A time-varying pattern design method and device of a broadband digital array radar

Abstract

This invention provides a method and apparatus for designing time-varying radiation patterns for a broadband digital array radar, relating to the field of radar processing technology. It includes: using a genetic algorithm to determine the airspace target waveform based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix; the airspace target waveform being a waveform with slowly varying rising and falling edges; determining the sub-objective function of the airspace target waveform based on the airspace target waveform, multiple main lobe pointing directions, the signal phase matrix, the expected power spectrum of each main lobe pointing direction, and the signal power spectrum of each main lobe pointing direction; determining the synthesized objective function and its gradient with respect to the signal phase matrix; and performing gradient descent search using the conjugate gradient method based on the gradient, correction coefficients, and an iteration termination threshold to determine the final waveform matrix and the final time-varying radiation pattern. This effectively reduces the probability of radar signals being intercepted by local forces, improves the radar signal's self-interference capability, and achieves modulation of the temporal distribution of airspace electromagnetic energy.

Description

Technical Field

[0001] This invention relates to the field of radar processing technology, and in particular to a method and apparatus for designing time-varying radiation patterns for a broadband digital array radar. Background Technology

[0002] In terms of bandwidth, wideband signals have emerged because the complex narrowband signals in the electromagnetic environment can no longer meet battlefield requirements. Wideband signals are transmitted by wideband radar, which has better range resolution and can obtain more target information, facilitating target imaging or identification. Regarding array structure, digital array radar has waveform diversity characteristics. Due to the diversity of its transmission patterns, the operating modes of digital array radar systems are more flexible. Digital array radar can implement simultaneous multi-beam technology, allocating the required power to targets pointed at by different beams to improve the resource utilization of the radar system; it can also transmit different signals to different targets, giving different beams different functions. In terms of anti-jamming, wideband digital array radar can flexibly design the time-frequency domain characteristics of the signal at the main beam. For example, it can distribute the signal in a fixed frequency band to reduce the power spectral density and thus reduce the probability of interception, or control the degree of variation in the rising and falling edges of the time domain. In electronic reconnaissance, jammers can detect enemy radar signals by receiving the rising and falling edge waveforms of signals through antennas.

[0003] Currently, the design of time-varying radiation patterns with rising and falling edges typically employs broadband waveform optimization methods for digital radar based on pattern matching or spatial power spectrum matching. However, these methods result in radar signals with rapidly changing rising and falling edges, making the radar signals easily intercepted and increasing the probability of enemy interception, thus reducing the radar signal's inherent anti-jamming capability. Furthermore, waveforms with rapidly changing rising and falling edges cannot modulate the temporal distribution of spatial electromagnetic energy. Summary of the Invention

[0004] The purpose of this invention is to provide a method and apparatus for designing time-varying radiation patterns for a broadband digital array radar, which solves the problems of low anti-interference capability of radar signals and the inability of the designed waveform to modulate the temporal distribution of electromagnetic energy in the spatial domain.

[0005] To address the aforementioned technical problems, the embodiments of the present invention provide the following technical solutions:

[0006] The first aspect of this invention provides a time-varying radiation pattern design method for a broadband digital array radar, the time-varying radiation pattern design method comprising:

[0007] Using a genetic algorithm, the spatial target waveform is determined based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix. The spatial target waveform is a waveform with slowly varying rising and falling edges, and the autocorrelation function is the autocorrelation function of the spatial target waveform after removing the main lobe.

[0008] Based on the spatial target waveform, multiple main lobe pointing, signal phase matrix, expected power spectrum of each main lobe pointing, and signal power spectrum of each main lobe pointing, determine the sub-objective function of the spatial target waveform;

[0009] Based on the sub-objective function, the scaling coefficients of multiple sub-objective functions, the time-varying radiation patterns pointed to by each main lobe, and the desired radiation patterns pointed to by each main lobe, the comprehensive objective function and the gradient of the comprehensive objective function with respect to the signal phase matrix are determined.

[0010] Based on the gradient, correction coefficient, and iteration termination threshold, gradient descent search is performed using the conjugate gradient method to determine the final waveform matrix and the final time-varying orientation pattern.

[0011] A second aspect of the present invention provides a time-varying radiation pattern design apparatus for a broadband digital array radar, the time-varying radiation pattern design apparatus comprising:

[0012] The first determination module is used to determine the spatial target waveform using a genetic algorithm based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix. The spatial target waveform is a waveform with slowly varying rising and falling edges, and the autocorrelation function is the autocorrelation function of the spatial target waveform after removing the main lobe.

[0013] The second determining module is used to determine the sub-objective function of the spatial target waveform based on the spatial target waveform, multiple main lobe pointing, signal phase matrix, expected power spectrum of each main lobe pointing and signal power spectrum of each main lobe pointing;

[0014] The third determining module is used to determine the comprehensive objective function and the gradient of the comprehensive objective function with respect to the signal phase matrix based on the sub-objective function, the scaling coefficients of multiple sub-objective functions, the time-varying radiation pattern pointed to by each main lobe, and the desired radiation pattern pointed to by each main lobe.

[0015] The search module is used to perform gradient descent search using the conjugate gradient method based on the gradient, correction coefficient, and iteration termination threshold to determine the final waveform matrix and the final time-varying orientation pattern.

