Security design method for MIMO (Multiple Input Multiple Output) sensing integrated system under extended clutter model

Abstract

The invention relates to a security design method for an MIMO (Multiple Input Multiple Output) integrated system under an extended clutter model. The security design method comprises the following specific steps: establishing the MIMO integrated system equipped with NT transmitting antennas and NR receiving antennas; constructing a detection model and a communication model, and constructing a joint optimization problem of a transmitted waveform and a receiving filter based on the detection model and the communication model to ensure that the system can safely communicate with a downlink user; aiming at the joint optimization problem, designing a joint optimization algorithm for optimization; and the performance of the joint optimization algorithm is tested through a simulation experiment, and the safety design of the MIMO general inductance integrated system is completed. According to the method, the total communication secrecy rate of all users is used as a target function, the stable detection performance of a radar system on a target is ensured, and the stability of the target detection probability is maintained by jointly designing an integrated transmitting waveform and a receiving filter.

Description

Technical Field

[0001] The present invention relates to the technical field of MIMO radar communication, and in particular to a security design method for a MIMO synaesthesia integrated system under an extended clutter model. Background Art

[0002] With the development and update 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 increased exponentially, resulting in increasingly scarce spectrum resources. In this context, spectrum sharing technology has achieved unprecedented development and has become an important means to solve spectrum congestion. Since a large part of the spectrum in the radar operating frequency can be used for wireless communication, the radar band is widely considered to be one of the best candidate bands for spectrum sharing. There are two main ways to implement radar and communication spectrum sharing technology (RSCC): radar and communication system coexistence (RCC) and radar and communication integration (JRC). In the former, the radar system and the communication system are usually implemented on different hardware platforms, and each independently completes the design of the transmission signal. Therefore, it usually requires the two systems to cooperate in real time and periodically exchange some information, such as radar beam pattern, transmission waveform parameters, communication modulation mode, and channel state information, to manage the cross-interference between the two to avoid losses. This process will lead to a more complex system design and a large communication overhead. This application uses the latter radar communication integration method, that is, the JRC system that can support the simultaneous operation of radar and communication systems. The system completes the sensing and communication functions simultaneously through a unified hardware platform, so it does not require the two systems to exchange information, reducing the system design complexity, implementation cost and communication overhead.

[0003] The existing integrated common waveform design can be divided into three categories: common waveform based on communication waveform, common waveform based on radar waveform, and common waveform based on joint design. Common waveform design based on communication waveform can realize sensing function without sacrificing communication performance. For example, pilot signal and frame preamble, which are usually used for channel estimation, have recently been used for radar detection due to their good autocorrelation characteristics. In addition, vehicle-mounted 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-mounted scenarios. However, since pilot signal and frame preamble are not specially designed for sensing, this method will cause radar detection to be too dependent on the detection scenario and limit the detection range of the radar. Common waveform design based on radar waveform is to embed communication information into radar waveform parameters. For example, communication information can be embedded in the selection method of MIMO radar transmitting antenna and the arrangement of orthogonal waveforms, or in the arrangement method of frequency agile radar carrier frequency. Similarly, the communication rate will be limited, far lower than the requirements of 5G and 6G, and the communication receiver needs to decode the radar waveform specifically, which increases the complexity of hardware design. Considering the limitations of the above two types of waveforms on sensing and communication performance, and because the signal-to-interference-pulse-noise ratio (SINR) of the echo directly affects the stable detection probability of the target, in order to further improve the target detection performance in different environments, the output SINR can be improved by jointly designing the transmit waveform and the receive filter. In the past few decades, people have conducted extensive research on the joint design of transmit waveforms and receive filters in various scenarios.

[0004] Compared with point targets, extended targets occupy multiple range units, thus generating target echoes. At this time, the extended target echo is no longer a scale transformation of the transmitted waveform, but a convolution of the target impulse response (TIR) ​​and the transmitted waveform. At present, there are some studies specifically targeting the design of extended target transmit waveforms and receive filters. In actual scenarios, due to the high sensitivity of TIR to line-of-sight (LOS), it is impractical to obtain the accurate TIR of extended targets before detection. Therefore, the above methods perform poorly when TIR is uncertain.

