节点观测到的稀疏信号向量，该向量服从的分布是伯努利高斯分布，即该向量中的每个元素都以概率p服从高斯分布

Figure GDA0003215297400000052
以概率1-p等于0，这里的p表示未知的稀疏度。wq表示第q个节点的加性高斯噪声，该噪声服从的分布是高斯分布
Figure GDA0003215297400000053
hq表示进行压缩操作的滤波器权重系数向量，作用是对原始的高维观测数据进行压缩。sq和hq都是N×1维的实值向量，yq是压缩后的观测数据。各个传感器观测到的原始数据是条件相互独立的，即在任意一种假设H0或H1下都相互独立。为了减少能量消耗，各传感器在发送数据前会首先对数据进行审查，并且对数据进行有选择的发送。在无线传感器网络中，窃听者亦想窃取关于稀疏信号是否存在的信息。窃听者具备的能力是可以探测各个传感器和融合中心之间有无信息发送活动，并据此推测稀疏信号是否存在。Among them, H 0 and H 1 represent the case where the target does not exist and the case where the target exists, respectively. s q is the sparse signal vector observed by the qth sensor node, the distribution of this vector is the Bernoulli Gaussian distribution, that is, each element in the vector obeys the Gaussian distribution with probability p
Figure GDA0003215297400000052
Equal to 0 with probability 1-p, where p represents the unknown sparsity. w q represents the additive Gaussian noise of the qth node, the distribution of which the noise obeys is Gaussian distribution
Figure GDA0003215297400000053
h q represents the filter weight coefficient vector for the compression operation, which is used to compress the original high-dimensional observation data. Both s q and h q are N×1-dimensional real-valued vectors, and y q is the compressed observation data. The raw data observed by each sensor are conditionally independent of each other, that is, they are independent of each other under any assumption H 0 or H 1 . In order to reduce energy consumption, each sensor will first review the data before sending it, and send the data selectively. In wireless sensor networks, eavesdroppers also want to steal information about the presence or absence of sparse signals. The eavesdropper has the ability to detect whether there is information sending activity between the various sensors and fusion centers, and infer the existence of sparse signals based on this.

下面参照附图描述根据本发明实施例提出的基于虚伪审查手段的防窃听稀疏信号检测方法及系统，首先将参照附图描述根据本发明实施例提出的基于虚伪审查手段的防窃听稀疏信号检测方法。The method and system for anti-eavesdropping sparse signal detection based on false censorship means proposed according to the embodiments of the present invention will be described below with reference to the accompanying drawings. First, the method and system for anti-eavesdropping sparse signal detection based on false censorship means proposed according to the embodiments of the present invention will be described with reference to the accompanying drawings. .

图1是本发明一个实施例的基于虚伪审查手段的防窃听稀疏信号检测方法流程图。FIG. 1 is a flowchart of an anti-eavesdropping sparse signal detection method based on a false censorship method according to an embodiment of the present invention.

如图1所示，该基于虚伪审查手段的防窃听稀疏信号检测方法包括以下步骤：As shown in Figure 1, the detection method for anti-eavesdropping and sparse signals based on false censorship means includes the following steps:

在步骤S1中，将无线传感器网络设置为常规传感器和虚伪传感器两部分。In step S1, the wireless sensor network is set as two parts: regular sensors and fake sensors.

具体地，如图2所示，在系统上电前，融合中心将全部传感器分为两部分，即常规传感器和虚伪传感器，其中，虚伪传感器数量占全部传感器总数的比例是α。设Th和Td分别表示包含所有常规传感器和虚伪传感器的索引集合。Specifically, as shown in Figure 2, before the system is powered on, the fusion center divides all sensors into two parts, namely conventional sensors and fake sensors, where the ratio of the number of fake sensors to the total number of sensors is α. Let Th and Td denote the index set containing all regular and fake sensors, respectively.

在步骤S2中，根据无线传感器网络和被检测稀疏信号的参数设置计算出本地审查阈值。In step S2, the local censorship threshold is calculated according to the parameter settings of the wireless sensor network and the detected sparse signal.

也就是说，根据之前的理论分析无线传感器网络和被检测稀疏信号的具体参数设置，计算出最佳的系数参数，即最佳的本地审查阈值β>0。That is to say, according to the previous theoretical analysis of the wireless sensor network and the specific parameter settings of the detected sparse signals, the optimal coefficient parameters are calculated, that is, the optimal local censorship threshold β>0.

在步骤S3中，比较被检测稀疏信号和本地审查阈值，利用常规传感器将被检测稀疏函数中信息含量高的数据发送至融合中心，利用虚伪传感器将被检测稀疏函数中信息含量低的数据发送至融合中心。In step S3, compare the detected sparse signal with the local censorship threshold, use conventional sensors to send data with high information content in the detected sparse function to the fusion center, and use fake sensors to send data with low information content in the detected sparse function to Fusion Center.