[0016] Compared to existing technologies, the broadband digital array radar time-varying pattern design method and apparatus provided by this invention utilizes a genetic algorithm to determine the spatial target waveform based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix. The spatial target waveform is a waveform with slowly varying rising and falling edges, and the autocorrelation function is the autocorrelation function of the spatial target waveform after removing the main lobes. Based on the spatial target waveform, multiple main lobe pointing directions, the signal phase matrix, the expected power spectrum of each main lobe pointing direction, and the signal power spectrum of each main lobe pointing direction, a sub-objective function of the spatial target waveform is determined. Based on the sub-objective function, the scaling factors of multiple sub-objective functions, the time-varying pattern of each main lobe pointing direction, and the expected pattern of each main lobe pointing direction, a comprehensive objective function and its gradient with respect to the signal phase matrix are determined. Based on the gradient, correction coefficients, and iteration termination threshold, a gradient descent search is performed using the conjugate gradient method to determine the final waveform matrix and the final time-varying pattern. Thus, based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix, the determined airspace target waveform has a slowly varying rising and falling edge, which can effectively reduce the probability of radar signal being intercepted by the enemy and improve the anti-interference capability of the signal itself. Based on the gradient, correction coefficient, and iteration termination threshold, the conjugate gradient method is used to perform gradient descent search to determine the final time-varying radiation pattern, so that the airspace target waveform forms a time-varying radiation pattern in the airspace. During a certain period of time, the electromagnetic energy in a certain direction in the airspace slowly and continuously rises (falls), but the comprehensive radiation pattern is a process of energy integration in the time dimension. The total distribution of airspace energy remains unchanged over the overall time, thus realizing the modulation of the distribution of airspace electromagnetic energy in time. Attached Figure Description

[0017] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent upon reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of the invention are illustrated by way of example and not limitation, with the same or corresponding reference numerals denoteing the same or corresponding parts, wherein:

[0018] Figure 1 A flowchart illustrating the time-varying pattern design method for a broadband digital array radar is shown schematically.

[0019] Figure 2 A schematic diagram illustrating the envelope shape of a spatial target waveform and its autocorrelation function is shown.

[0020] Figure 3 A schematic diagram of the convergence curve obtained using the conjugate gradient method is shown.

[0021] Figure 4 A schematic diagram illustrating the comparison between the actual time-varying radiation pattern and the ideal radiation pattern after convergence is shown.

[0022] Figure 5A schematic diagram illustrating the comparison between the power spectrum at the points of convergence of the actual beams 1 and 2 and the power spectrum at the points of convergence of the ideal beams 1 and 2 is shown.

[0023] Figure 6 A schematic diagram illustrating the comparison between the envelope at the direction of beam 3 and the ideal envelope is shown.

[0024] Figure 7 A schematic diagram illustrating the comparison between the signal autocorrelation and the ideal autocorrelation at the direction of beam 3 is shown.

[0025] Figure 8 A schematic diagram of a time-varying pattern design device for a broadband digital array radar is shown. Detailed Implementation

[0026] Exemplary embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0027] It should be noted that, unless otherwise stated, the technical or scientific terms used in this invention should have the ordinary meaning as understood by those skilled in the art.

[0028] The methods described in the embodiments of the present invention will be explained in detail below.

[0029] Figure 1 The flowchart illustrating the time-varying radiation pattern design method for broadband digital array radar according to an embodiment of the present invention is shown in the figure. See also... Figure 1 As shown, this time-varying radiation pattern design method may include:

[0030] S101. Using a genetic algorithm, determine the target waveform in the spatial domain based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix.

[0031] The spatial target waveform is a waveform with gradually varying rising and falling edges, and the autocorrelation function is the autocorrelation function of the spatial target waveform after removing the main lobe.

[0032] The spatial target waveform has slowly varying rise and fall edges and good correlation characteristics. The spatial target waveform is the composite waveform of the array transmitted signal in the spatial domain, therefore no constant modulus constraint is required. The rate of change of the rise and fall edges of the envelope of the spatial target waveform is determined by the set amplitude difference tolerance ε.

[0033] Specifically, using a genetic algorithm, the spatial target waveform is determined based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix, including:

[0034] Step A1: Construct an optimization model based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix.

[0035] Specifically, based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix, an optimization model is constructed, including:

[0036] Based on the autocorrelation function, the magnitude difference tolerance, and the magnitude difference matrix, an optimization model is constructed using the following first formula:

[0037]

[0038] Where x is the target waveform in the spatial domain, Let ε be the autocorrelation function, i.e., the autocorrelation function of the spatial target waveform x after removing the main lobe, A be the amplitude difference matrix, and ε be the amplitude difference tolerance.

[0039] Specifically, The objective function is the highest sidelobe of the autocorrelation function of the spatially synthesized signal, constraining the amplitude difference st.||Ax|| between any two adjacent sampling points. ∞ Not greater than the amplitude difference tolerance ε.

[0040] Step A2: Use a genetic algorithm to solve the optimization model and obtain the target waveform in the spatial domain.

[0041] Figure 2 The diagram schematically illustrates the envelope shape of a spatial target waveform and its autocorrelation function. The upper diagram shows the envelope shape of the spatial target waveform, and the lower diagram shows the autocorrelation function of the spatial target waveform. See [link / reference]. Figure 2 As shown, the signal envelope and its autocorrelation function are given when ε = 0.1. The spatial target waveform has slowly varying rising and falling edges, and also has low autocorrelation sidelobes, thus exhibiting good anti-interference and pulse compression characteristics.

[0042] S102. Based on the spatial target waveform, multiple main lobe pointing directions, signal phase matrix, expected power spectrum of each main lobe pointing direction, and signal power spectrum of each main lobe pointing direction, determine the sub-objective function of the spatial target waveform.

[0043] Among them, multiple main lobe pointings include multiple power spectrum main lobe pointings and multiple time domain main lobe pointings, and sub-objective functions include power spectrum similarity sub-objective functions and time domain similarity sub-objective functions.

