Intelligent reflecting surface auxiliary electromagnetic stealth method based on Lagrange duality

Abstract

The invention discloses an intelligent reflecting surface auxiliary electromagnetic stealth method based on Lagrange duality. The method comprises the following steps: S1, inputting the number of sensing units, the number of passive reflecting units of an intelligent reflecting surface, the number of units on the surface of an uncontrollable material, and wave absorbing efficiency and reflecting phase information of the units; s2, estimating an incoming wave direction of the enemy detection radar in a current coherent processing time interval and transmitting and receiving beam gain information of the enemy detection radar by using a sensor array; s3, constructing an electromagnetic stealth problem assisted by the intelligent reflecting surface; and S4, calculating the amplitude and phase of the passive reflection unit of the intelligent reflection surface by using a Lagrange duality method. According to the intelligent reflecting surface auxiliary electromagnetic stealth method based on the Lagrange duality, the algorithm complexity is remarkably reduced, and the stealth performance of the target is improved, so that the stealth combat requirement of a modern battlefield can be met, and the method adapts to the complex and changeable battlefield situation.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic stealth technology, and in particular to an intelligent reflective surface-assisted electromagnetic stealth method based on Lagrangian duality, which is applicable to aircraft, military equipment and other stealth application fields. Background Art

[0002] In today's increasingly complex military warfare environment, radar technology plays a vital role in detecting and tracking targets such as drones, aircraft, and missiles. However, the rapid development of radar technology in recent years has brought serious challenges to military equipment, so electromagnetic stealth technology has become an important tool to improve the survivability of military equipment. The main goal of this technology is to achieve stealth by minimizing the energy of electromagnetic waves reflected on combat equipment. Traditional electromagnetic stealth methods generally change the shape of the target to reduce the radar cross-sectional area, or use absorbing materials to absorb incident electromagnetic waves. However, the effectiveness of traditional electromagnetic stealth technology is restricted by multiple factors such as the characteristics of absorbing materials, the angle of incident electromagnetic waves, and the operating frequency. Especially in high-dynamic electromagnetic environments, it is impossible to achieve the ideal stealth effect. Therefore, the traditional "one-time molding" electromagnetic stealth method can no longer meet the needs of modern complex electromagnetic combat environments.

[0003] In recent years, with the rapid development of related disciplines such as metamaterials, electromagnetic information and interface electromagnetics, smart reflective surfaces have introduced new technical paradigms in the fields of wireless communications and radars with their high integration, low cost, strong reconfigurability, easy deployment and no loss. The advantage of smart reflective surfaces is that they can provide flexible and high-density deployment for future wireless communications and sensing systems by adopting compact, lightweight and customizable geometric structures. In addition, smart reflective surfaces also have the ability to reconstruct in real time and can adapt to fast time-varying and highly dynamic wireless environments. Therefore, smart reflective surfaces can provide effective assistance in highly dynamic wireless environments, make up for the shortcomings of traditional stealth technology, and open up new paths in the field of electromagnetic stealth. The current artificial electromagnetic metamaterials / metasurfaces can effectively reduce the backscattering of targets in a wide frequency band, but this material is still affected by the frequency band, direction and environment of the electromagnetic wave signal, and has not yet achieved the goals of low cost, low loss and easy manufacturing, and cannot face the complex and changing electromagnetic stealth environment. Summary of the invention

[0004] In order to solve at least one of the problems existing in the prior art, the present invention provides an intelligent reflective surface-assisted electromagnetic stealth method based on Lagrangian duality, which has the advantages of low complexity, intelligent controllability, high flexibility and strong adaptability.

[0005] In order to achieve the purpose of the present invention, the present invention provides an intelligent reflective surface-assisted electromagnetic stealth method based on Lagrangian duality, which is applied to avoid single-station radar or multi-station radar detection. The method is implemented based on a stealth system, and the stealth system includes at least one sensor array with L sensing units, at least one sensor array with N 1 The intelligent reflective surface of passive reflective units, at least one with N 2 The electromagnetic stealth method comprises the following steps:

[0006] S1, the number of input sensing units, the number of passive reflection units of the intelligent reflection surface, the number of reflection units on the surface of the uncontrollable material, and the absorption efficiency and reflection phase information of the surface of the uncontrollable material;

[0007] S2, using the sensor array to estimate the incoming wave direction and the transmit beam and receive beam gains of the other detection radar within the current coherent processing time interval;

[0008] S3. Constructing an intelligent reflective surface to assist in avoiding electromagnetic stealth detection by single-station radar or multi-station radar. The problem of using intelligent reflective surface to assist in achieving ideal electromagnetic stealth is expressed as follows:

[0009]

[0010]

[0011] Among them, θ n represents the reflection coefficient of the nth passive reflection unit of the intelligent reflection surface, K is the number of radars, is the receiving beam gain of radar k within the coherent processing time interval, is the transmitted beam of radar i within the coherent processing time interval, and the superscript H represents the conjugate transpose operation. and They represent the cascade array response vectors on the smart reflective surface and the non-adjustable material surface, θ is the reflection coefficient of the passive reflective unit of the smart reflective surface, and φ is the reflection coefficient of the non-adjustable material unit;

[0012] S4. Calculate the amplitude and phase of the passive reflection unit of the smart reflection surface using the Lagrangian duality method.

[0013] Furthermore, the sensors in the sensor array are arranged in a cross shape.

