CN117241361B - Short wave hidden communication method based on power control - Google Patents
Short wave hidden communication method based on power control Download PDFInfo
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Abstract
The invention discloses a short wave hidden communication method based on power control, which comprises the following steps: constructing a short-wave hidden communication model based on the short-wave communication transmission characteristics, and determining the detection error probability of an eavesdropper and a hidden communication judgment rule; calculating the transmitting power constraint corresponding to the hidden communication based on the detection error probability and the hidden communication judging rule; and under the condition that the transmitting power meets the constraint, an optimization model with the maximum hidden transmission rate as an optimization target is established, the optimization model is solved to obtain the optimal transmitting power, and communication work is carried out according to the optimal transmitting power. The invention realizes the purpose of short-wave hidden communication by controlling the signal transmitting power, and maximizes the communication efficiency while considering the hidden, thereby realizing the short-wave communication with double consideration of the communication efficiency and the hidden capability on the physical level.
Description
Technical Field
The invention belongs to the technical field of short-wave communication, and particularly relates to a short-wave hidden communication method based on power control.
Background
The short-wave communication uses the natural ionized layer as a relay, has long transmission distance, convenient networking and strong destruction resistance, and plays an important role in the scenes of military command and the like. Because of the fragile link, the countermeasure against enemy attack is insufficient, and the random variation of the ionosphere causes instability of the phase difference of signals arriving at the receiving end in different propagation paths, the correctness of the received signals is often required to be improved through one transmitter and one receiver. Meanwhile, the short wave system is a single antenna system at present, so that signals are transmitted omnidirectionally, information is easier to leak and easier to be stolen by malicious persons, an eavesdropper can eavesdrop on transmission signals from multiple directions, and the signals need to be protected omnidirectionally.
Short wave communication faces more serious security threats in a one-shot and one-shot scenario. Generally, data in a wireless communication network employs conventional encryption techniques at an application layer to prevent an eavesdropper's attack. The traditional encryption technology encrypts the plaintext through the key and then transmits the plaintext, and legal communication parties can decrypt the message through the key through sharing the key, and an illegal eavesdropper cannot decrypt the message because the illegal eavesdropper does not have the key. But the approach of encryption at the application layer can only be aimed at attackers of limited computing power, and the security of using encrypted messages is extremely vulnerable when there are adversaries with unlimited computing power. Meanwhile, in security-sensitive scenes such as military command, information leakage and even communication behavior leakage cannot be allowed.
Therefore, short wave covert communication technology at the physical level is particularly important.
Disclosure of Invention
In view of the above, the present invention aims to provide a short-wave covert communication method based on power control, which can control signal transmission power to perform short-wave covert communication, and maximize communication efficiency while considering covert, so as to implement short-wave communication with dual consideration of communication efficiency and covert capability on a physical level.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the invention provides a short wave hidden communication method based on power control, which comprises the following steps:
step S1, a short-wave hidden communication model is built based on short-wave communication transmission characteristics, and detection error probability of an eavesdropper and hidden communication judgment rules are deduced and determined;
s2, calculating the transmitting power constraint corresponding to the hidden communication based on the detection error probability and the hidden communication judging rule;
and step S3, establishing an optimization model with the maximum hidden transmission rate as an optimization target under the condition that the transmitting power of the transmitting party meets the constraint, solving the optimization model to obtain the optimal transmitting power, and carrying out communication work according to the optimal transmitting power.
