A covert communication method based on artificial noise-like and code index modulation

Abstract

This invention discloses a covert communication method based on artificial noise-like modulation and code index modulation. The sender generates a covert information block and a coordination information block for transmission to the covert information receiver and the coordination party. The sender divides the covert information block into covert modulation bits and covert mapping bits. The covert modulation bits are subjected to M-PSK modulation, and the covert mapping bits are mapped to the corresponding spreading code. The real and imaginary parts of the modulation symbol are spread using the spreading code. The sender performs a four-term weighted fractional Fourier transform on the spread covert information block and the coordination information block to establish a beamforming vector optimization model. Under specified covert constraints, the beam vector transmitted to the covert information receiver is decomposed to find the beamforming vector that maximizes the covert capacity. The covert information receiver performs the opposite operation to the sender's operation on the received signal, thus realizing covert communication based on artificial noise-like modulation and code index modulation. This invention features high system performance and high energy efficiency.

Description

Technical Field

[0001] This invention belongs to the field of covert communication technology, specifically relating to a covert communication method based on artificial noise and code index modulation. Background Technology

[0002] Covert communication is a wireless communication technology that employs various methods to achieve low-probability detection. Spread spectrum communication has played a significant role in this field, and the square root law of covert wireless communication explains its theoretical covert performance. In recent years, with the deepening of research in this area, in addition to the square root law, studies on covert constraint metrics, covert codebook construction, and optimal signal distribution have also become more in-depth, laying a solid foundation for the development and application of subsequent technologies.

[0003] In recent years, covert communication technology has emerged, and research on cooperative interference, priority block length, noise uncertainty, channel uncertainty, and multi-node covert networks has become the main research content in this field. In practical communication scenarios, noise uncertainty is almost unavoidable due to constantly changing environmental factors. Therefore, designing covert communication systems that address the impact of noise on covert wireless communication is of practical significance and necessity.

[0004] In practical wireless communication scenarios, completely concealing signals within background noise is extremely difficult. Most current covert communication systems operate under strong assumptions, such as the eavesdropper must occupy the same channel as the legitimate receiver, and the eavesdropper must have fewer antennas than the legitimate receiver. Furthermore, these systems require additional energy to generate artificial noise, significantly increasing power consumption. Therefore, this invention proposes a covert communication method based on artificial noise. Utilizing the Gaussian-like properties of a four-term weighted fractional Fourier transform, a beamforming algorithm is proposed to make the signal exhibit noise characteristics at the eavesdropping point. This allows the covert information to be transmitted within the covert constraints, and spreading code index modulation is employed to improve the system's transmission efficiency. Summary of the Invention

[0005] The purpose of this invention is to provide a covert communication method based on artificial noise and code index modulation, which has good system performance and high energy utilization.

[0006] The final solution to achieve the present invention is: a covert communication method based on artificial noise and code index modulation, comprising the following steps:

[0007] (10) The sender generates a covert information block and an assistance information block, wherein the covert information block is used to send to the covert information receiver and the assistance information block is used to send to the assisting party;

[0008] (20) The sender divides the covert information block into covert modulation bits (M bits) and covert mapping bits (2N bits). First, the covert modulation bits are M-PSK modulated to form modulation symbols. Then, the covert mapping bits are mapped to the corresponding spreading codes. The real and imaginary parts of the modulation symbols are spread using the spreading codes respectively. The same processing is performed on the assisting information block.

[0009] (30) The transmitter performs a four-term weighted fractional Fourier transform on the spread covert information block and the assist information block. With the goal of maximizing the covert capacity, a beamforming vector optimization model is established. Then, under specified covert constraints, the beam vector transmitted to the covert information receiver is decomposed in the null-forcing direction and the orthogonal direction of the null-forcing direction. Finally, the weighting factors are adjusted. By performing second-order differentiation, the beamforming vector that maximizes the concealment capacity is obtained. The transmitter uses this beamforming vector to send signals to the concealed information receiver and the assisting party. The two signals form superposition interference at the eavesdropping party.

