CN114337774A - Safe transmission method for double-satellite communication system - Google Patents
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Abstract
The invention discloses a safe transmission method facing a double-satellite communication system in the technical field of wireless communication, which comprises the steps of obtaining perfect channel information of a legal user and imperfect channel information of an eavesdropper; establishing a safe transmission problem model with the beamforming weight vector as a variable; considering the uncertainty caused by imperfect eavesdropper channel information, introducing a safety interruption probability constraint condition; solving the safety transmission problem model according to the actual conditions of each satellite in the double-satellite communication system to obtain a beam forming weight vector; the user signals are subjected to space-time coding and then multiplied by the beamforming weight vectors obtained in the front, and are sent to the corresponding satellite and forwarded to the ground user through the satellite, so that the communication quality of a double-satellite communication system is ensured, and the safety and reliability of information transmission between a legal user and the satellite are improved.
Description
Technical Field
The invention belongs to the field of satellite communication, and particularly relates to a secure transmission method for a dual-satellite communication system.
Background
The satellite communication has the advantages of wide coverage range, no influence from regions, large communication capacity and the like, and has wide application prospects in the fields of remote area communication, navigation, disaster relief and the like. However, due to the inherent broadcast nature and wide area coverage of satellites, security concerns have received a great deal of attention.
The traditional upper-layer encryption method is premised on the fact that an eavesdropper has limited computing capacity and cannot decipher an encryption algorithm. However, with the development of quantum computing and the enhancement of computing power of eavesdroppers, the traditional key mechanism has difficulty in ensuring the safe transmission of signals. Unlike the terrestrial wireless communication system, in the satellite communication system, there are many cases of malicious eavesdropping, and it is generally difficult to obtain perfect channel state information of an eavesdropper. Therefore, a physical layer secure transmission method under the condition of imperfect eavesdropper channel information is a technical problem to be solved urgently in the field of satellite communication.
In addition, in a satellite communication system, signals received by terrestrial users exhibit fading characteristics due to the shadow effect and multipath scattering, thereby affecting the communication quality thereof, and how to improve the communication reliability is another technical problem in the satellite communication field.
Disclosure of Invention
The invention aims to provide a safe transmission method facing a double-satellite communication system, which ensures the communication quality of the double-satellite communication system and simultaneously improves the safety and reliability of information transmission between a legal user and a satellite.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention provides a secure transmission method for a double-satellite communication system, which comprises the following steps:
acquiring perfect channel information of a legal user and imperfect channel information of an eavesdropper;
the method comprises the steps of establishing a safe transmission problem model with a beam forming weight vector as a variable by adding a safe interruption probability constraint condition, a transmission rate constraint condition and a satellite maximum transmitting power constraint condition of information transmission between a legal user and a satellite with the maximum safe rate of a double-satellite communication system as a target;
considering the uncertainty caused by imperfect eavesdropper channel information, introducing a safety interruption probability constraint condition;
solving the safety transmission problem model according to the actual conditions of each satellite in the double-satellite communication system to obtain a beam forming weight vector; and carrying out space-time coding on the user signals, multiplying the space-time coding by the beamforming weight vector obtained in the front, sending the space-time coding to a corresponding satellite, and forwarding the space-time coding to the ground user through the satellite.
Preferably, the expression formula of the interruption probability constraint condition is as follows:
wherein h isiDenoted as satellite channel, wiExpressed as a beamforming weight vector, R is expressed as a system security rate threshold, pk,sop∈(0,1]Is the system outage probability threshold value and is,
expressed as the noise power of the signal received by the legitimate user,
representing the noise power of the signal received by the eavesdropper, (.)HDenoted as the conjugate transpose operator.
Preferably, the transmission rate constraint is expressed by the following formula:
wherein R isminA transmission rate threshold value indicative of a legitimate user,
preferably, the maximum transmit power constraint of the satellite is expressed by the following formula:
||wi||2≤Pi，max
wherein, Pi,maxRepresenting the ith satellite maximum transmit power threshold.
Preferably, considering the uncertainty caused by the imperfect information of the eavesdropper channel, introducing a safety interruption probability constraint condition; the process comprises the following steps:
the uncertainty model for the kth eavesdropper channel is expressed as:
wherein, gi,kFor channel state information between the ith satellite and the kth eavesdropper,
for estimating channel state information between the ith satellite and the kth eavesdropper, Δ gi,kFor the estimated error between the ith satellite and the kth eavesdropper, obey a mean of 0 and a variance of Ei,kComplex gaussian distribution of (a);
substituting the uncertain model of the eavesdropper channel into the interruption probability constraint condition and converting by using a Bernstein inequality to obtain:
s+(A)＝max{λmax(A)，0}
wherein Tr (·) is a trace of the matrix; vec (·) denotes matrix vectorization.