进一步地，在本发明的一个实施例中，信息含量高的数据为被检测稀疏信号压缩后的观测数据的绝对值大于本地审查阈值的数据，采用常规传感器将被检测稀疏信号压缩后发送至融合中心；信息含量低的数据为被检测稀疏信号压缩后的观测数据的绝对值小于本地审查阈值的数据，采用虚伪传感器将被检测稀疏信号压缩后发送至融合中心。Further, in an embodiment of the present invention, the data with high information content is the data whose absolute value of the observation data compressed by the detected sparse signal is greater than the local censorship threshold, and the detected sparse signal is compressed and sent to the fusion using a conventional sensor. Center; the data with low information content is the data whose absolute value of the observed data compressed by the detected sparse signal is less than the local censorship threshold, and the detected sparse signal is compressed and sent to the fusion center by the false sensor.

具体地，如图3所示，接着上述的举例，若第q个传感器节点是常规传感器，那么其发送的是信息含量高的数据，即对应的似然比取值较大的数据。基于所考虑的信号模型，等价的审查发送方式如下：Specifically, as shown in FIG. 3 , following the above example, if the qth sensor node is a conventional sensor, it sends data with high information content, that is, data with a large corresponding likelihood ratio. Based on the considered signal model, the equivalent censorship is sent as follows:

Figure GDA0003215297400000061
Figure GDA0003215297400000061

其中，yq为被检测稀疏信号被压缩后的观测数据，β为本地审查阈值，q为第q个传感器节点，Th为包含所有常规传感器的索引集合。Among them, y q is the compressed observation data of the detected sparse signal, β is the local censorship threshold, q is the qth sensor node, and Th is the index set containing all regular sensors.

如图4所示，若第q个传感器节点是虚伪传感器，那么其发送的是信息含量低的数据，即对应的似然比取值较大的数据。基于所考虑的信号模型，等价的审查发送方式如下：As shown in Figure 4, if the qth sensor node is a fake sensor, then it sends data with low information content, that is, data with a large corresponding likelihood ratio. Based on the considered signal model, the equivalent censorship is sent as follows:

Figure GDA0003215297400000062
Figure GDA0003215297400000062

其中，yq为被检测稀疏信号被压缩后的观测数据，β为本地审查阈值，q为第q个传感器节点，Td为包含所有虚伪传感器的索引集合。Among them, y q is the compressed observation data of the detected sparse signal, β is the local censorship threshold, q is the qth sensor node, and T d is the index set containing all false sensors.

也就是说，无线传感器网络中的两类传感器采用相反的审查策略，从而隐瞒自己的发送活动中隐含的有用信息，使得窃听者无法单纯从传感器的发送状态判断目标是否存在。所有的系统参数都同时被融合中心和窃听者掌握和了解。但是只有融合中心知道各个传感器的身份，即各个传感器采用何种审查发送策略。所以，当无线传感器网络中存在大量传感器时，从窃听者的视角看，每个传感器是虚伪传感器的概率为α。That is to say, the two types of sensors in the wireless sensor network adopt opposite censorship strategies, so as to conceal the useful information hidden in their own sending activities, so that eavesdroppers cannot simply judge whether the target exists from the sending status of the sensors. All system parameters are grasped and understood by the fusion center and the eavesdropper at the same time. But only the fusion center knows the identity of each sensor, that is, which censorship and sending strategy each sensor adopts. Therefore, when there are a large number of sensors in the wireless sensor network, from the eavesdropper's point of view, the probability of each sensor being a fake sensor is α.

在步骤S4中，基于融合中心的自身信号模型，根据收到的数据和每个传感器的身份构建局部最大势检测器，以作出相应的全局判决。In step S4, based on the fusion center's own signal model, a local maximum potential detector is constructed according to the received data and the identity of each sensor to make a corresponding global decision.

因此，基于上述的虚伪审查策略，求得最佳的系统参数的具体过程为：Therefore, based on the above false review strategy, the specific process of obtaining the best system parameters is as follows:

首先分析融合中心的检测器及其检测性能。不失一般性，考虑

Figure GDA0003215297400000071
均匀情况下的检测问题。由于融合中心的检测问题是一个紧密单边参数检验问题，可以采用局部最大势检测器，具体如下：Firstly, the detector of fusion center and its detection performance are analyzed. Without loss of generality, consider
Figure GDA0003215297400000071
Detection problem in the uniform case. Since the detection problem of fusion center is a tight one-sided parameter test problem, a local maximum potential detector can be used, as follows:

