Intelligent reflecting surface assisted unauthorized detection area electromagnetic stealth method, device and equipment and medium

Abstract

The invention discloses an unauthorized detection area electromagnetic stealth method and device assisted by an intelligent reflecting surface, equipment and a medium, and the method comprises the following steps: calculating a closed expression of a signal-to-noise ratio of a radar receiving signal of an opposite side based on a constructed electromagnetic stealth system; constructing an optimization problem P1 for minimizing the maximum radar receiving SNR based on the closed expression of the SNR and the module value constraint of the I RS reflection unit; the original non-convex problem P1 is converted into a convex problem P2 by discretizing continuous spatial frequency deviation to approximate semi-infinite reflection gain constraint; obtaining a Lagrange duality problem corresponding to the optimization problem P2; and a semi-closed solution of the original problem P1 is obtained by solving the dual problem, so that the I RS reflection phase shift capable of realizing electromagnetic stealth is calculated. According to the Lagrange electromagnetic stealth method based on the intelligent reflecting surface, detection signals, reflected from a target to an unauthorized detection area, of a radar can be counteracted, and the maximum receiving SNR of the whole area is made to be minimum.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular, to an electromagnetic stealth method, device, equipment, and medium for an unauthorized detection area assisted by an intelligent reflecting surface. Background Art

[0002] With the development of wireless communication technologies and radar detection equipment, the electromagnetic stealth technology applied to aircraft can improve the survival and defense capabilities of aircraft and plays an increasingly important role in practice. The electromagnetic stealth technology reduces the strong scattering sources of the aircraft to radar signals to a minimum through specific means, thereby greatly reducing the electromagnetic wave energy that can be intercepted by the radar receiver, making the aircraft almost invisible in the radar system.

[0003] New types of absorbing / reflecting materials are applied to the field of electromagnetic stealth due to their high absorption efficiency. However, they cannot have perfect stealth performance and can only reduce the radar cross-section value of the target to a certain extent, especially in highly dynamic scenarios. In addition, certain types of electromagnetic stealth materials can only achieve the expected stealth performance at specific incident electromagnetic wave angles and frequencies. Therefore, the high mobility of the target and the rapid change of the combat radar mode will lead to a rapid change in the detection frequency and incident wave angle, making the electromagnetic stealth materials unable to adapt to the rapidly changing environment. Therefore, in addition to simply relying on electromagnetic stealth materials with fixed post-manufacture performance, it has become an urgent need to study intelligent adaptive electromagnetic stealth systems integrating reconfigurable / controllable metasurfaces from the perspective of signal processing to cope with increasingly complex scenarios.

[0004] Currently, among the candidate new technologies for 6G, the intelligent reflecting surface (IRS) stands out with its unique characteristics of low cost, low power consumption, programmable, easy deployment, and noise-free. The intelligent reflecting surface is a promising wireless channel reconstruction technology that makes the wireless propagation environment actively controllable from passively adaptive by introducing a wireless network, thereby constructing an intelligent wireless environment, bringing a new paradigm for the coverage design of future networks, and meeting the needs of future mobile communications. Although some work has considered applying the intelligent reflecting surface to directional signal suppression (such as physical layer security), its potential in the anti-radar detection of electromagnetic stealth systems has not been fully explored. Different from the traditional electromagnetic stealth technology that relies on fixed stealth material characteristics, limited operating frequencies, and angles / directions, the intelligent reflecting surface has flexible and real-time control over incident electromagnetic waves and a wider range of operating frequencies and angles / directions. This adaptability makes it more suitable to assist or supplement imperfect electromagnetic stealth in a highly dynamic wireless environment, making the wireless propagation environment actively controllable from passively adaptive. Summary of the Invention

[0005] To at least to some extent solve one of the technical problems existing in the prior art, the purpose of the present invention is to provide an electromagnetic stealth method, device, equipment and medium assisted by an intelligent reflecting surface for an unauthorized detection area, so that an object can achieve electromagnetic stealth under a bistatic radar detection system.

[0006] The first technical solution adopted by the present invention is:

[0007] An electromagnetic stealth method assisted by an intelligent reflecting surface for an unauthorized detection area, comprising the following steps:

[0008] Step 1: Establish a system model of an electromagnetic stealth system assisted by an intelligent reflecting surface under a bistatic radar, wherein both the intelligent reflecting surface installed on the target surface and the other party's radar are equipped with uniform planar arrays;

[0009] Step 2: Based on the constructed electromagnetic stealth system, calculate a closed-form expression of the signal-to-noise ratio of the received signal of the other party's radar;

[0010] Step 3: Based on the closed-form expression in Step 2 and the modulus constraint of the IRS reflection unit, construct an optimization problem P1 for minimizing the maximum radar received SNR;

[0011] Step 4: By discretizing the continuous spatial frequency deviation to approximate the semi-infinite reflection gain constraint, transform the non-convex problem P1 in Step 3 into a convex problem P2;

[0012] Step 5: Obtain the Lagrangian dual problem f(λ, u) corresponding to the optimization problem P2;

[0013] Step 6: Obtain a semi-closed solution of the original problem P1 by solving the dual problem f(λ, u), thereby calculating the IRS reflection phase shift capable of achieving electromagnetic stealth.

[0014] Further, the system model in Step 1 includes:

[0015] Both the radar transmitter and receiver in the system model are equipped with M antennas and are randomly located in a rectangular unauthorized plane to try to detect the target; the 3D coordinates of the radar transmitter and receiver are respectively represented by and ; the IRS installed on the target is parallel to the x-y plane and consists of a sub-wavelength uniform planar array (Uniform planar array, UPA), where N = N x N y passive reflection elements, where N x and N y represent the number of reflection elements along the x-axis and y-axis respectively.

