Method for correcting antenna radome below antenna radiation beam deflection based on time reversal

Abstract

The application discloses a method for correcting deflection of an antenna radiation beam under a radome based on time reversal, and belongs to the technical field of radars. The method is used for processing signals received by each array element in an array antenna by using the time reversal method, and re-emitting the processed time reversal signals from the corresponding array element, so that more accurate beam pointing is achieved, and the aiming error is reduced. Based on the time reversal technology, the application can realize the effect of adaptive direction backtracking, and ensure that the target angle has the maximum gain under the target frequency; compared with a traditional phased array feeding method under the radome, the method has a better aiming error index.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a method for correcting the deflection of the antenna radiation beam under the radome based on time reversal. Background Technology

[0002] In modern electronic warfare, array antennas have traditionally been concealed beneath radomes. These radomes, while protecting the antenna from environmental influences, are designed with symmetrical streamlined shapes, asymmetrical singular shapes, and multi-layered structures. They are functional structural components integrating electrical performance, structural strength, aerodynamic shape, and specific functional requirements. Traditionally, array antennas under radomes utilize phased array principles for feeding to achieve the desired pointing angle. According to Snell's law, when an array antenna radiates outward through a radome of uniform thickness, the difference in slope between the non-parallel inner and outer surfaces causes beam deflection, deviating from the original target direction. Units carrying antennas in warfare often require precise beam pointing, especially high-precision weapons such as missiles. Therefore, optimizing the beam pointing of array antennas under radomes is necessary to improve aiming accuracy.

[0003] Regarding theoretical research on optimizing the beam pointing of radomes, the article "Electromagnetic design and performance analysis of airborne radomes: Trends and perspectives" (IEEE Antennas & Propagation Magazine, vol. 56, no. 4, pp. 276-298, 2014) introduces various traditional radome analysis methods. These traditional methods generally analyze radomes using different approaches such as physical optics (ray tracing principle), geometric optics, finite element method, and equivalent transmission line method. Optimization is achieved by modifying the radome's thickness, shape, and internal metal doping to alter its electromagnetic performance, such as transmission coefficient and axial line error.

[0004] However, when simulating and optimizing radomes of equal thickness using computer simulations, it is necessary to know the model parameters and dielectric constant of the radome body in advance, and to model and process them in programming software such as MATLAB. This poses a challenge to the electromagnetic performance optimization of the radome, and the optimized variable-thickness radome or radomes with metal inclusions (such as adding FSS (Frequency Selective Surface) to change the electromagnetic performance of the radome) require high-precision manufacturing processes in the later stages of processing. This problem is particularly evident in non-axisymmetric singular radomes and radomes with multiple layers of different dielectrics. Furthermore, optimizing the radome in isolation does not consider the coupling effects between array elements covered by the radome. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for correcting antenna radiation beam deflection under a radome based on time reversal. Without requiring computer optimization of the radome, the method uses time reversal to process the signal received by each element in the array antenna, and then retransmits the processed time-reversed signal from the corresponding element to achieve more accurate beam pointing, thereby reducing aiming errors.

[0006] The technical solution adopted in this invention is:

[0007] A method for correcting antenna radiation beam deflection under a radome based on time reversal includes the following steps:

[0008] S1. Irradiate a plane wave containing the same polarization component as the array antenna from the target direction toward the array antenna covered by the radome;

[0009] S2. Record the signal received by each element of the array antenna, perform time-reversal processing on the signal, and obtain the time-reversed signal;

[0010] S3. Re-input the time-reversal signal into the corresponding array element and transmit it simultaneously to obtain a beam that is accurately pointed in the target direction.

[0011] Furthermore, step S1 is detailed as follows:

[0012] S11. Analyze the entire system in a spherical coordinate system, with the center of the array antenna as the origin of the spherical coordinate system. A plane wave s(t) is illuminated in a direction where θ d Let θ be the angle component of the plane wave relative to the array antenna in spherical coordinates. For plane waves relative to the array antenna in spherical coordinates The included angle component, s(t), is the expression for the amplitude of the plane wave signal as a function of time.

[0013] S12. Treat the complex environment as a linear time-invariant channel, and the array antenna covered by the radome as a linear time-invariant system; in the linear time-invariant system, the signal Y(t) of the electromagnetic wave emitted in the direction of the target after passing through the radome is written as:

[0014]

[0015] Where Y(t)=[y1(t),y2(t),...,y N (t)] T y represents the matrix composed of the signals received by each array element. n (t) represents the signal received by each array element, n = 1, 2, ..., N.T To perform a transpose transformation on this matrix; This indicates that the two expressions are convolved. The impulse response is for the accepting mode.

