A multi-user physical layer security transmission method based on time modulation array

Abstract

The application discloses a kind of multi-user physical layer security transmission methods based on time modulation array, belong to physical layer security technical field, construct space division multiple access security communication system based on time modulation array, including base station end and receiving end, base station end is equipped with time modulation array by N antenna, receiving end includes legal user and eavesdropper, and legal user is equipped with single antenna;In the case of single antenna eavesdropper, I group data streams are transmitted to I single antenna legal users in parallel by space division multiple access technology;Base station pre-encodes data signal, then the data signal after pre-encoding is mapped to OFDM signal, then time modulation technology is used to transmit OFDM signal to legal user.The application is particularly related to the realization of multi-user physical layer security communication using single radio frequency chain time modulation array, and further analyzes the lower bound of system security rate based on time modulation considering the harmonic characteristics of time modulation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of physical layer security, and particularly relates to a multi-user physical layer security transmission method based on a time modulation array. BACKGROUND

[0002] In the existing research on physical layer security based on a time modulation array, the security transmission performance is mainly evaluated by indicators such as bit error rate or signal-to-interference-and-noise ratio, and the physical layer security rate of the system still needs to be further discussed. In addition, considering that the eavesdropper can improve its sampling rate to extract information from the sideband signal, thereby improving its eavesdropping ability and bringing eavesdropping risk to the system, the eavesdropping risk brought by its oversampling needs to be further analyzed and eliminated.

[0003] Due to the openness of the wireless channel, the information transmitted through the wireless channel is easily intercepted by eavesdroppers. In addition to traditional cryptography, physical layer security as a complementary method to enhance data privacy has received more and more attention in recent years. Physical layer security mainly relies on techniques such as beamforming and artificial noise, but these methods require multiple radio frequency chains or need to provide additional interference signal sources, thereby increasing the cost and complexity. Therefore, time modulation array (TMA) as a single radio frequency chain technology has received extensive attention.

[0004] TMA has been applied to achieve physical layer security due to its multi-harmonic characteristics. The existing technology proposes a time modulation-based secure communication, which clarifies that as long as the time modulation frequency is less than the bandwidth of the transmitted signal, due to the aliasing effect, the time modulation signal cannot be correctly demodulated. On this basis, the existing technology can achieve secure communication without prior knowledge of the location of the legitimate receiver by combining enhanced directional modulation with 4D antenna arrays and reverse pointing technology. Subsequently, methods for using TMA to achieve signal distortion have been further extensively studied. In 2019, someone proposed a method for extending the directional modulation technology based on time modulation to OFDM signal transmission. This method combines time modulation with a phase shifter to control the fundamental and harmonic component radiation patterns, enabling the OFDM signal transmitted outside the legitimate user direction to produce controllable aliasing distortion. On this basis, it is pointed out that the eavesdropper can successfully extract data symbols and TMA parameters by using independent component analysis (ICA) technology, and a defense mechanism is proposed to improve the security of communication. In order to further improve the beam control accuracy and energy efficiency, someone proposes a method for 1bit metasurface omnidirectional transmission using time modulation. This method combines with the optimization modulation sequence based on the particle swarm optimization algorithm to improve the performance of secure transmission.

[0005] However, the secure transmission performance in the aforementioned studies was mainly evaluated using metrics such as bit error rate or signal-to-interference-plus-noise ratio (SINR). Secure transmission rates based on time modulation require further analysis. Due to the multi-harmonic characteristics of time modulation, increasing the sampling rate could pose a threat to the system's security performance; therefore, the eavesdropping risks associated with increasing the sampling rate need further investigation. Furthermore, the implementation of multi-user transmission using a single radio frequency chain requires in-depth research. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a multi-user physical layer secure transmission method based on a time modulation array, specifically involving the use of a single radio frequency chain time modulation array to realize multi-user physical layer secure communication, and considering the multi-harmonic characteristics of time modulation, further analyzing the lower bound of the system security rate based on time modulation.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for secure multi-user physical layer transmission based on time modulation array.

