Safety Design Method for MIMO Inductive System under Extended Clutter Model

Abstract

This application relates to a safety design method for a MIMO inductive integrated system under an extended clutter model, including the following specific steps: establishing a system equipped with N T One transmitting antenna and N R This application presents a MIMO sensing-enabled system with multiple receiving antennas. It constructs detection and communication models, and based on these models, establishes a joint optimization problem involving the transmit waveform and receive filter to ensure secure communication between the system and downlink users. A joint optimization algorithm is designed to optimize the problem. Simulation experiments are conducted to test the performance of the joint optimization algorithm, thus completing the security design of the MIMO sensing-enabled system. This application uses the total communication security rate of all users as the objective function to ensure stable target detection performance of the radar system. The stability of the target detection probability is maintained through the joint design of the integrated transmit waveform and receive filter.

Description

Technical Field

[0001] This invention relates to the field of MIMO radar communication technology, and specifically to a security design method for an integrated MIMO sensing system under a spread clutter model. Background Technology

[0002] With the development and upgrading of global mobile communication systems from the first generation to the sixth generation, the number of wireless devices has exploded, and the bandwidth required by various high data rate services has grown exponentially, leading to increasingly scarce spectrum resources. Against this backdrop, spectrum sharing technology has seen unprecedented development, becoming an important means of solving spectrum congestion. Since a large portion of the radar operating frequency spectrum can be used for wireless communication, the radar band is widely considered one of the best candidate bands for spectrum sharing. Radar and Communication Spectrum Sharing (RSCC) technology is implemented in two main ways: Radar and Communication System Coexistence (RCC) and Joint Radar and Communication (JRC). In the former, the radar system and communication system are usually implemented on different hardware platforms and each independently designs its transmission signals. Therefore, it typically requires the two systems to cooperate in real time, periodically exchanging information such as radar beam patterns, transmitted waveform parameters, communication modulation methods, and channel state information to manage cross-interference and avoid losses. This process leads to complex system design and high communication overhead. This application uses the latter radar-communication integrated approach, namely the JRC system that supports the simultaneous operation of radar and communication systems. This system performs sensing and communication functions simultaneously through a unified hardware platform, thus eliminating the need for information exchange between the two systems, reducing system design complexity, implementation costs, and communication overhead.

[0003] Existing integrated shared waveform designs can be categorized into three types: shared waveforms based on communication waveforms, shared waveforms based on radar waveforms, and shared waveforms based on joint designs. Shared waveform designs based on communication waveforms can achieve sensing functions without sacrificing communication performance. For example, pilot signals and frame preambles, commonly used for channel estimation, have recently been applied to radar detection due to their good autocorrelation properties. Furthermore, vehicle communication waveforms based on common communication standards such as IEEE 802.11ad or IEEE 802.11p have also been used for target detection in vehicle scenarios. However, since pilots and frame preambles are not specifically designed for sensing, this approach makes radar detection overly dependent on the detection scenario and limits the radar's detection range. Shared waveform designs based on radar waveforms embed communication information into radar waveform parameters. For example, communication information can be embedded into the selection of MIMO radar transmitting antennas and the arrangement of orthogonal waveforms, or into the arrangement of frequency-agile radar carrier frequencies. Similarly, the communication rate is limited, far lower than the requirements of 5G and 6G, and the communication receiver needs to specifically decode the radar waveform, increasing the complexity of the hardware design. Considering the limitations of these two types of waveforms on sensing and communication performance, and since the signal-to-interference-pulse-noise ratio (SINR) of the echo directly affects the stable detection probability of the target, the output SINR can be improved by jointly designing the transmitted waveform and the received filter to further enhance target detection performance in different environments. Over the past few decades, extensive research has been conducted on the joint design of transmitted waveforms and received filters in various scenarios.

[0004] Compared to point targets, extended targets occupy multiple range cells, thus generating target echoes. In this case, the extended target echo is no longer a scale transformation of the transmitted waveform, but rather a convolution of the target impulse response (TIR) ​​and the transmitted waveform. Currently, some research exists specifically addressing the design problems of the transmitted waveform and receiver filters for extended targets. However, in practical scenarios, due to the high sensitivity of TIR to line-of-sight (LOS), obtaining accurate TIR of the extended target before detection is impractical. Therefore, the methods described above perform poorly when TIR is uncertain.