[0014] Further, the sensor array is located at a central position on the surface of the stealth target.

[0015] Furthermore, in step S1, the stealth system includes at least one stealth target surface. Assume that a stealth target surface includes N 1Passive reflector units and N 2 The passive reflection units and the reflection units on the surface of the non-adjustable material are arranged in a uniform planar array; the sensor array with L sensing units is deployed at the center of the stealth target surface; the reflection coefficient of each passive reflection unit at time t is defined as in and Respectively represent the control amplitude and phase range of the nth passive reflection unit, e represents an exponential function, and the superscript T represents the transposition operation of a vector; the reflection coefficient of each uncontrollable material unit is defined as in represents the absorbing efficiency of the mth uncontrollable material unit, Represents the reflection phase determined by material properties and can be obtained in advance through a large number of actual measurements.

[0016] Furthermore, the estimation step of step S2 includes:

[0017] The one-dimensional steering vector function is defined as: Where φ is defined as the signal phase difference between two adjacent antennas, adjacent passive reflective elements, or adjacent non-adjustable material reflective elements, and N is defined as the size of a uniformly spaced linear array;

[0018] Assuming that the wavelength of the enemy detection radar signal is λ, the distance between two adjacent sensing units is expressed as Δ s The number of sensor units in the sensor array along the x-axis and y-axis directions is L respectively. x and L y ; At time t, the enemy radar k (denoted as R k ) reaches the stealth target surface (denoted as T a ) is and the pitch angle is is the array response of the sensor array, and its array response along the x-axis and y-axis directions are expressed as

[0019]

[0020] in, and is the phase offset

[0021] The received signal of the sensor array is expressed as

[0022]

[0023] in, Indicates that the sensor array receives a mean of 0 and a power of Gaussian white noise, represents the array response of the sensor array, s(t)=[s 1 (t), ..., s K (t)] T represents the transmission signal vector of K radars, represents the transmission signal of radar k, represents the radar pulse waveform, B is the signal bandwidth, t p is the pulse interval;

[0024] First, a multiple signal classification algorithm is used to estimate the direction of the incoming signal. Secondly, the least squares method is used to estimate the signal The estimated signal is expressed as

[0025]

[0026] in, represents the estimated value of the transmitted signal of radar K, represents the estimated noise vector, represents the noise estimate from radar K, express The conjugate transpose of .

[0027] Furthermore, define and are the transmit beam and receive beam gains of radar k in the coherent processing time interval, respectively. Based on channel reciprocity, the transmit beam and receive beam gains of each single-station radar are equal, that is, K is the number of radars, and the estimated value of the transmit beam gain is expressed as

[0028]

[0029] Among them, T p represents the pulse repetition interval, Indicates from radar The noise estimate of represents the real part operation, Express Take the conjugate.

[0030] Furthermore, the process of obtaining the electromagnetic stealth problem in step S3 includes:

[0031] Based on the estimation, the detection signal direction of each detection radar at time t and transmit beam gain and receive beam gain definition It means that the radar k is respectively in contact with the intelligent reflective surface I and the uncontrollable material surface N at time t a 、Stealth target surface T a The far-field line-of-sight channel, the stealth target surface and the array response of the radar r and Defined as:

[0032]

[0033]

[0034] in, and Respectively represent the azimuth and elevation angle of the radar transmitting or receiving signal Δ e and Δ a Respectively represent the distance between the stealth target surface and two adjacent units of the radar antenna array; N x and N y They represent the stealth target surface along the x-axis and The number of units in the coordinate axis direction; M x and M x Respectively represent the number of antennas along the x-axis and y-axis directions; the smart reflector array responds to and array responses of uncontrollable material surfaces The array response of the stealth target surface is defined in the same way. Given the positional relationship between the smart reflective surface, the uncontrollable material surface, and the stealth target surface, the array responses of the three have the following relationship:

[0035]

[0036] Therefore, the far-field line-of-sight channel matrix between any two points (denoted by X and Y) at time t is expressed as

[0037]

[0038] where X∈{I,N a , T a}and α is defined as the channel gain at a reference distance of 1 meter, Defined as radar Real-time propagation distance to the stealth target, represents the path gain;

[0039] Since the far-field line-of-sight channel between any two points satisfies channel reciprocity in uplink and downlink transmission,

[0040] Based on the co-location relationship between the stealth target surface, the intelligent reflective surface and the uncontrollable material surface, the channel matrix relationship between the radar and these three satisfies:

[0041] After applying intelligent reflective surfaces to assist stealth targets, radar The received signal at time t is expressed as

[0042]

[0043] in, w i and denote the transmit beam gain of radar i and the receive beam gain of radar k, respectively, and n k (t) means the mean is 0 and the variance is σ 2 Gaussian white noise;

[0044] Assuming that the position of the stealth target remains unchanged within each radar coherent processing time interval, and the changes in the channel and geometric parameters between the stealth target and the radar are negligible, and the time index [t] is omitted in the calculation process, the received echo signal power of radar k within a pulse repetition time interval is expressed as

[0045]

[0046] Then the total power of the received signal of the multi-station radar detection system is expressed as

[0047]

[0048] According to the above formula, the intelligent reflective surface is used to assist in reducing or completely eliminating the signal power reflected back to the radar detection system to achieve ideal stealth performance. First, st is defined as subject to the constraint of, min x f(x) is defined as minimizing the objective function f(x); therefore, the problem of minimizing the energy of radar received signals using smart reflective surfaces is expressed as

[0049]

[0050]

[0051] in, represents the cascade array response vector at the overall stealth target, and Represent the cascade array response vectors on the smart reflective surface and the uncontrollable material surface respectively.

