Electromagnetic deception and invisibility implementation method based on intelligent reflecting surface and related equipment

Abstract

The embodiment of the invention provides an electromagnetic deception and stealth implementation method based on an intelligent reflecting surface and related equipment, and belongs to the technical field of wireless communication and electronic countermeasure. The method is applied to a system formed by a moving target carrying an IRS, a plurality of distributed radars and an environment scatterer cluster, and comprises the following steps: establishing a system channel model, and deducing echo power expressions of the radars from a target direction and a scatterer cluster direction; constructing an optimization problem about an IRS reflection coefficient, and maximizing the total power received by all radars from a selected scatterer cluster direction on the premise that the receiving power of each radar from a target direction is constrained to be lower than a detection threshold value; the optimal or suboptimal reflection coefficient is obtained by solving the optimization problem, and the amplitude and phase shift of each unit of the IRS are configured in real time according to the optimal or suboptimal reflection coefficient. According to the method, the passive beam regulation and control capability of the IRS is utilized, radar signal energy is intelligently redirected to an environment scatterer to construct high-significance bait while real target echoes are inhibited to realize stealth, and thus integrated deception is realized.

Description

Technical Field

[0001] This application relates to the fields of wireless communication and electronic countermeasures, and in particular to a method and related equipment for electromagnetic deception and stealth based on a smart reflective surface. Background Technology

[0002] Electronic countermeasures (ECM) technology plays a crucial role in modern warfare in preventing target exposure and in jamming and deceiving enemy detection systems. Besides making targets "invisible" through electromagnetic stealth technology, electromagnetic deception technology, which creates false information about the target (such as decoys) to confuse radar, is also an important counter-detection strategy.

[0003] Existing electromagnetic deception technologies are mainly divided into two categories: passive deception and active deception. Passive deception technologies typically utilize specialized electromagnetic materials to manipulate the spectral distribution of harmonics, thereby achieving radar camouflage and deception. However, this passive approach has poor adaptability, usually only exhibiting the expected performance for specific incident directions and frequencies of the detection signal. On the other hand, active deception technologies utilize active transmitters based on Digital Radio Frequency Memory (DRFM) units to generate attack and jamming signals to mislead radar detection. However, this active approach is not only costly in terms of hardware and power consumption, but also carries the risk of revealing the true target direction due to the broadcasting characteristics of electromagnetic waves. Therefore, exploring a low-cost and adaptive electromagnetic deception strategy to cope with increasingly complex radar detection is particularly urgent.

[0004] In recent years, Intelligent Reflecting Surfaces (IRS), as a cutting-edge technology capable of reconstructing the wireless propagation environment, have been considered a strong candidate to overcome the limitations of traditional ECM (Electronic Coding Model) technology. By sensing environmental information and dynamically adjusting the reflection amplitude and / or phase of the IRS unit, echo signals can be eliminated or disguised. Currently, research has been conducted on IRS-assisted electromagnetic stealth systems, which reduce the echo of targets towards the radar by co-optimizing the IRS reflection pattern and imperfect absorbing materials, thereby reducing the probability of detection. However, existing research on IRS-based electronic countermeasures mainly focuses on simple electromagnetic stealth (i.e., making the target "invisible"). Research on using IRS to achieve electromagnetic deception (i.e., making the real target invisible while using the surrounding environment to create false targets to confuse the radar) remains largely unexplored. Traditional stealth technologies can reduce the detection rate, but cannot actively mislead the enemy's judgment; while simple deception technologies are difficult to balance with their own low detectability. How to use IRS to simultaneously achieve efficient stealth against multiple radars and high-fidelity deception is an urgent problem to be solved in the current technological field. Summary of the Invention

[0005] The main objective of this application is to propose a method, electronic device, storage medium, and program product for electromagnetic deception and stealth based on intelligent reflectors in multi-radar detection environments. This aims to address the problems of high hardware costs, poor environmental adaptability, and the ease with which active signal transmission exposes the real target in traditional electronic countermeasures technologies. By jointly optimizing the reflection phase shift and amplitude of the intelligent reflector, the radar detection signal is redirected to an environmental scattering array. This ensures the real target's stealth against multiple radars while simultaneously constructing highly realistic false targets using the scattering array to confuse radar detection. Furthermore, this method has low computational complexity and is suitable for real-time electromagnetic countermeasures scenarios.

[0006] To achieve the above objectives, one aspect of this application proposes an electromagnetic deception and stealth implementation method based on a smart reflector, applied to a system comprising a moving target equipped with a smart reflector IRS, K distributed radars, and J environmental scattering body clusters. The method includes the following steps: S1. Establish the electromagnetic signal transmission model of the system, and define the line-of-sight channel from the IRS to the radar, the line-of-sight channel from the target to the radar, and the non-line-of-sight channel reflected by the scatterer cluster. S2. Based on the electromagnetic signal transmission model, derive the expression for the power of the first echo signal received by each radar from the target direction, and the expression for the power of the second echo signal received by each radar from all scatterer clusters. S3. Construct the reflection coefficient vector of the IRS. The optimization problem is to maximize the total second echo signal power received by all radars from at least one selected scatterer cluster, while ensuring that the first echo signal power received by each radar from the target direction is below a preset detection threshold. and the reflection coefficient vector The modulus constraints of each element are conditions; S4. Solve the optimization problem to obtain the reflection coefficient vector. The optimal or suboptimal solution; S5. Based on the obtained reflection coefficient vector... The amplitude and phase shift of each reflective unit of the IRS are configured to suppress the echo in the direction of the target while enhancing the echo in the direction of the selected scatterer cluster, thereby achieving stealth and electromagnetic deception.

