阅读说明：本技术 一种基于广义多分数傅里叶变换的多分量安全传输方法 (Multi-component safe transmission method based on generalized multi-fraction Fourier transform ) 是由 李卓明 董衡 房宵杰 沙学军 于 2021-08-03 设计创作，主要内容包括：一种基于广义多分数傅里叶变换的多分量安全传输方法,它属于保密通信领域。本发明解决了现有基于人工噪声的方案中人工噪声的引入需要存在零空间导致系统的能量效率低以及基于WFRFT的物理层安全方法的安全性能受窃听方对变换参数估计能力影响的问题。本发明利用空域信道信息对广义多分数傅里叶变换的多个分量进行设计,同时利用广义多分数傅里叶变换多个分量之间的互干扰特性,在保证合作接收机不受干扰的情况下,有效降低了非合作接收机接收到信号的信干噪比。即使窃听者完全知道广义多分数傅里叶变换的知识和发射机所有变换参数,也无法消除导致其接收信号信噪比下降的干扰。本发明可以应用于保密通信领域。(A multi-component secure transmission method based on generalized multi-fraction Fourier transform belongs to the field of secret communication. The invention solves the problems that the introduction of artificial noise in the existing scheme based on artificial noise needs to have zero space to cause low energy efficiency of the system and the safety performance of the physical layer safety method based on WFRFT is influenced by the estimation capability of an eavesdropper on transformation parameters. The invention designs a plurality of components of generalized multi-fraction Fourier transform by utilizing the spatial domain channel information, and effectively reduces the signal-to-interference-and-noise ratio of signals received by a non-cooperative receiver by utilizing the mutual interference characteristic among the plurality of components of the generalized multi-fraction Fourier transform under the condition of ensuring that the cooperative receiver is not interfered. Even if the eavesdropper has full knowledge of the generalized multi-fractional fourier transform and all the transform parameters of the transmitter, it cannot eliminate the interference that causes the signal-to-noise ratio of its received signal to degrade. The invention can be applied to the field of secret communication.)

1. A multi-component secure transmission method based on generalized multi-fraction Fourier transform is characterized by specifically comprising the following steps:

at the transmitting end

Step A1: performing baseband mapping on 0 and 1 bit data generated by an information source to obtain a modulation result of a sequence x₀；

Step A2: for sequence x₀Performing 1-time normalization DFT to obtain a sequence x₁(ii) a For sequence x₀Performing normalized DFT for 2 times to obtain a sequence x₂(ii) a For sequence x₀Performing normalized DFT for 3 times to obtain a sequence x₃；

Step A3: for sequence x₀、x₁、x₂And x₃To carry outProcessing, namely respectively obtaining baseband signals to be transmitted on M antennas, wherein M represents the number of antennas of a transmitter;

baseband signal p to be transmitted on the l-th antenna_lComprises the following steps:

wherein, ω is_i(4l/M) is x_iI is 0,1,2,3, B_l(α_M) Is a weighting coefficient of a generalized multi-fractional Fourier transform, alpha_MIs the transformation order of the generalized multi-fraction Fourier transform, beta is the coefficient ensuring the constant total power of the transmitter, h_lRepresenting the channel coefficients between the ith antenna of the transmitter and the receiver,represents h_lConjugation of (1);

weighting coefficient B of generalized multi-fraction Fourier transform_l(α_M) Expressed as:

wherein j is an imaginary unit;

the weighting coefficient ω_i(4l/M) is expressed as:

step A4: respectively transmitting baseband signals p to be transmitted on M antennas_lObtaining M paths of analog signals p by a digital-to-analog converter_l'；

Step A5: for M analog signals p respectively_l' Up-conversion processing is carried out to obtain the signal p after the up-conversion processing on the M paths_l", and p is_l"transmit to channel through the ith antenna of the transmitter,l＝0,1,…,M-1；

at the receiving end

Step B1: the signal transmitted in the step A5 reaches a partner receiver after passing through a channel, the partner receiver receives the signal by using a single antenna, and performs down-conversion processing on the received signal to obtain a signal after down-conversion processing;

step B2: b, passing the signal obtained in the step B1 after the down-conversion treatment through an analog/digital converter to obtain a signal sequence y';

step B3: the partner receiver converts the signal sequence y' obtained in step B2 into an order of-4 α_MPerforming Fourier transform on four weighted scores of the/M to obtain a sequence y;

step B4: the partner receiver demaps the sequence y obtained in step B3 to recover 0 and 1 bits of data.