[0052] Furthermore, the cascade array response vector at the overall stealth target for

[0053]

[0054] Furthermore, step S4 includes:

[0055] According to the differences in the estimated parameters and optimized reflection coefficients required to avoid single-station radar and multi-station radar detection, the reflection coefficient of the intelligent reflective surface is designed in two scenarios:

[0056] In the case of single-station radar detection, there is no cross-link signal in the radar receiving signal, then the cascade array response vector of the smart reflective surface and the non-adjustable material surface is and It can be directly expressed as and The superscript H represents the conjugate transpose operation. In addition, it is only necessary to estimate the direction of the incoming signal without paying attention to the radar's transmit and receive beam gains. Therefore, the optimization problem of smart reflector-assisted electromagnetic stealth can be reconstructed as

[0057]

[0058]

[0059] in, represents the reflection gain of the uncontrollable material surface unit; then the Lagrangian dual method is applied to solve the optimal reflection coefficient;

[0060] In the case of multi-station radar (K ≥ 2) detection, the optimization problem of intelligent reflective surface assisted electromagnetic stealth can be restructured as

[0061]

[0062]

[0063] in, and is the joint gain of receive and transmit beamforming between radar i and radar k; then the Lagrangian dual method is used to solve the optimal reflection coefficient of the smart reflector.

[0064] Furthermore, the Lagrangian dual method is used to solve the optimal reflection coefficient of the smart reflector, where

[0065] In the case of single-station radar detection, the Lagrangian function of the optimization problem is defined as

[0066]

[0067] in, represents the Lagrange multiplier and satisfies

[0068] Then, the Lagrangian function Take the partial derivative of θ and set its derivative to 0:

[0069]

[0070] Then we can get the expression of θ about the Lagrange multiplier λ:

[0071] θ ＊ =-C(uu H +diag(λ) -1 u.

[0072] Secondly, θ ＊ Substitute the Lagrangian function Get the expression of the dual function:

[0073]

[0074] Given that the strong duality of the original problem and the dual problem holds, the optimal dual variable is obtained by solving the dual problem; the dual problem is transformed into a semi-positive definite optimization problem using the Schur complement theory.

[0075]

[0076]

[0077] Finally, the solver is used to solve the dual problem and substitute the required λ into θ ＊ The optimal intelligent reflection surface coefficient can be obtained; in the case of multi-station radar (K ≥ 2) detection, the Lagrangian function of the above optimization problem is defined as

[0078]

[0079] in, represents the Lagrange multiplier and satisfies

[0080] Then, the Lagrangian function Take the partial derivative of θ and set its derivative to 0:

[0081]

[0082] Then we can get the expression of θ about the Lagrange multiplier λ:

[0083]

[0084] Secondly, θ ＊ Substitute the Lagrangian function Get the expression of the dual function:

[0085]

[0086] Given that the strong duality of the original problem and the dual problem holds, the optimal dual variable is obtained by solving the dual problem; the dual problem is transformed into a semi-positive definite optimization problem using the Schur complement theory.

[0087]

[0088]

[0089] Finally, the solver is used to solve the dual problem and substitute the required λ into θ ＊ The optimal intelligent reflection surface coefficient can be obtained.

[0090] Furthermore, the solver is a CVX solver.

[0091] Compared with the prior art, the present invention has the following advantages and effects:

[0092] 1) The Lagrangian duality-based intelligent reflector-assisted electromagnetic stealth method proposed in the present invention can effectively reduce or even eliminate radar echo signals. This solution reduces or offsets the electromagnetic wave signals that are not absorbed by the surface of unadjustable materials by adjusting the reflection coefficient of the intelligent reflector, thereby reducing the echo signals reflected back to the radar system. Compared with traditional stealth technology, this method has the ability to adapt to high-speed flying targets and quickly switch radar working modes, significantly improving stealth performance in complex electromagnetic environments.

[0093] 2) For single-station radar and multi-station radar, the present invention proposes a low-complexity angle and channel gain estimation scheme. The sensor array of this scheme only needs a small number of sensor devices to effectively estimate the direction and path gain information of the incoming signal, thereby significantly reducing the hardware cost and simplifying the algorithm complexity.

[0094] 3) The present invention proposes a Lagrangian dual-based intelligent reflector-assisted electromagnetic stealth method to obtain a semi-closed solution for the reflection coefficient of the intelligent reflector. Compared with directly using a convex optimization solver to solve the problem, the stealth method has lower complexity. Moreover, the reflection coefficient can be adjusted in real time to improve the stealth performance of the target in both single-station radar detection and multi-station radar detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0096] Figure 1This is a system model diagram of an intelligent reflective surface assisting a stealth aircraft in avoiding radar detection in an embodiment of the present invention;

[0097] Figure 2 It is a flow chart of a Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method provided by an embodiment of the present invention;

[0098] Figure 3 1 is a performance comparison simulation diagram in Example 1 of the present invention, (a) is for a single-station radar, and (b) is for a multi-station radar;

