CN111970653B - Anti-eavesdropping sparse signal detection method and system based on false censoring - Google Patents
Anti-eavesdropping sparse signal detection method and system based on false censoring Download PDFInfo
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Abstract
The invention discloses an anti-eavesdrop sparse signal detection method and system based on a false censorship means, wherein the method comprises 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 a local examination threshold, sending data with high information content in the detected sparse function to a fusion center by using a conventional sensor, and sending data with low information content in the detected sparse function to the fusion center by using a false sensor; and constructing a local maximum potential detector based on a self signal model of the fusion center according to the received compressed data and the identity of each sensor so as to make corresponding global judgment. The method can realize effective secret detection with low energy consumption on the sparse signals with unknown sparsity, has higher realizability, and can almost reach the upper limit of the detection performance.
Description
Technical Field
The invention relates to the technical field of secret communication of wireless sensor networks, in particular to an anti-eavesdropping sparse signal detection method and system based on a false-false censoring means, which can be particularly applied to the sparse signal detection problem in the wireless sensor network with eavesdropping threat and limited energy supply.
Background
Due to the inherent sparsity of various signals in practical application, the problem of distributed detection of sparse signals in a wireless sensor network attracts much attention. The wireless sensor network is generally composed of a plurality of sensors and a fusion center, wherein the sensors are responsible for performing certain preliminary processing on local observation data and sending the local observation data to the fusion center, and the fusion center comprehensively utilizes the received data and makes global judgment on whether sparse signals exist or not. Because energy and bandwidth in a wireless sensor network are often extremely limited, how to efficiently utilize the resources is an urgent problem to be solved in distributed detection of sparse signals. The compressed sensing theory provides a new idea for solving the problem. Based on the theory, on the premise of ensuring certain detection performance, the local sensor only needs to send compressed data to the fusion center, so that the occupation of bandwidth resources and the consumption of energy are greatly reduced.
In a wireless sensor network, many sensors are placed in unattended locations and battery replacement of these sensors is difficult. If all the sensor nodes only send compressed data, the data transmission still consumes huge energy, so a more efficient information sending method should be selected. The existing low-energy-consumption Distributed Sparse Signal Detection method is provided With detectors based on an examination strategy, such as C.Li, G.Li, and P.K.Varshney, "Distributed Detection of spark Signals With centering Sensors Via Locally Power Test," IEEE Signal Process.Lett., vol.27, pp.346-350,2020. Specifically, each sensor calculates a local likelihood ratio based on the compressed data, and only transmits the likelihood ratio larger than a certain threshold to the fusion center, and the fusion center detects sparse signals with unknown sparsity by using a local maximum potential detector by using the received data and considering the inherent sparse features of the signals. However, this method is suitable for an ideally secure wireless sensor network, i.e. there is no threat from eavesdroppers in the network.
In some practical application scenarios, such as distributed radar networks and cognitive radio networks, since the wireless sensor network itself has a distributed characteristic and a broadcast characteristic, information transmitted therein is easily intercepted, and an eavesdropper also wants to steal relevant information about whether signals and targets exist. The existing low-energy-consumption anti-eavesdropping method aiming at the traditional Distributed Detection problem is a design examination interval method, such as S.Marano, V.Matta, and P.K.Willett, "Distributed Detection With center searching Sensors Underr Physical Layer secret," IEEE Trans.Signal Process., vol.57, No.5, pp.1976-1986, May.2009. An eavesdropper present in the system can observe whether data transmission activities exist between each local sensor and the fusion center, and deduce whether a target exists or not according to the data transmission activities. In order to ensure the absolute security of the system (i.e. ensure that an eavesdropper cannot steal any useful information), the method reasonably designs the examination interval to ensure that the two sending probabilities of the two sensor nodes under two assumptions are equal, thereby achieving the purpose of completely shielding the eavesdropper. However, the method has the disadvantage that the sensor node is required to grasp the accurate probability distribution of the data under two assumptions, which is difficult to realize in practical application, especially in the problem of sparse signal detection with unknown sparsity. Therefore, a low-energy-consumption distributed anti-eavesdropping sparse signal detection method is urgently needed.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, an object of the present invention is to provide an anti-eavesdropping sparse signal detection method based on a false censoring approach, which can achieve effective secret detection with low energy consumption for sparse signals with unknown sparsity.