[0016] Furthermore, step S2 is detailed as follows:

[0017] The signal received by each element in the array antenna is time-reversed to Y(-t) = [y1(-t), y2(-t), ..., y N (-t)] T The time-reversal signal is obtained:

[0018]

[0019] Furthermore, step S3 specifically includes:

[0020] In the time domain, neglecting propagation loss and time delay, the radiated electric field can be written as:

[0021]

[0022] in To excite the radiated electric field of the array antenna, The pulse response in transmit mode. c represents the relative position of the array element in the system. i (t) represents the excitation of the i-th transient element; when c i (t) is the time-reversal signal y i When (-t), the direction of the deflection beam is improved.

[0023] To illustrate the feasibility of this invention, further analysis is conducted in the frequency domain:

[0024] Performing a Fourier transform on equation (2) yields:

[0025]

[0026] Where (ω) is the corresponding frequency domain representation, * (.) represents the conjugate of the original expression; let:

[0027]

[0028] a(ω)=Y * (ω) (5)

[0029] Where a(ω) represents the excitation of the array antenna.

[0030] The radiation field is subjected to a Fourier transform and then calculated in matrix form:

[0031]

[0032] In the formula The far-field radiation pattern obtained using a(ω) is shown, where |.| denotes the absolute value of the corresponding expression. From the formula, we can see... Fundamentally depends on P tx (θ,φ,t) and P rx The inner product of (θ,φ,t) is because a(ω) in time-reversal beamforming already contains the intrinsic radiation information of the array antenna.

[0033] Further analysis of this formula reveals that, under ideal conditions, the radiation pattern obtained using the time-reversal excitation a(ω) in the target direction... Gain The gain is greater than that obtained using any excitation c(ω) (such as the traditional phase-shifting method of a phased array). In other words, the time-reversed electromagnetic wave "space-time" focusing characteristics can effectively improve the antenna beam deflection phenomenon caused by the radome.

[0034]

[0035] Where Z0 represents the free-space wave impedance, P in =c T (ω)c * (ω) represents the total input power. Assuming all incident power is completely radiated, the target direction under arbitrary excitation... Gain for:

[0036]

[0037] in(.) H To represent Hermitian conjugation, and further simplify the formula, let x(ω) = c * (ω), Therefore, the maximum gain can be obtained:

[0038]

[0039] As can be seen from matrix operations, the problem of finding the maximum value can be transformed into finding R. tx The problem of eigenvectors with the largest eigenvalue can be further simplified using the following formula:

[0040]

[0041] in express The maximum gain at the target direction frequency ω, ||.|| represents the constant in the corresponding expression, and the optimal excitation of the array antenna is obtained:

[0042]

[0043] Where γ is an arbitrary non-zero complexity factor, that is, the array received signal after time reversal processing is exactly... Find the solution that yields the maximum value.

[0044] Therefore, the time-reversed signal transmitted by the antenna array can achieve adaptive directional backtracking and ensure maximum gain at the target angle at the target frequency. It can be seen that during the time-reversal processing of the received signal, information such as coupling between each array element and coupling between the element and the radome is not presented separately and has been adaptively processed. Therefore, it is unnecessary to know information such as the shape and thickness of the radome; the influence of this information on the element radiation pattern is already included in the channel and eliminated when the reversed signal passes through the channel again and performs an inner product, thus achieving maximum gain in the target direction. Since the overall system gain is constant, and the target angle gain increases, according to the law of conservation of energy, the maximum beam pointing will inevitably shift towards the target angle. Therefore, compared to the traditional phased array feeding method under the radome, this method provides a better aiming error index.

[0045] Advantages of this invention:

[0046] 1) This method does not require knowledge of the model parameters of the enclosure;

[0047] 2) This method does not require computer simulation optimization;

[0048] 3) This method overcomes the problem of processing radomes with varying thickness.

[0049] 4) This method takes into account the coupling between elements and the near-field effects of the radome. Attached Figure Description

[0050] Figure 1 This is a top view of a unit of the array antenna used in an embodiment of the present invention;

[0051] Figure 2 This is a front view of a unit of the array antenna used in an embodiment of the present invention;

[0052] Figure 3 The S of the array antenna element used in the embodiments of the present invention 11 parameter;

[0053] Figure 4 This is the 6GHz far-field radiation pattern of the array antenna element used in the embodiment of the present invention;

[0054] Figure 5 This is a top view of the array antenna used in an embodiment of the present invention;

[0055] Figure 6 This is a front view of the array antenna used in an embodiment of the present invention;

[0056] Figure 7 This is the far-field radiation pattern of the array antenna used in this embodiment of the invention at 6 GHz with target angles of Phi = 0° and Theta = 30° and -30° in free space;

[0057] Figure 8 This is the far-field radiation pattern of the array antenna used in this embodiment of the invention at 6 GHz with target angles of Phi = 0° and Theta = 45° and -45° in free space;

[0058] Figure 9 This is a top view of the array antenna in an embodiment of the present invention located under an upright radome;

[0059] Figure 10 This is a front view of the array antenna under the upright radome according to an embodiment of the present invention;

[0060] Figure 11 In this embodiment of the invention, when the array antenna is located under the upright radome, port 5 receives a high-order modulated Gaussian pulse wave transmitted from Phi = 0° and Theta = -30°.