[0099] Figure 4 This is a performance comparison simulation diagram in Example 2 of the present invention, (a) is for a single-station radar, and (b) is for a multi-station radar;

[0100] Figure 5 This is a performance comparison simulation diagram in Example 3 of the present invention, (a) is for a single-station radar case, and (b) is for a multi-station radar case. DETAILED DESCRIPTION

[0101] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0102] See also Figure 1 , Figure 1 is a system model diagram of the intelligent reflective surface assisted electromagnetic stealth technology in all embodiments of the present invention. The stealth system includes at least one sensor array with L sensing units, at least one sensor array with N 1 The intelligent reflective surface of passive reflective units, at least one with N 2 The sensor array is used to estimate the direction of the radar detection signal and its transmit and receive beam gain, the smart reflective surface is used to control the amplitude and phase of the incident electromagnetic wave signal, and the non-controllable material surface is used to absorb the radar detection signal. The unabsorbed signal will be reflected and controlled by the smart reflective surface, thereby effectively reducing or even eliminating the signal returning to the radar.

[0103] In order to illustrate the technical advancement of the method of the present invention, the radar received signal energy size is compared on the MATLAB platform between the Lagrangian duality-based intelligent reflector-assisted electromagnetic stealth method proposed in the present invention and other methods under different embodiments, wherein the other methods include: 1) Intelligent reflector random phase shift method: the reflection phase is randomly generated within [0, 2π). 2) DFT-based codebook search method: in the codebook based on discrete Fourier transform (DFT) (using The reflection coefficient vector of the smart reflective surface is searched on the surface to minimize the total signal power received by the radar.

[0104] Example 1

[0105] In this embodiment, the specific parameters are set as follows:

[0106] Assume that the stealth target and the radar are located in the same two-dimensional plane, so that Only the arrival angle of the incoming signal needs to be considered Other parameters are set as follows: the number of radar transceiver antennas is M = 8 × 8 = 64, the intelligent reflective surface and the non-adjustable material surface have N passive reflective units respectively. 1 =N 1，x ×2(N 1，x represents the number of passive reflection units of the intelligent reflection surface along the x-axis direction) and the number of unadjustable reflection units N 2 =100×2=200, the number of sensing units L=9, the sensor array is deployed at the center of the stealth target surface, and the absorption efficiency of uncontrollable materials (such as radar absorbing materials or other materials on the aircraft surface) is The reflection phase of the reflection unit on the surface of the non-adjustable material is randomly generated and uniformly distributed in [0, 2π), and the maximum reflection amplitude of the smart reflection surface is 1. Assume that the radar system operates in the ultra-high frequency band of 150GHz, the wavelength of the wavelength transmission signal is λ=0.05m, and the distance between two adjacent antennas in the radar system is Δ a =λ / 2=0.025m, the distance between two adjacent passive reflectors is Δ e =λ / 4=0.0125m. The radar transmission waveform is The signal bandwidth is B = 100 MHz, and the pulse repetition interval and pulse interval are set to T p = 100μs and t p = 30μs, the shortest distance between the radar and the stealth target is set to 100 meters, and the channel gain at a reference distance of 1 meter is β 0 =-30dB, the transmit power of each radar is set to P = 15dBm.

[0107] Combine the following Figure 1 and Figure 2, specifically describing the process steps of a smart reflective surface-assisted electromagnetic stealth method based on Lagrangian duality disclosed in Example 1.

[0108] In this embodiment, step S1 is specifically implemented as follows:

[0109] Input the number of sensing units, the number of passive reflection units of the intelligent reflection surface, the number of reflection units on the surface of unadjustable materials, and their absorption efficiency and reflection phase information:

[0110] The stealth system includes at least one stealth target surface. Assume that a stealth target surface includes N 1 Passive reflector units and N 2 The passive reflective unit and the reflective unit on the surface of the non-adjustable material are arranged in a uniform planar array; the cross-shaped sensor array with L sensing units is deployed at the center of the stealth target surface; the reflection coefficient of each passive reflective unit at time t is defined as in and Respectively represent the control amplitude and phase range of the nth passive reflection unit, e represents an exponential function, and the superscript T represents the transposition operation of a vector; the reflection coefficient of each uncontrollable material unit is defined as in represents the absorbing efficiency of the mth uncontrollable material unit, represents the reflection phase determined by the material properties and can be obtained in advance through a large number of actual measurements. For N 1 The reflection coefficient of a passive reflection unit.

[0111] In this embodiment, step S2 uses the sensor array to estimate the direction of the incoming wave of the other detection radar within the current coherent processing time interval, which is specifically implemented as follows:

[0112] The one-dimensional steering vector function is defined as: Where φ is defined as the signal phase difference between two adjacent antennas, adjacent passive reflection units, or adjacent non-adjustable material reflection units, Defined as the size of a uniformly spaced linear array;

[0113] Assuming that the wavelength of the enemy detection radar signal is λ, the distance between two adjacent sensing units is expressed as Δ s The number of sensing units in the cross-shaped sensor array along the x-axis and y-axis directions is L respectively. x and L y ; At time t, the enemy radar k (denoted as R k ) reaches the stealth target (denoted as Ta ) is and the pitch angle is is the array response of the sensor array, and its array response along the x-axis and y-axis directions are expressed as

[0114]

[0115] in, and is the phase offset.

