CN115412195B - Generalized multi-fraction Fourier transform multi-component secure transmission method based on imperfect channel state information - Google Patents
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Abstract
A generalized multi-fraction Fourier transform multi-component secure transmission method based on imperfect channel state information belongs to the technical field of wireless communication. The invention solves the problem of low reachable safety rate of a physical layer safety transmission scheme designed based on imperfect channel state information in a wireless communication network with a passive eavesdropper. The invention introduces the signal domain as an extra dimension into the design of a physical layer safe transmission scheme under the condition of imperfect channel state information, and a transmitting end codes data across a plurality of transmitting antennas based on GMFRFT, so that a single-antenna legal receiving end receives signals which are naturally overlapped into a GMFRFT form, and the receiving signals are subjected to data recovery through corresponding transformation. Equivalent artificial noise is generated by utilizing the mismatch of the parameters of the main channel and the eavesdropping channel, and even if an eavesdropper is provided with a plurality of receiving antennas and adopts the same signal processing method as that of a legal receiving end, the data cannot be recovered. The method of the invention can be applied to the technical field of wireless communication.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a generalized multi-fraction Fourier transform (GMFRFT) multi-component secure transmission method based on imperfect channel state information.
Background
In recent years, the rapid development of wireless communication technology brings great convenience to the production and life of human beings, and the consequent information security problem is also widely focused. Traditional wireless communication security is generally realized based on cryptography theory, and information security is ensured through calculation complexity. However, due to the rapid increase of computer power in recent years and the requirement of secure communication in the scenes of multi-user dense access, internet of things and the like, the conventional encryption method faces serious challenges.
Unlike traditional cryptography encryption method, physical layer security technology uses the characteristics of randomness of wireless channel, etc. to ensure the secure transmission of information from the communication bottom layer. In a multi-antenna communication system, the physical layer safety transmission is ensured mainly by relying on spatial freedom, and the method mainly comprises two types of safety beam forming technology and artificial noise technology. The secure beamforming technology needs to simultaneously utilize channel state information of a main channel and a eavesdropping channel to perform precoding design, and when a passive eavesdropper exists in a communication network, the channel state information of the eavesdropping channel is generally difficult to acquire, so that the algorithm is difficult to practically apply; the artificial noise technology only needs the channel state information of the main channel to perform precoding design and can actively reduce the capacity of the eavesdropping channel. However, in a practical application scenario, it is often difficult to obtain perfect channel state information. Studies have shown that when the channel state information acquired by the transmitting end is imperfect, the artificial noise technology will generate serious artificial noise leakage, which results in a decrease in the system safety capacity and also reduces the achievable safety rate of the transmission scheme. This effect is more pronounced especially in the case of eavesdroppers with antennas whose number is close to that of the transmitting end.
Disclosure of Invention
The invention aims to solve the problem of low reachable safety rate of a physical layer safety transmission scheme designed based on imperfect channel state information in a wireless communication network with passive eavesdroppers, and provides a generalized multi-fraction Fourier transform multi-component safety transmission method based on imperfect channel state information.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a generalized multi-fraction Fourier transform multi-component secure transmission method based on imperfect channel state information specifically comprises the following steps:
the signal processing method of the transmitting end comprises the following steps:
step A1: after digital baseband mapping is carried out on 0 and 1 bit data generated by an information source, the obtained modulation result is marked as a sequence x;
step A2: after the generalized multi-fraction Fourier transform is carried out on the sequence x, the baseband signals to be transmitted of each antenna are respectively obtained, wherein the baseband signals to be transmitted of the first antenna are expressed as p l L=0, 1,2,., M-1, M is the number of antennas at the transmitting end;
the specific process of the step A2 is as follows:
step A21: respectively carrying out weighted fractional Fourier transform with the transformation order of 4l/M on the sequence x, and correspondingly respectively obtaining a transformed sequence s l ，l＝0,1,2,...,M-1；