2. The method of claim 1, wherein the sequence x is a sequence of a multi-component secure transmission based on generalized multi-fractional Fourier transform₁、x₂And x₃In the form of:

wherein:

wherein N is the sequence x₀Length of (1), x₀(n) is the sequence x₀N-th value of (1), x₁(n) is the sequence x₁N-th value of (1), x₂(n) is the sequence x₂N-th value of (1), x₃(n) is the sequence x₃Is the base of the natural logarithm, X₀(k) Is a sequence x₀The kth value, X, of the sequence obtained after normalized discrete Fourier transform₁(k) Is a sequence x₁Sequences obtained by normalized discrete Fourier transformThe kth value of the column, X₂(k) Is a sequence x₂The kth value of the sequence obtained after normalized discrete fourier transform, k being 0,1, …, N-1.

3. A method for multi-component secure transmission based on generalized multi-fractional fourier transform as claimed in claim 2, wherein the coefficient β is of the form:

4. the method according to claim 3, wherein the number M of antennas of the transmitter is an integer greater than or equal to 4.

5. The method of claim 4, wherein the signal-to-noise ratio γ obtained by the partner receiver is a multi-component secure transmission method based on generalized multi-fractional Fourier transform_bExpressed as:

in the formula: p₀Is the total power of the transmitter;

is the variance of white gaussian noise received by the cooperating receivers.

6. The method of claim 5, wherein the signal sequence y' is represented as:

wherein n is_b' represents an additive white gaussian noise signal between the transmitter and the partner receiver;is a transformation matrix of a four-term weighted fractional Fourier transform with a transformation order of 4 l/M.

7. A multi-component safe transmission method based on generalized multi-fraction Fourier transform is characterized in that the working process of the method at a transmitting end is as follows:

step A1: performing baseband mapping on 0 and 1 bit data generated by an information source to obtain a modulation result of a sequence x₀；

Step A2: for sequence x₀Performing 1-time normalization DFT to obtain a sequence x₁(ii) a For sequence x₀Performing normalized DFT for 2 times to obtain a sequence x₂(ii) a For sequence x₀Performing normalized DFT for 3 times to obtain a sequence x₃；

Step A3: for sequence x₀、x₁、x₂And x₃Processing is carried out, and baseband signals to be transmitted on M antennas are obtained respectively, wherein M represents the number of antennas of a transmitter;

baseband signal p to be transmitted on the l-th antenna_lComprises the following steps:

wherein, ω is_i(4l/M) is x_iI is 0,1,2,3, B_l(α_M) Is a weighting coefficient of a generalized multi-fractional Fourier transform, alpha_MIs the transformation order of the generalized multi-fraction Fourier transform, beta is the coefficient ensuring the constant total power of the transmitter, h_lRepresenting the channel coefficients between the ith antenna of the transmitter and the receiver,represents h_lConjugation of (1);

weighting coefficient B of generalized multi-fraction Fourier transform_l(α_M) Expressed as:

wherein j is an imaginary unit;

the weighting coefficient ω_i(4l/M) is expressed as:

step A4: respectively transmitting baseband signals p to be transmitted on M antennas_lObtaining M paths of analog signals p by a digital-to-analog converter_l'；

Step A5: for M analog signals p respectively_l' Up-conversion processing is carried out to obtain the signal p after the up-conversion processing on the M paths_l", and p is_l"transmit to channel through the ith antenna of the transmitter, l ═ 0,1, …, M-1.