[0116] The received signal of the sensor array is expressed as

[0117]

[0118] in, Indicates that the sensor array receives a mean of 0 and a power of Gaussian white noise, represents the array response of the sensor array, s(t)=[s 1 (t), ..., s K (t)] T represents the transmission signal vector of K radars, represents the transmission signal of radar k, represents the radar pulse waveform, B is the signal bandwidth, t p The Multiple Signal Classification (MUSIC) algorithm is used to estimate the direction of the incoming signal. Then, the least squares method (LS) is used to estimate the signal s(t), and the estimated signal is expressed as

[0119]

[0120] in, represents the estimated value of the transmitted signal of radar K, represents the noise vector after LS estimation, represents the noise estimate from radar K, express The conjugate transpose of . Definition and Radar The transmit beam and receive beam gains within the coherent processing time interval are equal to each other based on channel reciprocity, that is, K is the number of radars. Finally, the estimated value of the transmit beam gain can be expressed as

[0121]

[0122] Among them, T p represents the pulse repetition interval, Indicates from radar The noise estimate of represents the real part operation, Express Take the conjugate.

[0123] In this embodiment, step S3 constructs an intelligent reflective surface to assist in avoiding electromagnetic stealth detection by single-station radar or multi-station radar, which is specifically implemented as follows:

[0124] Based on step S2, the signal direction of each detection radar at time t is estimated and its transmit beam gain and receive beam gain definition It indicates that the radar k is respectively in contact with the intelligent reflective surface (denoted by I), the uncontrollable material surface (denoted by N) at time t. a represents), the far-field line-of-sight channel of the stealth target surface; N represents the number of units on the stealth target surface and satisfies N=N 1 +N 2 ; Stealth target surface and array response of radar k and Defined as:

[0125]

[0126]

[0127] in, and Respectively represent the azimuth and elevation angle of the radar transmitting or receiving signal; Δ e and Δ a Respectively represent the distance between the stealth target surface and two adjacent units of the radar antenna array; N x and N y Respectively represent the number of units on the surface of the stealth target along the x-axis and y-axis directions; M x and M x Respectively represent the number of antennas along the x-axis and y-axis directions; the smart reflector array responds to and array responses of uncontrollable material surfaces The array response is defined in the same way as the stealth target surface. Given the positional relationship between the smart reflective surface, the uncontrollable material surface, and the stealth target surface, the array responses of the three have the following relationship:

[0128]

[0129] Therefore, the far-field line-of-sight channel matrix between any two points (denoted by X and Y) at time t is expressed as

[0130]

[0131] where X∈{I,N a , T a}and α is defined as the channel gain at a reference distance of 1 meter, Defined as the real-time propagation distance between radar k and stealth target, represents the path gain; since the far-field line-of-sight channel between any two points satisfies the channel reciprocity in uplink and downlink transmission, Based on the co-location relationship between the target surface, the intelligent reflective surface and the non-adjustable material surface, the channel matrix relationship between the radar and these three satisfies:

[0132] After applying the intelligent reflective surface to assist the stealth target, the received signal of radar k at time t is expressed as

[0133]

[0134] in, represents the reflection coefficient of the target surface, w i and denote the transmit beam gain of radar i and the receive beam gain of radar k, respectively, and n k (t) means the mean is 0 and the variance is σ 2 Gaussian white noise.

[0135] Assuming that the position of the stealth target remains unchanged within each radar coherent processing time interval, the changes in the channel and geometric parameters between the stealth target and the radar can be ignored, and the time index [t] is omitted in the calculation process. Therefore, within a pulse repetition time interval, the received echo signal power of radar k can be expressed as

[0136]

[0137] in, represents the channel matrix from the kth radar to the stealth target; the superscript H represents the conjugate transpose operation; The cascade array response vector at the overall target is represented by

[0138]

[0139] in, and Represent the cascade array response vectors on the smart reflective surface and the uncontrollable material surface respectively; then the total power of the received signal of the multi-station radar detection system is expressed as

[0140]

[0141] According to the above formula, the intelligent reflective surface is used to assist in reducing or completely eliminating the signal power reflected back to the radar detection system to achieve ideal stealth performance. First, st is defined as subject to the constraints of, min x f(x) is defined as minimizing the objective function f(x); therefore, the problem of minimizing the energy of radar received signals (achieving ideal electromagnetic stealth) using smart reflective surfaces can be expressed as

[0142]

[0143]

[0144] Among them, θ n It represents the reflection coefficient of the nth passive reflection unit of the smart reflection surface.

[0145] In this embodiment 1, step S4 uses the Lagrange dual method to calculate the amplitude and phase of the passive reflection unit of the smart reflection surface, which is specifically implemented as follows:

[0146] According to the differences in the estimated parameters and optimized reflection coefficients required to avoid single-station radar and multi-station radar detection, the reflection coefficient of the intelligent reflective surface is designed in two scenarios:

[0147] S4.1. If it is a case of single-station radar (K=1) detection, and there is no cross-link signal in the radar receiving signal, then the cascade array response vector of the smart reflective surface and the non-adjustable material surface is and It can be directly expressed as and The superscript H represents the conjugate transpose operation. In addition, it is only necessary to estimate the direction of the incoming signal without paying attention to the radar's transmit and receive beam gains. Therefore, the optimization problem of smart reflector-assisted electromagnetic stealth can be reconstructed as

[0148]

[0149]

[0150] in, represents the reflection gain of the uncontrollable material surface unit; then the Lagrangian dual method is applied to solve the optimal reflection coefficient.