Specifically, step S1 includes:
establishing a communication structure consisting of a legal signal sender, a legal signal receiver and an eavesdropper;
setting upAnd->Path loss between the short wave communication signal from the sender to the receiver and the sender to the eavesdropper, respectively;
setting upAnd->Respectively small scale parameters of short wave communication signals from a sender to a receiver and from the sender to an eavesdropper;
for the actual receiver of the signalWherein b represents the recipient, < >>Representing an eavesdropper, determining the signal it receives as +.>And satisfies the following:
in the method, in the process of the invention,for the signal sent by the sender, < > and->Representing additive white gaussian noise +.>Sequence number indicating number of channel use, +.>Expressed as the transmit power of the signal;
the signals received by the eavesdropper are determined as follows:
wherein,for the null hypothesis in the binary check, i.e. the sender actually has no transmission signal, +.>For the alternative assumption that the sender actually takes place the transmission signal behaviour;
the eavesdropper is determined to perform binary judgment based on the received signal, and the detection error probability of the received signal after the eavesdropper performs binary judgment is determinedWherein the false alarm probability->Probability of missing detection，/>Indicating that the eavesdropper decides that the sender did not send information, < >>Indicating that the sender sends information;
setting when meetingDetermining the communication as a covert communication, wherein +.>To conceal the constraint, the smaller the concealing constraint, the more concealed the communication.
Specifically, step S2 includes:
assuming that an eavesdropper is to minimize the probability of detection errorsWith optimal detection, under this assumption:
according to the Pinmaker inequality, the total variation distance is converted into relative entropy constraint for analysis, namely:
wherein the method comprises the steps ofAnd->Respectively represent->And->Probability distribution of the observation of an eavesdropper in the case, +.>Is thatAnd->The total variation distance between them, thus determining when the concealment constraint satisfies:
when the communication is in use, the concealment of the communication can be ensured, wherein:
calculating the signal-to-noise ratio of the eavesdropper according to the relative entropy constraint and the hidden constraint conditionConstraint:
setting in the scene of multiple eavesdropping nodes, the eavesdropper carries out maximum score aggregation on the branch signals received by each node and then judges the communication condition in the channel, if the total signal-to-noise ratio is the sum of the signal-to-noise ratios of each branch, then the eavesdropper carries out signal-to-noise ratio under the conditionThe expression is:
wherein,receiving the number of nodes for an eavesdropper, < >>Is->An eavesdropper node;
obtaining a constraint of the transmitting power X according to the signal-to-noise ratio expression and the signal-to-noise ratio constraint:
in the case where the transmission power X satisfies this constraint, it is determined that the covert communication can be achieved.
Specifically, step S3 includes:
setting the receiver to combine the signals by using maximum ratio diversity combining and determining the signal-to-noise ratio of the signals received by the receiver：
Wherein,for the number of receiving nodes of the receiver, < > and->Is the j-th receiver node;
determining an expression of the hidden communication rate under the condition of a limited code length:
in the method, in the process of the invention,indicating the rate of covert communication->For the decoding error probability at the receiver, +.>Is +.>Function (F)>Signal to noise ratio at the receiver;
deriving the corresponding optimization problem of the concealment rate according to the derivation：
Determining whenWhen (I)>Maximum value is obtained and the transmission power at this time is +.>The presence is:
and calculating an optimal solution of the transmitting power according to the formula, taking the optimal solution as the optimal transmitting power, and carrying out communication work according to the optimal transmitting power.
The invention has at least the following beneficial effects:
1. short-wave covert communication is achieved by controlling the transmit power of the transmitter.