Another objective of the present invention is to provide an anti-eavesdropping sparse signal detection system based on a false censoring means. In order to achieve the above object, an embodiment of the present invention provides an anti-eavesdropping sparse signal detection method based on a false censoring means, including 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; and constructing a local maximum potential detector based on a self signal model of the fusion center according to the received data and the identity of each sensor so as to make corresponding global judgment.
The anti-eavesdropping sparse signal detection method based on the virtual censoring means of the embodiment of the invention utilizes the virtual censoring strategy to enhance the confidentiality of the system, can realize effective secrecy detection with low energy consumption on sparse signals with unknown sparsity, and simultaneously provides a calculation method of the optimal system parameters in the strategy, and the fusion center can reach the optimal detection performance under the condition of absolute secrecy, namely, under the condition that an eavesdropper cannot obtain any useful information.
In addition, the eavesdropping-preventing sparse signal detection method based on the fake-fake review means according to the above embodiment of the present invention may further have the following additional technical features:
further, in one embodiment of the present invention, the wireless sensor network is composed of a fusion center and a plurality of sensors.
Further, in an embodiment of the present invention, the data with high information content is data in which an absolute value of observation data after the compression of the detected sparse signal is greater than the local review threshold, and the detected sparse signal is compressed by using the conventional sensor and then sent to a 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.
Further, in an embodiment of the present invention, the data with high information content is data in which an absolute value of observation data after the compression of the detected sparse signal is greater than the local review threshold, and the detected sparse signal is compressed by using the conventional sensor and then sent to a 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.
Further, in an embodiment of the present invention, the audit transmission mode of the conventional sensor is as follows:
wherein, yqFor the observation data after the detected sparse signal is compressed, beta is a local inspection threshold value, and q is the secondq sensor nodes, ThIs an index set that contains all conventional sensors.
Further, in an embodiment of the present invention, the sending method of the audit of the fake sensor is as follows:
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.
In order to achieve the above object, another embodiment of the present invention provides an anti-eavesdropping sparse signal detection system based on a false censoring method, including: 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; and 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 the self signal model of the fusion center so as to make corresponding global judgment.
The anti-eavesdropping sparse signal detection system based on the virtual censoring means of the embodiment of the invention utilizes the virtual censoring strategy to enhance the confidentiality of the system, can realize effective secrecy detection with low energy consumption on sparse signals with unknown sparsity, and simultaneously provides a calculation method of optimal system parameters in the strategy.
In addition, the anti-eavesdropping sparse signal detection system based on the fake censorship method according to the above embodiment of the present invention may further have the following additional technical features:
further, in one embodiment of the present invention, the wireless sensor network is composed of a fusion center and a plurality of sensors.
Further, in an embodiment of the present invention, the data with high information content is data in which an absolute value of observation data after the compression of the detected sparse signal is greater than the local review threshold, and the detected sparse signal is compressed by using the conventional sensor and then sent to a 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.
Further, in an embodiment of the present invention, the audit transmission mode of the conventional sensor is as follows:
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.