[0151] First, the Lagrangian function of the above optimization problem is defined as

[0152]

[0153] in, represents the Lagrange multiplier and satisfies diag(λ) denotes a diagonal matrix whose diagonal elements are the elements of the vector λ.

[0154] Then, the Lagrangian function Take the partial derivative of θ and set its derivative to 0:

[0155]

[0156] Then we can get the expression of θ about the Lagrange multiplier λ:

[0157] θ ＊ =-C(uu H +diag(λ) -1 u.

[0158] Secondly, θ ＊ Substitute the Lagrangian function Get the expression of the dual function:

[0159]

[0160] in, Given the strong duality between the original problem and the dual problem, the optimal dual variable is obtained by solving the dual problem. Based on the Schur complement theory, the auxiliary variable q is introduced to transform the dual problem into a semi-positive definite optimization problem.

[0161]

[0162]

[0163] Finally, the CVX solver is used to solve the dual problem and substitute the required λ into θ ＊ The optimal intelligent reflection surface coefficient can be obtained.

[0164] S4.2. In the case of multi-station radar (K ≥ 2) detection, the optimization problem of intelligent reflective surface assisted electromagnetic stealth can be restructured as

[0165]

[0166]

[0167] in, and For radar i and radar The joint gain between receive and transmit beamforming.

[0168] The Lagrangian dual method is used to solve the optimal reflection coefficient of the smart reflector. First, the Lagrangian function of the above optimization problem is defined as

[0169]

[0170] in, represents the Lagrange multiplier and satisfies

[0171] Then, the Lagrangian function Take the partial derivative of θ and set its derivative to 0:

[0172]

[0173] Then we can get the expression of θ about the Lagrange multiplier λ:

[0174]

[0175] Secondly, θ ＊ Substitute the Lagrangian function Get the expression of the dual function:

[0176]

[0177] Given the strong duality between the original problem and the dual problem, the optimal dual variable is obtained by solving the dual problem. Based on the Schur complement theory, the auxiliary variable q is introduced to transform the dual problem into a semi-positive definite optimization problem.

[0178]

[0179]

[0180] Finally, the CVX solver is used to solve the dual problem and substitute the required λ into θ ＊ The optimal intelligent reflection surface coefficient can be obtained. It is understandable that other convex optimization solvers can also be used.

[0181] like Figure 3 As shown, Figure 3 The relationship between the radar received signal power and the arrival angle estimation error is plotted. The signal power received by the method of the present invention in the single-station radar and multi-station radar within the estimation error range of no more than 2 degrees is significantly lower than that of the smart reflector random phase shift method and the DFT codebook search method. In addition, the received signal power in the single radar scenario is only 6.3% of the DFT codebook search method and about 4.7% of the random phase shift method; the total signal power received in the multi-station radar scenario is only 6.4% of the DFT codebook search method and about 3.5% of the random phase shift method.

[0182] Example 2

[0183] In this embodiment 2, the specific parameters are set as follows:

[0184] Assume that the number of passive reflection units of the smart reflection surface is N 1 =4×2=8, the shortest distance between radar and target The distances are 0m, 30m, 40m, 50m, 60m, 70m, 80m, 90m and 100m respectively. For the setting of other parameters, please refer to Example 1.

[0185] In this embodiment 2, the distance between the radar and the target is After setting, change the distance between the radar and the target Related variables, and implement steps S1-S4 once, wherein steps S1-S4 please refer to steps S1-S4 in embodiment 1.

[0186] like Figure 4 As shown, Figure 4 The relationship between the radar received signal power and the shortest distance between the radar and the target is shown. First, the method of the present invention deploys an intelligent reflector-assisted electromagnetic stealth system on the target, which can significantly reduce the signal power received by the radar. Moreover, the stealth performance of the intelligent reflector-assisted electromagnetic stealth method based on Lagrangian duality is significantly better than that of the random phase shift design and the DFT codebook search-based method. This also verifies the effectiveness of the intelligent reflector design scheme in reducing or eliminating the reflected signal power, thereby preventing detection by enemy radars.

[0187] Example 3

[0188] In this embodiment 3, the specific parameters are set as follows:

[0189] Assume that the distance parameter between the radar and the target is Fixed, number of passive reflective units of the smart reflective surface N 1 Take 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 respectively. Please refer to Example 1 for the setting of other parameters.

[0190] In this embodiment 3, the number of passive reflection units N of the smart reflection surface is 1 After the value is taken, the number of passive reflection units N of the smart reflection surface is changed. 1 Related variables, and implement steps S1-S4 once, wherein steps S1-S4 please refer to steps S1-S4 in embodiment 1.

[0191] like Figure 5 As shown, Figure 5The relationship between the radar received signal power and the passive reflector unit is plotted. First, as the number of reflective units of the smart reflective surface increases, the total received signal power of the radar decreases significantly. This is because the signal cancellation capability improved by the smart reflective surface is used to eliminate or reduce the reflected signal to a single radar system. Secondly, even in the case of cross-connections between multi-station radars, the stealth method designed in this example can still achieve complete electromagnetic stealth when the number of reflective units is greater than 90, that is, the signal power received by each radar is zero. This is because relative to a single radar system, the minimum number of reflective units required is only needed to offset the detection signal from a single radar, while in a multi-station radar scenario, a larger number of reflective units is required to achieve ideal electromagnetic stealth to offset the detection signals superimposed from different detection radars. There is no change in the electromagnetic stealth system without the application of smart reflective surfaces, and the electromagnetic stealth method assisted by smart reflective surfaces based on random phases increases with the number of reflective units N. 1 This is because the lack of proper signal cancellation leads to an increase in the signal power reflected from the target.