[0044] Before determining the sub-objective function of the spatial target waveform based on the spatial target waveform, multiple main lobe directions, signal phase matrix, expected power spectrum of each main lobe direction, and signal power spectrum of each main lobe direction, it is also necessary to determine multiple main lobe directions, i.e. multiple spatial target azimuths, based on prior knowledge, and determine the expected spatial waveform attributes of each spatial target azimuth according to requirements.

[0045] Specifically, based on the spatial target waveform, multiple main lobe pointing directions, signal phase matrix, expected power spectrum of each main lobe pointing direction, and signal power spectrum of each main lobe pointing direction, the sub-objective function of the spatial target waveform is determined, including:

[0046] Step B1: Determine the power spectrum similarity sub-objective function based on the main lobe pointing of multiple power spectra, the signal phase matrix, the expected power spectrum of each main lobe pointing, and the actual spatial synthesized power spectrum of each main lobe pointing.

[0047] Specifically, based on multiple main lobe pointing directions, the signal phase matrix, the expected power spectrum of each main lobe pointing direction, and the actual spatial synthesized power spectrum of each main lobe pointing direction, a power spectrum similarity sub-objective function is determined, including:

[0048] Based on the main lobe pointing of multiple power spectra, the signal phase matrix, the expected power spectrum of each main lobe pointing, and the actual spatial synthesized power spectrum of each main lobe pointing, the power spectrum similarity sub-objective function is determined using the following second formula:

[0049]

[0050] Where h1(θ) i ,Φ) is the power spectrum similarity sub-objective function, θ i Let Φ be the main lobe direction of multiple power spectra, Φ be the signal phase matrix, N be the number of sub-band frequency points of the broadband signal, and p be the main lobe direction of multiple power spectra. n (θ i ,Φ) represents the actual spatial composite power spectrum pointed to by the main lobe of each power spectrum. Let be the expected power spectrum pointing to the main lobe of each power spectrum, α be the first scale factor, and i be the main lobe pointing to the i-th power spectrum. This is the transpose of the steering vector pointing to the main lobe of each power spectrum at the nth frequency point. This is the transform vector corresponding to the nth frequency point in the N-point discrete Fourier transform.

[0051] Step B2: Determine the time-domain similarity sub-objective function based on the spatial target waveform, the main lobe pointing directions of multiple time domains, the signal phase matrix, the signal power spectrum of each main lobe pointing direction, and the fast Fourier transform matrix.

[0052] Based on the spatial target waveform, the main lobe pointing directions in multiple time domains, the signal phase matrix, the signal power spectrum of each main lobe pointing direction, and the fast Fourier transform matrix, the time-domain similarity sub-objective function is determined, including:

[0053] Based on the spatial target waveform, the main lobe pointing directions in multiple time domains, the signal phase matrix, the signal power spectrum of each main lobe pointing direction, and the fast Fourier transform matrix, the time-domain similarity sub-objective function is determined using the following third formula:

[0054]

[0055] Where h2(θ) m ,Φ) is the temporal similarity sub-objective function, θ m The main lobe points to multiple time domains, Φ is the signal phase matrix, and v(θ) m Φ) represents the signal power spectrum pointing to the main lobe in each time domain, F is the Fast Fourier Transform matrix, x is the target waveform in the spatial domain, i.e., the ideal waveform in the spatial domain, β is the second scale factor, and m is the main lobe pointing in the m-th time domain. This is the transpose of the steering vector pointing to the main lobe in the time domain at the (N / 2)th frequency point. Let be the transform vector corresponding to the (N / 2)th frequency point in the N-point discrete Fourier transform. Let exp(jΦ) be the transform vector corresponding to the N / 2-1th frequency point in the N-point discrete Fourier transform, and let exp(jΦ) be the transmitted waveform matrix.

[0056] in, F is an N*N dimensional fast Fourier transform matrix.

[0057] Table 1 shows the expected attributes of the spatial target waveform pointed to by each main lobe. The expected attributes include the number of array elements, carrier frequency, bandwidth, number of snapshots, beam pointing / constraint. Three beams are given, namely beam 1, beam 2 and beam 3. The pointing of the three beams is different. See Table 1 for details.

[0058] Table 1 shows the desired properties of the spatial target waveform pointed to by each main lobe.

[0059]

[0060]

[0061] S103. Based on the sub-objective functions, the scaling coefficients of multiple sub-objective functions, the time-varying radiation patterns pointed to by each main lobe, and the desired radiation patterns pointed to by each main lobe, determine the comprehensive objective function and the gradient of the comprehensive objective function with respect to the signal phase matrix.

[0062] The scaling factors of the multiple sub-objective functions include the first scaling factor, the second scaling factor, and the third scaling factor.

[0063] Specifically, based on the sub-objective function, the scaling factors of multiple sub-objective functions, the time-varying radiation patterns pointed to by each main lobe, and the desired radiation patterns pointed to by each main lobe, the comprehensive objective function and its gradient with respect to the signal phase matrix are determined, including:

[0064] Step C1: Construct a comprehensive objective function based on the power spectrum similarity sub-objective function, the time domain similarity sub-objective function, the first proportional coefficient, the second proportional coefficient, the third proportional coefficient, the time-varying radiation pattern pointed to by each main lobe, and the expected radiation pattern pointed to by each main lobe.