[0005] Communication security is an indispensable part of integrated radar and communication systems, because the integrated waveform not only performs detection functions but also carries communication information. To prevent confidential information from being eavesdropped on by unauthorized users, it is essential to use a large amount of additional energy to generate artificial noise to disrupt potential malicious receivers. Summary of the Invention

[0006] The purpose of this invention is to provide a secure design method for a MIMO integrated sensing system under an extended clutter model. The method uses the total communication security rate of all users as the objective function to ensure the stable target detection performance of the radar system. By jointly designing an integrated transmit waveform and receive filter, the stability of the target detection probability is maintained.

[0007] To achieve the above objectives, embodiments of this application provide a security design method for a MIMO inductive integrated system under an extended clutter model, comprising the following specific steps:

[0008] Establish equipped with N T One transmitting antenna and N R A MIMO sensing system with one receiving antenna;

[0009] Construct a detection model and a communication model, and based on the detection model and the communication model, construct a joint optimization problem of the transmit waveform and the receive filter to ensure that the system can communicate securely with downlink users;

[0010] A joint optimization algorithm is designed to optimize the joint optimization problem.

[0011] Simulation experiments were conducted to test the performance of the joint optimization algorithm, and the safety design of the MIMO integrated sensing system was completed.

[0012] The specific steps for constructing the detection model are as follows:

[0013] Assuming that the signal transmitted by each transmitting element has L fast-time discrete sampling points, then at the t-th sampling point, the signal s transmitted by all transmitting antennas is... t It can be represented as

[0014] s t =p t +v t (1)

[0015] in integrated signal Artificial noise

[0016] For L fast-time sampling points, the transmitted signal matrix S of the MIMO radar can be expressed as:

[0017] S=P+V (2)

[0018] in Integrated signal matrix Artificial noise matrix Furthermore, assuming the target impact response TIR of the extended target occupies a total of Q fast time units, i.e.

[0019] After being reflected by the target, the signal received by the MIMO radar receiver is:

[0020] Y = HST H +N

[0021] =HPT H +HVT H +N (3)

[0022] Wherein, the guidance matrix H = b(θ,f)a T (θ,f), where the launch steering vector Receive guide vector f represents the radar's real-time operating frequency. When the radar's operating bandwidth is much smaller than the center frequency f... c In this case, the array steering vector can be described using a narrowband model, and f can be represented by a constant f. c Instead, the transmit and receive steering vectors can be approximated as independent of bandwidth, denoted as a(θ) and b(θ), respectively, extending the target TIR matrix. The shift matrix It can be represented as

[0023]

[0024] This represents the uninteresting echo components that are independent of the transmitted waveform, including system noise and radio frequency interference.

[0025] Let y = vec(Y), p = vec(P), v = vec(V), n = vec(N), then equation (3) can be expressed as

[0026]

[0027] in and

[0028]

[0029] Let w be the receiving filter vector. Based on equation (5), the output signal of the radar receiver is:

[0030]

[0031] According to equation (8), define the matrix. We can get z out Another expression:

[0032]

[0033] In the formula,

[0034]

[0035] According to equations (8) and (9), the expression for the output SINR is as follows:

[0036]

[0037] The construction of the communication model specifically involves...