[0005] Communication security is an important part of the radar communication integrated system, because the integrated waveform can not only realize the detection function, but also carry the communication information. In order to prevent confidential information from being eavesdropped by illegal users, it is necessary to use a large amount of additional energy to generate artificial noise to destroy potential malicious reception. Summary of the invention

[0006] The purpose of the present invention is to provide a MIMO synaesthesia integrated system security design method under an extended clutter model, taking the total communication confidentiality rate of all users as the objective function, ensuring the stable detection performance of the radar system to the target, and maintaining the stability of the target detection probability by jointly designing an integrated transmission waveform and a receiving filter.

[0007] To achieve the above object, the present application provides a MIMO synaesthesia integrated system security design method under an extended clutter model, including the following specific steps:

[0008] Established with N T transmit antennas and N R MIMO interaceptive integrated system with 10 receiving antennas;

[0009] Build detection model and communication model, and construct the joint optimization problem of transmission waveform and receiving filter based on the detection model and communication model to ensure that the system can communicate safely with downlink users;

[0010] Design joint optimization algorithms for joint optimization problems;

[0011] Through simulation experiments, the performance of the joint optimization algorithm is tested and the security design of the MIMO synaesthesia integrated system is completed.

[0012] The construction of the detection model is as follows:

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

[0014] s t =p t +v t (44)

[0015] in integrated signal Artificial noise

[0016] Then for L fast time sampling points, the transmit signal matrix S of the MIMO radar can be expressed as

[0017] S=P+V (45)

[0018] in Integrated signal matrix Artificial Noise Matrix In addition, it is assumed that the target impulse response TIR of the extended target occupies a total of Q fast time units, that is,

[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 (46)

[0022] Where, the steering matrix H = b(θ, f)a T (θ,f), where the launch steering vector Receive Steering Vector f represents the real-time operating frequency of the radar. When the radar operating bandwidth is much smaller than the center frequency f c When the array steering vector can be described by a narrowband model, f can be expressed by a constant f c Instead, at this time, the transmitting and receiving steering vectors can be approximately considered to be independent of the bandwidth, denoted as a(θ) and b(θ), and the extended target TIR matrix is The shift matrix It can be expressed as

[0023]

[0024] Indicates uninteresting echo components that are unrelated to the transmitted waveform, including system noise and RF 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]

[0030] Assume w is the receiving filter vector. Based on equation (5), the radar receiver output signal is:

[0031]

[0032] According to formula (8), the matrix is ​​defined as You can get z out Another expression of :

[0033]

[0034] In the formula,

[0035]

[0036] According to equations (8) and (9), the output SINR expression is as follows:

[0037]

[0038] The construction of the communication model is specifically as follows:

[0039] Assuming that the integrated system serves K single-antenna downlink legal communication users, and there are M single-antenna illegal communication users in the system, the signals received at the i-th legal communication user and the m-th illegal communication user can be expressed as:

[0040]

[0041]

[0042] where h bi and h em denote the communication channel vectors from the BS to the i-th legal communication user and the m-th illegal communication user, respectively. and denote the Gaussian white noise at the i-th legal communication user and the m-th illegal communication user, respectively, and p i represents a signal that carries information sent to the i-th legitimate communication user, and Assume that for all i≠j, p i With p j No matter, at this time Then the SINRs of the i-th legal communication user and the m-th illegal communication user can be expressed as:

[0043]

[0044] The joint optimization problem of constructing the transmission waveform and the receiving filter based on the detection model and the communication model to ensure that the system can safely communicate with the downlink user is specifically as follows:

[0045] The radar obtains the TIR prior information t0 of the target of interest through previous detection and estimation methods, but the estimated TIR has a certain error Δt. Assume that Δt is random and conforms to the complex Gaussian distribution. The target TIR is described as In actual radar detection tasks, in order to stably achieve target detection, the system requires the target SINR to be higher than a certain threshold. Considering that the output SINR of formula (11) is random, the waveform design is used to ensure that the probability of the target SINR exceeding the threshold is not less than the probability threshold required by the system, so as to achieve stable target detection, that is,

[0046]

[0047] 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 is.