2. And (3) setting an optimization target and an optimization problem to solve an optimization result, so that short-wave communication with double consideration of communication efficiency and hiding capacity is realized.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
Drawings
In order to make the objects, technical solutions and advantageous effects of the present invention more clear, the present invention provides the following drawings for description:
fig. 1 is a flow chart of steps of a short wave covert communication method based on power control in an embodiment of the invention;
fig. 2 is a schematic structural diagram of a short-wave communication network constructed in an embodiment of the present invention;
FIG. 3 is a flowchart illustrating the steps for deriving a transmit power constraint in accordance with an embodiment of the present invention;
FIG. 4 is a graph of simulation results of the change of the rate of covert communication with the transmission power in an embodiment of the invention;
fig. 5 is a diagram of simulation results of the change of the rate of covert communication with the number of times N of channel use in the embodiment of the present invention;
FIG. 6 is a graph of simulation results of bit error rate as a function of transmit power in an embodiment of the present invention;
FIG. 7 is a graph of simulation results of the change of the rate of covert communication with the covert constraint in an embodiment of the invention;
fig. 8 is a graph of simulation results of the probability of eavesdropping error according to the change of the transmission power in the embodiment of the invention.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
According to the characteristics of a short-wave communication channel, a short-wave hidden communication system model is established, and under the condition of single-receipt eavesdropping, the relative entropy is used as a hidden communication measurement index, so that the constraint condition of the transmitting power of a transmitting party is deduced. And combining the characteristics of omnidirectional transmission, unstable channel and the like of a short wave channel environment, expanding a single-receiving single-interception scene to a multi-receiving multi-interception scene, combining signals by using a maximum ratio diversity receiving technology, and obtaining a short wave hidden communication method through power control on the basis.
Short wave sky wave propagation uses an ionosphere as a relay, and signals need to undergo large-scale fading and small-scale fading in the process of propagation. Large-scale fading refers to attenuation in power due to factors such as propagation distance, channel environment, etc. when a short wave signal propagates in a relatively large distance. Path loss is a propagation characteristic of large-scale fading, reflecting the power loss of a signal in the propagation path due to various factors. Short wave path loss includes four parts of free space propagation loss, ionospheric absorption loss, ground reflection loss and other losses.
Free space propagation loss refers to the energy loss at the receiving site caused by the gradual increase of the energy diffusion area of a short wave signal due to the increase of the propagation distance. Free space propagation lossThe expression method of (2) is as follows:
the ionospheric absorption loss refers to the energy loss caused by the collision of short wave signals with particles in the ionosphere when the short wave signals are reflected by the ionosphere. Ionospheric absorption losses are generally divided into offset absorption and non-offset absorption, typically less than 1dB, which is negligible in the calculation. Ionospheric absorption lossCan be expressed as:
wherein,incident angle at a height of 110 km; />The average value of the sun black activity is 12 months, and is used for estimating the sun activity intensity; />Two control points are arranged in each jump for controlling the number of the points; />Is->The zenith angle of the sun at each control point,is +.>A value; />Is in the local noon and +.>The absorption factor of the time is a function of the geographic latitude and the month; />Is an absorption factor; />Is->Electronic slew frequency at the control points; />As a function of the zenith angle of the sun, it can be expressed as:
wherein,the day absorption index is related to the month and the corrected dip angle.
For losses above the maximum usable frequency, a function of the ratio of the two when the transmitted signal frequency is greater than the maximum usable frequency, is related to the reflective layer and can be expressed as:
ground reflection loss refers to loss caused by that a short wave signal cannot reach a receiving party after being reflected by an ionosphere once, and thus reflection is required to be carried out through the ground, and the loss only occurs in multi-hop propagation. The ground emission loss can be expressed as:
wherein,is the hop count. The loss caused by each reflection varies slightly depending on the different reflection media.
Other losses refer to all losses that are not easily counted except for all the losses described above. Other losses ofCan be expressed as:
wherein,and calculating according to geomagnetic latitude and local time for loss caused by aurora or other signal loss factors, and finally adopting an average value of all control points as a calculation result. />To calculate the correction value, 8.72dB is typically taken.
Small-scale fading refers to the variation of phase, amplitude and time delay of a short-wave signal in a short time or in short-distance transmission due to multipath factors, and the signal amplitude is generally subjected to rayleigh distribution. Major characteristics of small scale fading include multipath, fading, doppler shift, etc.