[0016] Further, the said Step 2 includes:

[0017] Since the flying target is located at high altitude, the propagation channel between each radar and the IRS is characterized by the far-field line-of-sight (LoS) model; in addition, the radar detections during a coherent-processing interval (CPI) \(T\) are concerned, during which the channel and geometry-related parameters are assumed to be constant; the positions of the target / IRS during the CPI are denoted by c During this period, the channel and geometric related parameters are assumed to be constant; the position of the target / IRS during the CPI is represented by Denoted by:

[0018] Define the one-dimensional steering vector of a uniform linear array (ULA) as:

[0019]

[0020] where \(\varphi\in[0, 2\pi)\) represents the constant phase shift difference between the signals of two adjacent antennas / elements, Denotes the number of antennas / elements in the ULA; Let and Represent the elevation angle and azimuth angle of arrival (AoAs) of the transmission link from the radar transmitter to the IRS respectively. The received array response vector of the IRS can be expressed as:

[0021]

[0022] where \(\lambda\) is the wavelength of the detection signal, Denotes the element spacing at the IRS, and Are the spatial frequencies along the x and y dimensions corresponding to the AoAs respectively, Denotes the Kronecker product; The array response of the radar transmitter Can also be obtained similarly;

[0023] Due to the movement of the target, the propagation link is affected by the Doppler shift. The \(N\times M\) channel from the transmitting radar to the IRS at time \(t\) for \(0\leq t\leq T\) c Is given by:

[0024]

[0025] where Is the complex-valued path gain, \(d\) T (q, w T ) = |q - w T$R$ is the propagation distance between the radar transmitter and the IRS, and $\alpha$ is the unit path gain when the propagation distance is 1 meter. $f_{d,t}$ represents the Doppler frequency of the transmit link, and $v$ is the velocity of the airborne target; the far-field LoS channel from the radar transmitter to the target at time $t$ is denoted as Specifically expressed as:

[0026]

[0027] Similarly, let and be respectively represented as the elevation angle and azimuth angle of departure (Angles-of-departure, AoDs) of the receive link from the IRS to the radar receiver , then the reflection array response vector of the IRS is expressed as:

[0028]

[0029] where and represent the spatial frequencies along the $x$ and $y$ dimensions corresponding to the AoD respectively; then, the channel from the IRS and the target to the radar receiver at time $t$ is denoted as Specifically expressed as:

[0030]

[0031] where is the complex-valued path gain $d$ R $(q, w$ R ) = |q - w R | is the propagation distance between the IRS and the radar receiver, represents the Doppler frequency of the receive link, is the array response of the radar receiver;

[0032] The pulse waveform vector of the radar transmitter is represented as The echo of the target / IRS from the radar receiver at time $t$ is characterized as:

[0033]

[0034] where represents the IRS reflection vector, corresponding to the IRS element at position $(n$ x , $n$ y ), and are respectively the reflection amplitude and phase shift of the $n$-th element at time $t$, $\tau_s$ represents the isotropic complex-valued RCS of the target surface, is additive white Gaussian noise (AWGN) with zero mean and variance σ 2 ;

[0035] According to Equation (8), the SNR at the radar receiver at time t is given by:

[0036]

[0037]

[0038] where represents the complex-valued reflection gain at the target / IRS, which depends on the AoAs and AoDs of the target / IRS and the IRS reflection and is the normalized received signal power when |R [t] (q, w T , w R , θ [t] )| 2 = 1.

[0039] Furthermore, step 3 includes:

[0040] To reduce the radar detection probability, the objective is to minimize the maximum SNR within the unauthorized detection region by optimizing the IRS reflection vector θ [t] for a given target location q. This problem is formulated as:

[0041]

[0042] According to Equations (2) and (5), the reflection gain defined in Equation (9) can be rewritten as:

[0043]

[0044] where ⊙ represents the Hadamard product; for any given target location q, φ min and φ max are respectively defined as the minimum and maximum differences between the spatial frequencies associated with the AoAs along the x-axis and the spatial frequencies associated with the AoDs within the unauthorized detection region , i.e.:

[0045]

[0046] The spatial frequency and the minimum and maximum deviations along the y-axis are respectively denoted as Ω min and Ω max .

[0047] Further, step 4 includes:

[0048] If it is defined that then the unauthorized detection area can be equivalently described by in the angular domain; by introducing the slack optimization variable η to represent the maximum reflection gain within, (P1) is equivalently written as:

[0049]

[0050] For the above problem, the design of θ should make the reflection gain For the angular domain roughly equivalent for all spatial frequency pairs (Φ, Ω) within; the reflection gain constraint equation (13b) involves a semi-infinite constraint, which makes the direct solution of problem (P2) challenging;

[0051] To address this challenge, first discretize the continuous spatial frequency deviation by sampling K points within the angular domain :

[0052] Discretized as where Φ k ∈ [Φ min , Φ max and Ω k ∈ [Ω min , Ω max , and k = 1, 2,..., K respectively represent the spatial frequency deviations along the x and y dimensions corresponding to the k-th sampling point; thus, problem (P2) is approximated as:

[0053]

[0054] where is the array response vector corresponding to the k-th sampling point within the angular domain , and if K → ∞ and the sampling points traverse the entire angular domain then (P3) is equivalent to (P2).

[0055] Further, step 5 includes:

[0056] Since (P3) is convex and satisfies the Slater condition, there is strong duality between (P3) and its Lagrangian dual problem; thus, (P3) can be solved by using the Lagrangian dual method:

[0057] Let and Denote the non - negative dual variables associated with the constraints (14b) and (13c) respectively; then, the Lagrangian function associated with (P3) is:

[0058]

[0059] where Therefore, the dual function of (P3) is given by:

[0060]

[0061] For the dual function \(f(\lambda,\mu)\) to have a lower bound, i.e., \(f(\lambda,\mu)>-\infty\), it must hold; otherwise, if or then setting \(\eta\rightarrow\infty\), or \(\eta\rightarrow-\infty\), will result in \(f(\lambda,\mu)\rightarrow-\infty\); thus, the dual problem of (P3) is given by:

[0062]

[0063] \(\lambda\) k \(\geq0\), \(k = 1,2,\cdots,K\) (17c)

[0064] \(\mu\) n \(\geq0\), \(n = 1,2,\cdots,N\) (17d).