[0061] Figure 12 It is Figure 11 The signal corresponding to port 5 is obtained by time reversal of the signal in the input;

[0062] Figure 13 The image shows a comparison of the far-field radiation at 6 GHz from the method of this invention and the conventional method when the array antenna is located under an upright radome, with the array antenna radiated toward Phi = 0° and Theta = -30°.

[0063] Figure 14 The array antenna is located under an upright radome, and the 5GHz far-field diagram of the method of the present invention radiating towards Phi = 0° and Theta = -30° is shown.

[0064] Figure 15 This is a comparison diagram of the far-field radiation at 6 GHz from the method of this invention and the conventional method, with the array antenna located under an upright radome, radiating towards Phi = 0° and Theta = -45°.

[0065] Figure 16 The array antenna is located under an upright radome, and the 5GHz far-field diagram of the method of the present invention is radiated towards Phi = 0° and Theta = -45°.

[0066] Figure 17 This is a top view of the array antenna under the inverted radome according to an embodiment of the present invention;

[0067] Figure 18 This is a front view of the array antenna under the inverted radome according to an embodiment of the present invention;

[0068] Figure 19 This is a comparison diagram of the far-field radiation at 6 GHz from the method of this invention and the conventional method towards Phi = 0° and Theta = -30°, with the array antenna located under the inverted radome.

[0069] Figure 20 The array antenna is located under the inverted radome, and the 5GHz far-field diagram of the method of the present invention is radiated towards Phi = 0° and Theta = -30°.

[0070] Figure 21 The image shows a comparison of the far-field radiation at 6 GHz from the method of this invention and the conventional method, with the array antenna located under the inverted radome.

[0071] Figure 22 This is a 5GHz far-field diagram of radiation radiated towards Phi = 0° and Theta = -45° using the method of this invention, with the array antenna located under the inverted radome. Detailed Implementation

[0072] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0073] Figure 1 , Figure 2 The antenna shown is a basic rectangular patch antenna with parasitic elements. The antenna shown in this invention is 30mm long, 25mm wide, and 4mm thick, and uses a coaxial back-feed method. Figure 3 It is the S of the single-unit antenna 11 The parameter diagram utilizes the unit's broadband characteristics, which are below -10dB in the 5GHz to 6GHz range, and combines... Figure 4 The far-field radiation pattern of the element shows that the element radiates directly upwards in both the xoz and yoz planes. Therefore, this element is used as the basic element of the array antenna in this embodiment.

[0074] Figure 5 , Figure 6 The image shows the free space formed by... Figure 1 The array antenna shown is a 1×8 linear array composed of elements arranged along the X-direction. Since the elements have good far-field radiation characteristics in both the xoz and yoz planes, the elements are arranged with a center-to-center spacing of 25mm (approximately 0.5λ corresponding to 6GHz). The phased array arrangement is based on the formula for linear arrays. Where α is the phase difference of the input signal to each array element, and θ is the angle along the normal on the xoz plane, i.e., the target angle. This embodiment uses ±30° and ±45° as examples, first observing the far-field radiation pattern of the linear array in free space at 6 GHz. For example... Figure 7 As shown, this linear array can be correctly oriented within ±30° in free space. Figure 8 As shown, the linear array can point normally at ±45° in free space.

[0075] During the manufacturing process of radomes, due to the specific manufacturing techniques and requirements, variations in thickness are common, such as transitioning from a thicker radome structure to a thinner one. In the transition region between these thicknesses, the slopes of the upper and lower surfaces will inevitably differ. According to Snell's Law, when a slope difference exists between the upper and lower surfaces, the electromagnetic wave beam will be deflected after passing through the dielectric layer, and this deflection is related to the slope difference. This significantly affects the beam pointing of the radome, making it difficult to target the intended target. This embodiment magnifies the transition phase of the radome to highlight the beam deflection correction effect of this solution. Figure 9 , Figure 10 As shown, an upright sloping dielectric layer with a lower surface parallel to the xoy plane, an upper surface and a counterclockwise angle of 10° between the upper and lower surfaces, and a dielectric constant of 4 serves as the transition stage for the varying thickness of the radome.

[0076] When the array antenna is located under an upright radome, this embodiment takes the signal at port 5 as an example. Figure 11 The diagram shows that port 5 receives electromagnetic information with a target direction of Phi = 0° and Theta = 30°, and the signal transmitted in the target direction is a modulated Gaussian signal of 4GHz-8GHz. Figure 12 The signal processed by this method at port 5 will be transmitted along port 5.