[0009] Construct a space division multiple access secure communication system based on time modulation array, including a base station and a receiver. The base station is equipped with a... N A time-modulated array consisting of several antennas is used at the receiver, which includes both legitimate users and eavesdroppers, with each legitimate user equipped with a single antenna. In the presence of a single-antenna eavesdropper, spatial division multiple access (SDMA) technology is used to transmit signals to... I Parallel transmission of single-antenna legitimate users I Group data stream;

[0010] The base station precodes the data signal, then maps the precoded data signal onto an OFDM signal, and then uses time modulation technology to transmit the OFDM signal to the legitimate user.

[0011] As a further preferred embodiment of the present invention, the calculation formula for the OFDM signal is as follows:

[0012] (1)

[0013] in, Indicates the total number of OFDM subcarriers; Indicates the first Complex-valued signals on each subcarrier Indicates the first The angular frequency of the subcarrier, and Indicates the first The center frequency of the subcarrier.

[0014] As a further preferred embodiment of the present invention, the OFDM signal is uniformly distributed among each antenna by a power divider, and after processing by an RF switch, the array factor is [value missing].

[0015] (3)

[0016] in, For RF switching sequences, This indicates the angle between the signal transmission direction and the array normal;

[0017] set up , ,in, For modulation frequency, The interval between adjacent subcarriers. The OFDM signal's first... The first subcarrier Harmonic aliasing to the 1st On the fundamental frequency component of the subcarrier.

[0018] As a further preferred embodiment of the present invention, the first i The received signal at each legitimate user is ,and The calculation formula is as follows:

[0019] (20)

[0020] in, For the equivalent channel matrix, For the first i The precoding matrix of each signal. This is the data that needs to be sent to legitimate users.

[0021] As a further preferred embodiment of the present invention, the transmission rate of the received signal by a legitimate user when the sampling rate is limited is: Transmission rate at finite sampling rate The calculation formula is:

[0022]

[0023] (twenty four)

[0024] in, Let covariance matrix be the variance matrix. , Indicates the first j The precoding matrix of each signal. Represented as a diagonal matrix, its diagonal elements are the noise power. .

[0025] As a further preferred embodiment of the present invention, the upper limit of the transmission rate for legitimate users is: The calculation formula is as follows:

[0026] (31)

[0027] in, They represent The trace of the perturbation matrices of the numerator and denominator. and These represent the non-1 eigenvalues ​​of the numerator and denominator matrices before the perturbation, respectively. This represents the largest eigenvalue of the denominator matrix before the perturbation.

[0028] As a further preferred embodiment of the present invention, the safe rate and its lower bound are calculated:

[0029] After calculating the transmission rates of the eavesdropper and the user, the first... i The security level of each signal is given by the following formula.

[0030] (42)

[0031] in, For legitimate users, the rate at which they receive signals when the sampling rate is limited. The transmission rate for the eavesdropper when the sampling rate is limited;

[0032] Therefore, the sum rate of the system is:

[0033] (43)

[0034] Introducing a lower bound for the confidentiality rate calculation, its first... i The formula for calculating the lower bound of the safe rate for a signal is:

[0035] (44)

[0036] in, This is the upper bound of the eavesdropping rate for the eavesdropper.

[0037] Therefore, the lower bound of the final safe rate of the system is:

[0038] (45)

[0039] As a further preferred embodiment of the present invention, the lower bound of the safe rate is maximized by jointly optimizing power allocation and modulation timing using a particle swarm optimization algorithm, and the calculation formula is as follows:

[0040]

[0041] in This indicates the maximum transmission power. This represents the power of all signals.

[0042] The beneficial effects of this invention are as follows:

[0043] This invention utilizes a single-RF-chain time-modulated array to achieve secure multi-user physical layer communication. Considering the multi-harmonic characteristics of time modulation, it further analyzes the lower bound of the system's secure rate based on time modulation. This invention uses the lower bound of the system's secure rate as the optimization objective, effectively eliminating the risk of eavesdropping and improving the system's security performance. The simulation consistently uses a modulation frequency of one subcarrier spacing, and the optimization schemes considered include maximizing the secure rate under the Nyquist sampling rate and maximizing the lower bound of the secure rate. Simulation results show that this invention can effectively eliminate the risk of eavesdropping, thereby improving system adaptability. Furthermore, the security performance of this invention is unaffected by changes in the eavesdropper's sampling rate. Compared with existing technologies, this invention exhibits superior confidentiality rate performance.