Further, in an embodiment of the present invention, the sending method of the audit of the fake sensor is as follows:
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.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a flowchart of an anti-eavesdropping sparse signal detection method based on a false censoring approach according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a wireless sensor system model under an anti-eavesdropping sparse signal detection method based on a false censoring approach according to an embodiment of the invention;
FIG. 3 is a schematic diagram of a review delivery strategy local to a conventional sensor, in accordance with one embodiment of the present invention;
FIG. 4 is a diagram illustrating an exemplary audit transmission strategy local to a counterfeit sensor in accordance with an embodiment of the present invention;
fig. 5 is a detailed flowchart of an anti-eavesdropping sparse signal detection method based on false censoring according to an embodiment of the present invention;
FIG. 6 is a graph comparing the detection performance of the false censoring method under absolute privacy conditions and different signal strengths with the upper limit of the detection performance;
fig. 7 is a schematic structural diagram of an anti-eavesdropping sparse signal detection system based on a false censoring approach according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
It should be noted that, in a wireless sensor network composed of one fusion center and Q sensors, the detection problem of sparse signals can be modeled as a binary hypothesis testing problem as follows:
wherein H0And H1Respectively, a case where the target does not exist and a case where the target exists. 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
With the probability 1-p equal to 0, where p denotes the unknown sparsity. w is aqAdditive Gaussian noise representing the q-th node, the noise obeying a distribution that is Gaussian
hqThe filter weight coefficient vector representing the compression operation is used for compressing the original high-dimensional observation data. sqAnd hqAre all real valued vectors of dimension Nx 1, yqIs the compressed observation data. The raw data observed by each sensor is conditional independently of each other, i.e. on any one hypothesis H0Or H1The following are independent of each other. To reduce power consumption, each sensor may first review the data and selectively transmit the data before transmitting the data. In wireless sensor networks, eavesdroppers also want to steal information about the presence of sparse signals. The eavesdropper has the ability to detect the presence or absence of information transmission activity between each sensor and the fusion center and infer the presence or absence of a sparse signal based thereon.
The method and system for detecting an anti-eavesdropping sparse signal based on a false censoring means according to an embodiment of the present invention will be described below with reference to the accompanying drawings.
Fig. 1 is a flowchart of an anti-eavesdropping sparse signal detection method based on a false censoring approach according to an embodiment of the invention.
As shown in fig. 1, the method for detecting an anti-eavesdropping sparse signal based on a false censoring method comprises the following steps:
in step S1, the wireless sensor network is set as two parts, a regular sensor and a dummy sensor.
Specifically, as shown in fig. 2, before the system is powered on, the fusion center divides all the sensors into two parts, namely a conventional sensor and a dummy sensor, wherein the ratio of the number of the dummy sensors to the total number of all the sensors is α. Let ThAnd TdRespectively, representing a set of indices containing all regular sensors and dummy sensors.
In step S2, a local audit threshold is calculated from the wireless sensor network and the parameter settings of the detected sparse signals.
That is, the optimal coefficient parameters, i.e. the optimal local censorship threshold β >0, are calculated according to the previous theoretical analysis of the wireless sensor network and the specific parameter settings of the detected sparse signals.
In step S3, the detected sparse signal is compared with the local censoring threshold, the data with high information content in the detected sparse function is sent to the fusion center by using the conventional sensor, and the data with low information content in the detected sparse function is sent to the fusion center by using the dummy sensor.
Further, in an embodiment of the invention, the data with high information content is the data that the absolute value of the observation data compressed by the detected sparse signal is larger than the local examination threshold, and the detected sparse signal is compressed by a 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 a virtual sensor and then is sent to the fusion center.
Specifically, as shown in fig. 3, following the above example, if the q-th sensor node is a conventional sensor, it sends data with high information content, that is, data with a large corresponding likelihood ratio value. Based on the signal model under consideration, the equivalent censorship transmission is as follows:
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.
As shown in fig. 4, if the q-th sensor node is a false sensor, it sends data with low information content, that is, data with a large corresponding likelihood ratio value. Based on the signal model under consideration, the equivalent censorship transmission is as follows:
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.
That is, the two types of sensors in the wireless sensor network employ opposite auditing strategies, thereby concealing useful information implicit in their own transmission activities, so that an eavesdropper cannot simply determine whether a target exists from the transmission status of the sensors. All system parameters are simultaneously mastered and known by the fusion center and the eavesdropper. But only the fusion center knows the identity of each sensor, i.e. what audit transmission strategy each sensor employs. Therefore, when there are a large number of sensors in the wireless sensor network, the probability that each sensor is a false sensor is α from the viewpoint of an eavesdropper.
