A Beam Nulling and Broadening Method for Conformal Array Antennas

Abstract

The present invention proposes a method for beam nulling and broadening of a conformal array antenna, which mainly solves the problem that the beamforming output performance severely degrades in the presence of interference angle errors in the prior art. The implementation scheme is as follows: construct a conformal array model; use the maximum likelihood method to perform original covariance estimation on the echo data received by the conformal array; expand the interference source position and calculate its broadening function; add the broadening function to the original covariance matrix to calculate the broadened covariance matrix; calculate the broadened adaptive weight vector from the broadened covariance matrix; perform beam scanning on the broadened adaptive weight vector and output the array pattern after nulling and broadening. The present invention can perform real-time matching with the weights of the beamformer when the interference exhibits non-stationarity, maintain strong robustness, improve the interference suppression performance, and can be used for electronic countermeasures.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and further relates to an antenna beam nulling and broadening method, which can be used for electronic countermeasures. Background Art

[0002] The confrontation between radar and interference is one of the eternal themes in the development of radar technology. Generally speaking, the incoming wave directions of signals and interference are different. By adaptively adjusting the array weighting coefficients to enhance the signal and suppress the interference, a beam can be formed in the signal azimuth, while a null can be formed at the interference location. Although anti-jamming algorithms have been studied for many years, in practical applications, the interference signals will show non-stationary changes both in the time domain and the space domain. In terms of the space domain, the non-stationarity of the interference signal is reflected in the change of the incident angle of the interference on the receiving antenna; in terms of the time domain, the non-stationarity of the interference signal is reflected in the characteristics that the parameters of the interference signal change with time or the interference signal exists intermittently in time.

[0003] In response to the non-stationarity caused by the change of the relative position between the interference source and the radar receiving platform, Zatman proposed a null broadening method based on covariance matrix tapering, which expounded the principle of null broadening from the perspective of space-time equivalence. The expansion of the interference source angle in the time domain is reflected as the diffusion of frequency in the frequency domain, and the degree of angle diffusion is proportional to the signal bandwidth. Therefore, the incident narrowband interference source can be transformed into a broadband interference source with a certain virtual frequency bandwidth to achieve the null broadening at the interference position. However, this method using space-time equivalence to achieve wide nulls can only be applied in linear arrays.

[0004] Xidian University proposed an adaptive beamforming method for array antennas based on diagonal loading in its patent document with the authorized announcement number: CN104360338B. First, it uses diagonal loading to correct the data covariance matrix, then estimates the steering vector of the target signal using the corrected data covariance matrix, and then solves the constrained optimization problem accordingly to achieve interference suppression. This method can improve the problems of inaccurate covariance matrix estimation and desired signal mismatch, and has robustness. However, since it can only handle the case where the support data set does not contain strong targets, it has a large data requirement, and the diagonal loading factor is obtained through experience, resulting in unstable interference suppression performance.

[0005] The method proposed by Li Rongfeng et al. in the literature "Research on the Method of Broadening the Interference Null of the Adaptive Antenna Pattern" published in Modern Radar starts from the statistical model, derives the null broadening technology when the interference follows a normal distribution, and proves that when the interference is uniformly distributed, its method is equivalent to the Zatman method. Using this method to broaden the null is based on the premise of accurately knowing the steering vector of the desired signal. When there is a pointing error in the direction of the desired signal, the performance drops severely, and the normal model it applies is only applicable to linear arrays.

[0006] In the article "Research on Null Widening Algorithm of Array Beams" published by Wu Sijun et al. in the Journal of Harbin Engineering University, an interference-independent adaptive null technology is derived by rotating the interference steering vector left and right and using numerical processing of the covariance matrix. In the case of a large number of interferences, due to a large number of nulls and dense nulls, the widening effect is limited. Moreover, when the number of array elements is very small, the width of the main lobe is very wide, and the main lobe may be deformed while forming nulls, affecting the angle expansion. That is, when the number of array elements is small, the effect of null widening is not obvious. After algorithm derivation, this method is equivalent to the Zatman method. Although it is simple to implement, it is only applicable to linear arrays.