[0007] In some embodiments, in step S1, the system model is: The IRS is a uniform planar array composed of N passive reflective units, mounted on the moving target; Each radar is a monostation radar with co-located transceiver and is equipped with M transceiver antennas; The target end is equipped with an intelligent controller, which is used to dynamically adjust the reflection coefficient of each reflection unit of the IRS in real time.

[0008] In some embodiments, in step S2, the power of the first echo signal and the The second echo signal power in the direction of the scatterer cluster The specific expression is:

[0009] in, For radar indexing, For the number of radars, The number of scatterer clusters, This represents the total number of radar transceiver antennas. and These represent the two-way complex path gains for the target / IRS–radar link and the scattering object cluster, respectively. and The target and the first Radar cross section of a cluster of scatterers and These are the conjugate transposes of the cascaded array response vectors in the corresponding directions. For the effective incident signal power to reach the IRS / target, This is the reflection coefficient vector of the IRS.

[0010] In some embodiments, in step S3, the optimization problem is specifically described as problem (P1):

[0011] in, The detection thresholds for each radar are... For the IRS The complex reflection coefficient of each reflecting unit. For IRS reflective cell index, For radar index set, This is the set of IRS reflection unit indices.

[0012] In some embodiments, in step S4, the optimization problem (P1) is solved using the Lagrange multiplier method, transforming it into a dual semidefinite programming problem, and the reflection coefficient vector is obtained by solving this problem. The semi-closed optimal solution is used as the theoretical performance benchmark.

[0013] In some embodiments, step S4 includes solving the problem using a low-complexity method based on the minimum mean square error (MMSE) criterion, specifically including the following sub-steps: S41. Constructing a system of linear equations , where the matrix sum vector The cascaded array response vector Target RCS and scaling factor constitute; S42. Solve the MMSE problem with regularization parameter δ: To obtain a closed-form solution ; S43. Optimize the scaling factor in the positive real number domain through a two-dimensional search. and the regularization parameter δ, such that the closed-form solution The configured IRS maximizes the total second echo signal power in the direction of the selected scatterer cluster while satisfying the detection threshold constraint. S44, the optimal Substituting δ into step S42, the reflection coefficient vector is obtained. The suboptimal closed-form solution.

[0014] In some embodiments, the method for determining the selected scatterer cluster is as follows: selecting from all scatterers whose distance from the target is greater than a preset distance threshold. Among the candidate scatterer clusters, the scatterer cluster that maximizes the effective incident signal power reaching the target is selected as the chosen scatterer cluster. .

[0015] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0016] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0017] To achieve the above objectives, another aspect of this application provides a computer program product, including a computer program that, when executed by a processor, implements the method described above.

[0018] Compared with the prior art, this application has the following significant advantages: 1) Integrated stealth and deception: Breaking through the limitations of traditional technologies that can only achieve a single function, through a unified optimization framework, while suppressing the echo of the real target, the energy is intelligently redirected to the environmental scattering body to construct a highly realistic decoy, achieving an integrated countermeasure effect of "concealing the truth and showing the falsehood".

[0019] 2) High concealment and low power consumption: IRS is a passive device, and its reflection modulation does not generate additional active radiation, which greatly reduces the probability of being detected by enemy passive detection equipment, and the system power consumption is much lower than that of traditional active jammers.

[0020] 3) Strong environmental adaptability: By solving optimization problems in real time, it can dynamically adjust the IRS reflection mode according to the real-time geometric position of the target, radar, and scattering cluster and the channel state, so as to adapt to complex multi-radar detection environments.

[0021] 4) Computationally efficient and suitable for real-time applications: The proposed low-complexity closed-form solution algorithm based on MMSE approaches the theoretical optimal solution in performance, while reducing the computational complexity to a level that can be processed in real time. This makes the technology practically valuable in real-time combat against high-speed moving targets.

[0022] 5) Significant deception effect: By focusing energy to enhance the echo of a single optimal scatterer cluster, significant false target signals can be formed at multiple radars, effectively attracting and misleading radar detection and tracking decisions. Attached Figure Description

[0023] Figure 1 This is a flowchart of an electromagnetic deception and stealth implementation method based on a smart reflective surface provided in an embodiment of this application.

[0024] Figure 2 This is a schematic diagram of a system scenario where a target equipped with an intelligent reflector, multiple distributed radars, and a cluster of environmental scatterers coexist, as provided in an embodiment of the present invention.

[0025] Figure 3 This is a performance curve showing the change in total received signal power in the direction of the scatterer cluster as a function of the target height during a simulation experiment.

[0026] Figure 4 This is a performance curve showing the change in total received signal power in the direction of the scatterer cluster as a function of the number of radars K in a simulation experiment.

[0027] Figure 5 This is a performance curve showing the total received signal power in the direction of the scatterer cluster as a function of the number of IRS reflective units N in a simulation experiment.