[0065] Furthermore, the said step 6 includes:

[0066] First, solve problem (16) to obtain \(f\{\lambda,\mu\}\) for any given feasible dual variables \(\{\lambda,\mu\}\), then solve (D3) to obtain the optimal \(\{\lambda,\mu\}\) to maximize \(f(\lambda,\mu)\), and finally construct the optimal primal solution of (P3):

[0067] 1) Obtain \(f(\lambda,\mu)\) by solving problem (16) for the given \(\{\lambda,\mu\}\): For any given \(\{\lambda,\mu\}\), problem (16) can be decomposed into the following two sub - problems:

[0068]

[0069] Denote the optimal solutions of (18) and (19) by \(\eta\) (λ，μ) and \(\theta\) (λ，μ) respectively; for problem (18), since holds for any given feasible dual variables, the value of the objective is always zero; thus, any arbitrary real number can be chosen as the optimal solution \(\eta\) (λ，μ) ; for problem (19), set the first - order derivative of the objective function with respect to \(\lambda\) to zero, i.e., Therefore, the optimal solution of problem (19) is:

[0070]

[0071] Find the optimal dual solution of (D3): Obtain η (λ，μ) and θ (λ，μ) , and then solve the dual problem (D3) to find the optimal {λ, μ} to maximize f(λ, μ); According to and substitute η (λ，μ) and θ (λ，μ) into f(λ, μ), we get:

[0072]

[0073] where In addition, by applying the Schur complement, the dual problem is transformed into an equivalent semidefinite optimization problem as follows:

[0074]

[0075] The problem (P4) is effectively solved by semidefinite programming (SDP) or linear matrix inequality (LMI) optimization. For a given solution accuracy ∈ > 0, the complexity is order; More sampling points will achieve some performance improvement, but inevitably increase the complexity, resulting in an extraordinary trade-off between electromagnetic stealth performance and computational complexity;

[0076] 2) Construct the optimal initial solution of (P3): Obtain the optimal dual variables λ ＊ and μ ＊ by solving (D3). The optimal solution of (P3), denoted as θ ＊ and η ＊ , is expressed as:

[0077]

[0078] According to the Karush-Kuhn-Tucker (KKT) conditions, the complementary slackness condition corresponding to the constraint (14b) is expressed as:

[0079]

[0080] For any given sampling index k, if then must hold; Conversely, if To satisfy the complementary slackness condition (25), must be true; As observed from equation (23), if then corresponding to the angular domain The array response vector u of the k-th sampling point inside k For the optimal reflection vector θ ＊ There is no impact; if defined Then there is Effective sampling points for optimizing IRS reflection; this phenomenon indicates that in addition to the number of sampling points, the distribution of sampling points also affects the performance and computational complexity of electromagnetic stealth.

[0081] The second technical solution adopted by the present invention is:

[0082] An electromagnetic stealth device for an unauthorized detection area assisted by an intelligent reflecting surface, comprising:

[0083] A model construction module for establishing a system model of an electromagnetic stealth system for an unauthorized detection area assisted by an intelligent reflecting surface under bistatic radar, where both the intelligent reflecting surface installed on the target surface and the other party's radar are equipped with uniform planar arrays;

[0084] A first calculation module for calculating a closed-form expression of the signal-to-noise ratio of the received signal of the other party's radar based on the constructed electromagnetic stealth system;

[0085] A problem construction module for constructing an optimization problem P1 for minimizing the maximum radar received SNR based on the closed-form expression and the modulus constraint of the IRS reflection unit;

[0086] A problem transformation module for converting the non-convex problem P1 into a convex problem P2 by discretizing the continuous spatial frequency deviation to approximate the semi-infinite reflection gain constraint;

[0087] A problem optimization module for obtaining the Lagrangian dual problem f(λ, u) corresponding to the optimization problem P2;

[0088] A second calculation module for obtaining a semi-closed solution of the original problem P1 by solving the dual problem f(λ, u), thereby calculating the IRS reflection phase shift that can achieve electromagnetic stealth.

[0089] The third technical solution adopted by the present invention is:

[0090] An electronic device, the electronic device includes a processor and a memory, and at least one instruction, at least one program, a code set or an instruction set is stored in the memory, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by the processor to implement an electromagnetic stealth method for an unauthorized detection area assisted by an intelligent reflecting surface as described above.

[0091] The fourth technical solution adopted by the present invention is:

[0092] A computer-readable storage medium stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by a processor to implement the electromagnetic stealth method for an unauthorized detection area assisted by an intelligent reflecting surface as described above.

[0093] The fifth technical solution adopted by the present invention is:

[0094] A computer program product or a computer program includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions to enable the computer device to execute the above method.

[0095] The beneficial effects of the present invention are as follows: The present invention proposes an algorithm based on Lagrangian duality for the design of the reflection phase shift vector of the intelligent reflecting surface, enabling the intelligent reflecting surface in the electromagnetic stealth system to eliminate or cancel the reflection signals of the target aircraft surface in all radar echoes and cross-links, achieving an almost complete electromagnetic stealth effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following introduces the related technical solution drawings in the embodiments of the present invention or the prior art. It should be understood that the drawings below only conveniently and clearly illustrate some embodiments of the technical solutions in the present invention, and those skilled in the art can also obtain other drawings based on these drawings without creative efforts.

[0097] Figure 1 is a schematic diagram of the electromagnetic stealth system in the embodiment of the present application.

[0098] Figure 2 is an optional flowchart of the intelligent reflecting surface design method provided by the embodiment of the present application.

[0099] Figure 3 is a comparison result curve graph of the horizontal reflection gain obtained by different methods and the spatial frequency φ.

[0100] Figure 4 is the maximum horizontal reflection gain obtained by different methods and the number N of intelligent reflecting surface elements in the embodiment of the present application x relation curve graph.

[0101] Figure 5 is a relation curve graph of the maximum horizontal reflection gain obtained by the electromagnetic stealth system in the embodiment of the present application and the number K of sampling points. Detailed implementation manners

[0102] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary only for explaining the present invention and should not be construed as limiting the present invention. For the step numbers in the following embodiments, they are only set for the convenience of elaboration and explanation, and no limitation is imposed on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0103] In the description of the present invention, it should be understood that for the orientation description, such as the orientation or positional relationship indicated by up, down, front, back, left, right, etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present invention.

[0104] In the description of the present invention, the meaning of several is one or more, the meaning of multiple is more than two, understand greater than, less than, exceeding, etc. as not including the present number, and understand above, below, within, etc. as including the present number. If there is a description of first and second, it is only for the purpose of distinguishing technical features and should not be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence relationship of the indicated technical features.

[0105] In the description of the present invention, unless otherwise clearly defined, words such as setting, installing, connecting, etc. should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above words in the present invention in combination with the specific content of the technical solution.