8. The method of claim 7, wherein the sequence x is a sequence of a multi-component secure transmission based on generalized multi-fractional Fourier transform₁、x₂And x₃In the form of:

wherein:

wherein N is the sequence x₀Length of (1), x₀(n) is the sequence x₀N-th value of (1), x₁(n) is the sequence x₁N-th value of (1), x₂(n) is the sequence x₂N-th value of (1), x₃(n) is the sequence x₃Is the base of the natural logarithm, X₀(k) Is a sequence x₀The kth value, X, of the sequence obtained after normalized discrete Fourier transform₁(k) Is a sequence x₁The kth value, X, of the sequence obtained after normalized discrete Fourier transform₂(k) Is a sequence x₂The kth value of the sequence obtained after normalized discrete fourier transform, k being 0,1, …, N-1.

9. A method for multi-component secure transmission based on generalized multi-fractional fourier transform as claimed in claim 8, wherein the coefficient β is of the form:

10. the method according to claim 9, wherein the number M of antennas of the transmitter is an integer greater than or equal to 4.

Technical Field

The invention relates to the field of secret communication, in particular to a multi-component secure transmission method based on generalized multi-fraction Fourier transform.

Background

With the development of wireless communication technology, wireless communication can meet the requirements of more and more industries on effectiveness and reliability. However, wireless networks are vulnerable to eavesdroppers due to the broadcast nature of the wireless channel. Traditional secure transmission is achieved by cryptographic methods, relying on the computational complexity of the network layer, and such schemes fail when an eavesdropper has sufficient computational power. At the same time, these schemes present challenges to the distribution and management of keys in many communication scenarios.

In recent years, the field of physical layer security has attracted more and more researchers' attention, which mainly utilizes the randomness of a wireless channel to realize secure transmission of signals. In a multi-antenna system, the physical layer security is mainly realized by depending on the degree of freedom of a spatial domain, and there are mainly a beamforming-based scheme and an artificial noise-based scheme. However, beamforming-based schemes can only adapt passively to the channel conditions, and when the channel conditions of the eavesdropping channel are better than the main channel, the performance of the schemes can be significantly degraded or even fail. Although the artificial noise based scheme can actively reduce the capacity of the eavesdropping channel through artificial noise, the introduction of artificial noise requires the existence of null space and the scheme may reduce the energy efficiency of the system.

The scholars have proposed the concept of Weighted fractional Fourier transform (WFRFT), and based on this, WFRFT is extended to a multi-parameter form, which is introduced into the physical layer security domain as a precoding method. But as the eavesdropper increases in computational power it can obtain more accurate weighted fractional fourier transform parameters, which can lead to a reduction in the security performance of the system.

Disclosure of Invention

The invention aims to solve the problems that zero space is needed to be existed in the introduction of artificial noise in the existing artificial noise-based scheme, so that the energy efficiency of the system is low, and the safety performance of a physical layer safety method based on WFRFT is affected by the estimation capability of an eavesdropper on transformation parameters, and provides a multi-component safety transmission method based on generalized multi-fraction Fourier transformation.

The technical scheme adopted by the invention for solving the technical problems is as follows:

based on one aspect of the invention, a multi-component secure transmission method based on generalized multi-fraction Fourier transform specifically comprises the following steps:

at the transmitting end

Step A1: performing baseband mapping on 0 and 1 bit data generated by an information source to obtain a modulation result of a sequence x₀；

Step A2: for sequence x₀Performing 1-time normalization DFT to obtain a sequence x₁(ii) a For sequence x₀Performing normalized DFT for 2 times to obtain a sequence x₂(ii) a For sequence x₀Performing normalized DFT for 3 times to obtain a sequence x₃；

Step A3: for sequence x₀、x₁、x₂And x₃Processing is carried out, and baseband signals to be transmitted on M antennas are obtained respectively, wherein M represents the number of antennas of a transmitter;

baseband signal p to be transmitted on the l-th antenna_lComprises the following steps:

wherein, ω is_i(4l/M) is x_iI is 0,1,2,3, B_l(α_M) Is a weighting coefficient of a generalized multi-fractional Fourier transform, alpha_MIs the transformation order of the generalized multi-fraction Fourier transform, beta is the coefficient ensuring the constant total power of the transmitter, h_lRepresenting the channel coefficients between the ith antenna of the transmitter and the receiver,represents h_lConjugation of (1);

weighting coefficient B of generalized multi-fraction Fourier transform_l(α_M) Expressed as:

wherein j is an imaginary unit;

the weighting coefficient ω_i(4l/M) is expressed as:

step A4: respectively transmitting baseband signals p to be transmitted on M antennas_lObtaining M paths of analog signals p by a digital-to-analog converter_l'；