[0044] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0045] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0046] Figure 1 This is a system model diagram of time-modulated multi-user secure communication based on the present invention;

[0047] Figure 2 This is a schematic diagram of the OFDM signal and received signal spectrum of the present invention;

[0048] Figure 3 This is a graph showing the relationship between eavesdropping rate, security rate, and eavesdropping sampling rate in a single-user scenario according to the present invention.

[0049] Figure 4 This is a graph showing the relationship between eavesdropping rate, security rate, and eavesdropping sampling rate in a multi-user scenario according to the present invention.

[0050] Figure 5 This is a graph showing the relationship between the safe rate and the transmission power under different optimization schemes of the present invention;

[0051] Figure 6 This is a graph showing the relationship between the lower bound of the safe rate and the transmission power for different schemes in a scenario where there is no risk of eavesdropping. Detailed Implementation

[0052] likeFigures 1-6 As shown, this invention proposes a multi-user secure transmission method based on a time-modulated array. A time-modulated space-division multiple access (SDMA) multi-user secure transmission system is established. Based on this, the system's security rate is analyzed, and considering the eavesdropping risk caused by the increase in the sampling rate of eavesdroppers, the lower bound of the system's security rate is analyzed. To improve security performance, a particle swarm optimization algorithm is used to jointly optimize the modulation timing and power allocation to maximize the lower bound of the system's security rate. Compared with an insecure time-modulated SDMA system, the method proposed in this invention significantly improves the system's security performance. Furthermore, by considering the impact of increased sampling rate, this invention effectively reduces the eavesdropping risk within the system.

[0053] 1. For example Figure 1 As shown, a space division multiple access secure communication system based on a time modulation array is constructed. In the system scenario, the base station (BS) is equipped with a... N A time-modulated array consisting of several antennas, in the presence of a single-antenna eavesdropper, can transmit signals via spatial division multiple access (SDMA). I Parallel transmission of single-antenna legitimate users (Bobs) I The system consists of multiple data streams, assuming each user has a single antenna. Specifically, the base station precodes the data signals, maps them onto OFDM signals, and then uses time modulation techniques to transmit these signals to legitimate users. Furthermore, because the receivers are located in the far field, the base station applies a plane wave approximation to the signal transmission.

[0054] 2. Time-modulated array transmitter:

[0055] OFDM signals can be mathematically formulated.

[0056] (1)

[0057] in, Represents the imaginary unit. It represents the base of the natural logarithm. This indicates the total number of OFDM subcarriers. Indicates the first Complex-valued signals on each subcarrier Indicates the first The angular frequency of the subcarrier, and Indicates the first The center frequency of the subcarrier. Assume the frequency spacing between adjacent subcarriers and the frequency of the first subcarrier are respectively determined by... and Therefore, the center frequency of the OFDM signal can be given as...

[0058] (2)

[0059] Subsequently, the signal is evenly distributed among each antenna by a power divider. After processing by the RF switch, the array factor can be given as...

[0060] (3)

[0061] in, It is defined as an RF switch sequence. This indicates the angle between the signal transmission direction and the array normal.

[0062] Single-pole single-throw switch It can be represented as

[0063] (4)

[0064] in, and These indicate the times when the device is "opened" and "closed," respectively.

[0065] Unlike single-pole single-throw switches, the timing sequence of a 1-bit phase shifter switch can be represented as follows:

[0066] (5)

[0067] in and Defined as switch to 0 and At that moment.