[0028] Figure 6 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0031] Before providing a detailed description of the embodiments of this application, some of the nouns and terms involved in the embodiments of this application will be explained first. The nouns and terms involved in the embodiments of this application are subject to the following interpretations.

[0032] 1) Intelligent Reflecting Surface (IRS) is a novel wireless communication technology, also known as Reconfigurable Intelligent Surface (RIS) or Intelligent Metasurface. IRS technology utilizes large-scale reflective elements, such as micro-antennas or phase-adjusting elements, to construct a dynamically controllable surface. These reflective elements can regulate the reflection, propagation, and reception of wireless signals by changing their phase, amplitude, or polarization state as needed. In wireless communication systems, IRS can serve as an infrastructure to enhance or optimize wireless signal propagation. For example, by manipulating IRS, the propagation path of wireless signals can be altered, coverage increased, interference reduced, and the performance of the communication system improved.

[0033] In recent years, intelligent reflective surfaces (IRS), as an emerging technology capable of reconfiguring wireless propagation environments, have provided new ideas for electronic warfare. IRS consists of a large number of low-cost, passive programmable reflective elements. By adjusting the reflection amplitude and phase of each element in real time, it can precisely control the wavefront of incident electromagnetic waves. Existing research has preliminarily explored the application of IRS in radar stealth, namely, by optimizing the IRS reflection mode to cancel or weaken the echo signal of the target towards the radar. However, these studies mainly focus on achieving a single "stealth" function.

[0034] While simple stealth can reduce the probability of detection, it cannot actively mislead the enemy and cause them to misjudge the situation. Traditional deception techniques, on the other hand, struggle to maintain their own low detectability. Therefore, how to achieve effective stealth for the target itself while actively and intelligently generating highly realistic false target information to deceive multiple radars has become a critical problem that urgently needs to be solved in the current technological field. Currently, there is no integrated technical solution that utilizes IRS (Infrared Detection System) to simultaneously achieve efficient stealth and deception against multiple distributed radars.

[0035] In view of this, this application provides an electromagnetic deception and stealth implementation method, electronic device, storage medium and program product based on intelligent reflector for multi-radar detection environments. The scheme optimizes the IRS reflection coefficient to suppress the echo of the real target and enhance the echo of the selected scatterer cluster to construct the decoy target while satisfying the detection threshold constraint, thereby achieving multi-radar cooperative stealth and deception effect. The scheme also uses the minimum mean square error criterion to derive a low-complexity closed-form solution of the IRS reflection coefficient to support real-time control.

[0036] like Figure 1 As shown, this embodiment provides an electromagnetic deception and stealth implementation method based on a smart reflector, applied to a system including a moving target equipped with a smart reflector IRS, K distributed radars, and J environmental scattering body clusters. The method includes the following steps: S1. Establish the electromagnetic signal transmission model of the system, and define the line-of-sight (LoS) channel from the IRS to the radar, the line-of-sight channel from the target to the radar, and the non-line-of-sight (NLoS) channel reflected by the scatterer cluster.

[0037] In a preferred embodiment, the system model is as follows: the IRS is a uniform planar array (UPA) composed of N passive reflective elements, mounted on the moving target; each radar is a monostation radar with co-located transmit and receive, equipped with M transmit and receive antennas; the target end is equipped with an intelligent controller for dynamically adjusting the reflection coefficient of each reflective element of the IRS in real time.

[0038] S2. Based on the electromagnetic signal transmission model, derive the closed-form expression for the power of the first echo signal received by each radar from the target direction, and the closed-form expression for the power of the second echo signal received by each radar from all scatterer clusters.

[0039] Specifically, through geometric channel modeling and signal analysis, the signal power received by the k-th radar from the target direction can be obtained. and the Signal power received from the direction of the scatterer cluster The expressions are as follows:

[0040]

[0041] in, This is the reflection coefficient vector of the IRS. For path gain, The target's radar cross section (RCS). For radar and scatterer clusters The cascaded array response vector is determined by the geometric relationship with the IRS. For the Kroneck delta function (when = (1 if it is 1, 0 otherwise) The selected cluster of scatterers used for deception.

[0042] S3. Construct the reflection coefficient vector of the IRS. The optimization problem is to maximize the total second echo signal power received by all radars from at least one selected scatterer cluster, while ensuring that the first echo signal power received by each radar from the target direction is below a preset detection threshold. and the reflection coefficient vector The modulus constraints of each element are conditions.

[0043] This optimization problem can be specifically formulated as problem (P1):

[0044]

[0045]

[0046] in, For the first Normalized detection thresholds for each radar. For radar collection, For IRS reflective unit set S4. Solve the optimization problem to obtain the reflection coefficient vector. The optimal or suboptimal solution.

[0047] This embodiment provides two solution paths: Firstly (as a theoretical performance benchmark), using the Lagrange multiplier method and optimization theory, the problem (P1) is transformed into a semidefinite programming problem (SDP) with zero duality gap, which is then solved using standard convex optimization tools, yielding the following results. The optimal solution for the semi-closed form.

