Multi-user physical layer secure transmission method based on time modulation array

Abstract

The invention discloses a multi-user physical layer secure transmission method based on a time modulation array, and belongs to the technical field of physical layer security, a space division multiple access secure communication system based on the time modulation array is constructed, the space division multiple access secure communication system comprises a base station end and a receiving end, the base station end is equipped with the time modulation array composed of N antennas, the receiving end comprises legal users and eavesdroppers, and each legal user is provided with a single antenna; in the presence of a single-antenna eavesdropper, transmitting I groups of data streams to I single-antenna legal users in parallel through a space division multiple access technology; a base station pre-codes a data signal, then maps the pre-coded data signal to an OFDM signal, and then transmits the OFDM signal to a legal user by adopting a time modulation technology. The invention particularly relates to a method for realizing multi-user physical layer security communication by using a time modulation array of a single radio frequency chain, and further analyzes a system security rate lower bound based on time modulation by considering the multi-harmonic characteristic of time modulation.

Description

Technical Field

[0001] The present invention belongs to the technical field of physical layer security, and in particular relates to a multi-user physical layer security transmission method based on a time modulation array. Background Art

[0002] In existing research on physical layer security based on time-modulated arrays, secure transmission performance is primarily evaluated using metrics such as bit error rate (BER) or signal-to-interference-and-noise ratio (SINR). Further research is needed to assess the physical layer security rate of these systems. Furthermore, given that an eavesdropper can increase the sampling rate to extract information from sideband signals, thereby enhancing their eavesdropping capabilities and posing an eavesdropping risk to the system, the eavesdropping risk posed by oversampling warrants further analysis and mitigation.

[0003] Due to the open nature of wireless channels, information transmitted through them is vulnerable to interception by eavesdroppers. In addition to traditional cryptographic techniques, physical layer security has garnered increasing attention in recent years as a complementary approach to enhancing data confidentiality. Physical layer security primarily relies on techniques such as beamforming and artificial noise. However, these methods require multiple RF chains or additional interference sources, increasing cost and complexity. Consequently, time-modulated arrays (TMAs) as a single RF chain technology have garnered significant attention.

[0004] Due to its multi-harmonic properties, TMA has been applied to physical layer security. Prior art proposes secure communications based on time modulation, stating that as long as the time modulation frequency is less than the bandwidth of the transmitted signal, the time-modulated signal cannot be correctly demodulated due to aliasing. Building on this, prior art combines enhanced directional modulation with 4D antenna arrays and reverse pointing techniques to achieve secure communications without prior knowledge of the authorized receiver's location. Subsequently, methods for using TMA to mitigate signal distortion have been further extensively studied. In 2019, a method was proposed to extend time-modulated directional modulation techniques to OFDM signal transmission. By combining time modulation with phase shifters, this method controls the radiation patterns of the fundamental and harmonic components, enabling controlled aliasing distortion in OFDM signals transmitted outside the direction of the authorized user. Building on this, it was shown that an eavesdropper could successfully extract data symbols and TMA parameters using independent component analysis (ICA) techniques, and a defense mechanism was proposed to enhance communication security. To further improve beam steering accuracy and energy efficiency, a method for 1-bit fully directional transmission using a metasurface using time modulation was proposed. This method is combined with an optimized modulation sequence based on a particle swarm optimization algorithm to improve the performance of secure transmission.

[0005] However, the secure transmission performance evaluated in these studies is primarily based on metrics such as bit error rate (BER) or signal-to-interference-and-noise ratio (SINR). Further analysis is needed to determine the security rate based on time modulation. Due to the multi-harmonic nature of time modulation, an eavesdropper increasing the sampling rate could potentially compromise system security. Therefore, the eavesdropping risks associated with increased sampling rates require further investigation. Furthermore, achieving multi-user transmission using a single RF chain requires further research. Summary of the Invention

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

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

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

[0009] A secure communication system based on a time-modulated array (TMA) using spatial division multiple access (SDMA) is constructed. The system consists of a base station and a receiver. The base station is equipped with a TDMA array consisting of N antennas. The receiver includes legitimate users and eavesdroppers, each of whom is equipped with a single antenna. In the presence of a single-antenna eavesdropper, SDMA is used to transmit I data streams in parallel to I legitimate users with a single antenna.