Figure GDA0003215297400000072
Figure GDA0003215297400000072

Figure GDA0003215297400000073
Figure GDA0003215297400000073

Figure GDA0003215297400000074
Figure GDA0003215297400000074

其中，

Figure GDA0003215297400000075
和
Figure GDA0003215297400000076
分别表示包含所有发送信息的常规节点和发送信息的虚伪节点的索引集合,λFC表示融合中心的判决阈值，
Figure GDA0003215297400000077
表示两个集合的并集。费雪信息量FIFC(0)的具体表达式为：in,
Figure GDA0003215297400000075
and
Figure GDA0003215297400000076
Represents the index set containing all regular nodes that send information and false nodes that send information, respectively, λ FC represents the decision threshold of the fusion center,
Figure GDA0003215297400000077
Represents the union of two sets. The specific expression of Fisher's information FI FC (0) is:

Figure GDA0003215297400000081
Figure GDA0003215297400000081

在上述两个表达式中，

Figure GDA0003215297400000082
表示在H0下压缩观测值yq在yq＝β处的概率密度函数值，
Figure GDA0003215297400000083
以及
Figure GDA0003215297400000084
当传感器网络中有大量传感器时，融合中心的局部最大势检测器服从的渐进分布为：In the above two expressions,
Figure GDA0003215297400000082
represents the probability density function value of the compressed observation y q at y q = β under H 0 ,
Figure GDA0003215297400000083
as well as
Figure GDA0003215297400000084
When there are a large number of sensors in the sensor network, the asymptotic distribution obeyed by the local maximum potential detector at the fusion center is:

Figure GDA0003215297400000085
Figure GDA0003215297400000085

从上述分布中可知，基于上述的虚伪审查策略下，融合中心的检测性能随费雪信息量FIFC(0)的增大而增大。It can be seen from the above distribution that, based on the above false censorship strategy, the detection performance of the fusion center increases with the increase of Fisher's information amount FI FC (0).

再者分析窃听者的检测性能。窃听者从传感器的发送活动中获取的信息服从的分布为：Then, the detection performance of the eavesdropper is analyzed. The distribution of the information obtained by the eavesdropper from the sending activity of the sensor is:

Figure GDA0003215297400000086
Figure GDA0003215297400000086

Figure GDA0003215297400000087
Figure GDA0003215297400000087

Figure GDA0003215297400000088
Figure GDA0003215297400000088

Figure GDA0003215297400000089
Figure GDA0003215297400000089

其中，Pr(A|B)表示条件概率，

Figure GDA00032152974000000810
表示第q个传感器的发送活动(
Figure GDA00032152974000000811
表示有信息发送，
Figure GDA00032152974000000812
表示无信息发送)。要想达到绝对保密的条件，即窃听者无法从本地传感器的发送活动中获取关于信号存在与否的任何信息，需保证在两种假设下
Figure GDA00032152974000000813
的分布相同，即要求where Pr(A|B) represents the conditional probability,
Figure GDA00032152974000000810
represents the sending activity of the qth sensor (
Figure GDA00032152974000000811
Indicates that there is information to send,
Figure GDA00032152974000000812
Indicates that no information is sent). In order to achieve the condition of absolute secrecy, that is, an eavesdropper cannot obtain any information about the presence or absence of the signal from the transmission activity of the local sensor, it is necessary to ensure that under two assumptions
Figure GDA00032152974000000813
distribution is the same, that is, the requirement

Figure GDA0003215297400000091
Figure GDA0003215297400000091

进一步地，在保证系统绝对保密性的条件下最大化融合中心的检测性能等价于建立如下的优化问题：Further, maximizing the detection performance of the fusion center under the condition of ensuring the absolute confidentiality of the system is equivalent to establishing the following optimization problem:

maxβFIFC(0)|α＝1/2,max β FI FC (0)| α=1/2 ,

s.t.β>0,s.t.β>0,

其中，in,

Figure GDA0003215297400000092
Figure GDA0003215297400000092

Figure GDA0003215297400000093
Figure GDA0003215297400000093

可以证明，上述目标函数FIFC(0)|α＝1/2是一个关于β的单峰函数，且函数的最大值出现在βmax∈(σw,2σw)；同时，βmax也是

Figure GDA0003215297400000094
在(0，+∞]上的唯一解。所以，可以采用二分法寻找上述优化问题的最优解，得到的最优解为：It can be proved that the above objective function FI FC (0)| α=1/2 is a unimodal function about β, and the maximum value of the function appears in β max ∈(σ w , 2σ w ); at the same time, β max is also
Figure GDA0003215297400000094
The only solution on (0, +∞]. Therefore, the optimal solution of the above optimization problem can be found by the bisection method, and the optimal solution obtained is:

βmax＝1.482σw.β max = 1.482σ w .