[0048] The total confidentiality rate of the system is defined as

[0049]

[0050] where λ i and λ m denote the non-negative weights of the i-th legal communication user and the m-th illegal communication user, respectively. represents the sum of the communication rates of K legitimate communication users, represents the sum of the communication rates of M illegal communication users,

[0051] The following optimization model is constructed to jointly optimize the transmit waveform and the receive filter:

[0052]

[0053] Where R p =pp H , R v =vv H , P0 is the transmit power budget of the system.

[0054] The joint optimization algorithm is designed for the joint optimization problem. Specifically,

[0055] When the receiving filter w (n) When fixed, the SINR ≥ Γ inside the stability probability constraint in (18) can be rewritten as

[0056]

[0057] in,

[0058] Known TIR error It can be rewritten as Δt = Ω 1 / 2 u, where Ω=Ω 1 / 2 Ω 1 / 2 , and then Formula (19) can be expressed as

[0059] u H Bu+2Re(u H r)+ω≥0 (63)

[0060] In the formula,

[0061] Then, using the decomposition-based large deviation inequality, Equation (20) is transformed into a convex constraint set containing only second-order cone constraints,

[0062] Known ρ∈(0,1], for any

[0063] Prob{e H Qe+2Re{e H r}+s≥0}≥1-ρ (64)

[0064] All of them, formula (21) is equivalent to the following constraint set

[0065]

[0066] Where x and y are slack variables,

[0067] By introducing slack variables m and n, for any given g, the stability probability constraint in equation (18) can be rewritten as

[0068]

[0069] Using the convex constraint set given by formula (23) to replace the stable detection probability constraint, the original optimization problem is reformulated as the following semidefinite programming form:

[0070]

[0071] A fast solution method based on Lagrangian dual transformation is used.

[0072] First, rewrite equation (17) as

[0073]

[0074] Among them, f i + (r) = λ i log(1+r) is a concave increasing function. is a concave decreasing function,

[0075] Introducing a set of auxiliary variables To replace each f i + (r) the internal fractional terms of the logarithm; introduce a set of auxiliary variables To replace each The fractional term inside the logarithm in , that is, the original optimization problem (24) is transformed into

[0076]

[0077] If and only if When it is the optimal solution of the optimization problem (26), the optimal solution of the original optimization problem (R p ＊ ,R v ＊ ), where the objective function is expressed as

[0078]

[0079] in,

[0080]

[0081] Auxiliary variables By (R p ,R v )and Alternating optimization effectively solves,

[0082] When R v When fixed, optimize We can directly find γ, The optimal closed-form solutions are

[0083]

[0084] when When fixed, optimize R v , introduce auxiliary variables and Convert the optimization problem (26) into

[0085]

[0086] in,

[0087]

[0088] If and only if When is the optimal solution to the optimization problem (31), the optimal solution R of problem (26) can be obtained. v ＊ , through R v and Alternating optimization to solve the problem, when R v When fixed, y and Can be updated to

[0089]

[0090] Among them, ε is a small positive number to prevent Approaching infinity,

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

[0092] When R p When fixed, update through equations (29) and (30) When R p and When fixed, update through 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 artificial noise v is p and R v When fixed, maximize the expected SINR at the radar output and solve the optimal w.

[0094] According to formula (11), the expected output SINR is

[0095]

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

[0097]

[0098] because Taking the expectation on both sides

[0099]

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

[0101]

[0102] Let W = ww H , Can Re-stated as R p Function

[0103]

[0104] Similarly, Re-stated as R v Function

[0105]

[0106] Therefore, the following optimization problem is constructed to directly solve W *

[0107]

[0108] Since W = ww H , by calculating W * The main eigenvalue of w can be directly obtained

[0109]

[0110] in, Represents the operation of computing the principal eigenvector of a matrix.