Step A5: for M analog signals p respectively_l' Up-conversion processing is carried out to obtain the signal p after the up-conversion processing on the M paths_l", and p is_l"transmit to channel through the ith antenna of the transmitter, l ═ 0,1, …, M-1;

at the receiving end

Step B1: the signal transmitted in the step A5 reaches a partner receiver after passing through a channel, the partner receiver receives the signal by using a single antenna, and performs down-conversion processing on the received signal to obtain a signal after down-conversion processing;

step B2: b, passing the signal obtained in the step B1 after the down-conversion treatment through an analog/digital converter to obtain a signal sequence y';

step B3: the partner receiver converts the signal sequence y' obtained in step B2 into an order of-4 α_MPerforming Fourier transform on four weighted scores of the/M to obtain a sequence y;

step B4: the partner receiver demaps the sequence y obtained in step B3 to recover 0 and 1 bits of data.

Based on another aspect of the invention, a multi-component secure transmission method based on generalized multi-fraction fourier transform comprises the following working processes at a transmitting end:

step A1: performing baseband mapping on 0 and 1 bit data generated by an information source to obtain a modulation result of a sequence x₀；

Step A2: for sequence x₀Performing 1-time normalization DFT to obtain a sequence x₁(ii) a For sequence x₀Performing normalized DFT for 2 times to obtain a sequence x₂(ii) a For sequence x₀Performing normalized DFT for 3 times to obtain a sequence x₃；

Step A3: for sequence x₀、x₁、x₂And x₃Processing is carried out, and baseband signals to be transmitted on M antennas are obtained respectively, wherein M represents the number of antennas of a transmitter;

baseband signal p to be transmitted on the l-th antenna_lComprises the following steps:

wherein, ω is_i(4l/M) is x_iI is 0,1,2,3, B_l(α_M) Is a weighting coefficient of a generalized multi-fractional Fourier transform, alpha_MIs the transformation order of the generalized multi-fraction Fourier transform, beta is the coefficient ensuring the constant total power of the transmitter, h_lRepresenting the channel coefficients between the ith antenna of the transmitter and the receiver,represents h_lConjugation of (1);

weighting coefficient B of generalized multi-fraction Fourier transform_l(α_M) Expressed as:

wherein j is an imaginary unit;

the weighting coefficient ω_i(4l/M) is expressed as:

step A4: respectively transmitting baseband signals p to be transmitted on M antennas_lObtaining M paths of analog signals p by a digital-to-analog converter_l'；

Step A5: for M analog signals p respectively_l' Up-conversion processing is carried out to obtain the signal p after the up-conversion processing on the M paths_l", and p is_l"transmit to channel through the ith antenna of the transmitter, l ═ 0,1, …, M-1.

The invention has the beneficial effects that: the invention provides a multi-component safe transmission method based on generalized multi-fraction Fourier transform, which designs a plurality of components of generalized multi-fraction Fourier transform by utilizing spatial domain channel information, and effectively reduces the signal-to-interference-plus-noise ratio of signals received by a non-cooperative receiver under the condition of ensuring that the cooperative receiver is not interfered by utilizing the mutual interference characteristic among the components of the generalized multi-fraction Fourier transform. Even if an eavesdropper completely knows the knowledge of the generalized multi-fractional Fourier transform and all the transformation parameters of the transmitter, the interference which causes the reduction of the signal-to-noise ratio of the received signal can not be eliminated, and the problem that when the eavesdropper can accurately obtain the transformation parameters of the weighted fractional Fourier transform, the safety performance of the physical layer safety method based on the WFRFT is influenced is solved. Meanwhile, the problem of low energy efficiency when the safety performance of a physical layer is improved by a scheme based on artificial noise is solved.