对应的目标函数的最大值为：The maximum value of the corresponding objective function is:

Figure GDA0003215297400000095
Figure GDA0003215297400000095

下面结合具体实施例对本发明实施例的基于虚伪审查手段的防窃听稀疏信号检测方法进一步说明。The method for detecting sparse signals against eavesdropping based on a false inspection method according to an embodiment of the present invention is further described below with reference to specific embodiments.

步骤一，本发明实施例使用的各种参数如下表1所示，首先根据之前的理论分析计算出最佳的系统参数，即最佳的本地审查阈值βmax＝1.482σw。Step 1, various parameters used in the embodiments of the present invention are shown in Table 1 below. First, the optimal system parameters, that is, the optimal local censorship threshold β max =1.482σ w , are calculated according to the previous theoretical analysis.

表1无线传感器网络和被检测稀疏信号的具体参数设置Table 1 Wireless sensor network and the specific parameter settings of the detected sparse signal

Figure GDA0003215297400000096
Figure GDA0003215297400000096

Figure GDA0003215297400000101
Figure GDA0003215297400000101

步骤二，按照图2的系统模型和图5的具体流程进行仿真。滤波器权重系数向量hq中的每个元素都由独立同分布的高斯分布

Figure GDA0003215297400000102
产生并归一化到
Figure GDA0003215297400000103
。所有传感器都首先对原始观测数据进行压缩，之后，常规传感器只发送绝对值大于审查阈值βmax的压缩数据到融合中心，虚伪传感器只发送绝对值小于审查阈值βmax的压缩数据到融合中心。In step 2, the simulation is performed according to the system model in FIG. 2 and the specific flow in FIG. 5 . Each element in the filter weight coefficient vector h q is distributed by an IID Gaussian
Figure GDA0003215297400000102
generated and normalized to
Figure GDA0003215297400000103
. All sensors first compress the original observation data, after that, conventional sensors only send compressed data whose absolute value is greater than the censorship threshold βmax to the fusion center, and fake sensors only send compressed data whose absolute value is less than the censorship threshold βmax to the fusion center.

步骤三，融合中心根据自身的信号模型，利用自己接收到的数据和各个传感器的身份构建局部最大势检测器，并作出相应的全局判决。在每组参数条件下各进行104次蒙特卡洛实验，画出融合中心的接收机特性(ROC)曲线，用于表征绝对保密情况下融合中心的检测性能。Step 3: According to its own signal model, the fusion center uses the data received by itself and the identity of each sensor to construct a local maximum potential detector, and makes a corresponding global decision. 10 4 Monte Carlo experiments were carried out under each set of parameters, and the receiver characteristic (ROC) curve of the fusion center was drawn, which was used to characterize the detection performance of the fusion center under absolute confidentiality.

进一步地，如图6所示，画出了在绝对保密情况和不同信号强度

Figure GDA0003215297400000104
下所提出的虚伪审查方法在融合中心的检测性能曲线，并且标记出了每条曲线对应的信号强度。从该簇曲线可以十分直观观察出，信号增强有助于在保证系统的保密性的前提下提升融合中心的检测性能。同时，图6中也画出了设计审查区间方法的ROC曲线作为上限进行对比，可以看出，本发明实施例提出的虚伪审查方法实现的性能几乎和检测性能上限相同，但是虚伪审查法不要求稀疏度已知，从而在实际应用中具有更强的可实现性。Further, as shown in Fig. 6, the absolute secrecy situation and different signal strengths are plotted
Figure GDA0003215297400000104
The detection performance curves of the proposed false detection method in the fusion center are shown below, and the corresponding signal intensity of each curve is marked. From the cluster curve, it can be observed intuitively that signal enhancement helps to improve the detection performance of fusion center on the premise of ensuring the confidentiality of the system. At the same time, the ROC curve of the design review interval method is also drawn as the upper limit for comparison. It can be seen that the performance achieved by the falsehood review method proposed in the embodiment of the present invention is almost the same as the upper limit of the detection performance, but the falsehood review method does not require The sparsity is known, resulting in stronger achievability in practical applications.