[0111] The beneficial effects of adopting the above embodiment are: taking the total communication confidentiality rate of all users as the objective function, ensuring the stable detection performance of the radar system for the target, and maintaining the stability of the target detection probability by jointly designing an integrated transmission waveform and a receiving filter. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0113] Figure 1 A flow chart of the method provided in the embodiment of the present application;

[0114] Figure 2 This is a comparison chart of confidentiality rates under different missed detection probabilities for this application. DETAILED DESCRIPTION

[0115] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0116] It should be noted that the descriptions of "first", "second", etc. in the present invention are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0117] In order to maximize the communication security of the radar communication integrated system in an environment with multiple illegal users, this application takes the total communication confidentiality rate of all users as the objective function. In order to ensure the stable detection performance of the radar system to the target, this application maintains the stability of the target detection probability by jointly designing an integrated transmission waveform and a receiving filter. This application proposes a cyclic optimization algorithm that combines a decomposition-based large deviation inequality (DBLDI) with a hybrid FP problem fast solution method based on Lagrangian dual transformation to solve the optimization problem.

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

[0119] See also Figure 1 The present application relates to a MIMO synaesthesia integrated system security design method under an extended clutter model, comprising the following specific steps:

[0120] Established with N T transmit antennas and N R MIMO interaceptive integrated system with 10 receiving antennas;

[0121] Build detection model and communication model, and construct the joint optimization problem of transmission waveform and receiving filter based on the detection model and communication model to ensure that the system can communicate safely with downlink users;

[0122] Design joint optimization algorithms for joint optimization problems;

[0123] Through simulation experiments, the performance of the joint optimization algorithm is tested and the security design of the MIMO synaesthesia integrated system is completed.

[0124] The construction of the detection model is as follows:

[0125] Assuming that the signal transmitted by each transmitting array element has L fast-time discrete sampling points, at the tth sampling point, the signal s transmitted by all transmitting antennas is t It can be expressed as

[0126] s t =p t +v t (87)

[0127] in integrated signal Artificial noise

[0128] Then for L fast time sampling points, the transmit signal matrix S of the MIMO radar can be expressed as

[0129] S=P+V (88)

[0130] in Integrated signal matrix Artificial Noise Matrix In addition, it is assumed that the target impulse response TIR of the extended target occupies a total of Q fast time units, that is,

[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 (89)

[0134] Where, the steering matrix H = b(θ, f)a T (θ,f), where the launch steering vector Receive Steering Vector f represents the real-time operating frequency of the radar. When the radar operating bandwidth is much smaller than the center frequency f c When the array steering vector can be described by a narrowband model, f can be expressed by a constant f c Instead, at this time, the transmitting and receiving steering vectors can be approximately considered to be independent of the bandwidth, denoted as a(θ) and b(θ), and the extended target TIR matrix is The shift matrix It can be expressed as

[0135]

[0136] Indicates uninteresting echo components that are unrelated to the transmitted waveform, including system noise and RF 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] Assume w is the receiving filter vector. Based on equation (5), the radar receiver output signal is:

[0142]

[0143] According to formula (8), the matrix is ​​defined as You can get z out Another expression of :

[0144]

[0145] In the formula,

[0146]

[0147] According to equations (8) and (9), the output SINR expression is as follows:

[0148]

[0149] The construction of the communication model is specifically as follows:

[0150] Assuming that the integrated system serves K single-antenna downlink legal communication users, and there are M single-antenna illegal communication users in the system, the signals received at the i-th legal communication user and the m-th illegal communication user can be expressed as:

[0151]

[0152]

[0153] where h bi and h em denote the communication channel vectors from the BS to the i-th legal communication user and the m-th illegal communication user, respectively. and denote the Gaussian white noise at the i-th legal communication user and the m-th illegal communication user, respectively, and p i represents a signal that carries information sent to the i-th legitimate communication user, and Assume that for all i≠j, p i With p j No matter, at this time Then the SINRs of the i-th legal communication user and the m-th illegal communication user can be expressed as:

[0154]

[0155]

[0156] The joint optimization problem of constructing the transmission waveform and the receiving filter based on the detection model and the communication model to ensure that the system can safely communicate with the downlink user is specifically as follows:

[0157] The radar obtains the TIR prior information t0 of the target of interest through previous detection and estimation methods, but the estimated TIR has a certain error Δt. Assume that Δt is random and conforms to the complex Gaussian distribution. The target TIR is described as In actual radar detection tasks, in order to stably achieve target detection, the system requires the target SINR to be higher than a certain threshold. Considering that the output SINR of formula (11) is random, the waveform design is used to ensure that the probability of the target SINR exceeding the threshold is not less than the probability threshold required by the system, so as to achieve stable target detection, that is,

[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 is.