[0007] In recent years, the research on conformal array antenna technology has become a hot issue of concern to scholars. Compared with conventional uniform linear arrays, conformal arrays have superior structural characteristics and good lateral performance. At the same time, they also have the advantages of saving the structural space of the carrier and reducing the radar cross section. They have been widely used in the aerospace field. Among them, cylindrical conformal array antennas are the most common form of conformal antennas. However, at present, most of the anti-interference methods for conformal array antennas are ordinary adaptive beamforming algorithms, such as LCMV. When affected by factors such as antenna rotation or disturbance of the interference source position, the interference often shows non-stationarity, and the weights of conventional adaptive algorithms cannot be matched with non-stationary interference in real time, resulting in a sharp decline in its interference suppression performance. Summary of the Invention

[0008] The purpose of the present invention is to propose a beam nulling and widening method for conformal array antennas in view of the above-mentioned deficiencies of the prior art, so as to reduce the decline in output performance when there is a pointing error in the direction of the interference signal, and be able to match the weights of the beamformer in real time when the interference shows non-stationarity, maintaining strong robustness, thereby improving the interference suppression performance.

[0009] To achieve the above purpose, the technical solution of the present invention includes the following:

[0010] (1) Determine the wavenumber vector k0, the signal arrival direction u0, the position vectors p of each array element, and the signal steering vector a(u0) according to the actually selected coordinate system and the desired signal model, and establish a conformal array model with this as prior information;

[0011] (2) According to the conformal array model, obtain the echo received data of the array, perform maximum likelihood estimation on the echo received data, and obtain the original covariance matrix R;

[0012] (3) Expand the interference source and determine the widening width:

[0013] (3a) Near each interference source, a number of virtual interference sources with equal power and uncorrelated envelopes are evenly distributed. According to the set expansion angle, calculate the angular interval of an actual single virtual interference source:

[0014]

[0015] Among them, u is the normalized direction vector corresponding to the direction of the incoming wave, θ, respectively represent the azimuth angle and elevation angle corresponding to the direction of the incoming signal, Δθ, respectively represent the expansion angles in the azimuth dimension and elevation dimension, [Δu] θ 、 respectively represent the angular intervals between the spatially discrete interference sources in the azimuth dimension and elevation dimension;

[0016] (3b) According to the angular interval and the number of virtual interference sources, obtain the final broadening function:

[0017] W θ =I·Δθ·[Δu] θ

[0018]

[0019] W θ 、 respectively represent the broadening functions in the azimuth dimension and elevation dimension, I represents the number of virtual interferences;

[0020] (4) Add I discrete virtual interference sources to the original covariance matrix R to obtain the broadened covariance matrix

[0021]

[0022] Among them, ⊙ represents the Hadamard product, T1 and T2 respectively represent the tapering matrices in the azimuth dimension and elevation dimension, and both of these tapering matrices are in the form of the sinc function. The elements in the m-th row and n-th column are respectively: p m and p n respectively represent the positions of the m-th array element and the n-th array element relative to the reference array element, and λ is the wavelength;

[0023] (5) According to the signal steering vector a(u0) and the broadened covariance matrix calculate the adaptive weight vector w after nulling and broadening:

[0024]

[0025] Among them, a(u0) is an N×1 signal steering vector, and N represents the number of array elements;

[0026] (6) Respectively perform beam scanning on the azimuth angle θ and elevation angle corresponding to the direction of the incoming signal, and obtain the spatio-temporal steering vector of the array according to the actually selected coordinate system and the desired signal model. As the spatial scanning angle changes, the spatio-temporal steering vector of the array Search for the interference angle that matches the adaptive weight vector w, and output the nulling and broadening pattern after interference suppression: where H represents the conjugate transpose,

[0027]

[0028] and is the pattern function.

[0029] The present invention has the following advantages compared with the prior art:

[0030] First, through the first-order approximation of the array steering vector, the present invention represents the covariance matrix taper as a function of the Euclidean distance between each array element and the pattern nulling and broadening coefficient, providing a basis for solving the broadening function expression.