[0068] Due to the periodicity of the modulation sequence, and It can be decomposed into Fourier series with different frequency components. It can be expanded into

[0069] (6)

[0070] in For modulation frequency, The Fourier coefficients can be calculated as follows:

[0071] (7)

[0072] in , and These are defined as the normalized on-time and normalized center time, respectively. Similarly, the Fourier coefficients of the 1-bit phase shifter expansion are calculated as follows:

[0073] (8)

[0074] in , For ease of discussion, the Fourier coefficients of the two switching sequences are uniformly represented as follows when no special distinction is required: They are only represented as [specific terms] when a clear distinction is required. and .when OFDM signals will experience aliasing. To simplify calculations, assume... ,in .in, For modulation frequency, The interval between adjacent subcarriers is denoted as . Therefore, the ... The first subcarrier Harmonics will be mixed up to the 1st On the fundamental frequency component of the subcarrier.

[0075] 3. Multi-user transmission and reception model:

[0076] To illustrate the impact of the sampling rate on the system, Bob i The sampling rates of and Eve are defined as follows: and Among them, when ( When ), it indicates that the signal is received at the Nyquist sampling rate; ( When ), it indicates that the receiver has oversampled. Define the base station to Bob. i The channel matrix is When the receiver receives the signal at the Nyquist sampling rate, the channel matrix is ​​defined as:

[0077] (9)

[0078] in , Indicates unit path loss. . This represents the path loss index. ,in, and They represent Bob i Distance and angle to Alice. When oversampling, assume a sampling rate of... The channel matrix is ​​defined as

[0079] (10)

[0080] By further definition Bob i The received signal can be represented as

[0081] (11)

[0082] in , Indicates from the first n root antenna to Bob i The channel coefficients. At the Nyquist sampling rate, Represented as During oversampling, Represented as .also, This represents Gaussian white noise in the frequency domain. . Defined as an aliasing matrix, used to describe the first... n The aliasing situation on the root antenna. For example, when the receiver receives a signal at the Nyquist sampling rate, such as Figure 2 As shown in (b), the aliasing matrix It can be defined as

[0083] (12)

[0084] In this case, all elements of the aliasing matrix are non-zero. However, for other modulation frequencies, zero elements will appear in the aliasing matrix. Furthermore, for... The modulated OFDM signal will not produce aliasing, therefore It will be a diagonal matrix containing only the fundamental frequency.

[0085] It is worth noting that in the case of oversampling, the received out-of-band harmonics will also experience aliasing effects caused by various subcarriers (e.g., Figure 2 (as shown in (c)). For example, the aliasing matrix becomes

[0086] (13)

[0087] Therefore, the general term of the aliasing matrix can be expressed as:

[0088] (14)

[0089] in ,and A conditional function is defined as follows:

[0090] (15)

[0091] To simplify formula (11), the equivalent channel matrix is ​​defined as follows: Therefore, the receiving model is further simplified to

[0092] (17)

[0093] Subsequently, the equivalent channel matrix The right singular vector matrix obtained by singular value decomposition (SVD) , can be represented as .in Represents the maximum The eigenvectors corresponding to the eigenvalues This represents the remaining eigenvectors.

[0094] For downlink multi-user transmission scenarios, the transmitted signal at the base station can be represented as:

[0095] (18)

[0096] in This means it needs to be sent to Bob. i Data, Indicates the first i The precoding matrix of a signal is defined as

[0097] (19)

[0098] Therefore, Bob i The final expression for the received signal can be represented as:

[0099] (20)

[0100] in, For the desired signal, Add noise to the interference.

[0101] 4. Performance analysis of safe rate and its lower bound

[0102] (1) Transmission rate under finite sampling rate

[0103] To clarify the rates corresponding to various sampling frequencies, the sampling rate is... The rate of the received signal is defined as The receiver received the first... i The signal sent by Alice is the first i The mutual information between signals can be given by the following formula.

[0104]

[0105] (twenty one)

[0106] Assuming both the signal and noise follow a Gaussian distribution, the covariance matrix of the signal is defined as follows: ,So It can be calculated as

[0107] (twenty two)

[0108] in Indicates the first j The covariance matrix of the signals, where ,. Because Bob i When receiving signals from the base station, interference from other signals is also received; therefore, the conditional differential entropy includes the effects of channel noise components and other signal interference. Given that the interference also follows a Gaussian distribution, therefore... It can be calculated as

[0109] (twenty three)

[0110] Therefore, the transmission rate can be expressed as

[0111]

[0112] (twenty four)

[0113] in, Let covariance matrix be the variance matrix. , Indicates the first j The precoding matrix of each signal. Represented as a diagonal matrix, its diagonal elements are the noise power. .