In step S4, based on the fusion center' S own signal model, a local maximum potential detector is constructed from the received data and the identity of each sensor to make a corresponding global decision.
Therefore, based on the above false and false censorship strategy, the specific process of finding the optimal system parameters is as follows:
the detector of the fusion center and its detection performance are first analyzed. Without loss of generality, consider
Detection problems in the homogeneous case. Because the detection problem of the fusion center is a close unilateral parameter detection problem, a local maximum potential detector can be adopted, and the method specifically comprises the following steps:
wherein,
and
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,
representing the union of the two sets. Snow information FIFC(0) The specific expression of (A) is as follows:
in the above-described two expressions,
is shown in H0Lower compression observed value yqAt yqThe value of the probability density function at beta,
and
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:
from the distribution, it can be seen that the detection performance of the fusion center depends on the snow information amount FI based on the false censoring policyFC(0) Is increased.
And furthermore, the detection performance of the eavesdropper is analyzed. The information obtained by the eavesdropper from the transmission activity of the sensor follows a distribution:
wherein Pr (A | B) represents a conditional probability,
indicating the transmission activity of the q-th sensor: (
It is indicated that there is information to be sent,
indicating no information transmission). To achieve the condition of absolute security that an eavesdropper cannot obtain any information about the presence or absence of a signal from the transmission activity of a local sensor, it is ensured under two assumptions
Are equally distributed, i.e. require
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,
s.t.β>0,
wherein,
it can be shown that the above-mentioned 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) (ii) a At the same time, betamaxIs also that
At (0, + ∞)]The unique solution of (c). Therefore, the optimal solution of the optimization problem can be found by adopting a dichotomy method to obtain the best solutionThe optimal solution is as follows:
βmax＝1.482σw.
the maximum value of the corresponding objective function is:
the eavesdropping-preventing sparse signal detection method based on the fake-fake review means according to the embodiment of the invention is further described below with reference to specific embodiments.
First, various parameters used in the embodiment of the present invention are shown in table 1 below, and an optimal system parameter, i.e., an optimal local review threshold β, is calculated according to the previous theoretical analysismax＝1.482σw。
TABLE 1 Wireless sensor network and specific parameter settings for detected sparse signals
And step two, carrying out simulation according to the system model of the figure 2 and the specific flow of the figure 5. Filter weight coefficient vector hqEach element in the group consisting of a Gaussian distribution with independent equal distribution
Is generated and normalized to
. All sensors first compress the raw observation data, after which conventional sensors only send absolute values greater than the audit threshold βmaxThe false sensor only sends the absolute value less than the examination threshold value betamaxTo the fusion center.
And step three, the fusion center constructs a local maximum potential detector by using the data received by the fusion center and the identities of the sensors according to the signal model of the fusion center, and makes corresponding global judgment. Each run 10 under each set of parameters4And (3) performing a secondary Monte Carlo experiment, and drawing a receiver characteristic (ROC) curve of the fusion center, wherein the ROC curve is used for representing the detection performance of the fusion center under the condition of absolute secrecy.
Further, as shown in FIG. 6, the absolute secrecy case and different signal strengths are plotted
The false censoring method proposed below fuses the performance curves of the detection at the center and marks the signal strength corresponding to each curve. The cluster curve can be observed visually, and the signal enhancement is helpful for improving the detection performance of the fusion center on the premise of ensuring the confidentiality of the system. Meanwhile, an ROC curve of a design examination interval method is also drawn in fig. 6 as an upper limit for comparison, and it can be seen that the performance of the pseudo examination method provided by the embodiment of the present invention is almost the same as the upper limit of the detection performance, but the pseudo examination method does not require known sparsity, so that the method has stronger realizability in practical application.