[0065] Specifically, based on the power spectrum similarity sub-objective function, the time-domain similarity sub-objective function, the first scaling factor, the second scaling factor, the third scaling factor, the time-varying radiation patterns of each main lobe, and the desired radiation patterns of each main lobe, the comprehensive objective function is constructed using the following formula:

[0066]

[0067] Where λ1 is the first scaling factor, λ2 is the second scaling factor, λ3 is the third scaling factor, K is the number of spatial grid points, k is the number of the kth spatial grid points, and θ k Let w be the angle of the k-th spatial grid cell. k Let be the scaling factor for the angle of the k-th spatial grid, Φ be the signal phase matrix, f1 be the pattern matching objective function, f2 be the power spectrum matching objective function, f3 be the time-domain matching objective function, I be the number of main lobes in the power spectrum fitting of the main lobe synthesized signal, i be the main lobe pointing direction of the i-th power spectrum, and P be the signal phase matrix. D (θ k ,Φ) represents the time-varying radiation pattern pointing to each main lobe, P d (θ k () represents the desired radiation pattern pointing to each main lobe, and α is the first scale factor. For θ i The scaling factor at the nth frequency point in the directional grid, h1(θ) i ,Φ) is the power spectrum similarity sub-objective function, h2(θ) m ,Φ) is the temporal similarity sub-objective function. For θ m The scaling factor at the nth frequency point of the directional grid, M is the number of main lobes in the time-domain fitting of the main lobe synthesized signal, and θ m Let be the direction of the main lobe fitted in the m-th time domain. θ at the nth frequency point k The transpose of the directional guide vector, f n =[1,e -j2πn / N ,…,e -j2πn(N-1) / N ] T This is the Fourier transform vector.

[0068] Step C2: Determine the first optimal scaling factor and the second optimal scaling factor based on the first scaling factor, the second scaling factor, the third scaling factor, the desired radiation pattern pointed to by each main lobe, and the time-varying radiation pattern pointed to by each main lobe.

[0069] Wherein, the first optimal scaling factor is the optimal scaling factor corresponding to the first scale factor in the power spectrum similarity sub-objective function, and the second optimal scaling factor is the optimal scaling factor corresponding to the second scale factor in the time domain similarity sub-objective function.

[0070] The expressions for the first and second optimal scaling factors are:

[0071]

[0072]

[0073] Where, α opt β is the first optimal scaling factor. opt λ1 is the second optimal scaling factor, λ2 is the first scaling coefficient, σ is the second scaling coefficient, and x is the fourth intermediate variable. H F is the inverse conjugate of the spatial target waveform, i.e., the inverse conjugate of the spatial ideal waveform. H It is the inverse conjugate of the Fast Fourier Transform matrix.

[0074] Step C3: Determine the gradient of the integrated objective function with respect to the signal phase matrix based on the integrated objective function, the first optimal scaling factor, and the second optimal scaling factor.

[0075] Specifically, based on the comprehensive objective function, the first optimal scaling factor, and the second optimal scaling factor, the gradient of the comprehensive objective function with respect to the signal phase matrix is ​​determined, including:

[0076] Based on the comprehensive objective function, the first optimal scaling factor, and the second optimal scaling factor, the gradient of the comprehensive objective function with respect to the signal phase matrix is ​​determined using the following fourth formula:

[0077]

[0078] in, Let λ1 be the gradient, λ1 be the first scaling factor, K be the number of spatial grid points, k be the number of the kth spatial grid points, and θ be the gradient. k Let w be the angle of the k-th spatial grid cell. k Φ is the scaling factor for the angle of the k-th spatial grid, Φ is the signal phase matrix, and f k (Φ) is the first intermediate variable, λ2 is the second proportionality coefficient, I is the number of main lobes required for fitting the power spectrum of the synthesized main lobe signal, and θ i Let N be the direction of the main lobe of the i-th power spectrum, and N be the number of sub-band frequency points of the broadband signal. For θ i The scaling factor h at the nth frequency point of the directional grid in(Φ) is the second intermediate variable, λ3 is the third proportionality coefficient, M is the number of main lobes in the time-domain fitting of the main lobe synthesis signal, and θ m The direction of the main lobe is the fit of the m-th time-domain region. For θ m The scaling factor at the nth frequency point of the directional grid, g(Φ) is the third intermediate variable, and P D (θ k ,Φ) represents the time-varying radiation pattern pointing to each main lobe, α opt P is the first optimal scaling factor. d (θ k ) represents the desired radiation pattern pointing to each main lobe, p n (θ i ,Φ) is θ i The actual spatial composite power spectrum of the direction, For θ i The expected power spectrum in the direction, v(θ) m ,Φ) is θ m The signal power spectrum in the direction, β opt Let x be the second optimal scaling factor, F be the fast Fourier transform matrix, and x be the second optimal scaling factor. H It is the inverse conjugate of the target waveform in the spatial domain, that is, the inverse conjugate of the ideal waveform in the spatial domain.

[0079] S104. Based on the gradient, correction coefficient, and iteration termination threshold, perform gradient descent search using the conjugate gradient method to determine the final waveform matrix and the final time-varying orientation pattern.

[0080] Specifically, based on the gradient, correction coefficients, and iteration termination threshold, gradient descent search is performed using the conjugate gradient method to determine the final waveform matrix and the final time-varying orientation pattern, including:

[0081] Step D1: Based on the gradient, correction coefficients, and iteration termination threshold, perform gradient descent search using the conjugate gradient method to determine the final gradient of the synthesized objective function with respect to the signal phase matrix.

[0082] The search direction can be determined by the conjugate gradient method, the step size can be determined by a one-dimensional linear search, and the search should be stopped only when the objective function converges during the gradient descent search operation.

[0083] Specifically, based on the gradient, correction coefficients, and iteration termination threshold, gradient descent is performed using the conjugate gradient method to determine the final gradient of the synthesized objective function with respect to the signal phase matrix, including:

[0084] Step D11: Initialize the waveform phase matrix Φ (0) Calculate the initial gradient based on the gradient expression in step C3. Set the initial search direction Determine the iteration termination threshold ε0, and set the iteration count s = 0.

[0085] The waveform phase matrix Φ can be initialized using a random generation method. (0) D (0) This sets the initial search direction.

[0086] Step D12: Determine the step size δ using a one-dimensional linear search. (s) And update the signal phase matrix Φ for the current round. (s+1) =Φ (s) +δ (s) D (s) .