Wherein F is a normalized discrete Fourier transform matrix, F i Represents i times F, omega i (4 l/M) is the i-th weighting coefficient corresponding to the weighted fractional fourier transform with a transform order of 4l/M, i=0, 1,2,3;
where j is an imaginary unit, k=0, 1,2,3;
step A22: for the sequence s obtained in step A21 l Designing to obtain a baseband signal p to be transmitted by the first antenna l ；
Where beta is the power normalization factor of the transmitter,for the channel state information between the first transmitting antenna and the legal receiving end single antenna obtained by channel estimation,/or->Is->Conjugate of B l (α M ) For the sequence s l Corresponding weighting coefficients;
wherein alpha is M To transform parameters, alpha M The value range of (2) is [0, M);
step A3: the baseband signal p to be transmitted by the first antenna obtained in the step A2 l The baseband signal p is obtained by a digital-to-analog converter l Corresponding analog signal p l '，l＝0,1,2,...,M-1；
Step A4: for the analog signal p obtained in step A3 l ' up-conversion processing is carried out to obtain a signal p after up-conversion processing l ", p is again l "map to the first antenna of the transmitter for transmission, l=0, 1,2, M-1;
the signal processing method of the legal receiving end comprises the following steps:
step B1: the legal receiver receives the signal transmitted in the step A4 after passing through the channel by utilizing a single antenna, and performs down-conversion processing on the received signal to obtain a signal y after the down-conversion processing 1 ；
Step B2: the legal receiver processes the down-converted signal y obtained in the step B1 1 Obtaining a signal sequence y' by an analog/digital converter;
step B3: b2, processing the signal sequence y 'obtained in the step B2 by a legal receiver, and recovering a useful signal y from the received signal y';
step B4: and B, the legal receiver demaps the signal y obtained in the step B3 to recover 0 and 1 bit data.
Further, the normalized discrete fourier transform matrix F is:
wherein [ F] m,n N is the length of the sequence x, which is the element of row N in the matrix F.
Further, the saidAnd the actual channel h l The relationship between them is expressed as:
wherein ρ ε [0,1 ] represents the error coefficient, e l Error representing imperfect channel, andare independently distributed in the same way.
Further, the power normalization factor β of the transmitter is:
wherein, l=0, 1,2,..m-1.
Further, the signal sequence y' is:
wherein n is b ' is additive white gaussian noise in the received signal of a legitimate receiver.
Further, the legal receiver processes the signal sequence y' obtained in the step B2, which specifically includes:
wherein,is of conversion order-4α M Weighted fractional Fourier transform matrix of/M, n b Is n b ' transformed order-4α M The result of the weighted fractional fourier transform of/M;
further, the signal to interference plus noise ratio gamma of the useful signal y B The method comprises the following steps:
wherein P is 0 For the total power of the transmitter,is the variance of the gaussian white noise received by a legitimate receiver.
The beneficial effects of the invention are as follows:
the invention introduces the signal domain as an extra dimension into the design of a physical layer safe transmission scheme under the condition of imperfect channel state information, and the transmitting end codes data across a plurality of transmitting antennas based on GMFRFT, so that a single-antenna legal receiving end receives signals which are naturally overlapped into a GMFRFT form, and the receiving signals can be subjected to data recovery through corresponding transformation. The quality of the signal received by the eavesdropper is reduced by generating equivalent artificial noise by utilizing the mismatch of the parameters of the main channel and the eavesdropper, and the recovery of the data cannot be realized even if the eavesdropper is provided with a plurality of receiving antennas and adopts the same signal processing method as that of a legal receiving end. The invention can ensure the safe transmission of information no matter the transformation parameters adopted by the transmitting end are unknown or known by the eavesdropping end, and compared with the problem that the traditional artificial noise scheme has artificial noise leakage when the available channel state information is imperfect, the method can improve the reachable safe rate of the system because no additional transmitting power is required to be distributed to artificial noise.
Drawings
Fig. 1 is a schematic diagram of a generalized multi-fractional fourier transform multi-component secure transmission method based on imperfect channel state information according to the present invention;
FIG. 2 is an overall workflow diagram of the method of the present invention;
FIG. 3 is a flow chart of a signal domain GMFRFT signal decomposition module implementation;
FIG. 4 is a flow chart of a spatial domain multi-component design module implementation;
FIG. 5 is a flow chart of an implementation of a legal receiver digital baseband signal processing module;
FIG. 6 is a graph of the safe rate achievable by the system with signal to noise ratio under imperfect channel state information conditions, with both GMFRFT conversion orders known and unknown to an eavesdropper;
in the figure, N t Indicating the number of antennas at the transmitting end, N e Indicating the number of antennas of the eavesdropper.