[0048] Secondly (as a low-complexity and practical solution), a heuristic method based on the minimum mean square error (MMSE) criterion is used for approximate solution, specifically including: S41. Constructing a system of linear equations , where the matrix sum vector The cascaded array response vector Target RCS and scaling factors used to enhance spoofing signals constitute.

[0049] S42. Solve the MMSE problem with regularization parameter δ: To obtain a closed-form solution ;in Used to control the modulus of the solution.

[0050] S43. Optimize the scaling factor jointly in the positive real number domain through a two-dimensional search. and regularization parameters Its optimization goal is to make the result from The configured IRS maximizes the total received power in the direction of the selected scatterer cluster while satisfying all radar detection threshold constraints.

[0051] S44, the optimal Substituting δ into step S42, the reflection coefficient vector is obtained. The suboptimal closed-form solution is found. The computational complexity of this scheme mainly involves matrix inversion, with an order of O(n). It can meet the real-time requirements.

[0052] S5. Based on the obtained reflection coefficient vector... The amplitude and phase shift of each reflective element of the IRS are configured so that the radar receiver can simultaneously suppress the echo in the direction of the real target (stealth) and enhance the echo in the direction of the selected scatterer cluster (deception).

[0053] To better illustrate the technological advancements of the method in this embodiment, the intelligent reflective surface-assisted electromagnetic deception method proposed in this invention is compared with different benchmark schemes on the MATLAB platform. These other benchmark schemes include: 1) Baseline system without IRS: In this scheme, since no IRS is installed on the target, it can be directly set... .

[0054] 2) Baseline system with random phase: In this scheme, the reflection coefficient vector of the IRS The phase shift in the interval The contents are randomly generated according to a uniform distribution.

[0055] To better understand the above technical solution, the following will describe in more detail an electromagnetic deception method assisted by an intelligent reflective surface disclosed in this embodiment, in conjunction with the accompanying drawings and specific implementation methods.

[0056] This embodiment proposes an electromagnetic deception and stealth implementation method based on a smart reflective surface, and its specific system design is as follows: This embodiment considers an IRS-assisted electromagnetic deception system model for evading detection and deceiving the system. A distributed radar. In this system, the IRS is mounted on a moving target. By significantly reducing the radar cross section of the real target and simultaneously increasing the RCS of the surrounding scattering aggregates (thus acting as decoy targets), it interferes with and misleads the detection and decision-making of the counter-radar. In the considered scenario, the number of scattering aggregates is denoted as . Without loss of generality, we assume that the target's IRS is a uniform planar array, and that... It consists of passive reflective units, among which and They represent along shaft and The number of IRS elements along the axial direction. For ease of description, the radar array, scatterer cluster array, and IRS reflection element array are respectively denoted as... , and Furthermore, it is assumed that each radar is a monostation radar (i.e., the transmitter and receiver are co-located) and equipped with a uniform planar array, with a total number of transmitting and receiving antennas of [missing information]. ,in and They represent along shaft and The number of transmit and receive antennas along the axial direction. The target end is equipped with an intelligent controller that can dynamically adjust the reflection amplitude or phase shift of the IRS in real time.

[0057] This embodiment provides a method for achieving electromagnetic deception and stealth with the assistance of a smart reflective surface, including the following steps: Step 1: Establish a model of an electromagnetic deception system assisted by an intelligent reflector; the model includes a moving target equipped with an intelligent reflector, multiple distributed monostation radars and multiple environmental scattering clusters, and defines the line-of-sight channel from the intelligent reflector to the radar, the line-of-sight channel from the target to the radar, and the non-line-of-sight channel reflected by the scattering clusters. Step 2: Based on the system model, derive the closed-form expression for the target echo signal power received by each radar from the target direction, and the closed-form expression for the cluster echo signal power received by each radar from all scatterer cluster directions. Step 3: Based on the closed expression in Step 2, maximize the total signal power received by all radars from the direction of the selected scatterer cluster. The constraints include that the signal power received by each radar from the target direction is lower than a preset detection threshold, and the magnitude constraint of the reflection coefficient of the smart reflector. Step 4: Solve the optimization problem using the Lagrange multiplier method to derive the semi-closed optimal solution expression for the reflection coefficient of the intelligent reflective surface, which serves as the upper bound or benchmark for theoretical performance. Step 5: To reduce the real-time computational complexity, a system of linear equations is constructed based on the minimum mean square error criterion, and a low-complexity closed-form solution for the reflection coefficient of the intelligent reflective surface is derived. Step Six: Determine the optimal intelligent reflector reflection coefficient based on the closed-form solution obtained in Step Five, and configure the phase shift and amplitude of each reflector element of the intelligent reflector accordingly, so as to form a false target deception signal at the radar and suppress the real target echo signal at the same time, thereby achieving the stealth and deception effect of the target.