综上，本发明提出的基于虚伪审查的低能耗分布式防窃听稀疏信号检测方法，通过将传感器分为常规传感器和虚伪传感器，并令两种传感器采用截然相反的数据审查策略，从而达到迷惑窃听者的目的，同时可以在保证系统绝对保密的情况下使融合中心获得最好的检测性能，且不需要掌握关于信号稀疏度的相关知识。另外，本发明实施例还计算并给出了系统的最佳参数，与相关技术中的设计审查区间法相比，本发明实施例不要求系统设计者掌握关于稀疏信号分布的全部信息，可以更好地应用于复杂环境下的实际场景中，且几乎可以达到融合中心检测性能的上限。To sum up, the low-energy distributed anti-eavesdropping sparse signal detection method based on false censorship proposed by the present invention achieves confusing eavesdropping by dividing sensors into conventional sensors and false sensors, and making the two sensors adopt diametrically opposite data censorship strategies. At the same time, the fusion center can obtain the best detection performance under the condition of ensuring the absolute confidentiality of the system, and it does not need to master the relevant knowledge about the signal sparsity. In addition, the embodiment of the present invention also calculates and provides the optimal parameters of the system. Compared with the design review interval method in the related art, the embodiment of the present invention does not require the system designer to master all the information about the sparse signal distribution, which can be better It can be applied to practical scenes in complex environments, and can almost reach the upper limit of fusion center detection performance.

其次参照附图描述根据本发明实施例提出的基于虚伪审查手段的防窃听稀疏信号检测系统。Next, an anti-eavesdropping sparse signal detection system based on a false inspection method proposed according to an embodiment of the present invention will be described with reference to the accompanying drawings.

图7是本发明一个实施例的基于虚伪审查手段的防窃听稀疏信号检测系统的结构示意图。FIG. 7 is a schematic structural diagram of an anti-eavesdropping sparse signal detection system based on a false censorship method according to an embodiment of the present invention.

如图7所示，该系统10包括：设置模块100、计算模块200、比较模块300和构建模块400。As shown in FIG. 7 , the system 10 includes: a setting module 100 , a calculation module 200 , a comparison module 300 and a construction module 400 .

其中，设置模块100用于将无线传感器网络设置为常规传感器和虚伪传感器两部分。计算模块200据无线传感器网络和被检测稀疏信号的参数设置计算出本地审查阈值。比较模块300较被检测稀疏信号和本地审查阈值，利用常规传感器将被检测稀疏函数中信息含量高的数据发送至融合中心，利用虚伪传感器将被检测稀疏函数中信息含量低的数据发送至融合中心。构建模块400于融合中心的自身信号模型，根据收到的数据和每个传感器的身份构建局部最大势检测器，以作出相应的全局判决。Wherein, the setting module 100 is used for setting the wireless sensor network into two parts: conventional sensors and fake sensors. The calculation module 200 calculates the local censorship threshold according to the parameter settings of the wireless sensor network and the detected sparse signal. The comparison module 300 compares the detected sparse signal with the local censorship threshold, uses conventional sensors to send data with high information content in the detected sparse function to the fusion center, and uses fake sensors to send data with low information content in the detected sparse function to the fusion center . The building module 400 builds a local maximum potential detector according to the received data and the identity of each sensor based on the fusion center's own signal model, so as to make a corresponding global decision.

进一步地，在本发明的一个实施例中，无线传感器网络由一个融合中心和多个传感器构成。Further, in an embodiment of the present invention, the wireless sensor network consists of a fusion center and a plurality of sensors.

进一步地，在本发明的一个实施例中，信息含量高的数据为被检测稀疏信号压缩后的观测数据的绝对值大于本地审查阈值的数据，采用常规传感器将被检测稀疏信号压缩后发送至融合中心；信息含量低的数据为被检测稀疏信号压缩后的观测数据的绝对值小于本地审查阈值的数据，采用虚伪传感器将被检测稀疏信号压缩后发送至融合中心。Further, in an embodiment of the present invention, the data with high information content is the data whose absolute value of the observation data compressed by the detected sparse signal is greater than the local censorship threshold, and the detected sparse signal is compressed and sent to the fusion using a conventional sensor. Center; the data with low information content is the data whose absolute value of the observed data compressed by the detected sparse signal is less than the local censorship threshold, and the detected sparse signal is compressed and sent to the fusion center by the false sensor.

进一步地，在本发明的一个实施例中，常规传感器的审查发送方式为：Further, in an embodiment of the present invention, the examination sending method of the conventional sensor is:

Figure GDA0003215297400000111
Figure GDA0003215297400000111

其中，yq为被检测稀疏信号被压缩后的观测数据，β为本地审查阈值，q为第q个传感器节点，Th为包含所有常规传感器的索引集合。Among them, y q is the compressed observation data of the detected sparse signal, β is the local censorship threshold, q is the qth sensor node, and Th is the index set containing all regular sensors.

进一步地，在本发明的一个实施例中，虚伪传感器的审查发送方式为：Further, in an embodiment of the present invention, the examination and sending method of the false sensor is:

Figure GDA0003215297400000112
Figure GDA0003215297400000112

其中，yq为被检测稀疏信号被压缩后的观测数据，β为本地审查阈值，q为第q个传感器节点，Td为包含所有虚伪传感器的索引集合。Among them, y q is the compressed observation data of the detected sparse signal, β is the local censorship threshold, q is the qth sensor node, and T d is the index set containing all false sensors.