[0010] The base station precodes the data signal, maps the precoded data signal to 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 of the OFDM signal is:

[0012]

[0013] Where K represents the total number of OFDM subcarriers; s k represents the complex value signal on the kth subcarrier, w k =2πf k represents the angular frequency of the kth subcarrier, and f k Indicates the center frequency of the kth subcarrier.

[0014] As a further preferred embodiment of the present invention, the OFDM signal is evenly distributed between each antenna through a power divider. After being processed by the RF switch, the array factor is

[0015]

[0016] Among them, U n (t) is the RF switching sequence, θ represents the angle between the signal transmission direction and the array normal;

[0017] Let f p =pf Δ , p={1,2,...,K}, where f p is the modulation frequency, f Δ The qth harmonic of the kth subcarrier of the OFDM signal is aliased onto the fundamental frequency component of the k+pqth subcarrier.

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

[0019]

[0020] in, is the equivalent channel matrix, is the precoding matrix of the i-th signal, x i 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 of the legitimate user when the sampling rate is limited is C i (S i ); Transmission rate C under finite sampling rate i (S i ) is calculated as:

[0022]

[0023] in, is the covariance matrix, represents the precoding matrix of the j-th signal, It is represented as a diagonal matrix whose diagonal elements are the noise power

[0024] As a further optimization of the present invention, the upper limit of the transmission rate of the legal user is The calculation formula is as follows:

[0025]

[0026] in, and Represents C i (S i →∞), the trace of the perturbation matrix of the numerator and denominator, and Respectively represent the non-1 eigenvalues of the numerator and denominator matrices before perturbation, Represents the largest eigenvalue of the denominator matrix before perturbation.

[0027] As a further optimization of the present invention, the safe rate and its lower bound are calculated:

[0028] After calculating the transmission rates of the eavesdropper and the user, the confidentiality rate of the i-th signal is given by

[0029] C s,i (S i ,S E )=C i (S i )-C E,i (S E ) (42)

[0030] Among them, C i (S i ) is the rate at which legitimate users receive signals when the sampling rate is limited, C E,i (S E ) is the transmission rate of the eavesdropper when the sampling rate is limited;

[0031] Therefore, the sum rate of the system is:

[0032]

[0033] The lower bound of the confidentiality rate is introduced, and the calculation formula for the lower bound of the security rate of the i-th signal is:

[0034]

[0035] in, is the upper bound of the eavesdropper's eavesdropping rate;

[0036] Therefore, the lower bound of the final system's safety rate is:

[0037]

[0038] As a further preferred embodiment of the present invention, the power allocation and modulation timing are jointly optimized by the particle swarm optimization algorithm to maximize the lower bound of the safe rate. The calculation formula is as follows:

[0039]

[0040] Where P represents the maximum transmit power, Represents the power of all signals.

[0041] The beneficial effects of the present invention are:

[0042] The present invention utilizes a time modulation array of a single radio frequency chain to achieve multi-user physical layer secure communication, and taking into account the multi-harmonic characteristics of time modulation, further analyzes the lower bound of the system security rate based on time modulation. The present invention takes the lower bound of the system security rate as the optimization target, effectively eliminating the risk of eavesdropping and improving the security performance of the system. During the simulation process, the modulation frequency is uniformly set to be a single times the subcarrier spacing, and the optimization schemes considered in the simulation include the eavesdropper's security rate maximization scheme at the Nyquist sampling rate and the security rate lower bound maximization scheme. The simulation results show that the present invention can effectively eliminate the risk of eavesdropping, thereby improving the adaptability of the system. In addition, the security performance of the invention is not affected by changes in the eavesdropper's sampling rate. Compared with the prior art, the present invention exhibits superior confidentiality rate performance.