[0031] Second, the present invention applies the nulling and broadening algorithm to the conformal antenna array to achieve pattern nulling and broadening, which can effectively combat non-stationary interference and improve the robustness of the anti-interference algorithm.

[0032] Third, the present invention realizes the suppression of non-stationary interference by adjusting the value of the adaptive weight vector, which is independent of the array configuration, so it is applicable to any array configuration, including linear arrays, planar arrays, and conformal arrays. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is the implementation flowchart of the present invention;

[0034] Figure 2 is the geometric model diagram of the conformal array constructed in the present invention;

[0035] Figure 3 is the comparison diagram of the patterns output before and after nulling and broadening of the present invention;

[0036] Figure 4 is Figure 3 the nulling and broadening pattern at different azimuths;

[0037] Figure 5 is the output signal-to-interference-plus-noise ratio loss diagram after interference suppression of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0038] The following further describes the embodiments and effects of the present invention in detail with reference to the accompanying drawings.

[0039] Refer to Figure 1 ​, the implementation steps of the present invention are as follows:

[0040] Step 1, construct a conformal array geometric model.

[0041] Refer to Figure 2 , the specific implementation of this step is as follows:

[0042] 1.1) Select an actual coordinate system such as Figure 2 (a), define the elevation angle as the angle between the array element position and the Z-axis, denoted as Define the azimuth angle as the angle between the projection of the array element position on the XOY plane and the X-axis, denoted as θ;

[0043] 1.2) Based on the actually selected coordinate system, use the position vectors of the azimuth angle and elevation angle defined in this coordinate system as the position vectors of each array element, and establish a conformal array geometric model in combination with the wave number vector k0, the signal incoming direction u0, the position vectors p of each array element, and the signal steering vector a(u0):

[0044] 1.2.1) Obtain the direction vector u0 corresponding to the signal incoming direction according to the azimuth angle and elevation angle:

[0045]

[0046] Among them, and θ0 respectively represent the elevation angle and azimuth angle of the incoming wave direction,

[0047] 1.2.2) Represent the narrowband model of the array of any useful signal as: s = a(u0)s(t),

[0048] where s(t) is the signal baseband envelope, a(u0) is the signal steering vector, and the steering vector corresponding to the nth unit in this steering vector is:

[0049]

[0050] In the formula, F n (·) represents the element pattern of the nth array element; F n (u0) represents the element pattern coefficient of the nth unit corresponding to the u0 direction; g(u n , u0) is the illumination function, which reflects the problem of array surface occlusion, and it indicates whether the array element can receive the signal; is the phase relationship corresponding to the electromagnetic wave propagation, u n is the normal direction vector of the nth array element, p n is the position coordinate vector of the nth array element, represents the wave number vector, represents the transpose;

[0051] In the finally obtained steering vector a(u0), the array element position vector information, the normal direction, and the illumination relationship are included. Based on this information, the basic conformal array model is obtained. Figure 2 As shown in (b).

[0052] Step 2: Calculate the covariance matrix R of the original received data.

[0053] According to the constructed conformal array model, in the actually obtained echo received data containing N array elements, there are desired target signals, several interference signals, and noise.

[0054] Set the positions of the m-th array element and the n-th array element relative to the reference array element as p m and p n , and the receiver noise power corresponding to the n-th array element is The power of the q-th interference signal is The elevation angle and azimuth angle of the interference position are respectively and θ q , and calculate its corresponding original covariance matrix R, where the element in the m-th row and the n-th column is expressed as:

[0055]

[0056] where m, n = 1, 2,..., N, q = 1, 2,..., Q, Q represents the number of interferences, and the normalized direction vector corresponding to the q-th interference is δ(n, m) is the two-dimensional Kronecker function, expressed as

[0057]

[0058] Step 3: Determine the broadening function.