[0058] In one embodiment, step one proceeds as follows: This embodiment considers an IRS-assisted electromagnetic deception system model for evading detection and deceiving the system. A distributed radar. In this system, the IRS is mounted on a moving target. By significantly reducing the radar cross section of the real target and simultaneously increasing the RCS of the surrounding scattering aggregates (thus acting as decoy targets), it interferes with and misleads the detection and decision-making of the counter-radar. In the considered scenario, the number of scattering aggregates is denoted as . Without loss of generality, we assume that the target's IRS is a uniform planar array, and that... It consists of passive reflective units, among which and They represent along shaft and The number of IRS elements along the axial direction. For ease of description, the radar array, scatterer cluster array, and IRS reflection element array are respectively denoted as... , and Furthermore, it is assumed that each radar is a monostation radar (i.e., the transmitter and receiver are co-located) and equipped with a uniform planar array, with a total number of transmitting and receiving antennas of [missing information]. ,in and They represent along shaft and The number of transmit and receive antennas along the axial direction. The target end is equipped with an intelligent controller that can dynamically adjust the reflection amplitude or phase shift of the IRS in real time.

[0059] In one embodiment, step two proceeds as follows: like Figure 2As shown, considering the mobility of the IRS / target, let and They represent the times respectively. Next "IRS → No" "one radar" link and "target → first" The equivalent line-of-sight (LoS) channel of a radar link. Since air targets usually have high flight altitudes, the relevant LoS propagation channel can be characterized using a far-field model of plane wave propagation. For ease of subsequent derivation, the following one-dimensional (1D) steering vector function is first defined for a Uniform Linear Array (ULA).

[0060] (1) in, The imaginary unit; Indicates the signal wavelength; Indicates the spacing between two adjacent antennas / array elements; This indicates the constant phase difference between signals at two adjacent antennas / array elements; This indicates the number of antennas / elements in the uniform linear array. Based on this, let... and Representing IRS and the first The common array response vector of a radar, where For any arrival / departure angle (AoA / AoD) pair, including both pitch and azimuth dimensions, in the uniform planar array model, each array response vector can be represented as along... Axis (horizontal) direction and The Kronecker product of the two guiding vector functions in the axial (perpendicular) direction. Specifically, the IRS and the... The array response vectors at each radar location are respectively represented as: (2) (3) Among them, the arrival angle / departure angle in the form of pitch / azimuth angle is a pair. The input variable to be given.

[0061] For the line-of-sight channel between the target-equipped IRS and each radar, and They represent the times at time 1 and 2 respectively. Below, the IRS end and the first The elevation / azimuth angles AoA / AoD pairs of each radar terminal, among which To simplify the symbolic representation, let... Represents a node From node The array response vector at incident / exit directions, where , .

[0062] Therefore, under far-field conditions, IRS to the first The Loss Channel of a radar can be modeled as the outer product of the response vectors of the two array ends, i.e.: (4) in, For the corresponding complex path gain, Indicates time Next IRS / Target and First The propagation distance between radars This is the path gain at a reference distance of 1 meter. Additionally, the target to the... The far-field LoS channel of a radar can be expressed as: (5) Since the IRS and the target use the same reference point, they share the same elevation / azimuth angles for the radar signal.

[0063] On the other hand, considering the existence between the IRS / target and the radar A cluster of scattering bodies (such as clouds, flocks of birds, and buildings) makes... and Representing time respectively Next IRS → Radar link and target → First The equivalent non-line-of-sight channel of each radar link; in addition, let Indicates coming from the surroundings The echo from the first scatterer cluster returns to the first... The echo channel of the radar. For the radar echo channel of the... The non-line-of-sight channel associated with each scatterer cluster, let and These respectively represent their positions at the IRS end and the first... The elevation / azimuth angles corresponding to each radar terminal, among which and Based on the geometric channel model, IRS to the... The non-line-of-sight channel of a radar can be represented as: (6) in, Indicates the first The isotropic complex radar cross section (RCS) of a cluster of scatterers, and This represents the corresponding complex path gain (two-way path loss), where and They represent from the first The scatterer cluster to the IRS / target and to the first The propagation range of the first radar. Similarly, the target to the... The non-LoS channel of a radar can be represented as: (7) In addition, from the surrounding The scatterer cluster returns to the first The echo channel of a radar can be represented as: (8) in This is the complex path gain corresponding to the echo channel. and .

[0064] Based on the above channel model, it is easy to verify that each link satisfies channel reciprocity in both forward and reverse transmission. On the other hand, let This represents the equivalent (adjustable) reflection coefficient vector of the target-mounted IRS, with the maximum reflection amplitude of each IRS unit set to 1. Furthermore, let This represents the isotropic complex radar cross section of the target.

[0065] Assume that the geometric positions of the IRS / target, scatterer cluster, and radar remain approximately constant within each Coherent-Processing Interval (CPI). The CPI represents the time period during which the detected signal is reflected by the target and received by each radar; therefore, variations in channel and geometrically relevant parameters (e.g., propagation range, elevation, and azimuth) are negligible within this time period; however, these parameters may vary between different CPIs. For ease of explanation, only a single CPI is considered below, and time indices are omitted without causing confusion. .

[0066] make This represents the stacked radar pulse waveform matrix, where For the first The pulse waveform vector of each radar. Based on the above definition, the radar detection echo signal reflected and transmitted back by the IRS / target / scatterer cluster and subsequently received by each radar can be expressed as: (9) in, for The stacked RCS vector of a cluster of scatterers, and For the first Zero-mean additive white Gaussian noise at a single-station radar location, with a noise variance of: It should be noted that the first and second terms in equation (9) exist only when the IRS / target is within the detection range; while the third term in equation (9) can be regarded as the background echo signal between the radar and the scattering cluster, which does not depend on the presence or absence of the target.