[0043] Other advantages, objectives and features of the present invention will be described in the following description and will be apparent to those skilled in the art to some extent, or those skilled in the art can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0045] Figure 1 This is a system model diagram of multi-user secure communication based on time modulation according to the present invention;

[0046] Figure 2 Schematic diagram of the OFDM signal and received signal spectrum of the present invention;

[0047] Figure 3 This is a relationship diagram between the eavesdropping rate, security rate, and eavesdropping sampling rate in a single-user scenario of the present invention;

[0048] Figure 4 This is a relationship diagram between the eavesdropping rate, security rate, and eavesdropping sampling rate in a multi-user scenario of the present invention;

[0049] Figure 5 This is a relationship diagram between the security rate and the transmission power under different optimization schemes of the present invention;

[0050] Figure 6 This is a relationship diagram between the lower bound of the security rate and the transmission power of different schemes in the scenario without eavesdropping risk of the present invention. DETAILED DESCRIPTION

[0051] like Figures 1 to 6As shown, the present invention proposes a multi-user secure transmission method based on a time modulation array. A time-modulated spatial division multiple access multi-user secure transmission system is established. Based on this, the confidentiality rate of the system is analyzed, and considering the eavesdropping risk caused by the increase in the eavesdropper's sampling rate, the lower bound of the system's security rate is analyzed. In order to improve the 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 the non-secure time modulation spatial division multiple access system, the method proposed in the present invention significantly improves the security performance of the system. In addition, by considering the impact of the increase in the sampling rate, the present invention effectively reduces the eavesdropping risk within the system.

[0052] 1. Such as Figure 1 As shown in the figure, a secure communication system based on spatial division multiple access (SDMA) using a time modulation array is constructed. In this system scenario, a base station (BS) is equipped with a time modulation array consisting of N antennas. In the presence of a single-antenna eavesdropper (Eve), SDMA technology is used to transmit I groups of data streams in parallel to I single-antenna legitimate users (Bobs), assuming that each user has a single antenna. Specifically, the BS precodes the data signals, maps them onto OFDM signals, and then uses time modulation techniques to transmit these signals to the legitimate users. In addition, since the receiver is located in the far field, the BS applies a plane wave approximation to the signal transmission.

[0053] 2. Time modulation array transmitter:

[0054] The OFDM signal can be mathematically formulated as

[0055]

[0056] Where j represents the imaginary unit, e represents the natural logarithm base, and K represents the total number of OFDM subcarriers. k represents the complex value signal on the kth subcarrier, w k =2πf k represents the angular frequency of the kth subcarrier, and f k represents the center frequency of the kth subcarrier. Assume that the frequency interval between adjacent subcarriers and the frequency of the first subcarrier are represented by f Δ and f0. Therefore, the center frequency of the OFDM signal can be given as

[0057]

[0058] The signal is then evenly distributed between each antenna through a power divider. After processing by the RF switch, the array factor can be given as

[0059]

[0060] Among them, U n (t) is defined as the RF switching sequence. θ represents the angle between the signal transmission direction and the array normal.

[0061] SPST switch U spst,n (t) can be expressed as

[0062]

[0063] Among them, t on,n and t off,n Indicates the moments of "opening" and "closing" respectively.

[0064] Unlike a single-pole single-throw switch, the switching timing of a 1-bit phase shifter can be expressed as

[0065]

[0066] where t 0,n and t π,n It is defined as the moment when the switch switches to 0 and π.

[0067] Due to the periodicity of the modulation sequence, U spst,n (t) and U 1-bit,n (t) can be decomposed into Fourier series with different frequency components. spst,n (t) can be expanded into

[0068]

[0069] where f p =1 / T p is the modulation frequency, α spst,q,n represents the Fourier coefficients, which can be calculated as

[0070]

[0071] where sinc(πqτ n )=sin(πqτ n ) / (πqτ n ), τ n and are defined as the normalized on-time and the normalized center moment, respectively. Similarly, the Fourier coefficients of the 1-bit phase shifter expansion are calculated as

[0072]

[0073] where τ n =(t π,n -t 0,n ) / T p , For the convenience of discussion, the Fourier coefficients of the two switching sequences are uniformly expressed as α when no special distinction is needed. q,n Only when they need to be clearly distinguished are they expressed as α spst,q,n and α 1-bit,q,n When f p ≤Kf Δ , OFDM signal will produce aliasing. To simplify the calculation, assume f p =pf Δ , where p = {1, 2, ..., K}. Where f p is the modulation frequency, f Δ Therefore, the qth harmonic of the kth subcarrier will be aliased onto the fundamental frequency component of the k+pqth subcarrier.