[0087] Φ (s) D is the signal phase matrix from the previous round. (s) This refers to the search direction from the previous round.

[0088] When s is 0, it represents the signal phase matrix Φ in the first iteration. (1) =Φ (0) +δ (0) D (0) When s is 1, it corresponds to the signal phase matrix Φ in the second iteration. (2) =Φ (1) +δ (1) D (1) .

[0089] Step D13: Calculate the gradient of the integrated objective function with respect to the signal phase matrix in the current round. And calculate the correction factor for the current round. Set the search direction for the current round to

[0090] Let λ be the gradient of the previous round. (s) This is the correction coefficient from the previous round. When s is 0, it is the correction coefficient for the first round. The gradient for the first round; the correction coefficient for the second round when s is 1. This is the gradient for the second round. When s is 0, the search direction for the first round is... λ (0) The initial correction coefficient is ; when s is 1, the search direction in the second round is .

[0091] Step D14: Determine the termination condition If the condition is true, determine the final gradient and terminate; otherwise, let s = s + 1 and jump to step D12 until the termination condition is met.

[0092] Step D2: Determine the final waveform matrix and the final time-varying orientation pattern based on the final gradient.

[0093] final gradient Given a corresponding final signal phase matrix, and based on the final signal phase matrix Φ′ corresponding to the determined final gradient, the final waveform matrix is ​​determined as X=e jΦ′ The final time-varying pattern is It can also be determined that the actual spatial composite power spectrum pointing to the main lobe of each power spectrum is as follows:

[0094] This invention first optimizes the desired synthesized waveform in the spatial domain, ensuring it possesses gradually varying rise and fall edges and good autocorrelation characteristics. Then, it optimizes the digital array's transmitted waveform to simultaneously match the spatial radiation pattern and spatial power spectrum, and synthesizes the waveform generated in the previous step in the desired direction. The essence of the gradually varying rise and fall edge waveform is the formation of a time-varying radiation pattern in the spatial domain. Over a certain period, the electromagnetic energy at a target location in the spatial domain slowly and continuously rises (falls). However, the synthesized radiation pattern is a process of energy integration over time; the total spatial energy distribution remains constant over the overall time period. Therefore, the temporal distribution of electromagnetic energy is modulated. The electromagnetic energy distribution pattern is dynamically planned from three aspects: spatial domain, frequency domain, and time domain.

[0095] Figure 3 A schematic diagram illustrating the convergence curve obtained using the conjugate gradient method is shown below. Figure 3 As shown, the convergence curve converged within 60 iterations, proving that the invention has a fast convergence speed.

[0096] Figure 4 The diagram illustrates the comparison between the converged time-varying radiation pattern and the ideal radiation pattern. The dashed line represents the desired radiation pattern, i.e., the ideal radiation pattern. The actual design of the radiation pattern is the time-varying radiation pattern, and the generated time-varying radiation pattern achieves a good match with the ideal radiation pattern.

[0097] Figure 5 The diagram schematically illustrates the comparison between the power spectrum of the actual beams 1 and 2 after convergence and the power spectrum of the ideal beams 1 and 2. The upper diagram shows the power spectrum comparison of the signal in the -40° direction, and the lower diagram shows the power spectrum comparison of the signal in the 0° direction. The designed power spectrum is the power spectrum of the actual beams 1 and 2, and the desired power spectrum is the power spectrum of the ideal beams 1 and 2. The power spectrum designed in this invention achieves good matching of the ideal spatial domain.

[0098] Figure 6A schematic diagram illustrating the comparison between the envelope at the direction of beam 3 and the ideal envelope is shown. The blue line represents the autocorrelation of the actual synthesized signal, and the red line represents the ideal autocorrelation. The generated spatial target waveform achieves a good fit to the ideal envelope and has gradually varying rising and falling edges.

[0099] Figure 7 The diagram schematically illustrates the comparison between the signal autocorrelation and the ideal autocorrelation at the direction of beam 3. The blue line represents the signal envelope at the main lobe 3:40°, and the red line represents the ideal envelope. The generated signal at beam 3 recovers the properties of the designed spatial target waveform quite well.

[0100] Based on the above Figure 1 As can be seen from the implementation method, the embodiments of the present invention utilize a genetic algorithm to determine the spatial target waveform based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix. The spatial target waveform is a waveform with slowly varying rising and falling edges, and the autocorrelation function is the autocorrelation function of the spatial target waveform after removing the main lobes. Based on the spatial target waveform, multiple main lobe pointing directions, the signal phase matrix, the expected power spectrum of each main lobe pointing direction, and the signal power spectrum of each main lobe pointing direction, the sub-objective function of the spatial target waveform is determined. Based on the sub-objective function, the scaling factors of multiple sub-objective functions, the time-varying radiation pattern of each main lobe pointing direction, and the expected radiation pattern of each main lobe pointing direction, the comprehensive objective function and the gradient of the comprehensive objective function with respect to the signal phase matrix are determined. Based on the gradient, correction coefficients, and iteration termination threshold, the conjugate gradient method is used to perform gradient descent search to determine the final waveform matrix and the final time-varying radiation pattern. Thus, based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix, the determined airspace target waveform has a slowly varying rising and falling edge, which can effectively reduce the probability of radar signal being intercepted by the enemy and improve the anti-interference capability of the signal itself. Based on the gradient, correction coefficient, and iteration termination threshold, the conjugate gradient method is used to perform gradient descent search to determine the final time-varying radiation pattern, so that the airspace target waveform forms a time-varying radiation pattern in the airspace. During a certain period of time, the electromagnetic energy in a certain direction in the airspace slowly and continuously rises (falls), but the comprehensive radiation pattern is a process of energy integration in the time dimension. The total distribution of airspace energy remains unchanged over the overall time, thus realizing the modulation of the distribution of airspace electromagnetic energy in time.