The method effectively improves the physical layer safety performance of the wireless communication system.

Drawings

FIG. 1 is a flow chart of a multi-component secure transmission method based on generalized multi-fractional Fourier transform according to the present invention;

FIG. 2 is a flow diagram of transmitter multi-component digital baseband signal processing;

FIG. 3 is a flow diagram of a partner receiver multi-component digital baseband signal processing;

FIG. 4 shows the safety capacity C of the system under different antenna number conditions of the transmitter and the non-cooperative receiver when the non-cooperative receiver knows the knowledge of the generalized multi-fractional Fourier transform and all the transformation parameters of the transmitter_sA plot of variation with signal to noise ratio;

in the figure, N represents the number of non-cooperative receiver antennas.

Detailed Description

First embodiment this embodiment will be described with reference to fig. 1,2, and 3. The method for multi-component secure transmission based on generalized multi-fraction fourier transform described in this embodiment specifically includes the following steps:

at the transmitting end

Step A1: performing baseband mapping on 0 and 1 bit data generated by an information source to obtain a modulation result of a sequence x₀；

Step A2: for sequence x₀Performing 1 normalization DFT (discrete Fourier transform) to obtain a sequence x₁(ii) a For sequence x₀Performing normalized DFT for 2 times to obtain a sequence x₂(ii) a For sequence x₀Performing normalized DFT for 3 times to obtain a sequence x₃；

As shown in fig. 2, after "digital baseband mapping", the four signals from top to bottom are: the first path is as follows: output original signal sequence x₀(ii) a And a second path: output sequence x₀Passing through the reverse module, equivalent to the sequence x₀The signal obtained after 2 times of normalized DFT processing corresponds to the sequence x₂(ii) a And a third path: output sequence x₀Passing through FFT module, equivalent to sequence x₀The signal obtained after 1 normalized DFT process corresponds to the sequence x₁(ii) a And a fourth path: output sequence x₀Sequentially passes through an FFT module and an inversion module, and is equivalent to a sequence x₀The signal obtained after 3 times of normalized DFT processing corresponds to the sequence x₃. The DFT is implemented with the FFT.

Step A3: for sequence x₀、x₁、x₂And x₃Processing is carried out, and baseband signals to be transmitted on M antennas are obtained respectively, wherein M represents the number of antennas of a transmitter;

baseband signal p to be transmitted on the l-th antenna_lComprises the following steps:

wherein, ω is_i(4l/M) is x_iI is 0,1,2,3, B_l(α_M) Is a weighting coefficient of a generalized multi-fractional Fourier transform, alpha_MIs the transformation order of the generalized multi-fraction Fourier transform, beta is the coefficient ensuring the constant total power of the transmitter, h_lRepresenting the channel coefficients between the ith antenna of the transmitter and the receiver,represents h_lConjugation of (1);

designing a signal through generalized multi-fraction Fourier transform;

weighting coefficient B of generalized multi-fraction Fourier transform_l(α_M) Expressed as:

wherein j is an imaginary unit;

the weighting coefficient ω_i(4l/M) is expressed as:

step A4: respectively transmitting baseband signals p to be transmitted on M antennas_lObtaining M paths of analog signals p by a digital-to-analog converter_l'；

Step A5: for M analog signals p respectively_l' Up-conversion processing is carried out to obtain the signal p after the up-conversion processing on the M paths_l", and p is_l"transmit to channel through the ith antenna of the transmitter, l ═ 0,1, …, M-1;

at the receiving end

Step B1: the signal transmitted in the step A5 reaches a partner receiver after passing through a channel, the partner receiver receives the signal by using a single antenna, and performs down-conversion processing on the received signal to obtain a signal after down-conversion processing;

step B2: b, passing the signal obtained in the step B1 after the down-conversion treatment through an analog/digital converter to obtain a signal sequence y';

step B3: the partner receiver converts the signal sequence y' obtained in step B2 into an order of-4 α_MPerforming Fourier transform on four weighted scores of the/M to obtain a sequence y;

step B4: the partner receiver demaps the sequence y obtained in step B3 to recover 0 and 1 bits of data.