The invention provides a micro-grid-connected operation control method provided by the invention, referring to fig. 1, comprising the following steps:
step S1, a short-wave hidden communication model is built based on short-wave communication transmission characteristics, and detection error probability of an eavesdropper and hidden communication judgment rules are deduced and determined;
s2, calculating the transmitting power constraint corresponding to the hidden communication based on the detection error probability and the hidden communication judging rule;
and step S3, establishing an optimization model with the maximum hidden transmission rate as an optimization target under the condition that the transmitting power of the transmitting party meets the constraint, solving the optimization model to obtain the optimal transmitting power, and carrying out communication work according to the optimal transmitting power.
The working principle and beneficial effects of the technical scheme are as follows: the establishment of a short-wave hidden communication model is realized, the detection error probability of an eavesdropper and a hidden communication judgment rule are deduced according to the short-wave hidden communication model, and the emission power constraint corresponding to the hidden communication is calculated according to the detection error probability and the hidden communication judgment rule; and finally, establishing an optimization model with the maximum hidden transmission rate as an optimization target under the condition that the transmitting power meets the constraint, solving the optimization model to obtain the optimal transmitting power, and carrying out communication work according to the optimal transmitting power. The invention realizes the purpose of short-wave hidden communication by controlling the signal transmitting power, and maximizes the communication efficiency while considering the hidden, thereby realizing the short-wave communication with double consideration of the communication efficiency and the hidden capability.
Specifically, referring to fig. 2, step S1 includes:
establishing a communication structure consisting of a legal signal sender, a legal signal receiver and an eavesdropper;
the communication structure comprises a legal sender Alice, a legal receiver Bob and an eavesdropper Willie, wherein Alice tries to send information to Bob through a pre-shared secret key, bob can decrypt a received message sequence according to the secret key shared with Alice in advance, willie is different from Bob, he needs to judge whether communication behaviors occur between Alice and Bob or not through observing the obtained signal sequence, namely, judges whether the received transmission information is noise or noise-included transmission information through an observed value, and considers the large-scale fading, small-scale fading and additive Gaussian white noise setting experienced by signals in short-wave communicationAnd->Path loss between the short wave communication signal from the sender to the receiver and the sender to the eavesdropper, respectively;
setting upAnd->Respectively small scale parameters of short wave communication signals from a sender to a receiver and from the sender to an eavesdropper;
for the actual receiver of the signalWherein b represents the recipient, < >>Representing an eavesdropper, determining the signal it receives as +.>And satisfies the following:
in the method, in the process of the invention,for the signal sent by the sender, < > and->Representing additive white gaussian noise +.>Sequence number indicating number of channel use, +.>Expressed as the transmit power of the signal;
the signals received by the eavesdropper are determined as follows:
wherein,for the null hypothesis in the binary check, i.e. the sender actually has no transmission signal, +.>For the alternative assumption that the sender actually takes place the transmission signal behaviour;
the eavesdropper is determined to perform binary judgment based on the received signal, and the detection error probability of the received signal after the eavesdropper performs binary judgment is determinedWherein the false alarm probability->Probability of missing detection，/>Indicating that the eavesdropper decides that the sender did not send information, < >>Indicating that the sender sends information;
setting when meetingDetermining the communication as a covert communication, wherein +.>To conceal the constraint, the smaller the concealing constraint, the more concealed the communication.
The beneficial effects of the technical scheme are as follows: the method realizes the construction of a short-wave hidden communication model based on the transmission characteristics of the short-wave communication, and deduces and determines the detection error probability of an eavesdropper and the judgment rule of hidden communication.