[0192] In summary, the intelligent reflector-assisted electromagnetic stealth method based on Lagrangian duality proposed in the present invention can significantly reduce the signal power reflected from the target to the opponent's radar system, and improve the flexibility and adaptability of the target stealth.

[0193] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A smart reflective surface-assisted electromagnetic stealth method based on Lagrangian duality, characterized in that: Applied to avoid detection by single-station radar or multi-station radar, the method is implemented based on a stealth system, the stealth system includes at least one sensor array with L sensing units, at least one intelligent reflection surface with N1 passive reflection units, and at least one non-adjustable material surface with N2 reflection units. The electromagnetic stealth method includes the following steps: S1, the number of input sensing units, the number of passive reflection units of the intelligent reflection surface, the number of reflection units on the surface of the uncontrollable material, and the absorption efficiency and reflection phase information of the surface of the uncontrollable material; S2, using the sensor array to estimate the incoming wave direction and the transmit and receive beam gains of the other detection radar within the current coherent processing time interval; S3. Constructing an intelligent reflective surface to assist in avoiding electromagnetic stealth detection by single-station radar or multi-station radar. The problem of using intelligent reflective surface to assist in achieving ideal electromagnetic stealth is expressed as follows: Among them, θ n represents the reflection coefficient of the nth passive reflection unit of the intelligent reflection surface, K is the number of radars, is the receiving beam gain of radar k within the coherent processing time interval, is the transmitted beam of radar i within the coherent processing time interval, and the superscript H represents the conjugate transpose operation. and They represent the cascade array response vectors on the smart reflective surface and the non-adjustable material surface, θ is the reflection coefficient of the passive reflective unit of the smart reflective surface, and φ is the reflection coefficient of the non-adjustable material unit; S4. Calculate the amplitude and phase of the passive reflection unit of the smart reflection surface using the Lagrangian duality method.

2. The Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to claim 1, characterized in that: The sensors in the sensor array are arranged in a cross shape.

3. The Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to claim 1, characterized in that: The sensor array is located at the center of the stealth target surface.

4. The Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to claim 1, characterized in that: In step S1, the stealth system includes at least one stealth target surface, assuming that one stealth target surface includes N1 passive reflection units and N2 reflection units on the surface of an unadjustable material, and the passive reflection units and the reflection units on the surface of the unadjustable material are arranged in the form of a uniform planar array; A sensor array with L sensing units is deployed at the center of the stealth target surface; the reflection coefficient of each passive reflection unit at time t is defined as in and Respectively represent the control amplitude and phase range of the nth passive reflection unit, e represents an exponential function, and the superscript T represents the transposition operation of a vector; the reflection coefficient of each uncontrollable material unit is defined as in represents the absorbing efficiency of the mth uncontrollable material unit, Represents the reflection phase determined by the material properties.

5. The Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to claim 1, characterized in that: The estimation step of step S2 includes: The one-dimensional steering vector function is defined as: Where φ is defined as the signal phase difference between two adjacent antennas, adjacent passive reflection units, or adjacent non-adjustable material reflection units, Defined as the size of a uniformly spaced linear array; Assuming that the wavelength of the enemy detection radar signal is λ, the distance between two adjacent sensing units is expressed as Δ s The number of sensor units in the sensor array along the x-axis and y-axis directions is L respectively. x and L y ; At time t, the enemy radar k (denoted as R k ) reaches the stealth target (denoted as T a ) is and the pitch angle is is the array response of the sensor array, and its array response along the x-axis and y-axis directions are expressed as in, and is the phase offset; The received signal of the sensor array is expressed as in, Indicates that the sensor array receives a mean of 0 and a power of Gaussian white noise, represents the array response of the sensor array, s(t)=[s1(t),...,s K (t)] T represents the transmission signal vector of K radars, represents the transmission signal of radar k, represents the radar pulse waveform, B is the signal bandwidth, t p is the pulse interval; First, a multiple signal classification algorithm is used to estimate the direction of the incoming signal. Secondly, the signal s(t) is estimated using the least squares method, and the estimated signal is expressed as in, represents the estimated value of the transmitted signal of radar K, represents the estimated noise vector, represents the noise estimate from radar K, express The conjugate transpose operation of .

6. The Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to claim 5, characterized in that: definition and are the transmit beam and receive beam gains of radar k within the coherent processing time interval respectively; based on channel reciprocity, the transmit beam and receive beam gains of each single-station radar are equal, that is, K is the number of radars; accordingly, the estimated value of the transmit beam gain is expressed as Among them, T p represents the pulse repetition interval, represents the noise estimate from radar k; represents the real part operation, Express Take the conjugate.