[0077] Figure 13 The diagram shows a comparison of results obtained using this embodiment and phased array phase shifting at 6GHz. It is evident that the electromagnetic wave radiated by traditional phased array phase shifting is affected by the slope difference between the upper and lower surfaces, causing the radiation direction to deviate by 30°. In contrast, this method pre-considers the impact of the slope difference in complex channels and adaptively eliminates this effect during time reversal and retransmission. It is clearly shown that compared to the traditional phase shifting method, the electromagnetic wave radiated by this method is closer to the target direction (Phi = 0°, Theta = 30°), and exhibits higher gain in the target direction.

[0078] Figure 14 Transmit to each port Figure 12 The signal far-field radiation pattern at 5 GHz is shown. Because the received and transmitted signal spectrum components include 5 GHz, this method can achieve accurate beam pointing even when radiating at 5 GHz, thus verifying the characteristic of this method to correct beam pointing over a wide frequency band.

[0079] Figure 15 A comparison of the 6GHz far-field radiation patterns of traditional phased arrays and the proposed method is presented to change the target direction to Phi = 0° and Theta = 45°. Figure 16The image shows the 5GHz far-field radiation pattern of this embodiment after changing the target direction. The maximum gain of the radiation from the method of this invention is lower than that of the traditional method, but the maximum beam pointing of this method is more accurate, and the gain in the target direction is also greater than that of the traditional phased array, proving that this method is applicable to multiple target angles.

[0080] The thickness of the radome has a transition from thick to thin, and the transition from thin to thick also needs to be considered. Figure 17 and Figure 18 The aforementioned slope medium layer is inverted to serve as an antenna radome. Figures 19-22 In order to be in Figure 18 In the case of repeating Figures 13-16 The operation. Figure 19 yes Figure 17 The image shows a 6GHz far-field comparison of the method of the present invention and the conventional method radiating toward Phi = 0° and Theta = -30° in the environment shown. Figure 20 yes Figure 17 The image shows a 5GHz far-field plot of radiation from the direction of the present invention, Phi = 0° and Theta = -30°, under the shown environment. Figure 21 yes Figure 17 The image shows a comparison of the far-field radiation at 6 GHz between the method of this invention and the conventional method towards Phi = 0° and Theta = -45° in the shown environment. Figure 22 yes Figure 17 The image shows a 5GHz far-field plot of radiation emanating from Phi = 0° and Theta = -45° in the environment described in this invention. Different thickness variations of the radome have a significant impact on the beam pointing of traditional methods, while this method can correct erroneous beam pointing.

[0081] In summary, this invention discloses a time-reversal method for correcting beam pointing. By performing time-reversal processing on the pre-received signal passing through the radome, a more accurate beam pointing can be achieved compared to traditional phased array phase shifting, and it also exhibits excellent broadband performance. This invention provides a novel approach to improving beam pointing without requiring optimization of the radome or knowledge of the radome's specific parameters, and is applicable to various radome designs.

Claims

1. A method for correcting the deflection of an antenna's radiation beam below the radome based on time reversal, characterized in that, The method comprises the following steps: S1. radiating a plane wave containing the same polarization component as the array antenna from a target direction to the array antenna covered by the radome; S2. recording the signal received by each element of the array antenna, and performing time reversal processing on the signal to obtain a time reversal signal; S3. re-inputting the time reversal signal into the corresponding element and simultaneously emitting to obtain a pointing accurate beam in the target direction; Step S1 is specifically as follows: S11. The whole system is placed in the spherical coordinate system for analysis, taking the center of the array antenna as the origin of the spherical coordinate system, and the direction of the array antenna as the Z axis of the spherical coordinate system. The plane wave is irradiated in the direction Wherein is the angle component of the plane wave relative to the array antenna in the spherical coordinate system, is the angle component of the plane wave relative to the array antenna in the spherical coordinate system, is the expression of the amplitude of the plane wave signal changing with time; S12. regarding the linear time-invariant radome as a linear time-invariant channel, and regarding the array antenna covered by the radome as a linear time-invariant system; Signal of electromagnetic wave emitted by target direction after passing through antenna cover in linear time-invariant system is written as: （1） wherein represents a matrix composed of signals received by each array element, is a signal received by each array element, n = 1, 2,..., N, is a transposed matrix of the matrix; represents a convolution operation of the two preceding equations, is an impulse response of the receiving pattern; Step S2 is specifically as follows: time-reversing the signal received by each element of the array antenna to obtain a time-reversed signal （2） Step S3 is specifically as follows: In the time domain, ignoring the propagation loss and time delay, the radiated electric field is written as: （6） wherein is the radiated electric field of the array antenna, is the impulse response of the transmit pattern, represents the relative position of the array element in the system, is the excitation of the i-th transient element; when is the time-reversed signal the pointing of the deflected beam is improved.

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