[0010] (40) The covert information receiver performs an inverse four-term weighted fractional Fourier transform on the received signal, and then multiplies it with each spreading code. The set of spreading codes with the largest energy is then mapped back to the recovered covert mapping bits. At the same time, the covert information receiver uses the set of spreading codes with the largest energy to despread the signal after the inverse four-term weighted fractional Fourier transform to obtain the recovered modulation symbols. The receiver then performs M-PSK demodulation on the recovered covert modulation bits. The recovered covert modulation bits are combined with the recovered covert mapping bits to obtain the recovered covert information, thus realizing covert communication based on artificial noise and code index modulation.

[0011] A covert communication system based on artificial noise and code index modulation is provided. Based on the aforementioned covert communication method, covert communication based on artificial noise and code index modulation is realized.

[0012] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements covert communication based on artificial noise and code index modulation according to the aforementioned covert communication method.

[0013] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements covert communication based on artificial noise and code index modulation according to the covert communication method described above.

[0014] Compared with existing technologies, the significant advantages of this invention are: 1) Noise generation requires no additional energy overhead: This invention performs four-term weighted fractional Fourier transform on both the covert signal and the assisting signal, and uses beamforming algorithms to make the signal have noise characteristics at the eavesdropping party, enabling transmission under covert constraints. Compared with directly generating artificial noise using jammers, this invention not only uses quasi-artificial noise to interfere with the eavesdropping party and achieve covert communication, but also does not generate additional energy consumption. 2) High covert channel capacity: This invention uses code index modulation, dividing the covert information block into covert modulation bits and covert mapping bits. The 2N bits of the covert mapping bits spread the real and imaginary parts of the modulation symbol separately. Compared with direct transmission of covert information, this invention significantly improves the system channel capacity without consuming additional channel resources. 3) Higher Practicality of Beamforming Algorithm: This invention proposes a beamforming algorithm under artificial noise background and concealment constraints. This algorithm decomposes the beam vector from the transmitter to the concealed information receiver in the zero-forcing direction and its orthogonal direction, and, combined with the concealment constraints, takes the second derivative of the weight parameters to obtain two possible values ​​for the weight parameters. Each information block only needs to select the weights according to the derived general formula. Compared with other methods for solving convex optimization problems (such as the Lagrange multiplier method), the proposed algorithm has lower computational complexity, is easier to implement, and is more practical. Attached Figure Description

[0015] Figure 1 A covert communication method based on artificial noise and code index modulation is presented.

[0016] Figure 2 A flowchart based on artificial noise and code index modulation is shown.

[0017] Figure 3 The design flow of beamforming vectors after adding artificial noise is shown.

[0018] Figure 4 The bit error rate of a covert communication system based on artificial noise and code index modulation is shown.

[0019] Figure 5 The covert channel capacity based on artificial noise and code index modulation is shown. Detailed Implementation

[0020] The covert communication method based on artificial noise and code index modulation of this invention is implemented in the following scenarios:

[0021] A wireless covert communication model is established, including a sender, a covert information receiver, an assistant, and an eavesdropper. The sender is equipped with multiple antennas, while the covert information receiver, assistant, and eavesdropper are equipped with a single antenna. The sender continuously transmits processed assistance signals to the assistant and randomly sends covert signals to the covert information receiver, while the eavesdropper attempts to capture the covert information. Figure 2 As shown, the covert communication method based on artificial noise and code index of the present invention includes the following steps: (10) The sender generates a covert information block and an assistance information block, wherein the covert information block is used to send to the covert information receiver and the assistance information block is used to send to the assisting party;

[0022] (20) The sender divides the covert information block into covert modulation bits (M bits) and covert mapping bits (2N bits). First, the covert modulation bits are M-PSK modulated to form modulation symbols. Then, the covert mapping bits are mapped to the corresponding spreading codes. The real and imaginary parts of the modulation symbols are spread using the spreading codes respectively. The same processing is performed on the assisting information block. The specific method for spreading the real and imaginary parts of the modulation symbols using the spreading codes is as follows:

[0023] ,

[0024] in The symbol is after spectral expansion. and For the real and imaginary parts of the modulation symbol, and These are the spreading codes for the hidden mapping bit mapping.