[0074] 3. Multi-user transmission and reception model:

[0075] To illustrate the effect of sampling rate on the system, the sampling rates of Bob i and Eve are defined as f sample,i =S i fΔ and f sample,E =S E fΔ. When S i =K(S E =K), it means the signal is received at the Nyquist sampling rate; S i >K(S E >K), it means the receiver is over-sampling. The channel matrix from the base station to Bob i is defined as When the receiver receives the signal at the Nyquist sampling rate, the channel matrix is defined as:

[0076]

[0077] in represents the unit path loss, λ c =ν / f c， ν=3×10 8 m / s. Represents the path loss exponent. Among them, d i and θ i Represent the distance and angle between Bob i and Alice respectively. When oversampling, assuming the sampling rate is f sample，i =(K+2Q)f Δ , the channel matrix is defined as

[0078]

[0079] By further defining s=[s1,s2,…,s K ]T , Bob i’s received signal can be expressed as

[0080]

[0081] in represents the channel coefficient from the nth antenna to Bob i. At the Nyquist sampling rate, h i,n,K Represented as h i,n,K =[h 1,n,i ,h 2,n,i ,…,h K,n,i ] T , when oversampling, h i,n,K+2Q Represented as h i,n,K+2Q =[h 1-Q,n,i ,h 2-Q,n,i ,…,h K+Q,n,i ] T .also, represents Gaussian white noise in the frequency domain, It is defined as the aliasing matrix, which is used to describe the aliasing situation on the nth antenna. p =f Δ For example, when the receiver receives the signal at the Nyquist sampling rate, Figure 2 As shown in (b), the aliasing matrix A n,1,K Can be defined as

[0082]

[0083] 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. In addition, for P = K, the modulated OFDM signal will not produce aliasing, so A n,K,K will be a diagonal matrix containing only the fundamental frequencies.

[0084] It is worth noting that in the case of oversampling, the received out-of-band harmonics will also experience aliasing effects caused by the various subcarriers (such as Figure 2 (c)). With f p =f Δ For example, the aliasing matrix becomes

[0085]

[0086] Therefore, the general term of the aliasing matrix can be expressed as

[0087]

[0088] in And I Q％p＝0represents a conditional function, defined as

[0089]

[0090] In order to simplify formula (11), the equivalent channel matrix is defined as Therefore, the receiving model is further simplified to

[0091]

[0092] Then, the equivalent channel matrix The right singular vector matrix obtained by the singular value decomposition (SVD) of It can be expressed as in represents the eigenvector corresponding to the maximum K / I eigenvalue, represents the remaining eigenvectors.

[0093] For the downlink multi-user transmission scenario, the transmitted signal at the base station can be expressed as

[0094]

[0095] where x i Indicates the data that needs to be sent to Bob i, The precoding matrix representing the i-th signal is defined as

[0096]

[0097] Therefore, the final expression of the received signal at Bob i can be expressed as

[0098]

[0099] in, is the expected signal, Add noise to interference.

[0100] 4. Performance Analysis of Safe Rate and Its Lower Bound

[0101] (1) Transmission rate under limited sampling rate

[0102] To clarify the rates corresponding to various sampling frequencies, the sampling rate is f sample,i =S i f Δ The rate of the received signal is defined as C i (S i ). The mutual information between the i-th signal received by the receiver and the i-th signal sent by Alice can be given by

[0103]

[0104] Assuming that both the signal and the noise follow Gaussian distribution, the covariance matrix of the signal is defined as Then h It can be calculated as

[0105]

[0106] in represents the covariance matrix of the jth signal, where j≠i,. Since Bob i receives interference from other signals while receiving the signal from the base station, the conditional differential entropy includes the channel noise component and the influence of other signal interference. Since the interference also follows a Gaussian distribution, h(z i ) can be calculated as

[0107]

[0108] Therefore, the transmission rate can be expressed as

[0109]

[0110] in, is the covariance matrix, represents the precoding matrix of the j-th signal, It is represented as a diagonal matrix whose diagonal elements are the noise power

[0111] It is worth noting that due to the multi-harmonic characteristics of time modulation, the increase in sampling rate will introduce additional out-of-band harmonics, thereby increasing the transmission rate of the system. sample,E =S E f Δ The transmission rate when E,i (S E ).