Detailed Description
The first embodiment is as follows: this embodiment will be described with reference to fig. 1 and 2. The generalized multi-fraction Fourier transform multi-component secure transmission method based on imperfect channel state information in the embodiment specifically comprises the following steps:
the signal processing method of the transmitting end comprises the following steps:
step A1: after digital baseband mapping is carried out on 0 and 1 bit data generated by an information source, the obtained modulation result is marked as a sequence x;
step A2: after the generalized multi-fraction Fourier transform is carried out on the sequence x, the baseband signals to be transmitted of each antenna are respectively obtained, wherein the baseband signals to be transmitted of the first antenna are expressed as p l L=0, 1,2,., M-1, M is the number of antennas at the transmitting end;
the specific process of the step A2 is as follows:
step A21: the sequences x are respectively subjected to weighted fractional Fourier transform (Weighted type fractional Fourier transform, WFRFT) with the transformation order of 4l/M, and corresponding sequences s after transformation are respectively obtained l ，l＝0,1,2,...,M-1；
Wherein F is a normalized discrete Fourier transform matrix, F i Represents i times F, omega i (4 l/M) is the i-th weighting coefficient corresponding to the weighted fractional fourier transform with a transform order of 4l/M, i=0, 1,2,3;
where j is an imaginary unit, k=0, 1,2,3;
step A22: based on the imperfect channel state information, the sequence s obtained in the step A21 is l Designing to obtain a baseband signal p to be transmitted by the first antenna l ；
Where beta is the power normalization factor of the transmitter,for the channel state information between the first transmitting antenna and the legal receiving end single antenna obtained by channel estimation,/or->Is->Conjugate of B l (α M ) For the sequence s l Corresponding weighting coefficients;
wherein alpha is M To transform parameters, alpha M The value range of (1) is [0, M ], and can be adjusted according to different requirements;
step A3: the baseband signal p to be transmitted by the first antenna obtained in the step A2 l The baseband signal p is obtained by a digital-to-analog converter l Corresponding analog signal p l '，l＝0,1,2,...,M-1；
Step A4: for the analog signal p obtained in step A3 l ' up-conversion processing is carried out to obtain a signal p after up-conversion processing l ", p is again l "map to the first antenna of the transmitter for transmission, l=0, 1,2, M-1;
the signal processing method of the legal receiving end comprises the following steps:
step B1: the legal receiver receives the signal transmitted in the step A4 after passing through the channel by utilizing a single antenna, and performs down-conversion processing on the received signal to obtain a signal y after the down-conversion processing 1 ；
Step B2: the legal receiver processes the down-converted signal y obtained in the step B1 1 Obtaining a signal sequence y' by an analog/digital converter;
step B3: b2, processing the signal sequence y 'obtained in the step B2 by a legal receiver, and recovering a useful signal y from the received signal y';
step B4: and B, the legal receiver demaps the signal y obtained in the step B3 to recover 0 and 1 bit data.
Step a21 in this embodiment is implemented by a signal domain GMFRFT signal decomposition module, and the implementation flow is shown in fig. 3. Step a22 in this embodiment is implemented by using a spatial domain multi-component design module, and the implementation flow is shown in fig. 4. Step B3 in the present embodiment is implemented by using a legal receiving-end digital baseband signal processing module, and the implementation flow is shown in FIG. 5.
The second embodiment is different from the first embodiment in that: the normalized discrete fourier transform matrix F is:
wherein [ F] m,n N is the length of the sequence x, which is the element of row N in the matrix F.
Other steps and parameters are the same as in the first embodiment.
The third embodiment is different from the first or second embodiment in that: the saidAnd the actual channel h l The relationship between them is expressed as:
wherein ρ ε [0,1 ] represents the error coefficient, e l Error representing imperfect channel, andare independently distributed in the same way.
Taking into account the existence of channel time variability and estimation errors in the actual communication sceneAnd the actual channel h l The relation between is expressed as the form of the present embodiment, and in particular, ρ=0 means that no relation with h is obtained l Related useful channel state information.