[0025] (30) The transmitter performs a four-term weighted fractional Fourier transform on the spread covert information block and the assist information block. With the goal of maximizing the covert capacity, a beamforming vector optimization model is established. Then, under specified covert constraints, the beam vector transmitted to the covert information receiver is decomposed in the null-forcing direction and the orthogonal direction of the null-forcing direction. Finally, the weighting factors are adjusted. By performing second-order differentiation, the beamforming vector that maximizes the concealment capacity is obtained. The transmitter uses this beamforming vector to send signals to both the concealed information receiver and the assisting party. The two signals create superposition interference at the eavesdropping party, such as... Figure 3 As shown, the method for generating artificial noise and the design of the beamforming vector include the following steps:

[0026] (31) The transmitter directly performs a four-term weighted fractional Fourier transform on the spread-spectrum covert information block, and the resulting sequence is called the covert sequence. The assisting information block is first M-PSK modulated, and then subjected to a four-term weighted fractional Fourier transform, and the resulting sequence is called the assisting sequence. The formula for the four-term weighted fractional Fourier transform is:

[0027] ,

[0028] Indicates to The four-term weighted fractional Fourier transform, This indicates a covert information block or a helper information block after spread spectrum processing. They represent The 1st, 2nd, and 3rd discrete Fourier transforms, For the transformation order, Let be the weights, and satisfy the following formula:

[0029] ,

[0030] Next, the channel gain from the sender to the covert information receiver, the assisting party, and the eavesdropping party is randomly generated. , , ,Will Multiplying with the hidden sequence, the sum of the results has a mean of 0 and a variance of . Gaussian noise, while... Multiplying with the assist sequence and summing the results, the mean is 0 and the variance is... Gaussian noise.

[0031] (32) Next, with the goal of maximizing concealment capacity, a beamforming vector optimization model is established, and the expression for concealment capacity is:

[0032] ,

[0033] in, The number of active spreading codes, The base of the M_PSK modulation is . , These represent the channel gain from the sender to the receiver of the covert information and the beamforming vector, respectively. The variance of the superimposed Gaussian noise from the sender to the receiver of the concealed information is denoted as .

[0034] Then, the hidden constraints are determined, and their derivation is as follows. The hidden constraints can be written as:

[0035] ,

[0036] in, This indicates that the sender will not send a hidden sequence. This indicates that the sender is sending a hidden sequence. It is worth noting that... , In both states, the sender will send an assistance sequence. for and The relative entropy, To detect the probability of error, Let be the number of times the channel is used. Expanding the left side of the above equation, we get:

[0037] ,

[0038] in

[0039] ,

[0040] These refer to the power of the signals transmitted by the concealed information receiver and the assisting party, respectively. The beamforming vector from the transmitter to the assisting party is set to... , and Let be the channel gain from the sender to the eavesdropper and the Gaussian noise variance. Therefore, the hidden constraint can be written as:

[0041] ,

[0042] because ,and exist Since the expression is monotonically increasing, the hidden constraint can be further written as:

[0043] ,

[0044] in for The inverse function of .

[0045] (33) The beam vector transmitted to the covert information receiver The decomposition is performed in the zero-forcing direction and in the orthogonal direction to the zero-forcing direction, as follows:

[0046] ,

[0047] in As a weighting factor, This is the zero-forcing beamforming vector from the sender to the receiver of the covert information. Indicates and Perpendicular beamforming vectors will Substitute the hidden constraint expression to find the weight values ​​that maximize the hidden capacity. The expression:

[0048] ,

[0049] Next, regarding the hidden capacity expression... Perform second-order differentiation:

[0050] ,

[0051] in, , , The identity matrix is ​​then used to obtain the poles. The value of is denoted as It is given by the following formula:

[0052] ,

[0053] Due to channel variations and noise, the values ​​are uncertain, therefore the analysis yields... The beamforming schemes corresponding to the two value ranges are as follows:

[0054] , ;

[0055] , .