[0112] (2) Upper bound of transmission rate

[0113] In order to simplify the calculation of the subsequent upper bound, the following definition is established

[0114]

[0115] By substituting formula (24), we can further define and in Since the energy of high-order harmonics gradually decays with the increase of sampling rate, the rate impact caused by further increasing the sampling rate at a sufficiently large sampling rate can be regarded as a rate disturbance. Assume that the maximum sampling rate before the disturbance is f sample,i =β M fΔ , then the sampling rate is based on f sample,i =β M f Δ Increase to f sample,i =∞f Δ , the channel equivalent matrix can be decomposed into

[0116]

[0117] Among them H dU,i and H dL,i Represent the upper perturbation and lower perturbation matrices of the channel respectively. In order to facilitate the subsequent calculation of the upper bound, taking the numerator as an example, Decompose into a fixed matrix and a perturbation matrix:

[0118]

[0119] in For a dimension S i ×S i The fixed matrix is defined as

[0120]

[0121] Furthermore, the perturbation matrix in (27) can be expressed as

[0122]

[0123] Therefore, when the sampling rate approaches infinity, the transmission rate can be described as

[0124]

[0125] In order to obtain C i (S i →∞), the upper bound is transformed using the eigenvalue perturbation theory. Its upper bound is defined as And further express the upper bound of the transmission rate as

[0126]

[0127] in, and Represents C i (S i →∞), the trace of the perturbation matrix of the numerator and denominator, and Respectively represent the non-1 eigenvalues of the numerator and denominator matrices before perturbation, Represents the largest eigenvalue of the denominator matrix before perturbation.

[0128] It can be seen that the key to obtaining the upper bound lies in solving the trace of the perturbation matrix. Taking the molecule as an example, the trace of the perturbation matrix can be expressed by calculation as

[0129]

[0130] Since the structure of the aliasing matrix changes with different modulation frequencies, η and It is related to the modulation frequency and can be defined as

[0131]

[0132] Among them J n,m (v,g) is calculated as

[0133]

[0134] Among them, due to The value of is independent of ζ, and its calculation is related to the configuration of the RF switch, so it is necessary to analyze the infinite series under the two configurations separately. When the RF switch is a single-pole single-throw switch, J n,m,spst (v,g) can be defined as

[0135]

[0136] Among them, simplified is (a).

[0137] In order to ensure is limited to the discrete time Fourier transform (DTFT) period, is defined as

[0138]

[0139] When the RF switch is a 1-bit phase shifter, J n,m,1-bit (v,g) is represented as

[0140]

[0141] in Calculated as

[0142]

[0143] It can be seen that the key to calculating infinite series lies in solving (a). (a) can be calculated by DTFT to get the final result:

[0144]

[0145] in and is a function associated with x1 and x2, which can be defined as

[0146]

[0147] In addition, b1, b2, b3, b4 are expressed as

[0148]

[0149] Through the above calculations, the trace of the perturbation matrix can be determined, and the upper bound of the rate can be further derived. Similarly, the upper bound of the eavesdropper's eavesdropping rate is It can be calculated in a similar way.

[0150] (3) Safe rate and its lower bound:

[0151] After calculating the transmission rates of the eavesdropper and the user, the confidentiality rate of the i-th signal can be given by

[0152] C s,i (S i ,S E )=C i (S i )-C E,i (S E ) (42)

[0153] Therefore, the sum rate of the system is

[0154]

[0155] In addition, in order to further improve the security of the system, the introduction of the lower bound of the confidentiality rate helps to describe the performance of the system in the worst case. The lower bound of the security rate of the i-th signal can be defined as

[0156]

[0157] Among them, C i (K) represents the transmission rate of the i-th user at the Nyquist sampling rate, is the upper bound of the eavesdropper's eavesdropping rate.