[0106] In order to better illustrate the technical progressiveness of the method of the present invention, an electromagnetic stealth method for unlicensed detection areas assisted by an intelligent reflecting surface proposed by the present invention is compared with different benchmark schemes on the MATLAB platform. Among them, other benchmark schemes include:

[0107] 1) Benchmark system without IRS: The radar detects the target without the help of IRS.

[0108] 2) Baseline system with a single sampling point: The IRS reflection vector is designed using a solution based on back alignment to reduce the reflection gain when Φ = 0.

[0109] 3) Random phase shift design: The phase shifts of the IRS elements are randomly generated after being uniformly distributed within [0, 2π).

[0110] To better understand the above technical solution, the following will combine the accompanying drawings of the specification and specific implementation manners to provide a more detailed description of an electromagnetic stealth method for unauthorized detection areas assisted by an intelligent reflecting surface disclosed in this embodiment.

[0111] Embodiment 1

[0112] As Figure 1 shown, the embodiment of the present invention is based on an IRS-assisted electromagnetic stealth system, and its specific system design is as follows:

[0113] This embodiment considers the system model of an intelligent reflecting surface-assisted electromagnetic stealth system under a bistatic radar, where both the radar transmitter and receiver are equipped with M antennas and are randomly located in a rectangular unauthorized plane to attempt to detect the target. The 3D coordinates of the radar transmitter and receiver are represented by and respectively. The IRS installed on the target is parallel to the x-y plane and consists of a sub-wavelength uniform planar array (UPA), where N = N x N y passive reflecting elements, where N x and N y represent the number of reflecting elements along the x-axis and y-axis respectively.

[0114] As Figure 2 shown, this embodiment provides an electromagnetic stealth method for unauthorized detection areas assisted by an intelligent reflecting surface, including the following steps:

[0115] Step S1: Establish a system model of an intelligent reflecting surface-assisted electromagnetic stealth system under a bistatic radar, where both the intelligent reflecting surface installed on the target surface and the opposing radar are equipped with uniform planar arrays;

[0116] Step S2: Based on the constructed electromagnetic stealth system, calculate the closed-form expression of the signal-to-noise ratio of the received signal of the opposing radar;

[0117] Step S3: Based on the closed-form expression in Step S2 and the modulus constraint of the IRS reflection unit, construct an optimization problem P1 for minimizing the maximum radar received SNR;

[0118] Step S4: By discretizing the continuous spatial frequency deviation to approximate the semi-infinite reflection gain constraint, transform the non-convex problem P1 in Step S3 into a convex problem P2;

[0119] Step S5: Obtain the Lagrangian dual problem f(λ, u) corresponding to the optimization problem P2;

[0120] Step S6: Obtain the semi-closed solution of the original problem P1 by solving the dual problem f(λ,u), thereby calculating the IRS reflection phase shift that can achieve electromagnetic invisibility.

[0121] In this embodiment, the process of step S1 is as follows:

[0122] This embodiment considers the system model of an intelligent reflecting surface-assisted electromagnetic invisibility system under a bistatic radar, where both the radar transmitter and receiver are equipped with M antennas and are randomly located in a rectangular unauthorized plane to attempt to detect the target. The 3D coordinates of the radar transmitter and receiver are represented by and respectively. The IRS installed on the target is parallel to the x-y plane and consists of a sub-wavelength uniform planar array, where N = N x N y passive reflection elements, where N x and N y represent the number of reflection elements along the x-axis and y-axis respectively.

[0123] In this embodiment, the process of step S2 is as follows:

[0124] Since the flying target is usually located at high altitude, the propagation channel between each radar and the IRS can be characterized by the far-field line-of-sight (LoS) model. In addition, we focus on the radar detection during a coherent-processing interval (CPI) T c during which the channel and geometry-related parameters are assumed to be constant. The position of the target / IRS during the CPI is represented by respectively.

[0125] We define the one-dimensional steering vector of a uniform linear array (ULA) as:

[0126]

[0127] where φ ∈ [0, 2π) represents the constant phase shift difference between the signals of two adjacent antennas / elements, represents the number of antennas / elements in the ULA. Denote and as the elevation angle and azimuth angle of arrival (AoAs) of the transmission link from the radar transmitter to the IRS respectively, and the receiving array response vector of the IRS can be expressed as:

[0128]

[0129] wherein λ is the wavelength of the detection signal, represents the element spacing at the IRS, and are the spatial frequencies along the x- and y-dimensions corresponding to the AoAs, respectively, represents the Kronecker product. The array response of the radar transmitter can also be obtained similarly.

[0130] Due to the movement of the target, the propagation link is affected by the Doppler shift. The N×M channel from the transmitting radar to the IRS at time t for 0 ≤ t ≤ T c is given by:

[0131]

[0132] where is the complex-valued path gain, d T (q, w T ) = |q - w T | is the propagation distance between the radar transmitter and the IRS, α is the unit path gain when the propagation distance is 1 meter, represents the Doppler frequency of the transmitting link, and v is the velocity of the airborne target. The far-field LoS channel from the radar transmitter to the target at time t, denoted as can be expressed as:

[0133]

[0134] Similarly, denoting and as the elevation angle and azimuth angle of departure (Angles-of-departure, AoDs) of the receiving link from the IRS to the radar receiver respectively, the reflected array response vector of the IRS can be expressed as:

[0135]

[0136] where and are the spatial frequencies along the x and y dimensions corresponding to the AoD, respectively. Then, the channel from the IRS and the target to the radar receiver at time t, denoted as can be expressed similarly to (3) and (4), i.e.:

[0137]

[0138] where is the complex-valued path gain d R (q, wR) = |q - w R | is the propagation distance between the IRS and the radar receiver, representing the Doppler frequency of the receiving link, is the array response of the radar receiver.

[0139] Represent the pulse waveform vector of the radar transmitter as The echo from the target / IRS at the radar receiver at time t can be characterized as:

[0140]

[0141] where represents the IRS reflection vector, n = (n x - 1)N y + n y corresponds to the IRS element at position (n x , n y ), and are the reflection amplitude and phase shift of the nth element at time t, respectively, and τ S represents the isotropic complex-valued RCS of the target surface, is zero-mean additive white Gaussian noise (AWGN) with variance σ 2 .

[0142] According to (8), the SNR of the radar receiver at time t is given by:

[0143]

[0144] where represents the complex-valued reflection gain at the target / IRS, which depends on the AoAs and AoD of the target / IRS and the IRS reflection and is the normalized received signal power when |R [t] (q, w T , w R , θ [t] )| 2 = 1.