[0038] Assuming the integrated system serves K single-antenna downlink legitimate communication users, and there are also M single-antenna illegitimate communication users in the system, then the signals received at the i-th legitimate communication user and the m-th illegitimate communication user can be represented as follows:

[0039]

[0040]

[0041] Where h bi and h em Let these represent the communication channel vectors from BS to the i-th legitimate user and the m-th illegitimate user, respectively. and Let p represent the Gaussian white noise at the i-th legitimate communication user and the m-th illegitimate communication user, respectively. i This indicates a signal carrying information sent to the i-th legitimate communication user, and Suppose that for all i ≠ j, p i With p j It's irrelevant at this time. Then the SINR at the i-th legitimate communication user and the m-th illegitimate communication user can be expressed as:

[0042]

[0043] The method of constructing a joint optimization problem of transmit waveform and receive filter based on detection and communication models to ensure that the system can communicate securely with downlink users specifically involves the following steps:

[0044] The radar obtains the prior TIR information t0 of the target of interest through previous detection and estimation methods. However, the estimated TIR has a certain error Δt. It is assumed that Δt is random and follows a complex Gaussian distribution. The target TIR is described as follows: In practical radar detection missions, to achieve stable target detection, the system requires the target's SINR to be higher than a certain threshold. Considering the randomness of the output SINR of equation (11), waveform design is used to ensure that the probability of the target's SINR exceeding the threshold is not less than the probability threshold required by the system, thereby achieving stable target detection.

[0045]

[0046] In the formula, Γ represents the target detection threshold, 1-ρ represents the stable detection probability, and the smaller ρ is, the better the detection performance of the system.

[0047] Define the total security rate of the system as

[0048]

[0049] Where λ i and λ m Let the weights of the i-th legitimate user and the m-th illegitimate user be represented respectively. This represents the sum of communication rates of K legitimate communication users. This represents the total communication rate of M illegal communication users.

[0050] The following optimization model is constructed to jointly optimize the transmitted waveform and the received filter:

[0051]

[0052] Where R p =pp H R v =vv H , P0 is the system's transmit power budget;

[0053] Specifically, a joint optimization algorithm is designed to optimize the joint optimization problem.

[0054] When the receiving filter w (n) When fixed, SINR≥Γ inside the stability probability constraint in equation (18) can be rewritten as

[0055]

[0056] in,

[0057] Known TIR error It can be rewritten as Δt = Ω 1 / 2 u, where Ω=Ω 1 / 2 Ω 1 / 2 , and then Equation (19) can be expressed as

[0058] u H Bu+2Re(u H r)+ω≥0 (20)

[0059] In the formula,

[0060] Then, using the decomposition-based large deviation inequality, equation (20) is transformed into a convex constraint set containing only second-order cone constraints.

[0061] Known ρ∈(0,1], for any

[0062] Prob{e H Qe+2Re{e H r}+s≥0}≥1-ρ(21)

[0063] Both are true, and equation (21) is equivalent to the following set of constraints.

[0064]

[0065] In the formula, x and y are slack variables.

[0066] Introducing slack variables m and n, for any given g, the stability probability constraint in equation (18) can be rewritten as follows:

[0067]

[0068] By replacing the stable detection probability constraint with the convex constraint set given in equation (23), the original optimization problem is reformulated as the following semidefinite programming form.

[0069]

[0070] A fast solution method based on Lagrange dual transformation is used.

[0071] First, rewrite equation (17) as follows:

[0072]

[0073] in, It is a concave increasing function. It is a concave decreasing function.

[0074] Introduce a set of auxiliary variables Used to replace each The rational terms inside the logarithm; then introduce a set of auxiliary variables. Used to replace each The rational terms inside the logarithm in the equation, that is, the original optimization problem (24) is transformed into

[0075]

[0076] If and only if When the optimal solution is the solution to the optimization problem (26), the optimal solution to the original optimization problem can be obtained. The objective function is expressed as follows:

[0077]

[0078] in,

[0079]

[0080] Auxiliary variables Through (R) p ,R v )and Alternating optimization provides an efficient solution.

[0081] When R v When fixed, optimize It can be calculated directly. The optimal closed-form solutions are respectively

[0082]

[0083]

[0084] when When fixed, optimize R v Introducing auxiliary variables and The optimization problem (26) is transformed into

[0085]

[0086] in,

[0087]

[0088] If and only if When the optimal solution to problem (31) is found, the optimal solution to problem (26) can be obtained. Through R v and Alternating optimization is used to solve the problem when R v When fixed, y and They can be updated separately to

[0089]

[0090] Where ε is a very small positive number, to prevent Approaching infinity

[0091] When auxiliary variables When all are fixed, the optimization problem (31) becomes a convex problem that can be solved directly.