Specifically, referring to fig. 3, the specific flow of deriving the transmit power constraint in step S2 is shown in fig. 2, the detection error probability is firstly converted into a more convenient relative entropy of the expression, then the relative entropy is scaled to obtain the signal-to-noise ratio constraint, diversity reception is performed on the signal under the condition of multi-reception and multi-interception by assuming that the maximum ratio combination is used to obtain the signal-to-noise ratio expression of the received signal, the transmit power constraint of the sender is obtained according to the signal-to-noise ratio constraint, and finally the maximum transmission rate under the condition of meeting the constraint is obtained by solving the problem of anxiety, and the sender can ensure the concealment of communication by enabling the transmit power to meet the constraint. The specific flow of step S2 is described as follows:
assuming that an eavesdropper is to minimize the probability of detection errorsWith optimal detection, under this assumption:
according to the Pinmaker inequality, the total variation distance is converted into relative entropy constraint for analysis, namely:
wherein the method comprises the steps ofAnd->Respectively represent->And->Probability distribution of the observation of an eavesdropper in the case, +.>Is thatAnd->The total variation distance between them, thus determining when the concealment constraint satisfies:
when the communication is in use, the concealment of the communication can be ensured, wherein:
calculating the signal-to-noise ratio of the eavesdropper according to the relative entropy constraint and the hidden constraint conditionConstraint:
due to the influence of multipath and Doppler effect in short wave communication, serious fading phenomenon exists in a channel, so that the amplitude of a signal severely fluctuates, and the anti-fading performance of a receiver needs to be improved. By increasing the number of receiving nodes, the receiving side combines a plurality of signals by the same signal from a plurality of independent fading paths by using a diversity combining method, and the quality of the received signal is improved. There is a need to extend research into the scenario of multiple legitimate recipients and multiple listeners.
The maximum ratio combining is a common diversity combining technology, and different weight values are given to different branches through the signal-to-noise ratio of the signals of the different branches and summed, so that the maximum signal-to-noise ratio of the signals output after combining is ensured. In practice, the maximum ratio combining requires the receiver to better grasp the channel state information, so as to estimate the signal to noise ratio of each branch, which is a common fading channel combining technology.
Setting in the scene of multiple eavesdropping nodes, the eavesdropper carries out maximum score aggregation on the branch signals received by each node and then judges the communication condition in the channel, if the total signal-to-noise ratio is the sum of the signal-to-noise ratios of each branch, then the eavesdropper carries out signal-to-noise ratio under the conditionThe expression is:
wherein,receiving the number of nodes for an eavesdropper, < >>Is->An eavesdropper node;
obtaining a constraint of the transmitting power X according to the signal-to-noise ratio expression and the signal-to-noise ratio constraint:
in the case where the transmission power X satisfies this constraint, it is determined that the covert communication can be achieved.
As can be seen from the transmit power constraint expression, the transmit power constraint at Alice is related to the number of listening nodes and the number of channel uses of the listener, and is independent of the number of receiving nodes of the legitimate receiver Bob. And the sender adjusts the power to meet the constraint, so that the hidden communication can be realized.
The beneficial effects of the technical scheme are as follows: based on the detection error probability and the hidden communication judgment rule, the transmission power constraint corresponding to the hidden communication is calculated.
The specific step S3 includes:
setting the receiver to combine the signals by using maximum ratio diversity combining and determining the signal-to-noise ratio of the signals received by the receiver：
Wherein,for the number of receiving nodes of the receiver, < > and->Is the j-th receiver node;
determining an expression of the hidden communication rate under the condition of a limited code length:
in the method, in the process of the invention,indicating the rate of covert communication->For the decoding error probability at the receiver, +.>Is +.>Function (F)>Signal to noise ratio at the receiver;
deriving the corresponding optimization problem of the concealment rate according to the derivation：
Determining whenWhen (I)>Maximum value is obtained and the transmission power at this time is +.>The presence is:
and calculating an optimal solution of the transmitting power according to the formula, taking the optimal solution as the optimal transmitting power, and carrying out communication work according to the optimal transmitting power.
The beneficial effects of the technical scheme are as follows: an optimization model with the maximum hidden transmission rate as an optimization target is established under the condition that the transmitting power meets the constraint, the optimization model is solved to obtain the optimal transmitting power, communication work is carried out according to the optimal transmitting power, a solving result of an optimal transmitting power problem corresponding to the maximum transmission rate under the condition that the hidden communication is ensured is obtained through the embodiment, and finally, the parallel of the hidden performance and the high efficiency of the short wave communication is realized.