[0145] In this embodiment, the process of step S3 is as follows:

[0146] To reduce the radar detection probability, our goal is to minimize the maximum SNR within the unauthorized detection region [t] by optimizing the IRS reflection vector θ for a given target position q. The problem is formulated as:

[0147]

[0148] Note that in (9), is a constant independent of θ [t] and can thus be omitted in the objective function.

[0149] According to (2) and (5), the reflection gain defined in (9) can be rewritten as:

[0150]

[0151] where ⊙ denotes the Hadamard product. For any given target location q, we define Φ min and Φ max as the spatial frequencies related to the AoAs along the x-axis and the spatial frequencies related to the AoDs in the unauthorized detection region respectively, i.e., the minimum and maximum differences between and which are:

[0152]

[0153] The spatial frequency and the minimum and maximum deviations along the y-axis are denoted as Ω min and Ω max respectively.

[0154] In this embodiment, the process of step S4 is as follows:

[0155] If we define and then the unauthorized detection region can be equivalently described by in the angular domain. By introducing the relaxation optimization variable η to represent the maximum reflection gain within , (P1) can be equivalently written as:

[0156]

[0157] For the above problem, the design of θ should make the reflection gain roughly equivalent for all spatial frequency pairs (Φ, Ω) within the angular domain . The reflection gain constraint (13b) involves a semi-infinite constraint, which makes the direct solution of problem (P2) challenging.

[0158] To address this challenge, we first discretize the continuous spatial frequency deviation by sampling K points within the angular domain . Specifically, is discretized into where Φk ∈ [Φ min , Φ max and Ω k ∈ [Ω min , Ω max , and k = 1, 2, ..., K respectively represent the spatial frequency deviations along the x and y dimensions corresponding to the k-th sampling point. Therefore, problem (P2) can be approximated as:

[0159]

[0160] where is the array response vector corresponding to the k-th sampling point in the angular domain . Note that if K → ∞ and the sampling points traverse the entire angular domain then (P3) is equivalent to (P2).

[0161] In this embodiment, the process of step S5 is as follows:

[0162] Since (P3) is convex and satisfies the Slater condition, there is strong duality between (P3) and its Lagrangian dual problem. Therefore, we can solve (P3) by using the Lagrangian dual method.

[0163] Let and respectively represent the non-negative dual variables associated with constraints (14b) and (13c). Then, the Lagrangian function associated with (P3) is:

[0164]

[0165] where Therefore, the dual function of (P3) is given by:

[0166]

[0167] For the dual function f(λ, μ) to have a lower bound (i.e., f(λ, μ) > -∞), must hold. Otherwise, if (or ), then setting η → ∞ (or η → -∞) will result in f(λ, μ) → -∞. Therefore, the dual problem of (P3) is given by:

[0168]

[0169] λ k ≥ 0, k = 1, 2, ..., K (17c)

[0170] μ n≥ 0, n = 1, 2, ..., N (17d)

[0171] In this embodiment, the process of step S6 is as follows:

[0172] In what follows, we first solve problem (16) to obtain f(λ, μ) for any given feasible dual variables {λ, μ}, then solve (D3) to obtain the optimal {λ, μ} to maximize f(λ, μ), and finally construct the optimal primal solution of (P3).

[0173] 1) Obtain f(λ, μ) by solving problem (16) for the given {λ, μ}: For any given {λ, μ}, problem (16) can be decomposed into the following two sub - problems.

[0174]

[0175] Denote the optimal solutions of (18) and (19) by η (λ，μ) and θ (λ，μ) respectively. For problem (18), since holds for any given feasible dual variables, the value of the objective is always zero. Thus, we can choose any arbitrary real number as the optimal solution η (λ，μ) . For problem (19), we set the first - order derivative of the objective function with respect to θ to zero, i.e., Thus, the optimal solution of problem (19) can be obtained as:

[0176]

[0177] Find the optimal dual solution of (D3): Having obtained η (λ，μ) and θ (λ，μ) , then we solve the dual problem (D3) to find the optimal {λ, μ} to maximize f(λ, μ). According to and substituting η (λ，μ) and θ (λ，μ) into f(λ, μ), we get:

[0178]

[0179] where Furthermore, by applying the Schur complement, the dual problem can be transformed into an equivalent semidefinite optimization problem as follows:

[0180]

[0181] The problem (P4) can be effectively solved by semidefinite programming (SDP) or linear matrix inequality (LMI) optimization. For a given solution accuracy ∈ > 0, the complexity is order. More sampling points will achieve some performance improvement, but inevitably increase the complexity, leading to an unusual trade-off between electromagnetic stealth performance and computational complexity.

[0182] 3) Construct the optimal initial solution of (P3): Obtain the optimal dual variables λ ＊ and μ ＊ , and the optimal solution of (P3), denoted as θ ＊ and η ＊ , can be expressed as:

[0183]

[0184] Note: According to the Karush-Kuhn-Tucker (KKT) conditions, the complementary slackness condition corresponding to constraint (14b) can be expressed as:

[0185]

[0186] For any given sampling index k, if then must hold. Conversely, if To satisfy the complementary slackness condition (25), must be true. As we observe from (23), if then the array response vector u corresponding to the k-th sampling point within the angular domain k has no effect on the optimal reflection vector θ ＊ . If we define then there is effective sampling points for optimizing the IRS reflection. This phenomenon indicates that in addition to the number of sampling points, the distribution of sampling points also affects the electromagnetic stealth performance and computational complexity.

[0187] Figure 3It is a curve graph comparing the horizontal reflection gain obtained by different methods with the spatial frequency provided by an embodiment of the present application. Observations show that compared with the baseline system without IRS and the random phase shift design, the proposed Lagrangian dual-based optimization achieves significantly lower reflection gain. Although the baseline system with a single sampling point can completely eliminate the reflection gain at Φ = 0, it cannot eliminate the radar detection signal in the entire unauthorized detection area. The above results verify that the IRS design derived in (23) can effectively reduce the reflection gain of the target, thereby neutralizing the echo signal in the radar direction. In addition, the reflection gain obtained by our proposed scheme is approximately constant within the interval [Φ min , Φ max , which indicates that the proposed IRS-assisted electromagnetic stealth system acts like a dynamic band-stop spatial filter, shielding the radar detection signal reflected from the target echo and reflected into the unauthorized detection area. We also observe that near Φ = -0.35 and Φ = 0.35, the reflection gain increases significantly, indicating that our proposed method transfers the reflected electromagnetic energy outside the unauthorized detection area.