[0092] When R p When fixed, update via equations (29) and (30). When R p and When fixed, update via equations (34) and (35). when When all are fixed, solve R by solving problem (31). p ＊ ;

[0093] When the covariance matrix R of the integrated signal p and the artificial noise v p and R v When fixed, maximize the expected SINR at the radar output and solve for the optimal w.

[0094] According to equation (11), the expected SINR at the output is:

[0095]

[0096] make but f in First-order Taylor expansion

[0097]

[0098] because Take the expected value from both sides simultaneously

[0099]

[0100] Therefore, equation (36) can be restated as follows:

[0101]

[0102] Let W = ww H , Can Rephrased as about R p function

[0103]

[0104] Similarly, Rephrased as about R v function

[0105]

[0106] Therefore, we construct the following optimization problem and solve W directly. *

[0107]

[0108] Since W = ww H By calculating W * The principal eigenvalues ​​can be directly obtained from w.

[0109]

[0110] in, This indicates the operation of calculating the principal eigenvectors of a matrix.

[0111] The beneficial effects of adopting the above embodiments are: by taking the total communication security rate of all users as the objective function, the stable detection performance of the radar system on the target is ensured; and by jointly designing an integrated transmission waveform and receiving filter, the stability of the target detection probability is maintained. Attached Figure Description

[0112] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0113] Figure 1 A flowchart illustrating the method provided in this application embodiment;

[0114] Figure 2 This is a comparison chart of the confidentiality rate under different false negative probabilities for this application. Detailed Implementation

[0115] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0116] It should be noted that the descriptions involving "first," "second," etc., in this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0117] To maximize the communication security of the integrated radar-communication system under multiple unauthorized user environments, this application uses the total secure communication rate of all users as the objective function. To ensure the stable target detection performance of the radar system, this application maintains the stability of the target detection probability by jointly designing an integrated transmit waveform and receive filter. This application proposes a cyclic optimization algorithm that combines Decomposition-Based Large Deviation Inequality (DBLDI) with a fast solution method for a hybrid FP problem based on Lagrange dual transformation to solve the optimization problem.

[0118] A represents a matrix; a represents a vector; a represents a variable; (·) T 、(·) H They represent transpose and conjugate transpose, respectively. Represents the field of complex numbers; Represents the mathematical expectation. represents the Euclidian norm of a vector and the Frobenius norm of a matrix, respectively; vec(·) represents the matrix straightening operation; This represents the Kronecker product of matrices A and B; A > 0 indicates that A is a positive definite matrix.

[0119] Please see Figure 1 This application relates to a safety design method for a MIMO integrated sensing system under an extended clutter model, comprising the following specific steps:

[0120] Establish equipped with N T One transmitting antenna and N R A MIMO sensing system with one receiving antenna;

[0121] Construct a detection model and a communication model, and based on the detection model and the communication model, construct a joint optimization problem of the transmit waveform and the receive filter to ensure that the system can communicate securely with downlink users;

[0122] A joint optimization algorithm is designed to optimize the joint optimization problem.

[0123] Simulation experiments were conducted to test the performance of the joint optimization algorithm, and the safety design of the MIMO integrated sensing system was completed.

[0124] The specific steps for constructing the detection model are as follows:

[0125] Assume that the signal transmitted by each transmitting element has L If there are several fast-time discrete sampling points, then at the t-th sampling point, the signal s transmitted by all transmitting antennas will be... t It can be represented as

[0126] s t=p t +v t (1)

[0127] in integrated signal Artificial noise

[0128] Then for L With a fast sampling time, the transmitted signal matrix S of the MIMO radar can be represented as:

[0129] S=P+V (2)

[0130] in Integrated signal matrix Artificial noise matrix Furthermore, assuming the target impact response TIR of the extended target occupies a total of Q fast time units, i.e.