The second embodiment is as follows: this embodiment differs from the first embodiment in that the sequence x₁、x₂And x₃In the form of:

wherein the content of the first and second substances,

wherein N is the sequence x₀Length of (1), x₀(n) is the sequence x₀N-th value of (1), x₁(n) is the sequence x₁N-th value of (1), x₂(n) is the sequence x₂N-th value of (1), x₃(n) is the sequence x₃Is the base of the natural logarithm, X₀(k) Is a sequence x₀The kth value, X, of the sequence obtained after normalized discrete Fourier transform₁(k) Is a sequence x₁The kth value, X, of the sequence obtained after normalized discrete Fourier transform₂(k) Is a sequence x₂The kth value of the sequence obtained after normalized discrete fourier transform, k being 0,1, …, N-1.

Other steps and parameters are the same as those in the first embodiment.

The third concrete implementation mode: in this embodiment, which is different from the first or second embodiment, the coefficient β is in the form of:

other steps and parameters are the same as those in the first or second embodiment.

The fourth concrete implementation mode: this embodiment is different from the first to third embodiments in that the number M of antennas of the transmitter is an integer greater than or equal to 4.

Other steps and parameters are the same as those in one of the first to third embodiments.

The fifth concrete implementation mode: this embodiment differs from one of the first to fourth embodiments in that the signal-to-noise ratio γ obtained by the partner receiver_bExpressed as:

in the formula: p₀Is the total power of the transmitter and is a constant greater than 0;

is the variance of white gaussian noise received by the cooperating receivers.

Other steps and parameters are the same as in one of the first to fourth embodiments.

The sixth specific implementation mode: this embodiment differs from one of the first to fifth embodiments in that the signal sequence y' is represented as:

wherein n is_b' represents an additive white gaussian noise signal between the transmitter and the partner receiver;is a transformation matrix of a four-item weighted fractional Fourier transform with a transformation order of 4l/M,represents a sequence x of pairs₀And performing four-term weighted fractional Fourier transform with the transform order of 4l/M to obtain a result.

The sequence y is represented as:

in the formula:is of transformation order-4 alpha_MTransformation matrix of a four-item weighted fractional Fourier transform of/M, n_bRepresents n for_b' conversion order of-4. alpha_MThe result of the four-term weighted fractional Fourier transform of/M can be expressed as:

other steps and parameters are the same as those in one of the first to fifth embodiments.

Seventh embodiment, this embodiment will be described with reference to fig. 1 and 2. In this embodiment, a multi-component secure transmission method based on generalized multi-fraction fourier transform includes:

step A1: performing baseband mapping on 0 and 1 bit data generated by an information source to obtain a modulation result of a sequence x₀；

Step A2: for sequence x₀Performing 1 normalization DFT (discrete Fourier transform) to obtain a sequence x₁(ii) a For sequence x₀Performing normalized DFT for 2 times to obtain a sequence x₂(ii) a For sequence x₀Performing normalized DFT for 3 times to obtain a sequence x₃；

As shown in fig. 2, after "digital baseband mapping", the four signals from top to bottom are: the first path is as follows: output original signal sequence x₀(ii) a And a second path: output sequence x₀Passing through a reverse module, and equivalentIn the sequence x₀The signal obtained after 2 times of normalized DFT processing corresponds to the sequence x₂(ii) a And a third path: output sequence x₀Passing through FFT module, equivalent to sequence x₀The signal obtained after 1 normalized DFT process corresponds to the sequence x₁(ii) a And a fourth path: output sequence x₀Sequentially passes through an FFT module and an inversion module, and is equivalent to a sequence x₀The signal obtained after 3 times of normalized DFT processing corresponds to the sequence x₃. The DFT is implemented with the FFT.