根据本发明实施例提出的基于虚伪审查手段的防窃听稀疏信号检测系统，通过将传感器分为常规传感器和虚伪传感器，并令两种传感器采用截然相反的数据审查策略，从而达到迷惑窃听者的目的，同时可以在保证系统绝对保密的情况下使融合中心获得最好的检测性能，且不需要掌握关于信号稀疏度的相关知识。另外，本发明实施例还计算并给出了系统的最佳参数，与相关技术中的设计审查区间法相比，本发明实施例不要求系统设计者掌握关于稀疏信号分布的全部信息，可以更好地应用于复杂环境下的实际场景中，且几乎可以达到融合中心检测性能的上限。According to the anti-eavesdropping sparse signal detection system based on the false censorship method proposed in the embodiment of the present invention, the sensors are divided into conventional sensors and false sensors, and the two sensors adopt diametrically opposite data censorship strategies, so as to confuse the eavesdropper. At the same time, the fusion center can obtain the best detection performance under the condition of ensuring the absolute confidentiality of the system, and it does not need to master the relevant knowledge about the signal sparsity. In addition, the embodiment of the present invention also calculates and provides the optimal parameters of the system. Compared with the design review interval method in the related art, the embodiment of the present invention does not require the system designer to master all the information about the sparse signal distribution, which can be better It can be applied to practical scenes in complex environments, and can almost reach the upper limit of fusion center detection performance.

此外，术语“第一”、“第二”仅用于描述目的，而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。由此，限定有“第一”、“第二”的特征可以明示或者隐含地包括至少一个该特征。在本发明的描述中，“多个”的含义是至少两个，例如两个，三个等，除非另有明确具体的限定。In addition, the terms "first" and "second" are only used for descriptive purposes, and should not be construed as indicating or implying relative importance or implying the number of indicated technical features. Thus, a feature delimited with "first", "second" may expressly or implicitly include at least one of that feature. In the description of the present invention, "plurality" means at least two, such as two, three, etc., unless otherwise expressly and specifically defined.

在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不必须针对的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任一个或多个实施例或示例中以合适的方式结合。此外，在不相互矛盾的情况下，本领域的技术人员可以将本说明书中描述的不同实施例或示例以及不同实施例或示例的特征进行结合和组合。In the description of this specification, description with reference to the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples", etc., mean specific features described in connection with the embodiment or example , structure, material or feature is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, those skilled in the art may combine and combine the different embodiments or examples described in this specification, as well as the features of the different embodiments or examples, without conflicting each other.

尽管上面已经示出和描述了本发明的实施例，可以理解的是，上述实施例是示例性的，不能理解为对本发明的限制，本领域的普通技术人员在本发明的范围内可以对上述实施例进行变化、修改、替换和变型。Although the embodiments of the present invention have been shown and described above, it should be understood that the above-mentioned embodiments are exemplary and should not be construed as limiting the present invention. Embodiments are subject to variations, modifications, substitutions and variations.

Claims (10)