[0188] Figure 4 It is a curve graph showing the relationship between the maximum horizontal reflection gain obtained by different methods and the number of intelligent reflecting surface elements provided by an embodiment of the present application. It shows the relationship between the maximum horizontal reflection gain within the interval [Φ min , Φ max obtained by the considered methods and the number of IRS elements N x . Observations show that regardless of N x , the maximum reflection gain of the baseline system without IRS remains unchanged because in this case, Since increasing the size of the IRS increases the degrees of freedom available for echo signal manipulation on the target-mounted IRS, the maximum reflection gain of the proposed method decreases with N x . Due to the discrete approximation of the continuous spatial frequency deviation, the designed beam inevitably generates gain fluctuations, so the maximum reflection gain of the proposed method tends to level off and cannot achieve complete electromagnetic stealth (i.e., η = 0). In contrast, the baseline system with a single sampling point and the baseline scheme with a randomly configured IRS actually enhance the reflection gain, which has the adverse effect of increasing the target detection probability. The above results confirm the effectiveness of appropriate passive IRS reflection design for achieving electromagnetic stealth in the unauthorized detection area.

[0189] Figure 5 It is a curve graph showing the relationship between the maximum horizontal reflection gain obtained by the electromagnetic stealth system provided by an embodiment of the present application and the number of sampling points. It is observed that as K increases, N x and Φ maxThe maximum horizontal reflection gain at different times is significantly reduced and quickly approaches a constant η. Since the beamwidth of the phased array is inversely proportional to the array aperture N x Δ e and a wider unauthorized detection area requires more sampling points to traverse it to continuously reduce the reflection gain, we can also observe that a larger N x and a larger Φ max require more sampling points to achieve the minimum η.

[0190] In summary, an electromagnetic stealth method for unauthorized detection areas assisted by an intelligent reflecting surface proposed by the present invention can evade potential radar detections within the unauthorized detection area. To cancel the radar detection signals reflected from the target to any possible radar positions in the unauthorized detection area, the design of the IRS reflection pattern minimizes the maximum received SNR of the entire area to achieve good stealth performance in the unauthorized detection area.

[0191] Embodiment 2

[0192] This embodiment provides an electromagnetic stealth device for unauthorized detection areas assisted by an intelligent reflecting surface, including:

[0193] A model construction module for establishing a system model of an electromagnetic stealth system for unauthorized detection areas assisted by an intelligent reflecting surface under bistatic radar, where the intelligent reflecting surface installed on the target surface and the opposing radar are both equipped with uniform planar arrays;

[0194] A first calculation module for calculating a closed-form expression of the signal-to-noise ratio of the received signal of the opposing radar based on the constructed electromagnetic stealth system;

[0195] A problem construction module for constructing an optimization problem P1 of minimizing the maximum radar received SNR based on the closed-form expression and the modulus constraint of the IRS reflection unit;

[0196] A problem transformation module for transforming the non-convex problem P1 into a convex problem P2 by discretizing the continuous spatial frequency deviation to approximate the semi-infinite reflection gain constraint;

[0197] A problem optimization module for obtaining the Lagrangian dual problem f(λ,u) corresponding to the optimization problem P2;

[0198] A second calculation module for obtaining a semi-closed solution of the original problem P1 by solving the dual problem f(λ,u), thereby calculating the IRS reflection phase shift capable of achieving electromagnetic stealth.

[0199] Since this device is an electromagnetic stealth device for unauthorized detection areas assisted by an intelligent reflecting surface in an embodiment of the present invention, and the principle of how this device solves problems is similar to that of the method, the implementation of this device can refer to the implementation process of the above method embodiment, and repeated parts will not be elaborated again.

[0200] Embodiment 3

[0201] An embodiment of the present invention further provides an electronic device, where the electronic device includes a processor and a memory. At least one instruction, at least one program, a code set, or an instruction set is stored in the memory, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement Figure 2 an electromagnetic stealth method for unauthorized detection areas assisted by an intelligent reflecting surface as shown.

[0202] It can be understood that the memory may include a random access memory (RAM), and may also include a read-only memory (ROM). Optionally, the memory includes a non-transitory computer-readable storage medium. The memory can be used to store instructions, programs, codes, code sets, or instruction sets. The memory may include a program storage area and a data storage area. Among them, the program storage area may store instructions for implementing an operating system, instructions for at least one function, instructions for implementing the above various method embodiments, etc.; the data storage area may store data created according to the use of the server, etc.

[0203] The processor may include one or more processing cores. The processor connects various parts within the entire server using various interfaces and lines. By running or executing instructions, programs, code sets, or instruction sets stored in the memory, and by calling data stored in the memory, the processor performs various functions of the server and processes data. Optionally, the processor may be implemented in at least one hardware form of digital signal processing (DSP), field-programmable gate array (FPGA), or programmable logic array (PLA). The processor may integrate a central processing unit (CPU) and a modem, etc. in one or several combinations. Among them, the CPU mainly processes the operating system and application programs, etc.; the modem is used to process wireless communications. It can be understood that the above modem may not be integrated into the processor and may be implemented separately through a single chip.

[0204] Since the electronic device is the electronic device corresponding to an electromagnetic stealth method for unauthorized detection areas assisted by an intelligent reflecting surface according to an embodiment of the present invention, and the principle of the electronic device to solve the problem is similar to that of the method, the implementation of the electronic device can refer to the implementation process of the above method embodiment, and the repeated parts will not be described again.

[0205] Embodiment 4

[0206] An embodiment of the present invention further provides a computer-readable storage medium, in which at least one instruction, at least one segment of program, code set or instruction set is stored, and the at least one instruction, the at least one segment of program, the code set or instruction set is loaded and executed by a processor to implement Figure 2 an electromagnetic stealth method for unauthorized detection areas assisted by an intelligent reflecting surface as shown.

[0207] Those of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium. The storage medium includes a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electrically-erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc memories, a magnetic disk memory, a tape memory, or any other computer-readable medium capable of carrying or storing data.