[0114] It is worth noting that, due to the multi-harmonic characteristics of time modulation, increasing the sampling rate introduces additional out-of-band harmonics, thereby increasing the system's transmission rate. Similarly, eavesdroppers at a sampling rate of... The transmission rate at that time is defined as .

[0115] (2) Upper bound of transmission rate

[0116] To simplify the calculation of the upper bound, the following definition is established.

[0117] (25)

[0118] By substituting the formula into (24), we can further define... and ,in Since the energy of higher-order harmonics gradually decays with increasing sampling rate, the rate effect of further increasing the sampling rate at a sufficiently high sampling rate can be considered as a rate perturbation. Assume the maximum sampling rate before the perturbation is... So the sampling rate is based on Increase to The channel equivalent matrix can be decomposed into

[0119] (26)

[0120] in and Let represent the upper and lower perturbation matrices of the channel, respectively. For ease of subsequent calculation of the upper bound, we will use the numerator as an example. Decomposed into a fixed matrix and a perturbation matrix:

[0121] (27)

[0122] in For a dimension A fixed matrix is ​​defined as

[0123] = (28)

[0124] Furthermore, the perturbation matrix in (27) can be represented as

[0125] (29)

[0126] Therefore, when the sampling rate approaches infinity, the transmission rate can be described as

[0127] (30)

[0128] In order to obtain The upper bound is defined using eigenvalue perturbation theory. Furthermore, the upper bound expression for the transmission rate is expressed as:

[0129] (31)

[0130] in, They represent The trace of the perturbation matrices of the numerator and denominator. and These represent the non-1 eigenvalues ​​of the numerator and denominator matrices before the perturbation, respectively. This represents the largest eigenvalue of the denominator matrix before the perturbation.

[0131] It can be seen that the key to obtaining the upper bound lies in solving for the trace of the perturbation matrix. Taking the molecule as an example, the trace of the perturbation matrix can be expressed as:

[0132]

[0133] (32)

[0134] Since the structure of the aliasing matrix changes with different modulation frequencies, and Related to the modulation frequency, it can be defined as

[0135] (33)

[0136] in Calculated as

[0137] (34)

[0138] Among them, due to The value and It is irrelevant, and its calculation depends on the configuration of the RF switch; therefore, it requires separate analysis of the infinite series under the two configurations. When the RF switch is a single-pole single-throw switch, It can be defined as

[0139]

[0140] (35)

[0141] Among them, simplification for 。

[0142] In order to ensure Constrained within the periodic interval of the discrete-time Fourier transform (DTFT), Defined as

[0143] (36)

[0144] When the RF switch is a 1-bit phase shifter Represented as

[0145] (37)

[0146] in Calculated as follows

[0147] (38)

[0148] It can be seen that the key to calculating infinite series lies in solving the problem. . The final result can be obtained through DTFT calculation:

[0149] (39)

[0150] in and Is with and The associated functions can be defined separately.

[0151] (40)

[0152] also, Represented as

[0153] (41)

[0154] The above calculations determine the trace of the perturbation matrix, allowing for the further derivation of the upper bound of the rate. Similarly, the upper bound of the eavesdropper's eavesdropping rate can be determined. It can be calculated using a similar method.

[0155] (3) Safe rate and its lower bound:

[0156] After calculating the transmission rates of the eavesdropper and the user, the first... i The security level of a signal can be given by the following formula.

[0157] (42)

[0158] Therefore, the sum and rate of the system are

[0159] (43)

[0160] Furthermore, to further improve system security, introducing a lower bound on the confidentiality rate helps describe the system's performance in the worst-case scenario. Its second... i The lower bound of the safe rate for a signal can be defined as follows:

[0161] (44)

[0162] in, Indicates the first i Transmission rate per user at the Nyquist sampling rate This is the upper bound of the eavesdropping rate for the eavesdropper.