[0101] Based on the same inventive concept, as an implementation of the above-mentioned time-varying radiation pattern design method for a broadband digital array radar, this embodiment of the invention also provides a time-varying radiation pattern design device for a broadband digital array radar. Figure 8 This is a structural diagram of the device in an embodiment of the present invention. See also: Figure 8 As shown, the time-varying radiation pattern design device may include:

[0102] The first determining module 801 is used to determine the spatial target waveform using a genetic algorithm based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix. The spatial target waveform is a waveform with slowly varying rising and falling edges, and the autocorrelation function is the autocorrelation function of the spatial target waveform after removing the main lobe.

[0103] The second determining module 802 is used to determine the sub-objective function of the spatial target waveform based on the spatial target waveform, multiple main lobe pointing, signal phase matrix, expected power spectrum of each main lobe pointing and signal power spectrum of each main lobe pointing;

[0104] The third determining module 803 is used to determine the comprehensive objective function and the gradient of the comprehensive objective function with respect to the signal phase matrix based on the sub-objective function, the scaling coefficients of multiple sub-objective functions, the time-varying radiation pattern pointed to by each main lobe, and the desired radiation pattern pointed to by each main lobe.

[0105] Search module 804 is used to perform gradient descent search using the conjugate gradient method based on the gradient, correction coefficient and iteration termination threshold, in order to determine the final waveform matrix and the final time-varying orientation pattern.

[0106] The first determining module 801 is specifically used to construct an optimization model based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix; and to solve the optimization model using a genetic algorithm to obtain the target waveform in the spatial domain.

[0107] The first determining module 801 constructs an optimization model based on the autocorrelation function, the amplitude difference tolerance, and the amplitude difference matrix, including: constructing the optimization model using the following first formula based on the autocorrelation function, the amplitude difference tolerance, and the amplitude difference matrix:

[0108]

[0109] in, Let be the autocorrelation function, x be the target waveform in the spatial domain, A be the amplitude difference matrix, and ε be the amplitude difference tolerance.

[0110] The second determining module 802 is specifically used to determine a power spectrum similarity sub-objective function based on the main lobe pointing of multiple power spectra, the signal phase matrix, the expected power spectrum of each main lobe pointing, and the actual spatial synthesized power spectrum of each main lobe pointing; and to determine a time-domain similarity sub-objective function based on the spatial domain target waveform, multiple time-domain main lobe pointing, the signal phase matrix, the signal power spectrum of each main lobe pointing, and the fast Fourier transform matrix. The multiple main lobe pointings include the main lobe pointings of multiple power spectra and the main lobe pointings of multiple time domains, and the sub-objective functions include the power spectrum similarity sub-objective function and the time-domain similarity sub-objective function.

[0111] The second determining module 802 determines the power spectrum similarity sub-objective function based on multiple main lobe pointing directions, the signal phase matrix, the expected power spectrum of each main lobe pointing direction, and the actual spatial synthesized power spectrum of each main lobe pointing direction. This includes determining the power spectrum similarity sub-objective function using the following second formula based on the main lobe pointing directions, the signal phase matrix, the expected power spectrum of each main lobe pointing direction, and the actual spatial synthesized power spectrum of each main lobe pointing direction:

[0112]

[0113] Where h1(θ) i ,Φ) is the power spectrum similarity sub-objective function, θ i Let Φ be the main lobe direction of multiple power spectra, Φ be the signal phase matrix, N be the number of sub-band frequency points of the broadband signal, and p be the main lobe direction of multiple power spectra. n (θ i ,Φ) represents the actual spatial composite power spectrum pointed to by the main lobe of each power spectrum. Let be the expected power spectrum pointing to the main lobe of each power spectrum, α be the first scale factor, and i be the main lobe pointing to the i-th power spectrum. This is the transpose of the steering vector pointing to the main lobe of each power spectrum at the nth frequency point. This is the transform vector corresponding to the nth frequency point in the N-point discrete Fourier transform.

[0114] The second determining module 802 determines the time-domain similarity sub-objective function based on the spatial target waveform, multiple time-domain main lobe pointing directions, signal phase matrix, signal power spectrum of each main lobe pointing direction, and fast Fourier transform matrix. This includes determining the time-domain similarity sub-objective function using the following third formula based on the spatial target waveform, multiple time-domain main lobe pointing directions, signal phase matrix, signal power spectrum of each main lobe pointing direction, and fast Fourier transform matrix:

[0115]

[0116] Where h2(θ) m ,Φ) is the temporal similarity sub-objective function, θ m The main lobe points to multiple time domains, Φ is the signal phase matrix, and v(θ) m Φ) represents the signal power spectrum pointing to the main lobe in each time domain, F is the Fast Fourier Transform matrix, x is the target waveform in the spatial domain, β is the second scale factor, and θ m The direction of the main lobe in the m-th time domain is... This is the transpose of the steering vector pointing to the main lobe in the time domain at the (N / 2)th frequency point. Let be the transform vector corresponding to the (N / 2)th frequency point in the N-point discrete Fourier transform. Let exp(jΦ) be the transform vector corresponding to the N / 2-1th frequency point in the N-point discrete Fourier transform, and let exp(jΦ) be the signal transmission matrix.