[0160] The total confidentiality rate of the system is defined as

[0161]

[0162] where λ i and λ m denote the non-negative weights of the i-th legal communication user and the m-th illegal communication user, respectively. represents the sum of the communication rates of K legitimate communication users, represents the sum of the communication rates of M illegal communication users,

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

[0164]

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

[0166] The joint optimization algorithm is designed for the joint optimization problem. Specifically,

[0167] When the receiving filter w (n) When fixed, the 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 △t=Ω 1 / 2 u where Ω=Ω 1 / 2 Ω 1 / 2 , and then Formula (19) can be expressed as

[0171] u H Bu+2Re(u H r)+ω≥0 (106)

[0172] In the formula,

[0173] Then, using the decomposition-based large deviation inequality, Equation (20) is transformed into a convex constraint set containing only second-order cone constraints,

[0174] Known ρ∈(0,1], for any

[0175] Prob{e H Qe+2Re{e H r}+s≥0}≥1-ρ (107)

[0176] All of them, formula (21) is equivalent to the following constraint set

[0177]

[0178] Where x and y are slack variables,

[0179] By introducing slack variables m and n, for any given g, the stability probability constraint in equation (18) can be rewritten as

[0180]

[0181] Using the convex constraint set given by formula (23) to replace the stable detection probability constraint, the original optimization problem is reformulated as the following semidefinite programming form:

[0182]

[0183] A fast solution method based on Lagrangian dual transformation is used.

[0184] First, rewrite equation (17) as

[0185]

[0186] Among them, f i + (r) = λ i log(1+r) is a concave increasing function. is a concave decreasing function,

[0187] Introducing a set of auxiliary variables To replace each f i + (r) the internal fractional terms of the logarithm; introduce a set of auxiliary variables To replace each The fractional term inside the logarithm in , that is, the original optimization problem (24) is transformed into

[0188]

[0189] If and only if When it is the optimal solution of the optimization problem (26), the optimal solution of the original optimization problem (R p ＊ ,R v ＊ ), where the objective function is expressed as

[0190]

[0191] in,

[0192]

[0193] Auxiliary variables By (R p ,R v )and Alternating optimization effectively solves,

[0194] When R v When fixed, optimize We can directly find γ, The optimal closed-form solutions are

[0195]

[0196] when When fixed, optimize R v , introduce auxiliary variables and Convert the optimization problem (26) into

[0197]

[0198] in,

[0199]

[0200] If and only if When is the optimal solution to the optimization problem (31), the optimal solution R of problem (26) can be obtained. v * , through R v and Alternating optimization to solve the problem, when R v When fixed, y and Can be updated to

[0201]

[0202]

[0203] Among them, ∈ is a small positive number to prevent Approaching infinity,

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

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

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

[0207] According to formula (11), the expected output SINR is

[0208]

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

[0210]

[0211] because Taking the expectation on both sides

[0212]

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

[0214]

[0215] Let W = ww H , Can Re-stated as R p Function

[0216]

[0217] Similarly, Re-stated as R v Function

[0218]

[0219] Therefore, the following optimization problem is constructed to directly solve W *

[0220]

[0221] Since W = ww H , by calculating W * The main eigenvalue of w can be directly obtained

[0222]

[0223] in, Represents the operation of computing the principal eigenvector of a matrix.

[0224] This application tests the performance of the above joint optimization algorithm through simulation experiments. Unless otherwise specified, this application assumes that the center frequency of the MIMO interawareness integrated system is 3 GHz and the number of transmitting antennas equipped in the system is N. T =5, the number of receiving antennas is N R=4, the arrays are all uniform linear arrays, the array element spacing is half a wavelength, and the transmission waveform length L = 8. The transmission power budget P0 = 13dB. There is Gaussian white noise inside the radar system, 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 in the θ=0° direction of the MIMO array, and according to the range resolution of the radar, the TIR of the reconnaissance aircraft occupies Q=5 fast time domain resolution units of the radar. This paper models the extended target TIR as a random model, that is, t=t0+Δt, assuming that Δt is a complex complex Gaussian distribution, that is, Among them C t represents the covariance matrix of Δt and C t =0.05I Q Assume that the prior knowledge t0 of TIR is:

[0226]

[0227] This application assumes that there are 3 legitimate communication users and 2 illegal users. The flat fading channel model is used to model the communication channel h, and each channel element is independent of each other, satisfying The noise power of legal users and illegal users is set as The termination condition of the algorithm is set to ζ=10 -4 All experiments were performed 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 confidentiality rate curve and the number of iterations under different missed detection probabilities ρ is shown, where the detection threshold is set to Γ = 20dB and the weights of all communication users are set to 1. Obviously, the proposed algorithm converges after several iterations, and its convergence is numerically verified. At the same time, it can be seen that as the missed detection probability increases, the communication confidentiality rate also increases. Therefore, in order to obtain better communication performance, the integrated system needs to sacrifice some target detection performance.

[0229] Those skilled in the art may implement the present invention in a variety of variations without departing from the scope and essence of the present invention, such as using a feature of one embodiment to obtain another embodiment. Any modification, equivalent substitution and improvement made within the technical concept of the present invention shall be within the scope of the present invention.

Claims

1. A MIMO synaesthesia integrated system security design method under an extended clutter model, characterized in that: The specific steps include: Established with N T transmit antennas and N R MIMO interaceptive integrated system with 10 receiving antennas; Build detection model and communication model, and construct the joint optimization problem of transmission waveform and receiving filter based on the detection model and communication model to ensure that the system can communicate safely with downlink users; Design joint optimization algorithms for joint optimization problems; Through simulation experiments, the performance of the joint optimization algorithm is tested and the security design of the MIMO synaesthesia integrated system is completed.

2. The method for designing a MIMO synaesthesia integrated system security under an extended clutter model according to claim 1, characterized in that: The construction of the detection model is as follows: Assuming that the signal transmitted by each transmitting array element has L fast-time discrete sampling points, at the tth sampling point, the signal s transmitted by all transmitting antennas is t It can be expressed as s t =p t +v t (1) in integrated signal Artificial noise Then for L fast time sampling points, the transmit signal matrix S of the MIMO radar can be expressed as S=P+V (2) in Integrated signal matrix Artificial Noise Matrix In addition, it is assumed that the target impulse response TIR of the extended target occupies a total of Q fast time units, that is, After being reflected by the target, the signal received by the MIMO radar receiver is: Y=HST H +N =HPT H +HVT H +N (3) Where, the steering matrix H = b(θ, f)a T (θ,f), where the launch steering vector Receive Steering Vector f represents the real-time operating frequency of the radar. When the radar operating bandwidth is much smaller than the center frequency f c When the array steering vector can be described by a narrowband model, f can be expressed by a constant f c Instead, at this time, the transmitting and receiving steering vectors can be approximately considered to be independent of the bandwidth, denoted as a(θ) and b(θ), and the extended target TIR matrix is The shift matrix It can be expressed as Indicates uninteresting echo components that are unrelated to the transmitted waveform, including system noise and RF interference. Let y = vec(Y), p = vec(P), v = vec(V), n = vec(N), then the formula can be expressed as in and Let w be the receiving filter vector, based on the formula, the radar receiver output signal is: According to the formula, define the matrix You can get z out Another expression of : In the formula, According to the formula, the output SINR expression is as follows:

3. The method for designing a MIMO synaesthesia integrated system security under an extended clutter model according to claim 1, characterized in that: The construction of the communication model is specifically as follows: Assuming that the integrated system serves K single-antenna downlink legal communication users, and there are M single-antenna illegal communication users in the system, the signals received at the i-th legal communication user and the m-th illegal communication user can be expressed as: where h bi and h em denote the communication channel vectors from the BS to the i-th legal communication user and the m-th illegal communication user, respectively. and denote the Gaussian white noise at the i-th legal communication user and the m-th illegal communication user, respectively, and p i represents a signal carrying information sent to the i-th legitimate communication user, and Assume that for all i≠j, p i With p j No matter, at this time Then the SINRs of the i-th legal communication user and the m-th illegal communication user can be expressed as:

4. The method for designing a MIMO synaesthesia integrated system security under an extended clutter model according to claim 1, characterized in that: The joint optimization problem of constructing the transmission waveform and the receiving filter based on the detection model and the communication model to ensure that the system can safely communicate with the downlink user is specifically as follows: The radar obtains the TIR prior information t0 of the target of interest through previous detection and estimation methods, but the estimated TIR has a certain error Δt. Assume that Δt is random and conforms to the complex Gaussian distribution. The target TIR is described as In actual radar detection tasks, in order to stably achieve target detection, the system requires the target's SINR to be higher than a certain threshold. Considering that the output SINR of the formula is random, the waveform design ensures that the probability of the target SINR exceeding the threshold is not less than the probability threshold required by the system to achieve stable target detection, that is, 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 is. The total confidentiality rate of the system is defined as where λ i and λ m denote the non-negative weights of the i-th legal communication user and the m-th illegal communication user, respectively. represents the sum of the communication rates of K legitimate communication users, represents the sum of the communication rates of M illegal communication users, The following optimization model is constructed to jointly optimize the transmit waveform and the receive filter: Where R p =pp H , R v =vv H , P0 is the transmit power budget of the system.

5. The method for designing a MIMO synaesthesia integrated system security under an extended clutter model according to claim 1, characterized in that: The joint optimization algorithm is designed for the joint optimization problem. Specifically, When the receiving filter w (n) When fixed, the SINR ≥ Γ inside the medium stability probability constraint can be rewritten as in, Known TIR error It can be rewritten as Δt = Ω 1 / 2 u, where Ω=Ω 1 / 2 Ω 1 / 2 , and then The formula can be expressed as u H Bu+2Re(u H r)+ω≥0(20) In the formula, Then, using the large deviation inequality based on decomposition, the equation is transformed into a convex constraint set containing only second-order cone constraints, Known ρ∈(0,1], for any Prob{e H Qe+2Re{e H r}+s 0}1-ρ (21) All of them are equivalent to the following constraint set Where x and y are slack variables, By introducing slack variables m and n, for any given g, the stability probability constraint in the formula can be rewritten as Using the convex constraint set given by the formula to replace the stable detection probability constraint, the original optimization problem is reformulated as the following semidefinite programming form: Using a fast solution method based on Lagrangian dual transformation, First, rewrite equation (17) as in, f i + (r) = λ i log(1+r) is a concave increasing function. is a concave decreasing function, Introducing a set of auxiliary variables To replace each f i + (r) the internal fractional terms of the logarithm; introduce a set of auxiliary variables To replace each The fractional term inside the logarithm in , that is, the original optimization problem is transformed into If and only if When it is the optimal solution to the optimization problem, the optimal solution of the original optimization problem can be obtained (R p ,R v ), where the objective function is expressed as in, Auxiliary variables By (R p ,R v )and Alternating optimization effectively solves, When R v When fixed, optimize We can directly find γ, The optimal closed-form solutions are when When fixed, optimize R v , introduce auxiliary variables and Convert the optimization problem into in, If and only if When it is the optimal solution to the optimization problem, the optimal solution R v ＊ , through R v and Alternating optimization to solve the problem, when R v When fixed, y and Can be updated to Among them, ε is a small positive number to prevent Approaching infinity, When auxiliary variables When all are fixed, the optimization problem becomes a convex problem and can be solved directly. When R p When fixed, update by When R p and When fixed, update by when When all are fixed, solve R by solving the problem p ＊ , When the covariance matrix R of the integrated signal p and artificial noise v is p and R v When fixed, maximize the expected SINR at the radar output and solve the optimal w. According to the formula, the expected SINR at the output is make but Put f in First-order Taylor expansion because Taking the expectation on both sides This can be restated as Let W = ww H , Can Re-stated as R p Function Similarly, Re-stated as R v Function Therefore, the following optimization problem is constructed to directly solve W * Since W = ww H , by calculating W * The main eigenvalue of w can be directly obtained in, Represents the operation of computing the principal eigenvector of a matrix.

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