[0163] Therefore, the lower bound of the final safe rate of the system is:

[0164] (45)

[0165] 5. Optimization objective description: Maximize the safe rate lower bound by jointly optimizing power allocation and modulation timing.

[0166]

[0167] in This indicates the maximum transmission power. This represents the total power of all transmitted signals.

[0168] As can be seen from (7) and (8), the modulation timing In and Changes in the fundamental frequency and harmonic modes simultaneously alter the fundamental frequency and harmonic modes. This demonstrates a clear coupling relationship between the variables in the optimization problem. Therefore, this invention employs the Particle Swarm Optimization (PSO) algorithm to solve this problem.

[0169] This invention uses the lower bound of the system's safe rate as the optimization objective, effectively eliminating the risk of eavesdropping and improving the system's security performance. The simulation consistently uses a modulation frequency of one subcarrier spacing, and the optimization schemes considered include maximizing the safe rate for the eavesdropper at the Nyquist sampling rate and maximizing the lower bound of the safe rate.

[0170] To assess the eavesdropping risk in a single-user system, Figure 3 The trends of eavesdropping rate and security rate with the eavesdropper sampling rate are shown. The results indicate that the proposed security rate maximization scheme achieves a significant improvement in confidentiality rate. Furthermore, increasing the eavesdropper sampling rate enhances the system's eavesdropping analysis capabilities. Figure 3 As can be seen, with the increase of the eavesdropper's sampling rate, the confidentiality rate of both the existing schemes and the security rate maximization scheme under the eavesdropper's Nyquist sampling rate significantly decreases. In contrast, the security rate lower bound maximization scheme exhibits extremely strong robustness in the face of increased eavesdropping sampling rates, and the confidentiality rate does not significantly decrease with the increase of the eavesdropping sampling rate. This result shows that the scheme proposed in this invention can effectively suppress the eavesdropping risk caused by high sampling rates, thereby ensuring the stability of the system's security performance.

[0171] To further assess the eavesdropping risk of multi-user systems, the comparison scheme was expanded to TDMA multi-user transmission. Figure 4 It can be seen that as the eavesdropper's sampling rate increases, the security rate of the comparison scheme will eventually drop to 0, thus hindering the system's ability to achieve secure communication. Figure 4 (b) illustrates the secure rate maximization scheme for eavesdroppers at the Nyquist sampling rate. Compared to a TDMA multi-user system based on a contrastive scheme, Figure 4 The security features described in (b) are significantly enhanced; however, the risk of eavesdropping still exists. In contrast, [the following text is incomplete and requires further context: "by..."] Figure 4 (c) It can be seen that the secure rate under the scheme of maximizing the lower bound of the secure rate does not decrease significantly with the increase of the eavesdropping sampling rate. This further illustrates that optimizing the lower bound of the secure rate significantly reduces the system's sensitivity to the eavesdropper's sampling rate, effectively enhancing the system's adaptability and security.

[0172] Figure 5 This study investigates the trade-off between eavesdropping risk and maximizing security rate. Based on the preceding analysis, it is evident that under the security rate maximization scheme, the system's security rate does not fluctuate significantly with increasing eavesdropping sampling rate. Based on this characteristic, Figure 5 The lower bound of the security rate is used as a representative indicator of the security rate maximization scheme. For the security rate maximization scheme under the Nyquist sampling rate of the eavesdropper, in order to comprehensively reflect its security performance changes, Figure 5 Simulation results also plotted the lower bound of the security rate and the security rate when the eavesdropper uses the Nyquist sampling rate. The simulation results show that maximizing the lower bound of the security rate effectively improves the security rate lower bound. Furthermore, after maximizing the security rate lower bound, the lower bound of the security rate approaches the performance limit. This indicates that eliminating the risk of eavesdropping does not require a significant sacrifice in the security rate, while effectively improving the system's security performance.