[0158] Therefore, the lower bound of the final system's safety rate is

[0159]

[0160] 5. Optimization objective description: Maximize the safe rate lower bound by jointly optimizing power allocation and modulation timing.

[0161]

[0162] Where P represents the maximum transmit power, Indicates the total power of all transmitted signals.

[0163] According to (7) and (8), the modulation sequence U n τ in (t) n and The change of causes the change of fundamental and harmonic modes at the same time. Thus, there is a clear coupling relationship between the variables in the optimization problem. Therefore, the present invention adopts the particle swarm optimization algorithm (PSO) to solve this problem.

[0164] This paper optimizes the system's lower bound on the security rate, effectively eliminating the risk of eavesdropping and improving system security. The simulations uniformly adopt a modulation frequency setting of single subcarrier spacing, and consider optimization schemes that maximize the security rate and the lower bound of the security rate for an eavesdropper at the Nyquist sampling rate.

[0165] To assess the eavesdropping risk in a single-user system, Figure 3 The trend of eavesdropping rate and security rate changing with the eavesdropper sampling rate is shown. The results show that the proposed security rate lower bound maximization scheme achieves a significant improvement in confidentiality rate. In addition, the increase in the eavesdropper sampling rate will improve the system's eavesdropping analysis concept, from Figure 3 As can be seen from the figure, as the eavesdropper's sampling rate increases, the confidentiality rate of both the conventional scheme and the scheme that maximizes the security rate at the eavesdropper's Nyquist sampling rate decreases significantly. In contrast, the scheme that maximizes the lower bound of the security rate demonstrates strong robustness in the face of increased eavesdropping sampling rates, and the confidentiality rate does not significantly decrease with the increase in the eavesdropping sampling rate. This result demonstrates that the proposed scheme can effectively mitigate the eavesdropping risk caused by high sampling rates, thereby ensuring the stability of the system's security performance.

[0166] In order to further evaluate the eavesdropping risk of multi-user systems, the comparison scheme is extended 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 eavesdropper’s secure rate maximization scheme at the Nyquist sampling rate. Compared with the TDMA multi-user system based on the contrast scheme, Figure 4 The security performance described in (b) is significantly improved, but the risk of eavesdropping still exists. Figure 4 (c) As can be seen, the security rate under the scheme that maximizes the security rate lower bound does not decrease significantly with the increase of the eavesdropping sampling rate. This further demonstrates that optimizing the security rate lower bound significantly reduces the system's sensitivity to the eavesdropper's sampling rate, effectively enhancing the system's adaptability and security.

[0167] Figure 5 Study the trade-off between eavesdropping risk and maximizing confidentiality rate. According to the previous analysis results, the confidentiality rate of the system will not fluctuate significantly with the increase of eavesdropping sampling rate under the scheme of maximizing the lower bound of security rate. Based on this characteristic, Figure 5 The confidentiality rate lower bound is used as a representative indicator of the security rate lower bound maximization scheme. For the security rate maximization scheme under the Nyquist sampling rate of the eavesdropper, in order to fully reflect the changes in its security performance, Figure 5 The lower bound of the security rate is also plotted, along with the security rate when the eavesdropper uses the Nyquist sampling rate. Simulation results show that the scheme that maximizes the lower bound of the security rate effectively improves the lower bound. Furthermore, after maximizing the lower bound of the security rate, the lower bound of the security rate approaches the performance limit. This demonstrates that eliminating the risk of eavesdropping does not require a significant sacrifice in the security rate while effectively improving system security.

[0168] Figure 6 The simulation compared the lower bounds of the security rates of different schemes in a scenario without the risk of eavesdropping. The benchmark schemes include a user and rate maximization scheme and a time division multiple access scheme based on an extension of the comparison scheme. The simulation results show that the scheme proposed in this invention has significant advantages in confidentiality performance. Specifically, the lower bound of the security rate of the comparison scheme is zero, indicating that it cannot achieve secure communication. When the same lower bound of the security rate is required, this scheme can reduce the transmission power by about 8dB compared to the user and rate optimization scheme. These results verify the effectiveness of the proposed scheme in eliminating the risk of eavesdropping. It can not only maintain a high confidential communication rate, but also significantly reduce system power consumption, demonstrating excellent practical value and security performance.