[0059] Near each interference source, set I uniformly distributed, equal-power, and envelope-uncorrelated virtual interference sources, and set the azimuth angle and elevation angle corresponding to the incident wave direction as θ, to obtain the corresponding normalized direction vector u:

[0060]

[0061] Perform a first-order approximation derivative of the direction vector u in the azimuth and elevation directions respectively to obtain the angular interval Δu between the spatially discrete interference sources, which can be respectively expressed as:

[0062]

[0063] where [Δu] θ , respectively represent the angular intervals between spatially distributed interference sources discretely distributed in the azimuth dimension and the elevation dimension;

[0064] According to the angular interval Δu between spatially distributed interference sources discretely distributed, the final broadening function is obtained:

[0065] W θ = I·Δθ·[Δu] θ

[0066]

[0067] where W θ and respectively represent the broadening functions in the azimuth dimension and the elevation dimension; Δθ, respectively represent the expansion angles in the azimuth dimension and the elevation dimension.

[0068] Step 4, construct a taper matrix according to the broadened covariance matrix.

[0069] In the two directions of elevation and azimuth corresponding to the interference, I uniformly distributed virtual interference sources are respectively set, so that the positions of the interference sources are expanded in both the elevation and azimuth dimensions. At this time, the echo reception data containing N array elements includes the desired target signal, interference signal, several virtual interference sources, and noise;

[0070] Set the positions of the m-th array element and the n-th array element relative to the reference array element as p m and p n , the receiver noise power corresponding to the n-th array element is The power of the q-th interference signal is The elevation angle and azimuth angle of the interference position are respectively and θ q , the angular intervals between spatially distributed interference sources discretely distributed are respectively Δu θ and The broadening functions corresponding in the azimuth and elevation directions are respectively W θ and Calculate its corresponding broadened covariance matrix The element in the m-th row and the n-th column is expressed as:

[0071]

[0072] where, m,n = 1,2,...,N, q = 1,2,...,Q, Q represents the number of interferences, λ represents the wavelength, and the normalized direction vector corresponding to the q-th interference is δ(n,m) is a two-dimensional Kronecker function, which can be expressed as

[0073] The covariance matrix after zeroing and broadening Compared with the covariance matrix R of the original interference sources, it has an added sinc function term. Since this sinc function is independent of the interference source angles and only depends on the signal wavelength λ and the relative positions of the array elements. Therefore, a known null width and a fixed number of virtual interference sources can determine a unique sinc function. Thus, the element in the m-th row and n-th column of the covariance matrix after zeroing and broadening is further expressed as:

[0074]

[0075] where, ⊙ represents the Hadamard product, the taper matrices in the azimuth dimension and elevation dimension are T1 and T2 respectively, and the elements in the m-th row and n-th column of this T1 and T2 are respectively:

[0076]

[0077] Step 5, construct the zeroing and broadening adaptive weight vector:

[0078] According to the desired signal steering vector a(u0) and the broadened covariance matrix obtain the zeroing and broadening adaptive weight vector w:

[0079]

[0080] where, a(u0) is an N×1 signal steering vector, and N represents the number of array elements.

[0081] Step 6, output the broadened radiation pattern.

[0082] Perform beam scanning on the azimuth angle θ and elevation angle corresponding to the incoming wave direction. From the selected coordinate system and the desired signal model, obtain the spatio-temporal steering vector of the array changing with the spatial scanning angle, the spatio-temporal steering vector of the array search for the interference matching the adaptive weight vector w, and output the zeroing and broadening radiation pattern after interference suppression:

[0083]

[0084] where, H represents the conjugate transpose, is the radiation pattern function.

[0085] The following further illustrates the effect of the present invention in combination with simulation experiments:

[0086] 1. Simulation experiment conditions:

[0087] The hardware platform for the simulation experiment of the present invention is: the processor is an Intel(R) Core(TM) i7-10700 CPU with a main frequency of 2.90 GHz and 16 GB of memory.

[0088] The software platform for the simulation experiment of the present invention is: Windows 10 operating system and MATLAB R2020b.