Other steps and parameters are the same as in the first or second embodiment.
The fourth embodiment is different from one of the first to third embodiments in that: the power normalization factor beta of the transmitter is as follows:
wherein, l=0, 1,2,..m-1.
Other steps and parameters are the same as in one to three embodiments.
The fifth embodiment is different from one to four embodiments in that: the signal sequence y' is:
wherein n is b ' is additive white gaussian noise in the received signal of a legitimate receiver.
Other steps and parameters are the same as in one to four embodiments.
The sixth embodiment is different from one of the first to fifth embodiments in that: the legal receiver processes the signal sequence y' obtained in the step B2, and the specific process is as follows:
wherein,is of conversion order-4α M Weighted fractional fourier transform matrix of/M (equivalent to-alpha M GMFRFT of order, i.e. alpha M Inverse transform corresponding to order GMFRFT), n b Is n b ' transformed order-4α M The result of the weighted fractional fourier transform of/M;
other steps and parameters are the same as in one of the first to fifth embodiments.
The seventh embodiment is different from one of the first to sixth embodiments in that: the signal to interference plus noise ratio gamma of the useful signal y B The method comprises the following steps:
wherein P is 0 The total power of the transmitter is a constant greater than 0;is the variance of the gaussian white noise received by a legitimate receiver.
Other steps and parameters are the same as in one of the first to sixth embodiments.
To illustrate the effect of the present invention in achieving physical layer security transmission of a communication system, assuming that an eavesdropper has the same receiver architecture as a legitimate receiver, the transformation parameters α employed in step A2 when the eavesdropper is unknown and known to the transmitting end, respectively, are analyzed M And when the communication system is in a safe state.
(1) Transformation parameter alpha adopted by eavesdropper unknown transmitting end M
At this point, the maximum signal-to-interference-and-noise ratio that the eavesdropper can obtainCan be expressed as:
wherein: g l,ns For the first antenna of the transmitting end and the nth antenna of the eavesdropper s Channel gain coefficients between the root antennas; n is n s For eavesdroppers to obtain maximum signal-to-interference-and-noise ratioSelected receiving antenna, +.>The variance of the gaussian white noise received for an eavesdropper.
n s Specifically, the method can be expressed as:
ω 0 (4 l/M) is a coefficient related to l and M, ω 0 (4 l/M) can be expressed specifically as:
under such conditions, the achievable safe rate of the communication system employing the present invention is based on the relevant definition of safe capacity in the information theoryThe method comprises the following steps:
wherein: [] + ＝max(·,0)。
(2) The eavesdropper knows the transformation parameter alpha adopted by the transmitting end M
At this point, the maximum signal-to-interference-and-noise ratio that the eavesdropper can obtainCan be expressed as:
wherein:for the first antenna of the transmitting end and the nth antenna of the eavesdropper s The gain coefficient of the channel between the root antennas, theta is the WFRFT conversion order adopted by an eavesdropper, and the value range of theta is [0,4 ], -the ratio of the gain coefficient to the value of the channel is->The variance of the gaussian white noise received for an eavesdropper.
n s As an eavesdropperObtaining maximum signal-to-interference-and-noise ratioSelected receiving antennas, n s Specifically, the method can be expressed as:
ω 0 (4 l/M-theta) is a coefficient related to l, M, theta, omega 0 (4 l/M- θ) can be expressed specifically as:
under such conditions, the achievable safe rate of the communication system employing the present invention is based on the relevant definition of safe capacity in the information theoryThe method comprises the following steps:
wherein: [] + ＝max(·,0)。
When the channel error coefficient ρ=0.95 (i.e. under imperfect channel state information conditions), the achievable safe rate of the system is plotted as a function of the signal-to-noise ratio for both known and unknown transformation parameters for an eavesdropper as shown in fig. 6.
The above examples of the present invention are only for describing the calculation model and calculation flow of the present invention in detail, and are not limiting of the embodiments of the present invention. Other variations and modifications of the above description will be apparent to those of ordinary skill in the art, and it is not intended to be exhaustive of all embodiments, all of which are within the scope of the invention.