[0208] Since the storage medium is the storage medium corresponding to an electromagnetic stealth method for unauthorized detection areas assisted by an intelligent reflecting surface according to an embodiment of the present invention, and the principle of the storage medium to solve the problem is similar to that of the method, the implementation of the storage medium can refer to the implementation process of the above method embodiment, and the repeated parts will not be described again.

[0209] Embodiment 5

[0210] In some possible embodiments, various aspects of the method of the embodiments of the present invention can also be implemented in the form of a program product, which includes program code. When the program product runs on a computer device, the program code is used to cause the computer device to execute the steps of an unauthorized detection area electromagnetic stealth method assisted by an intelligent reflecting surface according to various exemplary embodiments described above in this specification. Among them, the executable computer program code or "code" for executing each embodiment can be written in high-level programming languages such as C, C++, C#, Smalltalk, Java, JavaScript, Visual Basic, structured query language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0211] It should be understood that each part of the present invention can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits with logic gate circuits for implementing logical functions on data signals, application-specific integrated circuits with appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0212] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples.

[0213] The above embodiments are only for illustrating the technical concept and characteristics of the present invention, and the purpose is to enable those of ordinary skill in the art to understand the content of the present invention and implement it accordingly. It cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the essence of the content of the present invention should be covered by the protection scope of the present invention.

Claims

1. An electromagnetic stealth method for an unauthorized detection area assisted by an intelligent reflecting surface, characterized in that, It includes the following steps: Step 1: Establish a system model of an electromagnetic stealth system for an unauthorized detection area assisted by an intelligent reflecting surface under a bistatic radar, where both the intelligent reflecting surface installed on the target surface and the other party's radar are equipped with uniform planar arrays; Step 2: Based on the constructed electromagnetic stealth system, calculate the closed-form expression of the signal-to-noise ratio of the received signal by the other party's radar; Step 3: Based on the closed-form expression in Step 2 and the modulus constraint of the IRS reflection unit, construct an optimization problem P1 for minimizing the maximum radar received SNR; Step 4: By discretizing the continuous spatial frequency deviation to approximate the semi-infinite reflection gain constraint, transform the non-convex problem P1 in Step 3 into a convex problem P2; Step 5: Obtain the Lagrangian dual problem f(λ, u) corresponding to the optimization problem P2; Step 6: Obtain the semi-closed solution of the original problem P1 by solving the dual problem f(λ, u), so as to calculate the IRS reflection phase shift that can achieve electromagnetic stealth.

2. The electromagnetic stealth method for unauthorized detection areas assisted by an intelligent reflecting surface according to claim 1, characterized in that, The system model in Step 1 includes: Both the radar transmitter and receiver in the system model are equipped with M antennas and are randomly located in a rectangular unlicensed plane to attempt to detect a target; the 3D coordinates of the radar transmitter and receiver are represented by and respectively; the IRS installed on the target is parallel to the x-y plane and consists of a sub-wavelength uniform planar array, where N = N x N y passive reflection elements, where N x and N y represent the number of reflection elements along the x-axis and y-axis respectively.

3. An electromagnetic stealth method for an unauthorized detection area assisted by an intelligent reflecting surface according to claim 1, characterized in that, The said Step 2 includes: Since the flying target is located at high altitude, the propagation channels between each radar and the IRS are characterized by the far-field line-of-sight model; in addition, the radar detections during a coherent processing interval T c are concerned, during which the channel and geometric-related parameters are assumed to be constant; the positions of the target / IRS during the CPI are represented by as follows: Define the one-dimensional steering vector of the uniform linear array as: where φ ∈ [0, 2π) represents the constant phase shift difference between the signals of two adjacent antennas / elements, denotes the number of antennas / elements in the ULA; Let and respectively denote the elevation angle and azimuth angle of arrival of the transmission link from the radar transmitter to the IRS. The received array response vector of the IRS is expressed as: where λ is the detection signal wavelength, denotes the element spacing at the IRS, and are the spatial frequencies along the x- and y-dimensions corresponding to the AoAs, respectively, denotes the Kronecker product; Due to the movement of the target, the propagation link is affected by Doppler frequency shift, and the N×M channel from the transmitting radar to the IRS at time t is 0≤t≤T c which is given by: where is the complex-valued path gain, d T (q, w T ) = |q - w T | is the propagation distance between the radar transmitter and the IRS, α is the unit path gain at a propagation distance of 1 meter, represents the Doppler frequency of the transmit link, v is the velocity of the airborne target; the far-field LoS channel from the radar transmitter to the target at time t is denoted as Specifically expressed as: Similarly, let and represent the elevation angle and azimuth angle departure angles of the receiving link from the IRS to the radar receiver respectively. Then, the reflection array response vector of the IRS is expressed as: where and represent the spatial frequencies along the x and y dimensions corresponding to the AoD, respectively; then, the channel from the IRS and the target to the radar receiver at time t, denoted as is specifically expressed as: where is the complex-valued path gain d R (q, w R ) = |q - w R | is the propagation distance between the IRS and the radar receiver, represents the Doppler frequency of the receiving link, is the array response of the radar receiver; The pulse waveform vector of the radar transmitter is represented as The echo from the target / IRS at time t received by the radar receiver is characterized as: Among them represents the IRS reflection vector, n = (n x - 1)N y + n y corresponds to the IRS element at position (n x , n y ); and are respectively the reflection amplitude and phase shift of the n-th element at time t, τ s represents the isotropic complex-valued RCS of the target surface, is zero-mean additive Gaussian white noise with variance σ 2 ; According to Equation (8), the SNR of the radar receiver at time t is given by: where represents the complex-valued reflection gain at the target / IRS, which depends on the AoAs and AoDs of the target / IRS as well as the IRS reflection and is |R [t] (q, w T , w R , θ [t] )| 2 is the normalized received signal power when = 1.

4. An electromagnetic stealth method for unauthorized detection areas assisted by intelligent reflecting surfaces according to claim 3, characterized in that The said Step 3 includes: To reduce the radar detection probability, the goal is to minimize the maximum SNR within the unauthorized detection area by optimizing the IRS reflection vector θ for a given target position q [t] and minimize the unauthorized detection area The problem is formulated as follows: Note that the in (9) is a constant independent of θ [t] and thus can be omitted in the objective function; According to Eqs. (2) and (5), the reflection gain defined in Eq. (9) can be rewritten as: where ⊙ denotes the Hadamard product; for any given target location q, Φ min and Φ max are respectively defined as the minimum and maximum differences between the spatial frequencies associated with the AoAs along the x-axis in the unauthorized detection region and the spatial frequencies associated with the AoD , that is: ​ Spatial frequency and the minimum and maximum deviations along the y-axis, denoted as Ω min and Ω max .