[0173] Figure 6 Simulations compared the lower bounds of the security rate for different schemes in scenarios without eavesdropping risk. The baseline schemes included a user and rate maximization scheme and a time-division multiple access scheme extended from the comparison scheme. Simulation results show that the proposed scheme has significant advantages in confidentiality performance. Specifically, the lower bound of the security rate for the comparison scheme is zero, indicating that it cannot achieve secure communication. When the same lower bound of the security rate is required, the proposed scheme can reduce the transmit power by approximately 8 dB compared to the user and rate optimization scheme. These results verify the effectiveness of the proposed scheme in eliminating eavesdropping risk, not only maintaining a high secure communication rate but also significantly reducing system power consumption, demonstrating excellent practical value and security performance.

[0174] Simulation results demonstrate that the proposed scheme effectively eliminates the risk of eavesdropping, thereby improving system adaptability. Furthermore, the security performance of this scheme is unaffected by changes in the eavesdropper's sampling rate. Compared to benchmark schemes in the prior art, this invention exhibits superior confidentiality rate performance.

[0175] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A multi-user physical layer secure transmission method based on a time-modulated array, characterized in that: Construct a space division multiple access secure communication system based on time modulation array, including a base station and a receiver. The base station is equipped with a... N A time-modulated array consisting of several antennas is used at the receiver, which includes both legitimate users and eavesdroppers, with each legitimate user equipped with a single antenna. In the presence of a single-antenna eavesdropper, spatial division multiple access (SDMA) technology is used to transmit signals to... I Parallel transmission of single-antenna legitimate users I Group data stream; The base station precodes the data signal, then maps the precoded data signal onto the OFDM signal, and then uses time modulation technology to transmit the OFDM signal to the legitimate user. The formula for calculating the OFDM signal is: (1) in, Indicates the total number of OFDM subcarriers; Indicates the first Complex-valued signals on each subcarrier Indicates the first The angular frequency of the subcarrier, and Indicates the first The center frequency of the subcarrier; The OFDM signal is evenly distributed among each antenna by a power divider, and after processing by an RF switch, the array factor is... (3) in, For RF switching sequences, This indicates the angle between the signal transmission direction and the array normal; set up , ,in, For modulation frequency, The interval between adjacent subcarriers is the first of the OFDM signals. The first subcarrier Harmonic aliasing to the 1st On the fundamental frequency component of the subcarrier; No. i The received signal at each legitimate user is ,and The calculation formula is as follows: (20) in, For the equivalent channel matrix, For the first i The precoding matrix of each signal. This is the data that needs to be sent to legitimate users.

2. The multi-user physical layer secure transmission method based on time modulation array according to claim 1, characterized in that: The transmission rate of the received signal for a legitimate user at a limited sampling rate is: Transmission rate at finite sampling rate The calculation formula is: (24) in, For the first The covariance matrix of each signal. , Indicates the first j The precoding matrix of each signal. Represented as a diagonal matrix, its diagonal elements are the noise power. .

3. The multi-user physical layer secure transmission method based on time modulation array according to claim 2, characterized in that: The upper limit of the transmission rate for legitimate users is The calculation formula is as follows: (31) in, They represent The trace of the perturbation matrices of the numerator and denominator. and These represent the non-1 eigenvalues ​​of the numerator and denominator matrices before the perturbation, respectively. This represents the largest eigenvalue of the denominator matrix before the perturbation.

4. The multi-user physical layer secure transmission method based on time modulation array according to claim 3, characterized in that: Calculate the safe rate and its lower bound: After calculating the transmission rates of the eavesdropper and the user, the first... i The security level of each signal is given by the following formula. (42) in, For legitimate users, the rate at which they receive signals when the sampling rate is limited. The transmission rate for the eavesdropper when the sampling rate is limited; Therefore, the sum rate of the system is: (43) Introducing a lower bound for the confidentiality rate calculation, its first... i The formula for calculating the lower bound of the safe rate for a signal is: (44) in, Indicates the first i Transmission rate per user at the Nyquist sampling rate This is the upper bound of the eavesdropping rate for the eavesdropper. Therefore, the lower bound of the final safe rate of the system is: (45)。 5. A multi-user physical layer secure transmission method based on a time-modulated array according to claim 4, characterized in that: The lower bound of the safe rate is maximized by jointly optimizing power allocation and modulation timing using a particle swarm optimization algorithm, as shown in the following formula: in This indicates the maximum transmission power. This represents the total power of all transmitted signals.

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