[0089] The parameter settings for the simulation experiment of the present invention are as follows:

[0090] The entire conformal array antenna surface of the radar consists of 106 array elements, and the specific array layout is as shown in Figure 2 (b).

[0091] Set the signal center frequency to f0 = 1.3 GHz, the radar operating wavelength to λ = 0.23 m, the signal-to-noise ratio to SNR = -10, and the elevation angle corresponding to the signal incoming direction The azimuth angle θ0 = 0°. There is 1 interference, the interference-to-noise ratio is JNR = 60, and the interference position corresponds to the elevation angle The azimuth angle θ j = 40°, and the broadening angles Δθ and are 1° respectively.

[0092] 2. Simulation content and result analysis:

[0093] Simulation 1: Using the present invention to suppress the interference of the signal echo generated under the above simulation conditions, the output pattern before and after nulling and broadening is obtained, as shown in Figure 3 shown. The Figure 3 nulling and broadening pattern in different azimuths is as shown in Figure 4 shown, where:

[0094] Figure 3 (a) is the result of the normalized pattern output before nulling and broadening. The X-axis represents the azimuth angle, the Y-axis represents the elevation angle, and the Z-axis is the normalized output power;

[0095] Figure 3 (b) is the normalized pattern output after anti-interference using the present invention. The X-axis represents the azimuth angle, the Y-axis represents the elevation angle, and the Z-axis is the normalized output power;

[0096] Figure 4 (a) is the broadening result of the pattern after nulling and broadening in the azimuth dimension. The X-axis represents the azimuth angle, and the Y-axis is the normalized output power;

[0097] Figure 4 (b) is the broadening result of the pattern after nulling and broadening in the elevation dimension. The X-axis represents the azimuth angle, and the Y-axis is the normalized output power.

[0098] Comparison Figure 3(a) and Figure 3 (b). Before zeroing broadening, the null formed by anti-interference is very narrow, and its anti-interference performance is vulnerable to the influence of interference pointing error. After zeroing broadening, the null at the position corresponding to the interference in the radiation pattern is significantly broadened. It can be clearly seen from Figure 4 (a) and Figure 4 (b) the broadening effects in the azimuth dimension and elevation dimension after zeroing broadening, indicating that the present invention can reduce the degradation of the output performance when there is a pointing error in the direction of the interference signal, maintain strong robustness when the interference is non-stationary, and improve the anti-interference robustness.

[0099] Simulation 2: 100 Monte Carlo experiments were carried out on the output results after interference suppression using the present invention, and the output signal-to-interference-plus-noise ratio (SINR) loss curve was obtained. The results are as shown in Figure 5 where the X-axis represents the output SINR and the Y-axis represents the output SINR loss.

[0100] From Figure 5 the simulation results, it can be seen that under the condition of zeroing broadening, the output SINR loss of the present invention remains at 1 - 2 dB, indicating that the present invention can effectively counter non-stationary interference pointing error and improve the anti-interference robustness on the premise of ensuring the output performance.

[0101] The above simulation results verify the correctness, effectiveness and reliability of the present invention. Under the condition of ensuring the output performance, it can broaden the null and improve the anti-interference robustness of the conformal array.