[0117] The third determining module 803 is specifically used to construct a comprehensive objective function based on the power spectrum similarity sub-objective function, the time-domain similarity sub-objective function, the first scaling factor, the second scaling factor, the third scaling factor, the time-varying radiation pattern pointed to by each main lobe, and the desired radiation pattern pointed to by each main lobe; to determine the first optimal scaling factor and the second optimal scaling factor based on the first scaling factor, the second scaling factor, the third scaling factor, the desired radiation pattern pointed to by each main lobe, and the time-varying radiation pattern pointed to by each main lobe, wherein the first optimal scaling factor is the optimal scaling factor corresponding to the first scale factor in the power spectrum similarity sub-objective function, and the second optimal scaling factor is the optimal scaling factor corresponding to the second scale factor in the time-domain similarity sub-objective function; and to determine the gradient of the comprehensive objective function with respect to the signal phase matrix based on the comprehensive objective function, the first optimal scaling factor, and the second optimal scaling factor, wherein the scaling factors of the multiple sub-objective functions include the first scaling factor, the second scaling factor, and the third scaling factor of the sub-objective functions.

[0118] The search module 804 is specifically used to perform gradient descent search using the conjugate gradient method based on the gradient, correction coefficient and iteration termination threshold, so as to determine the final gradient of the comprehensive objective function with respect to the signal phase matrix; and to determine the final waveform matrix and the final time-varying orientation pattern based on the final gradient.

[0119] It should be noted that the above description of the time-varying radiation pattern design device embodiment for broadband digital array radar is similar to the description of the above-described time-varying radiation pattern design method embodiment for broadband digital array radar, and has similar beneficial effects. For technical details not disclosed in the embodiments of the time-varying radiation pattern design device for broadband digital array radar of the present invention, please refer to the description of the time-varying radiation pattern design method embodiment for broadband digital array radar of the present invention for understanding.

[0120] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for designing time-varying radiation patterns for a broadband digital array radar, characterized in that, The time-varying orientation pattern design method includes: Using a genetic algorithm, a spatial target waveform is determined based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix. The spatial target waveform is a waveform with slowly varying rising and falling edges, and the autocorrelation function is the autocorrelation function of the spatial target waveform after removing the main lobe. Based on the spatial target waveform, multiple main lobe pointing, signal phase matrix, expected power spectrum of each main lobe pointing, and signal power spectrum of each main lobe pointing, determine the sub-objective function of the spatial target waveform; Based on the sub-objective function, the scaling coefficients of the multiple sub-objective functions, the time-varying radiation patterns pointed to by each main lobe, and the desired radiation patterns pointed to by each main lobe, the comprehensive objective function and the gradient of the comprehensive objective function with respect to the signal phase matrix are determined. Based on the gradient, correction coefficient, and iteration termination threshold, gradient descent search is performed using the conjugate gradient method to determine the final waveform matrix and the final time-varying orientation pattern.

2. The time-varying orientation pattern design method according to claim 1, characterized in that, The method of using a genetic algorithm to determine the spatial target waveform based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix includes: An optimization model is constructed based on the autocorrelation function, the amplitude difference tolerance, and the amplitude difference matrix; The optimization model is solved using the genetic algorithm to obtain the target waveform in the spatial domain.

3. The time-varying orientation pattern design method according to claim 2, characterized in that, The step of constructing an optimization model based on the autocorrelation function, the amplitude difference tolerance, and the amplitude difference matrix includes: Based on the autocorrelation function, the amplitude difference tolerance, and the amplitude difference matrix, an optimization model is constructed using the following first formula: in, Let be the autocorrelation function, x be the spatial target waveform, A be the amplitude difference matrix, and ε be the amplitude difference tolerance.

4. The time-varying orientation pattern design method according to claim 1, characterized in that, The multiple main lobe pointers include multiple power spectrum main lobe pointers and multiple time domain main lobe pointers. The sub-objective functions include a power spectrum similarity sub-objective function and a time domain similarity sub-objective function. Determining the sub-objective function of the spatial domain target waveform based on the spatial domain target waveform, the multiple main lobe pointers, the signal phase matrix, the expected power spectrum of each main lobe pointer, and the signal power spectrum of each main lobe pointer includes: The power spectrum similarity sub-objective function is determined based on the main lobe pointing of the multiple power spectra, the signal phase matrix, the expected power spectrum of each main lobe pointing, and the actual spatial synthesized power spectrum of each main lobe pointing. The time-domain similarity sub-objective function is determined based on the spatial target waveform, the main lobe pointing in the multiple time domains, the signal phase matrix, the signal power spectrum of each main lobe pointing, and the fast Fourier transform matrix.

5. The time-varying orientation pattern design method according to claim 4, characterized in that, The step of determining the power spectrum similarity sub-objective function based on the multiple main lobe directions, the signal phase matrix, the expected power spectrum of each main lobe direction, and the actual spatial synthesized power spectrum of each main lobe direction includes: Based on the main lobe directions of the multiple power spectra, the signal phase matrix, the expected power spectrum of each main lobe direction, and the actual spatially synthesized power spectrum of each main lobe direction, the power spectrum similarity sub-objective function is determined using the following second formula: Where h1(θ) i ,Φ) is the power spectrum similarity sub-objective function, θ i The main lobe direction of the multiple power spectra is denoted by Φ, the phase matrix of the signal is denoted by N, and the number of sub-band frequency points of the broadband signal is denoted by p. n (θ i ,Φ) represents the actual spatial composite power spectrum pointed to by the main lobe of each power spectrum. Let α be the expected power spectrum pointing to the main lobe of each power spectrum, and θ be the first scaling factor. i Let be the main lobe direction of the i-th power spectrum. This is the transpose of the steering vector pointing to the main lobe of each power spectrum at the nth frequency point. This is the transform vector corresponding to the nth frequency point in the N-point discrete Fourier transform.