5. An electromagnetic stealth method for an unauthorized detection area assisted by an intelligent reflecting surface according to claim 4, characterized in that, The said Step 4 includes: If defined and then the unauthorized detection area can be equivalently described by in the angular domain; by introducing the slack optimization variable η to represent the maximum reflection gain within, (P1) is equivalently written as: For the above problem, the design of θ should make the reflection gain for the angular domain be approximately equivalent for all spatial frequency pairs (Φ, Ω) within; the reflection gain constraint equation (13b) involves a semi-infinite constraint, which makes the direct solution of problem (P2) challenging; To address this challenge, first, the continuous spatial frequency deviation is discretized by sampling K points within the angular domain : Discretized into where Φ k ∈ [Φ min , Φ max and Ω k ∈ [Ω min , Ω max , and k = 1, 2,..., K respectively represent the spatial frequency deviations along the x and y dimensions corresponding to the k-th sampling point; thus, problem (P2) is approximated as: wherein is the array response vector corresponding to the k-th sampling point in the angular domain If K→∞ and the sampling points traverse the entire angular domain then (P3) is equivalent to (P2).

6. An electromagnetic stealth method for an unauthorized detection area assisted by an intelligent reflecting surface according to claim 5, characterized in that, The said Step 5 includes: Since (P3) is convex and satisfies the Slater condition, there is strong duality between (P3) and its Lagrangian dual problem; therefore, (P3) can be solved by using the Lagrangian dual method: Let and denote the non - negative dual variables associated with the constraints (14b) and (13c), respectively; then, the Lagrangian function associated with (P3) is: Among them Therefore, the dual function of (P3) is given by: For the dual function f(λ, μ) to have a lower bound, i.e., f(λ, μ) > -∞, it must hold; otherwise, if or then setting η → ∞ or η → -∞ will result in f{λ, μ} → -∞; thus, the dual problem of (P3) is given by: λ k ≥ 0, k = 1, 2, ..., K (17c) μ n ≥ 0, n = 1, 2, ..., N (17d).

7. An electromagnetic stealth method for unauthorized detection areas assisted by intelligent reflecting surfaces according to claim 6, characterized in that The said Step 6 includes: First, solve problem (16) to obtain f{λ, μ} for any given feasible dual variables {λ, μ}, then solve (D3) to obtain the optimal {λ, μ} to maximize f(λ, μ), and finally construct the optimal primal solution of (P3): 1) Obtain f{λ, μ} by solving problem (16) for a given {λ, μ}: For any given {λ, μ}, problem (16) can be decomposed into the following two sub-problems: Let η (λ，μ) and θ (λ，μ) represent the optimal solutions of (18) and (19) respectively; for problem (18), since holds for any given feasible dual variable, the value of the objective is always zero; thus, any arbitrary real number can be chosen as the optimal solution η (λ，μ) ; for problem (19), set the first derivative of the objective function with respect to θ to zero, i.e., Therefore, the optimal solution of problem (19) is: Find the optimal dual solution of (D3): obtain η (λ,μ) and θ (λ,μ) , then solve the dual problem (D3) to find the optimal {λ, μ} to maximize f(λ, μ); according to and substitute η (λ,μ) and θ (λ,μ) into f (λ，μ) , obtain: Among them In addition, by applying the Schur complement, the dual problem is transformed into an equivalent semidefinite optimization problem as follows: (17b)-(17d) (22c) The problem (P4) can be effectively solved by semidefinite programming or linear matrix inequality optimization. For a given solution accuracy ∈ > 0, the complexity is of order; more sampling points will achieve some performance improvement, but inevitably increase the complexity, leading to an unusual trade-off between electromagnetic stealth performance and computational complexity; 2) Optimal initial solution of the structure (P3): Obtain the optimal dual variables λ ＊ and μ ＊ , and the optimal solution of (P3). Denoted as θ ＊ and η ＊ , denoted as: According to the Karush-Kuhn-Tucker (KKT) conditions, the complementary slackness condition corresponding to constraint (14b) is expressed as: For any given sampling index k, if then must hold; conversely, if To satisfy the complementary slackness condition (25), must be true; as observed from Eq. (23), if then it corresponds to the angular domain the array response vector u of the k-th sampling point within k has no effect on the optimal reflection vector θ ＊ If it is defined that then there is effective sampling points for optimizing IRS reflection; this phenomenon indicates that in addition to the number of sampling points, the distribution of sampling points also affects the performance and computational complexity of electromagnetic stealth.

8. An electromagnetic stealth device for an unlicensed detection area assisted by an intelligent reflecting surface, characterized in that, It includes: A model construction module for establishing a system model of an electromagnetic stealth system for an unauthorized detection area assisted by an intelligent reflecting surface under a bistatic radar, where both the intelligent reflecting surface installed on the target surface and the other party's radar are equipped with uniform planar arrays; A first calculation module for calculating the closed-form expression of the signal-to-noise ratio of the received signal by the other party's radar based on the constructed electromagnetic stealth system; A problem construction module for constructing an optimization problem P1 for minimizing the maximum radar received SNR based on the closed-form expression and the modulus constraint of the IRS reflection unit; A problem transformation module for transforming the non-convex problem P1 into a convex problem P2 by discretizing the continuous spatial frequency deviation to approximate the semi-infinite reflection gain constraint; A problem optimization module for obtaining the Lagrangian dual problem f(λ, u) corresponding to the optimization problem P2; A second calculation module for obtaining the semi-closed solution of the original problem P1 by solving the dual problem f(λ, u), so as to calculate the IRS reflection phase shift that can achieve electromagnetic stealth.

9. An electronic device, characterized in that, The electronic device includes a processor and a memory. At least one instruction, at least one program, a code set, or an instruction set is stored in the memory. The at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, At least one instruction, at least one program, a code set, or an instruction set is stored in the storage medium. The at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the method according to any one of claims 1 to 7.

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