In a specific embodiment, the simulation is performed based on the above technical scheme, and the simulation process is as follows:
setting simulation condition values:
concealed restraint：0.1
Probability of error：0.001
Channel usage number：800
Noise power：-110dbm
Number of receivers：20
Sender location: (116.4E, 39.9N)
Receiver position: (118.8E, 32.0N) and (117.3E, 39.7N)
Listener position: (141.4E, 40.7N) and (131.0E, 32.9N)
Modulation mode: 8PSK (phase shift keying)
Channel environment: medium latitude and mid-range environment
The simulation results obtained are as follows:
as can be seen from fig. 4, in the preset short wave covert communication scenario, the transmitting power constraint of the transmitting side can reach 300W, because the path loss of the short wave in the main channel and the eavesdropping channel is greatly different when the short wave propagates in the sky wave, so that the transmitting power constraint can reach hundreds of watts. Meanwhile, the concealment rate becomes larger as the transmission power increases, and as the number of receiving nodes increases, the concealment rate becomes larger. This is because when maximum ratio combining is used, the total signal-to-noise ratio at the receiving site is the sum of the signal-to-noise ratios of the respective branches, and when the number of receiving nodes becomes large, the number of branches increases, and the total signal-to-noise ratio increases, so that the concealment rate also becomes large. And when the transmitting power increases, the signal-to-noise ratio at the receiving position also increases, so that the concealment rate becomes continuously larger.
As can be seen from the results in fig. 5, when the channel is used a number of timesAs this increases, the rate of concealment decreases. This is because when the number of channel uses +.>Increasing the transmit power constraint decreases, resulting in a decrease in the signal-to-noise ratio at the receiver, which ultimately affects the rate of concealment. When the number of receiving nodes +.>Increasing the signal-to-noise ratio at the receiver increases, resulting in an increase in the concealment rate.
Under the condition that the power constraint is satisfied, the error rate of the legal receiver is measured from fig. 6, and the receiving performance of the covert communication is verified. It can be seen that the bit error rate of the receiver gradually increases as the transmit power increases, since an increase in transmit power increases the signal-to-noise ratio at the receiver, which decreases the bit error rate. In addition, it can be seen that the bit error rate can be reduced toThe following is given.
As can be seen from fig. 7, as the concealment constraint increases gradually, the constraint of the transmit power also increases gradually, resulting in an increase in the signal-to-noise ratio at the receiver, resulting in an increase in the concealment rate; and when the error probability becomes smaller, the Q function increases, resulting in a smaller concealment rate.
FIG. 8 shows the probability of detection errors of listeners in listening to communications between legitimate parties, it can be seen that the probability of detection errors of listeners decreases gradually when the transmit power increases gradually, but is still greater when the transmit power satisfies the constraint。
In conclusion, the short-wave hidden communication is realized by controlling the transmitting power of the transmitting party, and the method has important significance in strong safety scenes such as military command and the like. Compared with the previous research, the method and the device for realizing the short-wave communication based on the short-wave communication model are used in the military field, a short-wave communication model is built according to the transmission characteristics, and the characteristics of one-shot and multi-shot of the short-wave communication, the fact that the omni-directional transmission is easier to monitor and the like are combined, and the hidden transmission is realized by controlling the transmitting power of a transmitting party under the multi-shot and multi-eavesdropping scene, so that the method and the device can be applied to the military short-wave hidden communication.