Claims (6)
1. A generalized multi-fraction Fourier transform multi-component secure transmission method based on imperfect channel state information is characterized in that the method specifically comprises the following steps:
the signal processing method of the transmitting end comprises the following steps:
step A1: after digital baseband mapping is carried out on 0 and 1 bit data generated by an information source, the obtained modulation result is marked as a sequence x;
step A2: after the generalized multi-fraction Fourier transform is carried out on the sequence x, the baseband signals to be transmitted of each antenna are respectively obtained, wherein the baseband signals to be transmitted of the first antenna are expressed as p l L=0, 1,2,., M-1, M is the number of antennas at the transmitting end;
the specific process of the step A2 is as follows:
step A21: respectively carrying out weighted fractional Fourier transform with the transformation order of 4l/M on the sequence x, and correspondingly respectively obtaining a transformed sequence s l ，l＝0,1,2,...,M-1；
Wherein F is a normalized discrete Fourier transform matrix, F i Represents i times F, omega i (4 l/M) is the i-th weighting coefficient corresponding to the weighted fractional fourier transform with a transform order of 4l/M, i=0, 1,2,3;
where j is an imaginary unit, k=0, 1,2,3;
the normalized discrete fourier transform matrix F is:
wherein [ F] m,n For row m and column n in matrix FElement N is the length of sequence x;
step A22: for the sequence s obtained in step A21 l Designing to obtain a baseband signal p to be transmitted by the first antenna l ；
Where beta is the power normalization factor of the transmitter,for the channel state information between the first transmitting antenna and the legal receiving end single antenna obtained by channel estimation,/or->Is->Conjugate of B l (α M ) For the sequence s l Corresponding weighting coefficients;
wherein alpha is M To transform parameters, alpha M The value range of (2) is [0, M);
step A3: the baseband signal p to be transmitted by the first antenna obtained in the step A2 l The baseband signal p is obtained by a digital-to-analog converter l Corresponding analog signal p l '，l＝0,1,2,...,M-1；
Step A4: for the analog signal p obtained in step A3 l ' up-conversion processing is carried out to obtain a signal p after up-conversion processing l ", p is again l "map to the first antenna of the transmitter for transmission, l=0, 1,2, M-1;
the signal processing method of the legal receiving end comprises the following steps:
step B1: the legal receiver receives the signal transmitted in the step A4 after passing through the channel by utilizing a single antenna, and performs down-conversion processing on the received signal to obtain a signal y after the down-conversion processing 1 ；
Step B2: the legal receiver processes the down-converted signal y obtained in the step B1 1 Obtaining a signal sequence y' by an analog/digital converter;
step B3: b2, processing the signal sequence y 'obtained in the step B2 by a legal receiver, and recovering a useful signal y from the received signal y';
step B4: and B, the legal receiver demaps the signal y obtained in the step B3 to recover 0 and 1 bit data.
2. The generalized multi-fractional fourier transform multi-component secure transmission method according to claim 1, wherein the following is performed based on imperfect channel state informationAnd the actual channel h l The relationship between them is expressed as:
wherein ρ ε [0,1 ] represents the error coefficient, e l Error representing imperfect channel, andare independently distributed in the same way.
3. The generalized multi-fractional fourier transform multi-component secure transmission method according to claim 2, wherein the power normalization factor β of the transmitter is:
wherein, l=0, 1,2,..m-1.
4. A generalized multi-fractional fourier transform multi-component secure transmission method according to claim 3, wherein the signal sequence y' is:
wherein n is b ' is additive white gaussian noise in the received signal of a legitimate receiver.
5. The method for secure transmission of generalized multi-fractional fourier transform multi-component according to claim 4, wherein the legal receiver processes the signal sequence y' obtained in step B2, and the specific process is as follows:
wherein,is of conversion order-4α M Weighted fractional Fourier transform matrix of/M, n b Is n b ' transformed order-4α M The result of the weighted fractional fourier transform of/M;
6. the generalized multi-fractional Fourier transform multi-component secure transmission method based on imperfect channel state information as claimed in claim 5, wherein the method comprises steps ofIn that the signal to interference plus noise ratio gamma of the useful signal y B The method comprises the following steps:
wherein P is 0 For the total power of the transmitter,is the variance of the gaussian white noise received by a legitimate receiver.
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