Preferably, the solving of the safety transmission problem model to obtain the beamforming weight vector includes:
converting the safety rate maximization problem into a transmission power minimization problem, and further converting the safety rate maximization problem into a convex optimization problem through a semi-positive definite relaxation method; solving the convex optimization problem to obtain a beam forming weight vector wi。
Preferably, the safety rate maximization problem is converted into the transmission power minimization problem, and further converted into the convex optimization problem by a semi-positive definite relaxation method, wherein the process comprises the following steps:
by introducing a relaxation variable mui,kAnd a relaxation variable λi,kA semi-positive planning problem can be obtained:
μi，kI-Ai，k≥0
rank(Wi)＝1，Wi≥0
wherein rank (·) represents the rank of the matrix, and I is the identity matrix.
Preferably, solving the convex optimization problem to obtain the beamforming weight vector wiThe process comprises the following steps:
solving through a semi-definite relaxation principle and a binary search method to obtain the beam forming matrix weight Wi opt；
Judgment of Wi optWhether the rank is 1; if the rank is 1, for Wi optResolving the eigenvalue to obtain a beamforming weight vector wi(ii) a Otherwise, solving the beam forming weight vector w by using a Gaussian randomization techniquei。
Compared with the prior art, the invention has the following beneficial effects:
(1) according to the actual situation of each satellite in a double-satellite communication system, solving a safe transmission problem model to obtain a beam forming weight vector; the user signals are subjected to space-time coding and then multiplied by the beamforming weight vectors obtained in the front, and the signals are sent to the corresponding satellite and forwarded to the ground user through the satellite, so that the safety and the reliability of information transmission between legal users and the satellite are improved.
(2) The method comprises the steps of establishing a safe transmission problem model with a beam forming weight vector as a variable by taking the maximum safe rate of a double-satellite communication system as a target and adding a satellite maximum transmitting power constraint condition, an interruption probability constraint condition and a transmission rate constraint condition for information transmission between a legal user and a satellite; the communication quality of the dual-satellite communication system is ensured through the safe transmission problem model.
(3) In the invention, uncertainty caused by imperfect eavesdropper channel information is introduced into an interruption probability constraint condition of information transmission between a legal user and a satellite; considering probability constraint under a non-conservative strategy, seeking the maximum safe reachable rate under the interruption probability constraint, namely seeking the maximum confidentiality rate; the burden of the system can be reduced on the premise of ensuring the safety of the double-satellite communication system.
Drawings
FIG. 1 is a schematic diagram of a satellite communication system in accordance with an embodiment of the present invention;
fig. 2 is a flowchart of a secure transmission method for a dual-satellite communication system according to the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in fig. 1-2, a secure transmission method for a dual-satellite communication system includes:
acquiring perfect channel information of a known legal user and imperfect channel information of an eavesdropper;
the method comprises the steps of adding a safety interruption probability constraint condition, a transmission rate constraint condition and a satellite maximum transmitting power constraint condition of information transmission between a legal user and a satellite to a maximum target of a safety rate of a double-satellite communication system, and establishing a safety transmission problem model with a beam forming weight vector as a variable;
the expression formula of the interruption probability constraint condition is as follows:
wherein h isiDenoted as satellite channel, wiExpressed as a beamforming weight vector, R is expressed as a system security rate threshold, pk,sop∈(0,1]Is the system outage probability threshold value and is,
expressed as the noise power of the signal received by the legitimate user,
representing the noise power of the received signal for the legitimate user, (.)HDenoted as the conjugate transpose operator.
The expression formula of the transmission rate constraint condition is as follows:
wherein R isminA transmission rate threshold value indicative of a legitimate user,
the expression formula of the constraint condition of the maximum transmitting power of the satellite is as follows:
||wi||2≤Pi，max
wherein, Pi,maxRepresenting the ith satellite maximum transmit power threshold.
Considering the uncertainty caused by imperfect eavesdropper channel information, introducing a safety interruption probability constraint condition; the process comprises the following steps:
the uncertainty model for the kth eavesdropper channel is expressed as:
wherein, gi,kFor channel state information between the ith satellite and the kth eavesdropper,
for estimating channel state information between the ith satellite and the kth eavesdropper, Δ gi,kFor the estimated error between the ith satellite and the kth eavesdropper, obey a mean of 0 and a variance of Ei,kComplex gaussian distribution of (a);
substituting the uncertain model of the eavesdropper channel into the interruption probability constraint condition and converting by using a Bernstein inequality to obtain:
s+(A)＝max{λmax(A)，0}
the probability constraint is reduced to:
wherein Tr (·) is a trace of the matrix; vec (·) denotes matrix vectorization. According to the actual situation of each satellite in the double-satellite communication system, solving the safety transmission problem model to obtain a beam forming weight vector, wherein the calculation process comprises the following steps:
converting the safety rate maximization problem into a transmission power minimization problem, and further converting the safety rate maximization problem into a convex optimization problem through a semi-positive definite relaxation method; solving the convex optimization problem to obtain a beam forming weight vector wi。
Converting the safe rate maximization problem into a transmission power minimization problem, and further converting the safe rate maximization problem into a convex optimization problem by a semi-positive definite relaxation method, wherein the process comprises the following steps:
by introducing a relaxation variable mui,kAnd a relaxation variable λi,kA semi-positive planning problem can be obtained:
μi，kI-Ai，k≥0
rank(Wi)＝1，Wi≥0
wherein rank (·) represents the rank of the matrix, and I is the identity matrix.