[0067] Since the background echo signal always exists between the radar and the scattering cluster (regardless of whether the target exists), it can be eliminated by the radar before target detection. After eliminating the background echo signal and ignoring the noise term in equation (9), the remaining received signal of each radar can be decomposed into two parts: received signals from the IRS / target direction and the scattering cluster direction, respectively, and their expressions are as follows: (10) (11) To simplify the symbolic representation, let (12) Indicates from radar or scattering cluster The effective incident signal incident on the IRS / target in the direction of the incident signal is denoted as . Furthermore, let (the vector defined below) (13) This indicates that there is a node at the IRS. Incident and reflected back to the node via IRS The response vector of the cascaded array, where Furthermore, substituting equations (4)–(7), (12), and (13) into equation (10), and after certain mathematical simplification operations, the received signal from the IRS / target direction can be simplified as follows: (14) Similarly, by substituting equations (4)–(7), (12), and (13) into equation (11), we can obtain the results from... The overall received signal from the direction of the scatterer cluster is simplified as follows: (15) in, Indicates the first The radar from the first Signal received from the direction of a cluster of scatterers.

[0068] According to equation (14), the first The signal power received by each radar from the IRS / target direction is: (16) Similarly, according to equation (15), the first... The radar from the first The signal power received by the scatterer cluster in the direction is: (17) And the first A radar from The sum of the signal power received by each scatterer cluster in the direction is: (18) In one embodiment, step three is as follows: In this embodiment, to achieve shielding of the target body, we first need to reduce its visibility by lowering the equivalent RCS value of the real target (using IRS), which is equivalent to reducing the visibility of each radar. The signal power received from the target direction, i.e., in equation (16) Building upon achieving target "invisibility," we further hope to simultaneously enhance the capabilities of each radar system. The signal power received from the direction of the scatterer cluster, i.e., in equation (18) To achieve electromagnetic deception, an optimized design for the reflection of the IRS is proposed: while constraining each... Maximize the detection threshold below a given detection threshold. Therefore, the problem can be formulated as follows (constants / irrelevant terms are omitted for brevity). ):

[0069]

[0070] in, This indicates the detection threshold for each radar, and is listed according to the number of radar antennas. Normalize.

[0071] It should be noted that although an IRS can simultaneously reflect light towards multiple scatterer clusters to construct multiple decoy targets and thus confuse radar detection, this method disperses the overall reflection energy of the IRS, resulting in a suboptimal deception effect. Compared to dispersing reflection energy, focusing and redirecting the entire reflection power of the IRS to a single scatterer cluster to construct the strongest decoy target, thereby attracting / deceiving the radar, is generally more efficient. Therefore, without loss of generality and for simplicity, this embodiment selects a single scatterer cluster for electromagnetic deception. Generally speaking, the selected scatterer cluster should not be too close to the target, otherwise it may increase the risk of exposing the real target; at the same time, it should not be too far from the target, otherwise it will increase the two-way path loss, resulting in lower reflection power in the direction of the selected scatterer cluster, thereby reducing the deception effect. Let... This represents the set of candidate scatterer clusters that maintain a sufficient distance from the target, i.e. ,in The distance threshold is used. To maximize the effective reflection gain of electromagnetic deception, the selected scatterer cluster can be defined as... ,in The effective incident signal power reaching the IRS / target.

[0072] Based on the above analysis, and given a cluster of scatterers In this case, the problem (P1) can be restated as follows (constants / irrelevant terms are omitted for brevity):

[0073] It can be verified that although the constraints in equations (20) and (21) are convex constraints, the objective function in equation (22a) is a concave function, thus making problem (P2) a non-convex optimization problem.

[0074] In one embodiment, step four is as follows: By examining problem (P2), it can be found that the objective function of equation (22a) and the constraints of equation (20) contain the same cross terms, that is, for any ,have This corresponds to the array response gain of the radar-IRS / target-scatterer cluster cascade link. It can be further deduced that at the detection threshold... In the case of smaller values, to satisfy all constraints in equation (20), for any , The value should be small and not exceed In this situation, these common intersections The contribution to the overall value of the objective function in equation (22a) is limited; otherwise, the constraints in equation (20) will be violated, and the real target will also be exposed to the countermeasure radar. Based on this, the common cross terms in the objective function of equation (22a) are... After removal, the problem (P2) can be further simplified to the following form (constants / irrelevant terms are omitted for brevity):

[0075] in, Indicates the first The normalized detection threshold at each radar location. Two efficient algorithms will be proposed below to solve the problem (P3).

[0076] Problem (P3) can be restated as:

[0077] in , , , ,as well as Therefore, the Lagrangian function for problem (P4) is defined as: (29) in, , ,as well as ,in and These are the Lagrange multiplier vectors corresponding to equations (27) and (28), respectively.

[0078] Subsequently, we about Taking the derivative, we get: (30) make We can obtain: (31) It is a Lagrange multiplier vector and The function. Although it involves cross-links between multiple radars, the problem (P4) is still a quadratically constrained quadratic program (QCQP) with zero duality gap, which indicates that the dual variables and It can be obtained through its dual programming. Therefore, its dual function can be expressed as: (32) Similarly, using the Schur complement, the dual problem can be equivalently represented as a semidefinite optimization problem, i.e.:

[0079] It can be efficiently solved using standard semidefinite programming or linear matrix inequality optimization methods; given a certain solution accuracy... Under the given conditions, its computational complexity is of order O. .