7. The Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to claim 1, characterized in that: The process of obtaining the electromagnetic stealth problem in step S3 includes: Based on the estimation, the detection signal direction of each detection radar at time t can be obtained and its transmit beam gain and receive beam gain definition The radar k is respectively connected to the intelligent reflective surface I and the uncontrollable material surface N at time t a 、Stealth target surface T a The far-field line-of-sight channel between the stealth target surface and the array response of the radar k and Defined as: in, and Respectively represent the azimuth and elevation angle of the radar transmitting or receiving signal, Δ e and Δ a Respectively represent the distance between the stealth target surface and two adjacent units of the radar antenna array; N x and N y Respectively represent the number of units on the surface of the stealth target along the x-axis and y-axis directions; M x and M x Respectively represent the number of antennas along the x-axis and y-axis directions; the smart reflector array responds to and array responses of uncontrollable material surfaces The array response is defined in the same way as the stealth target surface; given the positional relationship between the smart reflective surface, the uncontrollable material surface, and the stealth target surface, the array responses of the three have the following relationship: Therefore, the far-field line-of-sight channel matrix between any two points (denoted by X and Y) at time t is expressed as where X∈{I,N a , T a }and α is defined as the channel gain at a reference distance of 1 meter, Defined as the real-time propagation distance between radar k and stealth target, represents the real-time path gain; Since the far-field line-of-sight channel between any two points satisfies channel reciprocity in uplink and downlink transmission, Based on the co-location relationship between the stealth target surface, the intelligent reflective surface, and the uncontrollable material surface, the channel matrix relationship between the radar transmission signal reaching these three satisfies: After applying the intelligent reflective surface to assist the stealth target, the received signal of radar k at time t is expressed as in, w i and denote the transmit beam gain of radar i and the receive beam gain of radar k, respectively, and n k (t) means the mean is 0 and the variance is σ 2 Gaussian white noise; Assume that the position of the stealth target remains unchanged within each radar coherent processing time interval, and then ignore the changes in the channel and geometric parameters between the stealth target and the radar, and omit the time index [t] in the calculation process; therefore, within a pulse repetition time interval, the received echo signal power of radar k can be expressed as Then the total power of the received signal of the multi-station radar detection system is expressed as According to the above formula, the intelligent reflective surface is used to assist in reducing or completely eliminating the signal power reflected back to the radar detection system to achieve ideal stealth performance; first, st is defined as subject to the constraint, min x f(x) is defined as minimizing the objective function f(x); therefore, the problem of minimizing the energy of radar received signals using smart reflective surfaces is expressed as in, represents the cascade array response vector at the overall stealth target, and Represent the cascade array response vectors on the smart reflective surface and the uncontrollable material surface respectively.

8. The Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to claim 7, characterized in that: Cascade array response vector at the overall stealth target for and Represent the cascade array response vectors of the smart reflective surface and the uncontrollable material surface respectively.

9. A Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to any one of claims 1 to 8, characterized in that: The steps of step S4 include: According to the differences in the estimated parameters and optimized reflection coefficients required to avoid single-station radar and multi-station radar detection, the reflection coefficient of the smart reflective surface is designed in two scenarios: In the case of single-station radar detection, there is no cross-link signal in the radar receiving signal, then the cascade array response vector of the smart reflective surface and the non-adjustable material surface is and It can be directly expressed as u H and The superscript H represents the conjugate transpose operation. In addition, only the direction of the incoming signal needs to be estimated without paying attention to the radar's transmit and receive beam gains. Therefore, the optimization problem of smart reflector-assisted electromagnetic stealth can be reconstructed as in, represents the reflection gain of the uncontrollable material surface unit; then, the Lagrangian dual method is applied to solve the optimal reflection coefficient; In the case of multi-station radar (K ≥ 2) detection, the optimization problem of intelligent reflective surface assisted electromagnetic stealth can be restructured as in, and is the joint gain of receive and transmit beamforming between radar i and radar k; then, the Lagrangian dual method is applied to solve the optimal reflection coefficient of the smart reflector.

10. The Lagrangian duality-based intelligent reflective surface-assisted electromagnetic stealth method according to claim 9, characterized in that: The Lagrangian dual method is used to solve the optimal reflection coefficient of the smart reflector, where In the case of single-station radar detection, the Lagrangian function of the optimization problem is defined as in, represents the Lagrange multiplier and satisfies Then, the Lagrangian function Take the partial derivative of θ and set its derivative to 0: The expression of θ with respect to the Lagrange multiplier λ can be obtained: i ＊ =-C(uu H +diag(λ)) -1 u. Secondly, θ ＊ Substitute the Lagrangian function Get the expression of the dual function: Given that the strong duality of the original problem and the dual problem holds, the optimal dual variable is obtained by solving the dual problem; the dual problem is transformed into a semi-positive definite optimization problem using the Schur complement theory. Finally, the solver is used to solve the dual problem and substitute the required λ into θ ＊ The optimal intelligent reflection surface coefficient can be obtained; In the case of multi-station radar (K ≥ 2) detection, the Lagrangian function of the above optimization problem is defined as in, represents the Lagrange multiplier and satisfies Then, the Lagrangian function Take the partial derivative of θ and set its derivative to 0: The expression of θ with respect to the Lagrange multiplier λ can be obtained: Secondly, θ ＊ Substitute the Lagrangian function Get the expression of the dual function: Given that the strong duality of the original problem and the dual problem holds, the optimal dual variable is obtained by solving the dual problem; The dual problem is transformed into a semi-positive definite optimization problem using Schur complement theory: Finally, the solver is used to solve the dual problem and substitute the required λ into θ ＊ The optimal intelligent reflection surface coefficient can be obtained.

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