Claims

1. A beam nulling and broadening method for a conformal array antenna, characterized in that, Including: (1) Determine the wavenumber vector k0, the signal incoming direction u0, the position vectors p of each array element, and the signal steering vector a(u0) according to the actually selected coordinate system and the desired signal model, and use these as prior information to establish a conformal array model; (2) According to the conformal array model, obtain the echo received data of the array, perform maximum likelihood estimation on the echo received data, and obtain the original covariance matrix R; (3) Expand the interference sources and determine the broadening width: (3a) Near each interference source, evenly distribute a number of virtual interference sources with equal power and uncorrelated envelopes, and calculate the angular interval of an actual single virtual interference source according to the set expansion angle; where, u is the normalized direction vector corresponding to the incident wave direction, θ, respectively represent the azimuth angle and elevation angle corresponding to the incident wave direction, Δθ, respectively represent the extended angles in the azimuth dimension and elevation dimension, [Δu] θ and respectively represent the angular intervals between spatially distributed interference sources discretely distributed in the azimuth dimension and elevation dimension; (3b) Obtain the final broadening function according to the angular interval and the number of virtual interference sources; Among them, W θ and respectively represent the broadening functions in the azimuth dimension and the elevation dimension; I represents the number of virtual interferences; (4) Add I discrete virtual interference sources to the original covariance matrix R to obtain the broadened covariance matrix R: where, ⊙ represents the Hadamard product, T1 and T2 respectively represent the taper matrices in the azimuth dimension and the elevation dimension, and both of these taper matrices are expressed in the form of the sinc function. The elements in the m-th row and the n-th column are respectively: p m and p n respectively represent the positions of the m-th array element and the n-th array element relative to the reference array element, and λ is the wavelength; (5) According to the signal steering vector a(u0) and the broadened covariance matrix Calculate the adaptive weight vector w after null broadening: where a(u0) is an N×1 signal steering vector, and N represents the number of array elements; (6) Respectively perform beam scanning on the azimuth angle θ and elevation angle corresponding to the direction of arrival of the signal. According to the actually selected coordinate system and the desired signal model, obtain the spatio-temporal steering vector of the array. As it changes with the spatial scanning angle, the spatio-temporal steering vector of the array Search for the interference angle that matches the adaptive weight vector w, and output the nulling and broadening direction pattern after interference suppression: ​ where H represents the conjugate transpose, is the pattern function.

2. The method according to claim 1, characterized in that, (1) The establishment of the conformal array model in (1) is realized as follows: (1a) Define the pitch angle as the angle between the element position and the Z-axis, denoted as Define the azimuth angle as the angle between the projection of the element position on the XOY plane and the X-axis, denoted as θ; (1b) Calculate the inner product of the expected signal arrival direction vector u0 and different normal direction vectors u n of the vectors, Unit radiation pattern coefficient F n (u0): Among them, is the included angle between the incoming wave direction vector u0 of the desired signal and different normal direction vectors u n and (1c) The inner product of the desired signal arrival direction vector u0 and different normal direction vectors u n yields the illumination function g(u n , u0): (1d) Transpose the wave number vector k0 and the position coordinate vector p of the n-th array element n Perform an exponential operation to obtain an electromagnetic wave propagation phase vector with a dimension of N×1 Calculate the signal steering vector [a(u0)] of the n-th array element n : (1e) Calculate the signal steering vector of the nth array element, obtain the signal steering vectors of all array elements with a dimension of N×1, and complete the establishment of the conformal array model.

3. The method according to claim 1, wherein (2) The calculation of the original covariance matrix R in (2) is realized as follows: (2a) Obtain the training sample data X with a dimension of N×L from the received echo data, where N is the number of array elements included in the conformal array, and L is the selected spatial snapshot number; (2b) According to the training sample data X, calculate the original covariance matrix R with a dimension of N×N through maximum likelihood estimation: where H represents conjugate transpose.

4. The method according to claim 1, wherein The spatio-temporal steering vector described in (6) is obtained according to the following steps: (6a) Calculate the incoming wave direction vector of the omnidirectional scan and the vector inner product of different normal direction vectors u n of Element radiation pattern coefficient : Among them, is the direction vector of the incoming wave for omnidirectional scanning and the included angle with different normal direction vectors u n is (6b) The inner product of the omnidirectionally scanned incoming wave direction vector and different normal direction vectors u n gives the illumination function ： (6c) Calculate the scanning beam vector k through the incoming direction vector of the omnidirectional scan; (6d) Transpose the scanning wave number vector k and the position coordinate vector p of the nth array element n Perform an exponential operation to obtain a large dimension The electromagnetic wave propagation phase vector with a size of N×1 Calculate the spatio-temporal steering vector of the nth array element : (6e) Calculate the spatio-temporal steering vector of each array element to obtain the spatio-temporal steering vectors of all array elements with a dimension size of N×1

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