[0080] In one embodiment, step five is as follows: For problem (P3), the constraints in equation (24) can be decomposed into: Each term, that is, for any , All include Since all the above terms are non-negative, and their sum is... No more than Therefore, it can be deduced that each individual item does not exceed [a certain number]. ,Right now: (37) It should be noted that in practical applications, They are usually set to small values, and to achieve complete electromagnetic stealth of the target under multiple radars, we tend to reduce each term in Equation (36) to its minimum value of 0 as much as possible.

[0081] On the other hand, the objective function (23) of problem (P3) can be decomposed into: Each term, that is, for any ,Include To achieve electromagnetic deception against adversarial radar, this paper proposes to simultaneously maximize the values ​​of each term in equation (23), namely: (38) However, due to the unit mode constraint in equation (25) and the existence of cross links between multiple radar and scatterer clusters, it is usually difficult (or even impossible) to minimize all terms in equation (36) while simultaneously maximizing all terms in equation (37). Based on the above analysis, this paper proposes a method based on minimum mean square error as a low-complexity solution to approximate the solution of problem (P3) in a heuristic manner. Specifically, to satisfy the complete electromagnetic stealth condition corresponding to equation (36), we have: (39) On the other hand, the introduction of scaling factor To increase the values ​​of each term in equation (37), we have: (40) in, To simultaneously achieve electromagnetic stealth and electromagnetic deception, the reflection coefficient of the IRS needs to be designed. This ensures that both equation (38) and equation (39) are satisfied simultaneously, i.e.: (41) in, ,and Therefore, the following solution scheme based on MMSE is proposed: (42) in, These are regularization parameters used to ensure the reflection design of the IRS. The modulus constraint in equation (25) must be satisfied. In particular, equation (41) can be substituted into problem (P3), and the following binary optimization problem can be solved to determine the modulus constraint. and .

[0082]

[0083] in, for identity matrix The The optimal solution in problem (P6) is... and The solution can be obtained with low complexity through a two-dimensional search over the positive real number domain. Furthermore, the MMSE-based solution requires matrix inversion (e.g., using Gaussian-Jordan elimination), which has a computational complexity of O(n log n). .

[0084] Figure 3 This is a performance curve of the total received signal power in the direction of the scatterer cluster as a function of target height, according to an embodiment of this application. It can be observed that as the target height increases, the total received power from the scatterer cluster direction for each electromagnetic deception scheme decreases. This is because the increased distance between the target and the selected scatterer cluster leads to increased two-way path loss, thus reducing the reflected echo power in the cluster direction. Furthermore, it can be seen that the proposed MMSE-based electromagnetic deception scheme, with lower computational complexity, performs close to the optimal scheme based on Lagrange multiplier solutions. Compared to the baseline schemes without IRS and random phase, both schemes proposed in this invention significantly improve the total received power in the direction of the scatterer cluster, indicating that they can effectively optimize the IRS reflection design, redirecting reflected energy to the direction of the selected scatterer cluster, making the counter-radar more likely to identify the scatterer cluster as a decoy target, thereby achieving a deception effect against multiple radars.

[0085] Figure 4 This is a performance curve of the total received signal power in the direction of the scatterer cluster as a function of the number of radars, according to an embodiment of this application. It can be observed that as... With the increase in the number of distributed radars, the total received power in the cluster direction at multiple radars all show an upward trend. This is because the increased number of distributed radars means a stronger effective incident signal received by the IRS / target, and the joint reception capability of multiple radars from different directions of the selected scatterer cluster is enhanced, thereby increasing the total received power in the cluster direction. Furthermore, compared with the baseline schemes without IRS and random phase, the IRS-assisted electromagnetic deception scheme proposed in this invention (including implementations based on Lagrange multipliers and MMSE) shows an upward trend in power received by multiple radars. The increased gain indicates that the IRS reflection design can effectively suppress the target direction echo while enhancing the echo in the direction of the scatterer cluster and improving the salience of the decoy target, thus making it more conducive to the coordinated deception of multiple distributed radars.

[0086] Figure 5 This is a performance curve of the total received signal power in the direction of the scatterer cluster as a function of the number of passive reflective elements in the IRS, according to an embodiment of this application. It can be observed that as... As the number of reflective elements increases, the total received power in the direction of the scatterer cluster generally shows an upward trend. This is because the coherent superposition and directional reflection capabilities of the IRS enhance with the increase in the number of reflective elements, thus enabling more incident signals to be focused and reflected towards the selected scatterer cluster. Furthermore, with... As the complexity increases, the performance advantage of the electromagnetic deception scheme based on Lagrange multipliers over the low-complexity scheme based on MMSE gradually expands, indicating that the former can more fully coordinate each reflection unit to achieve a higher effective reflection gain, thereby improving the decoy construction effect of the electromagnetic deception system described in this invention.