[0056] According to the above formula, we can obtain the result that maximizes the concealment capacity. The sender uses and Signals are sent to both the recipient of the concealed information and the assisting party, causing superposition and interference between the two signals at the eavesdropping party. For example... Figure 5 As shown, the covert channel capacity obtained by the beamforming vector calculation method of the present invention is significantly higher than that of other schemes.

[0057] (40) The covert information receiver performs an inverse four-term weighted fractional Fourier transform on the received signal, and then multiplies it by each spreading code. The set of spreading codes with the highest energy is then mapped back to the recovered covert mapping bits. Simultaneously, the covert information receiver uses the set of spreading codes with the highest energy to despread the signal after the inverse four-term weighted fractional Fourier transform to obtain the recovered modulation symbols. These symbols are then demodulated using M-PSK to obtain the recovered covert modulation bits. The recovered covert modulation bits are combined with the recovered covert mapping bits to obtain the recovered covert information, thus realizing covert communication based on artificial noise and code index modulation. The specific steps are as follows:

[0058] (41) The receiver of the concealed information performs an inverse four-term weighted fractional Fourier transform on the received signal, as shown in the following equation:

[0059] ,

[0060] express Four-term weighted fractional Fourier transform, The signal received by the receiver of the concealed information. for The sequence after inverse four-term weighted fractional Fourier transform, and Satisfy the following formula

[0061] ,

[0062] express Four-term weighted fractional Fourier transform, It is Gaussian white noise with a mean of 0 and a variance of . Next, utilizing the autocorrelation properties of the spreading code, the receiver of the concealed information... Perform the following processing:

[0063] ,

[0064] in, The modulated symbol after despreading. For the first One spreading code, The energy for each spreading code, for After inverse four-term weighted fractional Fourier transform, and then with The noise obtained after multiplication is used by the covert information receiver to reverse-map the spreading code with the highest energy to the recovered covert mapping bits, as shown in the following formula:

[0065] ,

[0066] These are the hidden mapping bits obtained from the reverse mapping.

[0067] (42) Combine the recovered covert modulation bits with the recovered covert mapping bits and compare them with the sender's covert information block. Each possible combination will have a different number of error bits, and the remaining... The probability of each combination is the same, and the bit error probability of the hidden mapping bit is given by the following formula:

[0068] ,

[0069] in, This represents the bit error probability of the hidden mapping bit. The number of bits in the covert mapping bit combination detected by the covert information receiver. The error probability of the spreading code corresponding to the detected hidden mapping bit.

[0070] Next, the bit error probability of the recovered hidden information block is calculated using the following formula:

[0071] ,

[0072] in, This represents the bit error probability of the recovered hidden information block. The bit error rate of conventional direct sequence spread spectrum is given by the following formula:

[0073] ,

[0074] This is a complementary error function. For example... Figure 5 As shown, when the signal-to-noise ratio is greater than 10dB, the bit error probability of the recovered hidden information block is already lower than... This meets the needs of covert communication and enables covert communication based on artificial noise and code index modulation.

[0075] like Figure 4 The method uses QPSK modulation, and within the allowable bit error rate range, the maximum number of bits for the covert mapping bits is 3. Compared with existing methods that directly transmit covert information, the covert communication method based on artificial noise and code index modulation proposed in this invention significantly improves the covert channel capacity.

[0076] This invention performs a four-term weighted fractional Fourier transform on the signal, mapping normal information to the transform domain. It then utilizes a proposed beamforming algorithm to impart artificial noise-like characteristics, misleading eavesdroppers into perceiving it as noise, thus achieving covert communication. Compared to directly generating artificial noise using a jammer, this invention does not incur additional energy consumption, and the beamforming algorithm is easier to implement. Compared to covert communication schemes that do not employ artificial noise, its covert performance and capacity are significantly improved.