[0131] After being reflected by the target, the signal received by the MIMO radar receiver is:

[0132] Y = HST H +N

[0133] =HPT H +HVT H +N (3)

[0134] Wherein, the guidance matrix H = b(θ,f)a T (θ,f), where the launch steering vector Receive guide vector f represents the radar's real-time operating frequency. When the radar's operating bandwidth is much smaller than the center frequency f... c In this case, the array steering vector can be described using a narrowband model, and f can be represented by a constant f. c Instead, the transmit and receive steering vectors can be approximated as independent of bandwidth, denoted as a(θ) and b(θ), respectively, extending the target TIR matrix. The shift matrix It can be represented as

[0135]

[0136] This represents the uninteresting echo components that are independent of the transmitted waveform, including system noise and radio frequency interference.

[0137] Let y = vec(Y), p = vec(P), v = vec(V), n = vec(N), then equation (3) can be expressed as

[0138]

[0139] in and

[0140]

[0141]

[0142] Let w be the receiving filter vector. Based on equation (5), the output signal of the radar receiver is:

[0143]

[0144] According to equation (8), define the matrix. We can get z out Another expression:

[0145]

[0146] In the formula,

[0147]

[0148] According to equations (8) and (9), the expression for the output SINR is as follows:

[0149]

[0150] The construction of the communication model specifically involves...

[0151] Assuming the integrated system serves K single-antenna downlink legitimate communication users, and there are also M single-antenna illegitimate communication users in the system, then the signals received at the i-th legitimate communication user and the m-th illegitimate communication user can be represented as follows:

[0152]

[0153] Where h bi and h em Let these represent the communication channel vectors from BS to the i-th legitimate user and the m-th illegitimate user, respectively. and Let p represent the Gaussian white noise at the i-th legitimate communication user and the m-th illegitimate communication user, respectively. i This indicates a signal carrying information sent to the i-th legitimate communication user, and Suppose that for all i ≠ j, p i With p j It's irrelevant at this time. Then the SINR at the i-th legitimate communication user and the m-th illegitimate communication user can be expressed as:

[0154]

[0155]

[0156] The method of constructing a joint optimization problem of transmit waveform and receive filter based on detection and communication models to ensure that the system can communicate securely with downlink users specifically involves the following steps:

[0157] The radar obtains the prior TIR information t0 of the target of interest through previous detection and estimation methods. However, the estimated TIR has a certain error Δt. It is assumed that Δt is random and follows a complex Gaussian distribution. The target TIR is described as follows: In practical radar detection missions, to achieve stable target detection, the system requires the target's SINR to be higher than a certain threshold. Considering the randomness of the output SINR of equation (11), waveform design is used to ensure that the probability of the target's SINR exceeding the threshold is not less than the probability threshold required by the system, thereby achieving stable target detection.

[0158]

[0159] In the formula, Γ represents the target detection threshold, 1-ρ represents the stable detection probability, and the smaller ρ is, the better the detection performance of the system.

[0160] Define the total security rate of the system as

[0161]

[0162] Where λ i and λ m Let the weights of the i-th legitimate user and the m-th illegitimate user be represented respectively. This represents the sum of communication rates of K legitimate communication users. This represents the total communication rate of M illegal communication users.

[0163] The following optimization model is constructed to jointly optimize the transmitted waveform and the received filter:

[0164]

[0165] Where R p =pp H R v =vv H , P0 is the system's transmit power budget.

[0166] Specifically, a joint optimization algorithm is designed to optimize the joint optimization problem.

[0167] When the receiving filter w (n)When fixed, SINR≥Γ inside the stability probability constraint in (18) can be rewritten as

[0168]

[0169] in,

[0170] Known TIR error It can be rewritten as Δt = Ω 1 / 2 u, where

[0171] Ω=Ω 1 / 2 Ω 1 / 2 , and then Equation (19) can be expressed as

[0172] u H Bu+2Re(u H r)+ω≥0 (20)

[0173] In the formula,

[0174] Then, using the decomposition-based large deviation inequality, equation (20) is transformed into a convex constraint set containing only second-order cone constraints.

[0175] Known ρ∈(0,1], for any

[0176] Prob{e H Qe+2Re{e H r}+s≥0}≥1-ρ (21)

[0177] Both are true, and equation (21) is equivalent to the following set of constraints.