Step A3: for sequence x₀、x₁、x₂And x₃Processing is carried out, and baseband signals to be transmitted on M antennas are obtained respectively, wherein M represents the number of antennas of a transmitter;

baseband signal p to be transmitted on the l-th antenna_lComprises the following steps:

wherein, ω is_i(4l/M) is x_iI is 0,1,2,3, B_l(α_M) Is a weighting coefficient of a generalized multi-fractional Fourier transform, alpha_MIs the transformation order of the generalized multi-fraction Fourier transform, beta is the coefficient ensuring the constant total power of the transmitter, h_lRepresenting the channel coefficients between the ith antenna of the transmitter and the receiver,represents h_lConjugation of (1);

designing a signal through generalized multi-fraction Fourier transform;

weighting coefficient B of generalized multi-fraction Fourier transform_l(α_M) Expressed as:

wherein j is an imaginary unit;

the weighting coefficient ω_i(4l/M) is expressed as:

step A4: respectively transmitting baseband signals p to be transmitted on M antennas_lObtaining M paths of analog signals p by a digital-to-analog converter_l'；

Step A5: for M analog signals p respectively_l' Up-conversion processing is carried out to obtain the signal p after the up-conversion processing on the M paths_l", and p is_l"transmit to channel through the ith antenna of the transmitter, l ═ 0,1, …, M-1.

The specific implementation mode is eight: this embodiment differs from the seventh embodiment in that the sequence x₁、x₂And x₃In the form of:

wherein the content of the first and second substances,

wherein N is the sequence x₀Length of (1), x₀(n) is the sequence x₀N-th value of (1), x₁(n) is the sequence x₁N-th value of (1), x₂(n) is the sequence x₂N-th value of (1), x₃(n) is the sequence x₃Is the base of the natural logarithm, X₀(k) Is a sequence x₀The kth value, X, of the sequence obtained after normalized discrete Fourier transform₁(k) Is a sequence x₁The kth value, X, of the sequence obtained after normalized discrete Fourier transform₂(k) Is a sequence x₂The kth value of the sequence obtained after normalized discrete fourier transform, k being 0,1, …, N-1.

Other steps and parameters are the same as those in the seventh embodiment.

The specific implementation method nine: this embodiment differs from the seventh or eighth embodiment in that the coefficient β is in the form of:

other steps and parameters are the same as those of the seventh or eighth embodiment.

The detailed implementation mode is ten: this embodiment is different from one of the seventh to ninth embodiments in that the number M of antennas of the transmitter is an integer equal to or greater than 4.

Other steps and parameters are the same as those in one of the seventh to ninth embodiments.

Examples

The overall working flow diagram of the invention is shown in fig. 1, the flow diagram of the processing of the digital baseband signal in the transmitter is shown in fig. 2, and the flow diagram of the processing of the digital baseband signal in the cooperative receiver is shown in fig. 3.

The signal processing method of the transmitter comprises the following steps:

step A1: performing baseband mapping on 0 and 1 bit data generated by an information source to obtain a modulation result of a sequence x₀；

Step A2: respectively to the sequence x₀Performing normalized DFT for 1-3 times to obtain sequences x₁，x₂And x₃. Wherein the normalized DFT is defined in the form:

in the formula: j is an imaginary unit.

Sequence x₁，x₂And x₃The elements in (a) may be represented as:

wherein the content of the first and second substances,

step A3: sequence x obtained in transmitter pair step a2₀～x₃And processing to respectively obtain baseband signals to be transmitted on M antennas, wherein M represents the number of antennas of a transmitter and is an integer greater than or equal to 4. Baseband signal p to be transmitted on the l-th antenna_lCan be expressed as:

in the formula: h is_lRepresenting channel coefficients between the ith antenna of the transmitter and the receiver;

α_Mis the transform order of the generalized multi-fractional fourier transform;

B_l(α_M) The weighting coefficients, which are generalized multi-fractional fourier transforms, can be expressed as:

ω_i(4l/M) is x_iThe weighting coefficient of (2) can be expressed as:

β is a coefficient that ensures the total power of the transmitter is constant, and can be expressed as:

step A4: respectively passing the M-path signals obtained in the step A3 through digital-to-analog converters to respectively obtain digital signals p_lCorresponding analog signal p_l'；