[0169] Simulation results demonstrate that the proposed scheme effectively eliminates the risk of eavesdropping, thereby improving system adaptability. Furthermore, the scheme's security performance is unaffected by variations in the eavesdropper's sampling rate. Compared to existing baseline schemes, the proposed scheme demonstrates superior confidentiality rate performance.

[0170] 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 limiting. 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 in form and details 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 modulation array, characterized by: A secure communication system based on a time-modulated array (TMA) using spatial division multiple access (SDMA) is constructed. The system consists of a base station and a receiver. The base station is equipped with a TDMA array consisting of N antennas. The receiver includes legitimate users and eavesdroppers, each of whom is equipped with a single antenna. In the presence of a single-antenna eavesdropper, SDMA is used to transmit I data streams in parallel to I legitimate users with a single antenna. The base station precodes the data signal, maps the precoded data signal to an OFDM signal, and then uses time modulation technology to transmit the OFDM signal to the legitimate user.

2. The multi-user physical layer secure transmission method based on a time modulation array according to claim 1, characterized in that: The calculation formula of the OFDM signal is: Where K represents the total number of OFDM subcarriers; s k represents the complex value signal on the kth subcarrier, w k =2πf k represents the angular frequency of the kth subcarrier, and f k Indicates the center frequency of the kth subcarrier.

3. The multi-user physical layer secure transmission method based on a time modulation array according to claim 2, characterized in that: The OFDM signal is evenly distributed between each antenna through the power divider. After being processed by the RF switch, the array factor is Among them, U n (t) is the RF switching sequence, θ represents the angle between the signal transmission direction and the array normal; Let f p =pf Δ , p={1,2,...,K}, where f p is the modulation frequency, f Δ The adjacent subcarrier spacing is used to alias the qth harmonic of the kth subcarrier of the OFDM signal onto the fundamental frequency component of the k+pqth subcarrier.

4. The multi-user physical layer secure transmission method based on a time modulation array according to claim 2, characterized in that: The received signal at the i-th legal user is and The calculation formula is as follows: in, is the equivalent channel matrix, is the precoding matrix of the i-th signal, x i Data that needs to be sent to legitimate users.

5. The multi-user physical layer secure transmission method based on a time modulation array according to claim 4, characterized in that: The transmission rate of the received signal of the legitimate user when the sampling rate is limited is C i (S i ); Transmission rate C under finite sampling rate i (S i ) is calculated as: in, is the covariance matrix, represents the precoding matrix of the j-th signal, It is represented as a diagonal matrix whose diagonal elements are the noise power 6. The multi-user physical layer secure transmission method based on a time modulation array according to claim 5, characterized in that: The upper bound of the transmission rate of legitimate users is The calculation formula is as follows: in, and Represents C i (S i →∞), the trace of the perturbation matrix of the numerator and denominator, and Respectively represent the non-1 eigenvalues of the numerator and denominator matrices before perturbation, Represents the largest eigenvalue of the denominator matrix before perturbation.

7. The multi-user physical layer secure transmission method based on a time modulation array according to claim 6, characterized in that: Calculate the safe rate and its lower bound: After calculating the transmission rates of the eavesdropper and the user, the confidentiality rate of the i-th signal is given by C s,i (S i ,S E )=C i (S i )-C E,i (S E ) (42) Among them, C i (S i ) is the rate at which legitimate users receive signals when the sampling rate is limited, C E,i (S E ) is the transmission rate of the eavesdropper when the sampling rate is limited; Therefore, the sum rate of the system is: The lower bound of the confidentiality rate is introduced, and the calculation formula for the lower bound of the security rate of the i-th signal is: Among them, C i (K) represents the transmission rate of the i-th user at the Nyquist sampling rate, is the upper bound of the eavesdropper's eavesdropping rate; Therefore, the lower bound of the final system's safety rate is:

8. The multi-user physical layer secure transmission method based on a time modulation array according to claim 7, characterized in that: The particle swarm optimization algorithm is used to jointly optimize power allocation and modulation timing to maximize the lower bound of the safe rate. The calculation formula is as follows: Where P represents the maximum transmit power, Indicates the total power of all transmitted signals.

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