[0077] Furthermore, this invention employs code index modulation technology, which, compared to directly transmitting covert information, improves channel capacity by changing the ratio of plaintext bits to covert information bits within a single information block without consuming additional channel resources. Therefore, it is also an efficient method for transmitting covert information.

Claims

1. A steganographic communication method based on artificial-like noise and code index modulation, characterized by, Includes the following steps: (10) The sender generates a covert information block and an assistance information block, wherein the covert information block is used to send to the covert information receiver and the assistance information block is used to send to the assisting party; (20) The sender divides the covert information block into covert modulation bits and covert mapping bits. First, the covert modulation bits are M-PSK modulated to form modulation symbols. Then, the covert mapping bits are mapped to the corresponding spreading codes. The real and imaginary parts of the modulation symbols are spread using the spreading codes respectively. The same processing is performed on the assisting information block. The specific method for spreading the real and imaginary parts of the modulation symbols using the spreading codes is as follows: ， in The symbol is after spectral expansion. and For the real and imaginary parts of the modulation symbol, and These are the spreading codes for the hidden mapping bit mapping; (30) The transmitter performs a four-term weighted fractional Fourier transform on the spread covert information block and the assisting information block. With the maximum covert capacity as the objective, a beamforming vector optimization model is established. Then, under specified covert constraints, the beam vector transmitted to the covert information receiver is decomposed in the zero-forcing direction and the orthogonal direction of the zero-forcing direction. The weight factor is then differentiated in the second order to solve for the beamforming vector that maximizes the covert capacity. The transmitter uses this beamforming vector to send signals to the covert information receiver and the assisting party. The two signals form superimposed interference at the eavesdropping party. (40) The covert information receiver performs an inverse four-term weighted fractional Fourier transform on the received signal, and then multiplies it with each spreading code. The set of spreading codes with the largest energy is then mapped back to the recovered covert mapping bits. At the same time, the covert information receiver uses the set of spreading codes with the largest energy to despread the signal after the inverse four-term weighted fractional Fourier transform to obtain the recovered modulation symbols. The receiver then performs M-PSK demodulation on the recovered covert modulation bits. The recovered covert modulation bits are combined with the recovered covert mapping bits to obtain the recovered covert information, thus realizing covert communication based on artificial noise and code index modulation.