Step A5: respectively comparing the M paths of analog signals p obtained in the step A4_l' Up-conversion processing is carried out to obtain the signal p after the up-conversion processing on the M paths_l", and separately p_l"transmit to channel through the ith antenna of the transmitter;

the signal processing method of the cooperative receiver comprises the following steps:

step B1: the signal transmitted in the step A5 reaches a receiver after passing through a channel, the receiver receives the signal through a single antenna, and performs down-conversion processing on the received signal to obtain a signal after down-conversion processing;

step B2: the signal obtained by the step B1 after down-conversion processing is passed through an analog/digital converter, and the obtained signal sequence y' can be represented as:

in the formula: n is_b' represents an additive white gaussian noise signal between the transmitter and the cooperating receiver;

represents a sequence x of pairs₀Performing four-term weighted fractional Fourier transform with the transform order of 4l/M to obtain a result;

to verify the reliability of the present invention, it is assumed herein that the non-cooperative receiver has N receiving antennas, where N is a positive integer and satisfies 1 ≦ N < M. The baseband signal on the nth antenna of the non-cooperative receiver can be represented as:

in the formula: g_l，nRepresenting the channel coefficient between the ith antenna of the transmitter and the nth antenna of the uncooperative receiver, wherein N is 0,1, …, N-1;

n_e,n' denotes additive white gaussian noise between the nth antenna of the transmitter and the non-cooperative receiver;

step B3: the cooperative receiver converts the signal y' obtained in step B2 to an order of-4 alpha_MThe four-weighted fractional Fourier transform of/M yields a sequence y, which can be expressed as:

in the formula: n is_bRepresents n for_b' conversion order of-4. alpha_MThe result of the four-term weighted fractional Fourier transform of/M can be expressed as:

at this time, the signal-to-noise ratio γ that can be obtained by the cooperative receiver_bCan be expressed as:

in the formula: p₀Is the total power of the transmitter and is a constant greater than 0;

variance of white gaussian noise received for the partner;

to verify the reliability of the invention, it is assumed here that the non-cooperating receiver knows the transformation parameters used by the transmitter, at which time the non-cooperating receiver can obtain the maximum signal-to-interference-and-noise ratio γ_eCan be expressed as:

in the formula: p₀Is the total power of the transmitter and is a constant greater than 0;

a variance corresponding to white gaussian noise received by a non-partner;

n_sandrespectively non-cooperative receivers by gamma_eNumber and component number of the receiving antenna selected at maximum as target, n_s∈{0,1,…,N-1}，

Can be expressed as:

where l is 0,1, …, M-1, j is an imaginary unit.

According to the related definition of the safe capacity in the information theory, the invention can ensure that the system can reach the safe capacity C_sCan be expressed as the difference between the two channel capacities of the transmitter and the cooperating receiver and the transmitter and the non-cooperating receiver. Namely:

C_s＝[C_b-C_e]⁺

＝[log₂(1+γ_b)-log₂(1+γ_e)]⁺

in the formula: [. the]⁺＝max(·，0)。

Step B4: and the cooperative receiver demaps the sequence y obtained in the step B3 to recover 0 and 1 bit data.

Fig. 4 shows the safety capacity of the system as a function of the signal-to-noise ratio under the condition of different antenna numbers of the transmitter and the non-cooperative receiver when the non-cooperative receiver knows the knowledge of the generalized multi-fractional fourier transform and all the transformation parameters of the transmitter.

The invention adopts generalized multi-fraction Fourier transform to decompose the signal into a plurality of components, and the components are respectively corresponding to a plurality of antennas of a transmitter for transmission. For a cooperative receiver, all the received signal energy can be used for information recovery, thus no energy loss is caused. But for a non-cooperative receiver, the characteristics of the signal domain are destroyed because the received signal no longer satisfies the constraint relation between the components of the generalized multi-fractional fourier transform. Therefore, even if the non-cooperative receiver knows the knowledge of the generalized multi-fractional fourier transform and all the transform parameters, the mutual interference between the multiple components of the generalized multi-fractional fourier transform cannot be completely eliminated. The mutual interference can cause the signal-to-interference-and-noise ratio of the signals received by the non-cooperative receiver to be reduced, and further, the safety performance of a physical layer of the communication system is ensured.

The above-described calculation examples of the present invention are merely to explain the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.