[0178]

[0179] In the formula, x and y are slack variables.

[0180] Introducing slack variables m and n, for any given g, the stability probability constraint in equation (18) can be rewritten as follows:

[0181]

[0182] By replacing the stable detection probability constraint with the convex constraint set given in equation (23), the original optimization problem is reformulated as the following semidefinite programming form.

[0183]

[0184] A fast solution method based on Lagrange dual transformation is used.

[0185] First, rewrite equation (17) as follows:

[0186]

[0187] Among them, f i + (r)=λ i log(1+r) is a concave increasing function. It is a concave decreasing function.

[0188] Introduce a set of auxiliary variables Used to replace each f i + The rational terms inside the logarithm of (r); and then introduce a set of auxiliary variables. Used to replace each The rational terms inside the logarithm in the equation, that is, the original optimization problem (24) is transformed into

[0189]

[0190] If and only if When the optimal solution is the solution to the optimization problem (26), the optimal solution to the original optimization problem (R) can be obtained. p ＊ ,R v ＊ ), where the objective function is expressed as

[0191]

[0192] in,

[0193]

[0194] Auxiliary variables Through (R) p ,R v )and Alternating optimization provides an efficient solution.

[0195] When R v When fixed, optimize γ can be calculated directly. The optimal closed-form solutions are respectively

[0196]

[0197] when When fixed, optimize R v Introducing auxiliary variables and The optimization problem (26) is transformed into

[0198]

[0199] in,

[0200]

[0201] If and only if When the optimal solution to problem (31) is found, the optimal solution R of problem (26) can be obtained. v ＊ Through R v and Alternating optimization is used to solve the problem when R v When fixed, y and They can be updated separately to

[0202]

[0203] Where ε is a very small positive number, to prevent Approaching infinity

[0204] When auxiliary variables When all are fixed, the optimization problem (31) becomes a convex problem that can be solved directly.

[0205] When R p When fixed, update via equations (29) and (30). When R p and When fixed, update via equations (34) and (35). when When all are fixed, solve R by solving problem (31). p ＊

[0206] When the covariance matrix R of the integrated signal p and the artificial noise v p and R v When fixed, maximize the expected SINR at the radar output and solve for the optimal w.

[0207] According to equation (11), the expected SINR at the output is:

[0208]

[0209] make but f in First-order Taylor expansion

[0210]

[0211] because Take the expected value from both sides simultaneously

[0212]

[0213] Therefore, equation (36) can be restated as follows:

[0214]

[0215] Let W = ww H , Can Rephrased as about R p function

[0216]

[0217] Similarly, Rephrased as about R v function

[0218]

[0219] Therefore, we construct the following optimization problem and solve W directly. *

[0220]

[0221] Since W = ww H By calculating W * The principal eigenvalues ​​can be directly obtained from w.

[0222]

[0223] in, This indicates the operation of calculating the principal eigenvectors of a matrix.

[0224] This application uses simulation experiments to test the performance of the aforementioned joint optimization algorithm. Unless otherwise specified, this application assumes that the MIMO sensing system operates at a center frequency of 3 GHz and that the system is equipped with N transmit antennas. T =5, the number of receiving antennas is N R =4, the array consists of uniform linear arrays with an element spacing of half a wavelength, and the transmitted waveform length L = 8. The transmitted power budget P0 = 13dB. The radar system contains Gaussian white noise with a power of σ. 2 =0.002.

[0225] The extended target model considered in this application is a 5-meter-long unmanned reconnaissance aircraft located at θ = 0° in the MIMO array. Based on the radar's range resolution, the aircraft's TIR occupies Q = 5 fast time-domain resolution cells. This paper models the extended target TIR as a stochastic model, i.e., t = t0 + Δt, assuming Δt is a complex Gaussian distribution. Where C t Let C represent the covariance matrix of Δt and C t=0.05I Q Assume the prior knowledge t0 of the TIR is:

[0226]

[0227] This application assumes the existence of 3 legitimate communication users and 2 illegitimate users. A flat fading channel model is used to model the communication channel h, and all channel elements are independent of each other, satisfying the following conditions: Noise power settings for legitimate and illegitimate users The termination condition for the algorithm is set to ζ = 10. -4 All experiments were conducted on a personal computer equipped with a Core i7-13700H 2.4GHz CPU and 16GB RAM, using the MATLAB 2022 software environment.