2. The covert communication method based on artificial noise and code index modulation according to claim 1, characterized in that, The transmitter (30) performs a four-term weighted fractional Fourier transform on the spread-spectrum covert information block and the assisting information block, and establishes a beamforming vector optimization model with the goal of maximizing the covert capacity. Then, under specified covert constraints, the beam vector transmitted to the covert information receiver is decomposed in the null-forcing direction and the orthogonal direction of the null-forcing direction. The weighting factors are then differentiated in the second order to solve for the beamforming vector that maximizes the covert capacity. The transmitter uses this beamforming vector to send signals to the covert information receiver and the assisting party. The two signals form superimposed interference at the eavesdropping party. The specific method is as follows: (31) The transmitter directly performs a four-term weighted fractional Fourier transform on the spread-spectrum covert information block, and the resulting sequence is called the covert sequence. The assisting information block is first M-PSK modulated, and then subjected to a four-term weighted fractional Fourier transform, and the resulting sequence is called the assisting sequence. The formula for the four-term weighted fractional Fourier transform is: ， Indicates to The four-term weighted fractional Fourier transform, This indicates a covert information block or a helper information block after spread spectrum. They represent The 1st, 2nd, and 3rd discrete Fourier transforms, For the transformation order, Let be the weights, and satisfy the following formula: ， Next, the channel gain from the sender to the covert information receiver, the assisting party, and the eavesdropping party is randomly generated. , , ,Will Multiplying with the hidden sequence, the sum of the results has a mean of 0 and a variance of . Gaussian noise, while... Multiplying with the assist sequence and summing the results, the mean is 0 and the variance is... Gaussian noise; (32) Next, with the goal of maximizing concealment capacity, a beamforming vector optimization model is established, and the expression for concealment capacity is: ， in, The number of active spreading codes, The base of the M_PSK modulation is . , These represent the channel gain from the sender to the receiver of the covert information and the beamforming vector, respectively. The variance of the superimposed Gaussian noise from the sender to the receiver of the concealed information; Then, the hidden constraints are determined, expressed as follows: ， in, This indicates that the sender will not send a hidden sequence. This indicates that the sender is sending a hidden sequence. , In both states, the sender will send an assistance sequence. for and The relative entropy, To detect the probability of error, The number of times the channel is used, where: ， ， These refer to the power of the signals transmitted by the concealed information receiver and the assisting party, respectively. The beamforming vector from the transmitter to the assister is set to... , and Let be the channel gain from the sender to the eavesdropper and the variance of the Gaussian noise. Therefore, the hidden constraint condition is written as: ， because ,and exist Since the expression is monotonically increasing, the hidden constraint can be further written as: ， in for The inverse function; (33) The beam vector transmitted to the covert information receiver The decomposition is performed in the zero-forcing direction and in the orthogonal direction to the zero-forcing direction, as follows: ， in As a weighting factor, This is the zero-forcing beamforming vector from the sender to the receiver of the covert information. Indicates and Perpendicular beamforming vectors will Substituting the hidden constraint expression, we find the weight value that maximizes the hidden capacity, denoted as . ,expression: ， Next, regarding the hidden capacity expression... Perform second-order differentiation: ， in, , , The identity matrix is ​​then used to obtain the poles. The value of is denoted as It is given by the following formula: ， Due to channel variations and noise, the values ​​are uncertain; therefore, the analysis yields... The beamforming schemes corresponding to the two value ranges are as follows: ， ; ， ； According to the above formula, the maximum concealment capacity is achieved. The sender uses and Signals are sent to both the recipient of the concealed information and the assisting party, and the two signals cause superposition interference at the eavesdropping party.

3. The covert communication method based on artificial noise and code index modulation according to claim 1, characterized in that, The (40) covert information receiver performs an inverse four-term weighted fractional Fourier transform on the received signal, and then multiplies it by each spreading code. The set of spreading codes with the highest energy is then mapped back to the recovered covert mapping bits. At the same time, the covert information receiver uses the set of spreading codes with the highest energy to despread the signal after the inverse four-term weighted fractional Fourier transform to obtain the recovered modulation symbols. The receiver then performs M-PSK demodulation on these symbols to obtain the recovered covert modulation bits. The recovered covert modulation bits are combined with the recovered covert mapping bits to obtain the recovered covert information, thus realizing covert communication based on artificial noise and code index modulation. The specific method is as follows: (41) The receiver of the concealed information performs an inverse four-term weighted fractional Fourier transform on the received signal, as shown in the following equation: ， express Four-term weighted fractional Fourier transform, The signal received by the receiver of the concealed information. for The sequence after inverse four-term weighted fractional Fourier transform, and Satisfy the following formula ， express Four-term weighted fractional Fourier transform, It is Gaussian white noise with a mean of 0 and a variance of . Next, utilizing the autocorrelation properties of the spreading code, the receiver of the concealed information... Perform the following processing: ， in, The modulated symbol after despreading. For the first One spreading code, The energy for each spreading code, for After inverse four-term weighted fractional Fourier transform, and then with The noise obtained after multiplication is used by the covert information receiver to reverse-map the spreading code with the highest energy to the recovered covert mapping bits, as shown in the following formula: ， These are the hidden mapping bits obtained from the reverse mapping; (42) Combine the recovered covert modulation bits with the recovered covert mapping bits to realize covert communication based on artificial noise and code index modulation.

4. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements covert communication based on artificial noise and code index modulation according to the covert communication method of any one of claims 1-3.

5. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements covert communication based on artificial noise and code index modulation according to the covert communication method of any one of claims 1-3.

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