[0087] In summary, this embodiment optimizes the reflection coefficient of the target-mounted IRS, satisfying the multi-distributed radar detection threshold constraint and suppressing echoes from the real target direction. Simultaneously, it effectively focuses and redirects reflected energy to the direction of the selected scatterer cluster, significantly improving the total received power in the cluster direction and enhancing the decoy target's salience, thus achieving coordinated stealth and deception against multiple radars. Simulation results further demonstrate that the proposed MMSE low-complexity scheme can approach the performance of the optimal scheme with lower computational overhead, while increasing the number of reflection units and radars can further amplify the deception gain and system advantages of this embodiment.

[0088] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0089] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0090] Please see Figure 6 , Figure 6 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes: The processor 601 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application. The memory 602 can be implemented as a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 602 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 602 and is called and executed by the processor 601 using the methods described in the embodiments of this application. The input / output interface 603 is used to implement information input and output; The communication interface 604 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 605 transmits information between various components of the device (e.g., processor 601, memory 602, input / output interface 603, and communication interface 604); The processor 601, memory 602, input / output interface 603, and communication interface 604 are connected to each other within the device via bus 605.

[0091] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0092] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0093] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0094] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0095] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented in the embodiments of this program product are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments. The executable computer program code or "code" used to perform the various embodiments can be written in high-level programming languages ​​such as C, C++, Python, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0096] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0097] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0098] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0099] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0100] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0101] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0102] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0103] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0104] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0105] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0106] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for electromagnetic deception and stealth based on intelligent reflective surfaces, characterized in that, Applied to a system comprising a moving target equipped with a smart reflector IRS, K distributed radars, and J clusters of environmental scatterers, the method includes the following steps: S1. Establish the electromagnetic signal transmission model of the system, and define the line-of-sight channel from the IRS to the radar, the line-of-sight channel from the target to the radar, and the non-line-of-sight channel reflected by the scatterer cluster. S2. Based on the electromagnetic signal transmission model, derive the expression for the power of the first echo signal received by each radar from the target direction, and the expression for the power of the second echo signal received by each radar from all scatterer clusters. S3. Construct the reflection coefficient vector of the IRS. The optimization problem is to maximize the total second echo signal power received by all radars from at least one selected scatterer cluster, while ensuring that the first echo signal power received by each radar from the target direction is below a preset detection threshold. and the reflection coefficient vector The modulus constraints of each element are conditions; S4. Solve the optimization problem to obtain the reflection coefficient vector. The optimal or suboptimal solution; S5. Based on the obtained reflection coefficient vector... The amplitude and phase shift of each reflective unit of the IRS are configured to suppress the echo in the direction of the target while enhancing the echo in the direction of the selected scatterer cluster, thereby achieving stealth and electromagnetic deception.

2. The method according to claim 1, characterized in that, In step S1, the system model is as follows: The IRS is a uniform planar array composed of N passive reflective units, mounted on the moving target; Each radar is a monostation radar with co-located transceiver and is equipped with M transceiver antennas; The target end is equipped with an intelligent controller, which is used to dynamically adjust the reflection coefficient of each reflection unit of the IRS in real time.

3. The method according to claim 2, characterized in that, In step S2, the power of the first echo signal and the The second echo signal power in the direction of the scatterer cluster The specific expression is: in, For radar indexing, For the number of radars, The number of scatterer clusters, This represents the total number of radar transceiver antennas. and These represent the two-way complex path gains for the target / IRS–radar link and the scattering object cluster, respectively. and The target and the first Radar cross section of a cluster of scatterers and These are the conjugate transposes of the cascaded array response vectors in the corresponding directions. For the effective incident signal power to reach the IRS / target, This is the reflection coefficient vector of the IRS.

4. The method according to claim 3, characterized in that, In step S3, the optimization problem is specifically described as problem (P1): in, The detection thresholds for each radar are... For the IRS The complex reflection coefficient of each reflecting unit. For IRS reflective cell index, For radar index set, This is the set of IRS reflection unit indices.

5. The method according to claim 4, characterized in that, In step S4, the optimization problem (P1) is solved using the Lagrange multiplier method, transforming it into a dual semidefinite programming problem, and the reflection coefficient vector is obtained by solving this problem. The semi-closed optimal solution is used as the theoretical performance benchmark.

6. The method according to claim 4 or 5, characterized in that, Step S4 involves solving the problem using a low-complexity method based on the minimum mean square error (MMSE) criterion, specifically including the following sub-steps: S41. Constructing a system of linear equations , where the matrix sum vector The cascaded array response vector Target RCS and scaling factor constitute; S42. Solve the MMSE problem with regularization parameter δ: To obtain a closed-form solution ; S43. Optimize the scaling factor in the positive real number domain through a two-dimensional search. and the regularization parameter δ, such that the closed-form solution The configured IRS maximizes the total second echo signal power in the direction of the selected scatterer cluster while satisfying the detection threshold constraint. S44, the optimal Substituting δ into step S42, the reflection coefficient vector is obtained. The suboptimal closed-form solution.

7. The method according to claim 1, characterized in that, The method for determining the selected scatterer cluster is as follows: starting from all scatterers whose distance from the target is greater than a preset distance threshold. Among the candidate scatterer clusters, the scatterer cluster that maximizes the effective incident signal power reaching the target is selected as the chosen scatterer cluster. .

8. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method according to any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

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