[0228] Figure 2 The relationship between the communication security rate curve and the number of iterations under different false negative probabilities ρ is shown, where the detection threshold is set to Γ = 20dB, and the weight of all communication users is set to 1. It is evident that the proposed algorithm converges after several iterations, numerically verifying its convergence. It can also be seen that the communication security rate increases with the increase of the false negative probability; therefore, to achieve better communication performance, this integrated system needs to sacrifice some target detection performance.

[0229] Those skilled in the art can implement the present invention in various variations without departing from its scope and spirit. For example, a feature of one embodiment can be used in another embodiment to obtain yet another embodiment. Any modifications, equivalent substitutions, and improvements made within the scope of the present invention's technical concept should be within the scope of the present invention.

Claims

1. A safety design method for a MIMO inductive integrated system under an extended clutter model, characterized in that, The specific steps include the following: Established with equipment One transmitting antenna and A MIMO sensing system with one receiving antenna; Construct a detection model and a communication model, and based on the detection model and the communication model, construct a joint optimization problem of the transmit waveform and the receive filter to ensure that the system can communicate securely with downlink users; For joint optimization problems, a joint optimization algorithm is designed and proposed. A cyclic optimization algorithm combining a decomposition-based large deviation inequality and a fast solution method for hybrid FP problems based on Lagrange dual transformation is proposed to solve the optimization problem. Simulation experiments were conducted to test the performance of the joint optimization algorithm, and the safety design of the MIMO integrated sensing system was completed. The method of constructing a joint optimization problem of transmit waveform and receive filter based on detection and communication models to ensure that the system can communicate securely with downlink users specifically involves the following steps: The radar obtains the TIR prior information of the target of interest through previous detection and estimation methods. However, the estimated TIR has a certain error. Assuming It exhibits randomness and conforms to a complex Gaussian distribution. The target TIR is described as follows: In actual radar detection missions, in order to achieve stable target detection, the system requires the target's SINR to be higher than a certain threshold. Considering that the output SINR of equation (11) has randomness, waveform design is used to ensure that the probability of the target's SINR exceeding the threshold is not less than the probability threshold required by the system, so as to achieve stable target detection. （16） In the formula, Indicates the target detection threshold. Indicates the probability of stable detection. The smaller the value, the better the system's detection performance. Define the total security rate of the system as （17） in and They represent the first The first legitimate communication user and the first The non-negative weight of an illegal communication user express The total communication rate of a legal communication user express The total communication rate of each illegal communication user. The following optimization model is constructed to jointly optimize the transmitted waveform and the received filter: （18） in , , , This is the system's transmit power budget.