1. An anti-eavesdropping sparse signal detection method based on a false censoring means is characterized by comprising the following steps:
setting a wireless sensor network into a conventional sensor and a false sensor;
calculating a local audit threshold value according to the wireless sensor network and the parameter setting of the detected sparse signal;
comparing the detected sparse signal with the local examination threshold, sending data with high information content in the detected sparse function to a fusion center by using the conventional sensor, and sending data with low information content in the detected sparse function to the fusion center by using the false sensor;
based on a self signal model of the fusion center, constructing a local maximum potential detector according to the received data and the identity of each sensor so as to make corresponding global judgment;
in the wireless sensor network formed by a fusion center and Q sensors, the detection problem of sparse signals is modeled as the following binary hypothesis testing problem:
Figure FDA0003215297390000011
wherein H0And H1Respectively representing the case where the target is absent and the case where the target is present, sqIs a sparse signal vector observed by the q-th sensor node, the vector obeying a distribution that is a Bernoulli Gaussian distribution, i.e., each element in the vector obeys a Gaussian distribution with a probability p
Figure FDA0003215297390000012
With probability 1-p equal to 0, p representing unknown sparsity, wqAdditive Gaussian noise representing the q-th node, the noise obeying a distribution that is Gaussian
Figure FDA0003215297390000013
hqRepresenting the vector of filter weight coefficients, s, subjected to a compression operationqAnd hqAre all real valued vectors of dimension Nx 1, yqIs the compressed observation data, and the raw data observed by each sensor is independent of each other, namely, H is assumed in any one of the assumptions0Or H1The lower parts are mutually independent, beta is a local examination threshold value, and the probability that each sensor is a false sensor is alpha;
wherein, a local maximum potential detector is adopted, which is specifically as follows:
Figure FDA0003215297390000021
Figure FDA0003215297390000022
wherein,
Figure FDA0003215297390000023
and
Figure FDA0003215297390000024
set of indices, λ, representing regular nodes containing all transmitted information and dummy nodes of transmitted information, respectivelyFCA decision threshold value representing the fusion center is indicated,
Figure FDA0003215297390000025
representing a union of two sets, the amount of snow information FIFC(0) The specific expression of (A) is as follows:
Figure FDA0003215297390000026
wherein,
Figure FDA0003215297390000027
is shown in H0Lower compression observed value yqAt yqThe value of the probability density function at beta,
Figure FDA0003215297390000028
and
Figure FDA0003215297390000029
when there are a large number of sensors in the sensor network, the local maximum potential detector of the fusion center obeys a progressive distribution of:
Figure FDA00032152973900000210
based on the false and false examination strategy, the detection performance of the fusion center is along with the snow information amount FIFC(0) Is increased by an increase in;
analyzing the detection performance of the eavesdropper, and the information acquired by the eavesdropper from the transmission activity of the sensor follows the distribution:
Figure FDA0003215297390000031
Figure FDA0003215297390000032
Figure FDA0003215297390000033
Figure FDA0003215297390000034
wherein Pr (A | B) represents a conditional probability,
Figure FDA0003215297390000035
indicating the transmission activity of the q-th sensor: (
Figure FDA0003215297390000036
It is indicated that there is information to be sent,
Figure FDA0003215297390000037
indicating no information transmission), an eavesdropper cannot obtain any information about the presence or absence of a signal from the transmission activity of the local sensor, ensuring under both assumptions
Figure FDA0003215297390000038
Are equally distributed, i.e. require
Figure FDA0003215297390000039
Maximizing the detectability of the fusion center under the condition of ensuring the absolute confidentiality of the system is equivalent to establishing the following optimization problem:
maxβFIFC(0)|α＝1/2,
s.t.β>0,
wherein,
Figure FDA00032152973900000310
Figure FDA00032152973900000311
objective function FIFC(0)|α＝1/2Is a unimodal function with respect to beta, and the maximum of the function occurs at betamax∈(σw,2σw) At the same time, betamaxIs also that
Figure FDA00032152973900000312
At (0, + ∞)]Finding the optimal solution of the optimization problem by adopting a dichotomy to obtain the optimal solution as follows:
βmax＝1.482σw.
the maximum value of the corresponding objective function is:
Figure FDA0003215297390000041
2. an anti-eavesdropping sparse signal detection method based on a fake censoring approach as claimed in claim 1, wherein the wireless sensor network is composed of a fusion center and a plurality of sensors.
3. The eavesdropping-preventing sparse signal detection method based on the fake-fake review means as claimed in claim 1, wherein the data with high information content is data in which the absolute value of observation data compressed by the detected sparse signal is larger than the local review threshold, and the detected sparse signal is compressed by the conventional sensor and then sent to the fusion center; and the data with low information content is the data of which the absolute value of the observation data compressed by the detected sparse signal is smaller than the local examination threshold, and the detected sparse signal is compressed by adopting the false sensor and then sent to the fusion center.
4. The eavesdropping-proof sparse signal detection method based on the fake audit approach as claimed in claim 3, wherein the audit transmission mode of the conventional sensor is as follows:
Figure FDA0003215297390000042
wherein, yqFor the observation data after the detected sparse signal is compressed, beta is a local inspection threshold value, q is a q-th sensor node, and ThIs an index set that contains all conventional sensors.
5. The eavesdropping-preventing sparse signal detection method based on the fake audit means as claimed in claim 3, wherein the audit transmission mode of the fake sensor is as follows:
Figure FDA0003215297390000043
wherein, yqFor the observation data after the detected sparse signal is compressed, beta is a local inspection threshold value, q is a q-th sensor node, and TdIs an index set that contains all false sensors.