Finally, it is noted that the above-mentioned preferred embodiments are only intended to illustrate rather than limit the invention, and that, although the invention has been described in detail by means of the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (1)
1. The short wave covert communication method based on power control is characterized by comprising the following steps of:
step S1, a short-wave hidden communication model is built based on short-wave communication transmission characteristics, and detection error probability of an eavesdropper and hidden communication judgment rules are deduced and determined;
s2, calculating the transmitting power constraint corresponding to the hidden communication based on the detection error probability and the hidden communication judging rule;
step S3, an optimization model with the maximum hidden transmission rate as an optimization target is established under the condition that the transmitting power meets the constraint, the optimization model is solved to obtain the optimal transmitting power, and communication work is carried out according to the optimal transmitting power;
the step S1 includes:
establishing a communication structure consisting of a legal signal sender, a legal signal receiver and an eavesdropper;
setting upAnd->Path loss between the short wave communication signal from the sender to the receiver and the sender to the eavesdropper, respectively;
setting upAnd->Respectively small scale parameters of short wave communication signals from a sender to a receiver and from the sender to an eavesdropper;
for the actual receiver of the signalWherein b represents the recipient, < >>Representing an eavesdropper, determining the signal it receives as +.>And satisfies the following:
in the method, in the process of the invention,for the signal sent by the sender, < > and->Representing an additive gaussian white noise and,sequence number indicating number of channel use, +.>Expressed as the transmit power of the signal;
the signals received by the eavesdropper are determined as follows:
wherein,for the null hypothesis in the binary check, i.e. the sender actually has no transmission signal, +.>For the alternative assumption that the sender actually takes place the transmission signal behaviour;
the eavesdropper is determined to perform binary judgment based on the received signal, and the detection error probability of the received signal after the eavesdropper performs binary judgment is determinedWherein the false alarm probability->Probability of missing detection，/>Indicating that the eavesdropper decides that the sender did not send information, < >>Indicating judgment transmissionThe party sent the information;
setting when meetingDetermining the communication as a covert communication, wherein +.>For concealment constraints, the smaller the concealment constraints are, the higher the communication concealment is;
the step S2 includes:
assuming that an eavesdropper is to minimize the probability of detection errorsWith optimal detection, under this assumption:
according to the Pinmaker inequality, the total variation distance is converted into relative entropy constraint for analysis, namely:
wherein the method comprises the steps ofAnd->Respectively represent->And->Probability distribution of the observation of an eavesdropper in the case, +.>Is->Andthe total variation distance between them, thus determining when the concealment constraint satisfies:
when the communication is in use, the concealment of the communication can be ensured, wherein:
calculating the signal-to-noise ratio of the eavesdropper according to the relative entropy constraint and the hidden constraint conditionConstraint:
setting in the scene of multiple eavesdropping nodes, the eavesdropper carries out maximum score aggregation on the branch signals received by each node and then judges the communication condition in the channel, if the total signal-to-noise ratio is the sum of the signal-to-noise ratios of each branch, then the eavesdropper carries out signal-to-noise ratio under the conditionThe expression is:
wherein,receiving the number of nodes for an eavesdropper, < >>Is->An eavesdropper node;
obtaining a constraint of the transmitting power X according to the signal-to-noise ratio expression and the signal-to-noise ratio constraint:
in case the transmit power X satisfies this constraint, it is determined that covert communication can be achieved;
the step S3 includes:
setting the receiver to combine the signals by using maximum ratio diversity combining and determining the signal-to-noise ratio of the signals received by the receiver：
Wherein,for the number of receiving nodes of the receiver, < > and->Is the j-th receiver node;
determining an expression of the hidden communication rate under the condition of a limited code length:
in the method, in the process of the invention,indicating the rate of covert communication->For the decoding error probability at the receiver, +.>Is +.>Function (F)>Signal to noise ratio at the receiver;
deriving the corresponding optimization problem of the concealment rate according to the derivation：
Determining whenWhen (I)>Maximum value is obtained and the transmission power at this time is +.>The presence is:
and calculating an optimal solution of the transmitting power according to the formula, taking the optimal solution as the optimal transmitting power, and carrying out communication work according to the optimal transmitting power.
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| CN115915139A (en) * | 2022-10-28 | 2023-04-04 | 大连理工大学 | Intelligent reflector assisted unequal prior probability covert communication method |
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