2. The security design method for a MIMO inductive integrated system under an extended clutter model according to claim 1, characterized in that, The specific steps for constructing the detection model are as follows: Assume that the signal transmitted by each transmitting element has Then at the nth fast-time discrete sampling point, the nth At each sampling point, the signals transmitted by all transmitting antennas It can be represented as （1） in , integrated signal Artificial noise , Then for The transmit signal matrix of the MIMO radar at a fast sampling point. It can be represented as （2） in Integrated signal matrix Artificial noise matrix Furthermore, assuming the extended target's impact response TIR occupies a total of A fast time unit, that is , After being reflected by the target, the signal received by the MIMO radar receiver is: （3） Wherein, the guiding matrix The launch steering vector Receive guide vector , This indicates the real-time operating frequency of the radar. When the radar's operating bandwidth is much smaller than the center frequency... At that time, the array steering vector can be described using a narrowband model. Constants can be used Instead, in this case, the transmit and receive steering vectors can be approximated as independent of bandwidth, denoted as... and Expand the target TIR matrix , where the shift matrix It can be represented as （4） This represents the uninteresting echo components that are independent of the transmitted waveform, including system noise and radio frequency interference. make , , , Then equation (3) can be expressed as （5） in ,and （6） （7） set up Given the receiving filter vector, based on equation (5), the output signal of the radar receiver is: （8） According to equation (8), define the matrix. You can get Another expression: （9） In the formula, （10） According to equations (8) and (9), the expression for the output SINR is as follows: （11）。 3. The security design method for a MIMO inductive integrated system under an extended clutter model according to claim 1, characterized in that, The construction of the communication model specifically involves... Assuming the integrated system serves There are single-antenna downlink legitimate communication users, and there are also existing ones in the system. For a single-antenna illegal communication user, then in the... The first legitimate communication user and the first The signals received by each illegal communication user can be represented as follows: （12） （13） in and They represent from BS to the number The first legitimate communication user and the first The communication channel vector of an illegal communication user. and They represent the first The first legitimate communication user and the first Gaussian white noise at the location of an illegal communication user Indicates that the bearer is sent to the first A signal of legitimate communication user information, and Assuming for all , and It's irrelevant at this time. Then the first The first legitimate communication user The SINR of each illegal communication user can be represented as follows: （14） （15）。 4. The security design method for a MIMO inductive integrated system under an extended clutter model according to claim 1, characterized in that, Specifically, a joint optimization algorithm is designed to optimize the joint optimization problem. When receiving filter When fixed, the internal stability probability constraint in equation (18) It can be rewritten as （19） in, , Known TIR error It can be rewritten as ,in , , and then , Equation (19) can be expressed as （20） In the formula, , , , Then, using the decomposition-based large deviation inequality, equation (20) is transformed into a convex constraint set containing only second-order cone constraints. Known , , , , For any , （21） Both are true, and equation (21) is equivalent to the following set of constraints. （22） In the formula , It is a slack variable. Introducing slack variables , For any given The stability probability constraint in equation (18) can be rewritten as follows: （23） By replacing the stable detection probability constraint with the convex constraint set given in equation (23), the original optimization problem is reformulated as the following semidefinite programming form. （24） A fast solution method based on Lagrange dual transformation is used. First, rewrite equation (17) as follows: （25） in, It is a concave increasing function. It is a concave decreasing function. Introduce a set of auxiliary variables , used to replace each The rational terms inside the logarithm; then introduce a set of auxiliary variables. , used to replace each The rational terms inside the logarithm in the equation transform the original optimization problem (24) into... （26） If and only if When the optimal solution is found in the optimization problem (26), the optimal solution to the original optimization problem can be obtained. The objective function is expressed as （27） in, （28） Auxiliary variables ,pass and Alternating optimization provides an efficient solution. when When fixed, optimize It can be calculated directly. , The optimal closed-form solutions are respectively （29） （30） when When fixed, optimize Introducing auxiliary variables and The optimization problem (26) is transformed into （31） in, （32） （33） If and only if When the optimal solution to problem (31) is found, the optimal solution to problem (26) can be obtained. ,pass and Alternating optimization is used to solve the problem when When fixed, and They can be updated separately to （34） （35） in, It is a very small positive number, to prevent Approaching infinity When auxiliary variables When everything is fixed, the optimization problem (31) becomes a convex problem, which can be solved directly. when When fixed, update via equations (29) and (30). ;when and When fixed, update via equations (34) and (35). ;when When everything is fixed, the solution is obtained by solving problem (31). , When the integrated signal and artificial noise covariance matrix and When the value is fixed, the optimal solution is to maximize the expected SINR at the radar output. , According to equation (11), the expected SINR at the output terminal is: （36） make ,but ,Will exist First-order Taylor expansion （37） because Take the expected value from both sides simultaneously （38） Therefore, equation (36) can be restated as follows: （39） make , can Rephrased as about function （40） Similarly, Rephrased as about function （41） Therefore, we construct the following optimization problem and solve it directly. , （42） because Through calculation The principal eigenvalues ​​can be obtained directly. , （43） in, This indicates the operation of calculating the principal eigenvectors of a matrix.

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