Solving through a semi-definite relaxation principle and a binary search method to obtain the beam forming matrix weight Wi opt(ii) a Judgment of Wi optWhether the rank is 1; if the rank is 1, for Wi optResolving the eigenvalue to obtain a beamforming weight vector wi(ii) a Otherwise, solving the beam forming weight vector w by using a Gaussian randomization techniquei。
The user signals are subjected to space-time coding and then multiplied by the beamforming weight vectors obtained in the front, and are sent to respective satellites through high-capacity feeder links, and the satellites transmit the signals to ground legal users after adopting a satellite-borne beamforming technology, so that the whole information transmission process is completed.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (8)
1. A secure transmission method for a dual-satellite communication system, comprising:
acquiring perfect channel information of a known legal user and imperfect channel information of an eavesdropper;
the method comprises the steps of establishing a safe transmission problem model with a beam forming weight vector as a variable by adding a safe interruption probability constraint condition, a transmission rate constraint condition and a satellite maximum transmitting power constraint condition of information transmission between a legal user and a satellite with the maximum safe rate of a double-satellite communication system as a target;
considering the uncertainty caused by imperfect eavesdropper channel information, introducing a safety interruption probability constraint condition;
solving the safety transmission problem model according to the actual conditions of each satellite in the double-satellite communication system to obtain a beam forming weight vector; and carrying out space-time coding on the user signals, multiplying the space-time coding by the beamforming weight vector obtained in the front, sending the space-time coding to a corresponding satellite, and forwarding the space-time coding to the ground user through the satellite.
2. The method of claim 1, wherein the safety outage probability constraint is expressed by the following formula:
wherein h isiExpressed as a satellite downlink channel vector, wiExpressed as a beamforming weight vector, R is expressed as a system security rate threshold, pk，sop∈(0，1]Is the system outage probability threshold value and is,
expressed as the noise power of the signal received by the legitimate user,
representing the noise power of the signal received by the eavesdropper, (.)HDenoted as the conjugate transpose operator.
3. The method of claim 2, wherein the transmission rate constraint is expressed by the following formula:
wherein R isminIndicating a transmission rate threshold for legitimate users.
4. A method for secure transmission in a dual-satellite oriented communication system according to claim 3, wherein the maximum transmit power constraint is expressed by the following formula:
||wi||2≤Pi，max
wherein, Pi，maxRepresenting the ith satellite maximum transmit power threshold.
5. The secure transmission method for the dual-satellite communication system according to claim 4, wherein a security outage probability constraint is introduced in consideration of uncertainty caused by imperfect eavesdropper channel information; the process comprises the following steps:
the uncertainty model for the kth eavesdropper channel is expressed as:
wherein, gi，kChannel state information between the ith satellite and the kth eavesdropper;
estimating channel state information for the ith satellite and the kth eavesdropper; Δ gi，kFor the estimated error between the ith satellite and the kth eavesdropper, obey a mean of 0 and a variance of Ei，kComplex gaussian distribution of (a);
substituting the uncertain model of the eavesdropper channel into the interruption probability constraint condition, and then converting by using a Bernstein inequality to obtain:
s+(A)＝max{λmax(A)，0}
wherein Tr (·) is a trace of the matrix; vec (·) denotes matrix vectorization.
6. The method of claim 1, wherein the solving of the security transmission problem model to obtain the beamforming weight vector comprises:
converting the safety rate maximization problem into a transmission power minimization problem, and further converting the safety rate maximization problem into a convex optimization problem through a semi-positive definite relaxation method; solving the convex optimization problem to obtain a beam forming weight vector wi。
7. The method of claim 6, wherein the safety rate maximization problem is transformed into a transmit power minimization problem, which is further transformed into a convex optimization problem by a semi-positive relaxation method, and the process comprises:
by introducing a relaxation variable mui，kAnd relaxationVariable lambdai，kA semi-positive planning problem can be obtained:
s.t.
wherein rank (·) represents the rank of the matrix, and I is the identity matrix.
8. The method of claim 7, wherein the convex optimization problem is solved to obtain a beamforming weight vector wiThe process comprises the following steps:
solving through a semi-definite relaxation principle and a binary search method to obtain a beam forming matrix
Judgment of
Whether the rank is 1; if the rank is 1, for
Resolving the eigenvalue to obtain a beamforming weight vector wi(ii) a Otherwise, solving the beam forming weight vector w by using a Gaussian randomization techniquei。
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