In summary, the low-energy-consumption distributed eavesdropping-preventing sparse signal detection method based on the false-false censoring provided by the invention achieves the purpose of confusing eavesdroppers by dividing the sensors into the conventional sensors and the false-false sensors and enabling the two sensors to adopt the data censoring strategies which are opposite, and meanwhile, the fusion center can obtain the best detection performance under the condition of ensuring the absolute secrecy of the system without mastering the related knowledge about the signal sparsity. In addition, the embodiment of the invention also calculates and provides the optimal parameters of the system, and compared with a design examination interval method in the related technology, the embodiment of the invention does not require a system designer to master all information about sparse signal distribution, can be better applied to an actual scene in a complex environment, and can almost reach the upper limit of the detection performance of a fusion center.
Next, an anti-eavesdropping sparse signal detection system based on a false censoring method according to an embodiment of the present invention will be described with reference to the drawings.
Fig. 7 is a schematic structural diagram of an anti-eavesdropping sparse signal detection system based on a false censoring approach according to an embodiment of the present invention.
As shown in fig. 7, the system 10 includes: a setup module 100, a calculation module 200, a comparison module 300 and a construction module 400.
The setting module 100 is configured to set the wireless sensor network as two parts, namely a regular sensor and a dummy sensor. The calculation module 200 calculates the local censorship threshold according to the wireless sensor network and the parameter setting of the detected sparse signal. The comparison module 300 compares the detected sparse signal with the local review threshold, and transmits the data with high information content in the detected sparse function to the fusion center by using the conventional sensor, and transmits the data with low information content in the detected sparse function to the fusion center by using the false sensor. The building block 400 builds a local maximum potential detector from the received data and the identity of each sensor in the signal model of the fusion center itself to make a corresponding global decision.
Further, in one embodiment of the present invention, the wireless sensor network is composed of a fusion center and a plurality of sensors.
Further, in an embodiment of the invention, the data with high information content is the data that the absolute value of the observation data compressed by the detected sparse signal is larger than the local examination threshold, and the detected sparse signal is compressed by a 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 a virtual sensor and then is sent to the fusion center.
Further, in one embodiment of the present invention, the audit transmission mode of the conventional sensor is as follows:
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.
Further, in an embodiment of the present invention, the method for sending the audit of the fake sensor includes:
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.
According to the anti-eavesdropping sparse signal detection system based on the false censoring means, the sensors are divided into the conventional sensor and the false sensor, and the two sensors adopt the data censoring strategies which are opposite, so that the purpose of confusing an eavesdropper is achieved, meanwhile, the fusion center can obtain the best detection performance under the condition of ensuring the absolute secrecy of the system, and related knowledge about signal sparsity does not need to be mastered. In addition, the embodiment of the invention also calculates and provides the optimal parameters of the system, and compared with a design examination interval method in the related technology, the embodiment of the invention does not require a system designer to master all information about sparse signal distribution, can be better applied to an actual scene in a complex environment, and can almost reach the upper limit of the detection performance of a fusion center.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer 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, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
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:
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
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
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:
wherein,
and
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,
representing a union of two sets, the amount of snow information FIFC(0) The specific expression of (A) is as follows:
wherein,
is shown in H0Lower compression observed value yqAt yqThe value of the probability density function at beta,
and
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:
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:
wherein Pr (A | B) represents a conditional probability,
indicating the transmission activity of the q-th sensor: (
It is indicated that there is information to be sent,
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
Are equally distributed, i.e. require
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,
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
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:
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:
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:
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:
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
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
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:
wherein,
and
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,
representing a union of two sets, the amount of snow information FIFC(0) The specific expression of (A) is as follows:
wherein,
is shown in H0Lower compression observed value yqAt yqThe value of the probability density function at beta,
and
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:
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:
wherein Pr (A | B) represents a conditional probability,
indicating the transmission activity of the q-th sensor: (
It is indicated that there is information to be sent,
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
Are equally distributed, i.e. require
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,
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
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:
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:
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:
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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