6. An anti-eavesdropping sparse signal detection system based on a false censoring means, comprising:
the wireless sensor network is set into a conventional sensor and a false sensor;
the calculation module is used for calculating a local inspection threshold according to the wireless sensor network and the parameter setting of the detected sparse signal;
the comparison module is used for comparing the detected sparse signal with the local examination threshold, sending data with high information content in the detected sparse function to a fusion center by using the conventional sensor, and sending data with low information content in the detected sparse function to the fusion center by using the false sensor;
the building module is used for building a local maximum potential detector according to the received data and the identity of each sensor based on a self signal model of the fusion center so as to make corresponding global judgment;
in the wireless sensor network formed by a fusion center and Q sensors, the detection problem of sparse signals is modeled as the following binary hypothesis testing problem:
Figure FDA0003215297390000051
wherein H0And H1Respectively representing the case where the target is absent and the case where the target is present, sqIs a sparse signal vector observed by the q-th sensor node, the vector obeying a distribution that is a Bernoulli Gaussian distribution, i.e., each element in the vector obeys a Gaussian distribution with a probability p
Figure FDA0003215297390000052
With probability 1-p equal to 0, p representing unknown sparsity, wqAdditive Gaussian noise representing the q-th node, the noise obeying a distribution that is Gaussian
Figure FDA0003215297390000053
hqRepresenting the vector of filter weight coefficients, s, subjected to a compression operationqAnd hqAre all real valued vectors of dimension Nx 1, yqIs the compressed observation data, the original data observed by each sensor are mutually independent,i.e. at any one hypothesis H0Or H1The lower parts are mutually independent, beta is a local examination threshold value, and the probability that each sensor is a false sensor is alpha;
wherein, a local maximum potential detector is adopted, which is specifically as follows:
Figure FDA0003215297390000054
Figure FDA0003215297390000055
wherein,
Figure FDA0003215297390000057
and
Figure FDA0003215297390000058
set of indices, λ, representing regular nodes containing all transmitted information and dummy nodes of transmitted information, respectivelyFCA decision threshold value representing the fusion center is indicated,
Figure FDA0003215297390000056
representing a union of two sets, the amount of snow information FIFC(0) The specific expression of (A) is as follows:
Figure FDA0003215297390000061
wherein,
Figure FDA0003215297390000062
is shown in H0Lower compression observed value yqAt yqThe value of the probability density function at beta,
Figure FDA0003215297390000063
and
Figure FDA0003215297390000064
when there are a large number of sensors in the sensor network, the local maximum potential detector of the fusion center obeys a progressive distribution of:
Figure FDA0003215297390000065
based on the false and false examination strategy, the detection performance of the fusion center is along with the snow information amount FIFC(0) Is increased by an increase in;
analyzing the detection performance of the eavesdropper, and the information acquired by the eavesdropper from the transmission activity of the sensor follows the distribution:
Figure FDA0003215297390000066
Figure FDA0003215297390000067
Figure FDA0003215297390000068
Figure FDA0003215297390000069
wherein Pr (A | B) represents a conditional probability,
Figure FDA00032152973900000610
indicating the transmission activity of the q-th sensor: (
Figure FDA00032152973900000611
It is indicated that there is information to be sent,
Figure FDA00032152973900000612
indicating no information transmission), an eavesdropper cannot obtain any information about the presence or absence of a signal from the transmission activity of the local sensor, ensuring under both assumptions
Figure FDA00032152973900000613
Are equally distributed, i.e. require
Figure FDA0003215297390000071
Maximizing the detectability of the fusion center under the condition of ensuring the absolute confidentiality of the system is equivalent to establishing the following optimization problem:
maxβFIFC(0)|α＝1/2,
s.t.β>0,
wherein,
Figure FDA0003215297390000072
Figure FDA0003215297390000073
objective function FIFC(0)|α＝1/2Is a unimodal function with respect to beta, and the maximum of the function occurs at betamax∈(σw,2σw) At the same time, betamaxIs also that
Figure FDA0003215297390000074
At (0, + ∞)]Finding the optimal solution of the optimization problem by adopting a dichotomy to obtain the optimal solution as follows:
βmax＝1.482σw.
the maximum value of the corresponding objective function is:
Figure FDA0003215297390000075
7. an eavesdropping-preventing sparse signal detecting system based on false censoring means as claimed in claim 6, wherein the wireless sensor network is composed of a fusion center and a plurality of sensors.
8. The eavesdropping-preventing sparse signal detection system based on the fake-fake inspection means as claimed in claim 6, wherein the data with high information content is data of which the absolute value of observation data after the detected sparse signal is compressed is larger than the local inspection threshold, and the detected sparse signal is compressed by the conventional sensor and then sent to the fusion center; and the data with low information content is the data of which the absolute value of the observation data compressed by the detected sparse signal is smaller than the local examination threshold, and the detected sparse signal is compressed by adopting the false sensor and then sent to the fusion center.
9. The system according to claim 6, wherein the regular sensor audit is transmitted by:
Figure FDA0003215297390000081
wherein, yqFor the observation data after the detected sparse signal is compressed, beta is a local inspection threshold value, q is a q-th sensor node, and ThIs an index set that contains all conventional sensors.
10. The system according to claim 6, wherein the transmission mode of the dummy sensor for checking is:
Figure FDA0003215297390000082
wherein, yqFor the observation data after the detected sparse signal is compressed, beta is a local inspection threshold value, q is a q-th sensor node, and TdIs an index set that contains all false sensors.
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