6. The time-varying orientation pattern design method according to claim 5, characterized in that, The step of determining the time-domain similarity sub-objective function based on the spatial domain target waveform, the multiple time-domain main lobe directions, the signal phase matrix, the signal power spectrum of each main lobe direction, and the fast Fourier transform matrix includes: Based on the spatial target waveform, the main lobe directions in the multiple time domains, the signal phase matrix, the signal power spectrum of each main lobe direction, and the fast Fourier transform matrix, the time-domain similarity sub-objective function is determined using the following third formula: Where h2(θ) m ,Φ) is the temporal similarity sub-objective function, θ m The main lobe direction in the multiple time domains is denoted by Φ, and the signal phase matrix is ​​denoted by v(θ). m Φ) represents the signal power spectrum pointing to the main lobe in each time domain, F is the Fast Fourier Transform matrix, x is the target waveform in the spatial domain, β is the second scale factor, and m is the main lobe pointing in the m-th time domain. This is the transpose of the steering vector pointing to the main lobe in the time domain at the (N / 2)th frequency point. Let be the transform vector corresponding to the (N / 2)th frequency point in the N-point discrete Fourier transform. Let exp(jΦ) be the transform vector corresponding to the N / 2-1th frequency point in the N-point discrete Fourier transform, and let exp(jΦ) be the transmitted waveform matrix.

7. The time-varying orientation pattern design method according to claim 6, characterized in that, The scaling coefficients of the plurality of sub-objective functions include a first scaling coefficient, a second scaling coefficient, and a third scaling coefficient of the sub-objective functions; The step of determining the integrated objective function and its gradient with respect to the signal phase matrix based on the sub-objective function, the scaling coefficients of the multiple sub-objective functions, the time-varying radiation patterns pointed to by each main lobe, and the desired radiation patterns pointed to by each main lobe includes: A comprehensive objective function is constructed based on the power spectrum similarity sub-objective function, the time domain similarity sub-objective function, the first scaling factor, the second scaling factor, the third scaling factor, the time-varying radiation pattern pointed to by each main lobe, and the expected radiation pattern pointed to by each main lobe. Based on the first scaling factor, the second scaling factor, the third scaling factor, the desired radiation pattern pointed to by each main lobe, and the time-varying radiation pattern pointed to by each main lobe, a first optimal scaling factor and a second optimal scaling factor are determined. The first optimal scaling factor is the optimal scaling factor corresponding to the first scale factor in the power spectrum similarity sub-objective function, and the second optimal scaling factor is the optimal scaling factor corresponding to the second scale factor in the time domain similarity sub-objective function. The gradient of the integrated objective function with respect to the signal phase matrix is ​​determined based on the integrated objective function, the first optimal scaling factor, and the second optimal scaling factor.

8. The time-varying orientation pattern design method according to claim 7, characterized in that, Determining the gradient of the integrated objective function with respect to the signal phase matrix based on the integrated objective function, the first optimal scaling factor, and the second optimal scaling factor includes: Based on the comprehensive objective function, the first optimal scaling factor, and the second optimal scaling factor, the gradient of the comprehensive objective function with respect to the signal phase matrix is ​​determined using the following fourth formula: in, Let λ1 be the gradient, λ1 be the first scaling factor, K be the number of spatial grid points, k be the number of the kth spatial grid points, and θ be the gradient. k Let w be the angle of the k-th spatial grid cell. k Φ is the scaling factor for the angle of the k-th spatial grid, Φ is the signal phase matrix, and f k (Φ) is the first intermediate variable, λ2 is the second proportionality coefficient, I is the number of main lobes in the power spectrum fitting of the main lobe synthesized signal, and θ i Let N be the main lobe direction of the i-th power spectrum, and N be the number of sub-band frequency points of the broadband signal. h is the scaling factor for the nth frequency point at the grid point pointed to by the main lobe of multiple power spectra. in (Φ) is the second intermediate variable, λ3 is the third proportionality coefficient, M is the number of main lobes in the time-domain fitting of the main lobe synthesis signal, and θ m The direction of the main lobe in the m-th time domain is... For θ m The scaling factor for the nth frequency point at the grid, g(Φ) is the third intermediate variable, and P D (θ k ,Φ) represents the time-varying pattern pointing to each main lobe, α opt P is the first optimal scaling factor. d (θ k ) represents the desired radiation pattern pointing to each main lobe, and pn(θi,Φ) represents θ. i The actual spatial composite power spectrum of the direction, For θ i The expected power spectrum in the direction, v(θ) m ,Φ) is θ m The signal power spectrum in the direction, β opt Let x be the second optimal scaling factor, F be the fast Fourier transform matrix, and x be the second optimal scaling factor. H It is the inverse conjugate of the target waveform in the spatial domain.

9. The time-varying orientation pattern design method according to claim 1, characterized in that, The step of performing gradient descent search using the conjugate gradient method based on the gradient, correction coefficient, and iteration termination threshold to determine the final waveform matrix and the final time-varying orientation pattern includes: Based on the gradient, the correction coefficient, and the iteration termination threshold, gradient descent search is performed using the conjugate gradient method to determine the final gradient of the comprehensive objective function with respect to the signal phase matrix; Based on the final gradient, the final waveform matrix and the final time-varying orientation pattern are determined.

10. A time-varying pattern design device for a broadband digital array radar, characterized in that, The time-varying orientation pattern design device includes: The first determining module is used to determine the spatial target waveform using a genetic algorithm based on the autocorrelation function, amplitude difference tolerance, and amplitude difference matrix. The spatial target waveform is a waveform with slowly varying rising and falling edges, and the autocorrelation function is the autocorrelation function of the spatial target waveform after removing the main lobe. The second determining module is used to determine the sub-objective function of the spatial target waveform based on the spatial target waveform, multiple main lobe pointing, signal phase matrix, expected power spectrum of each main lobe pointing and signal power spectrum of each main lobe pointing; The third determining module is used to determine the comprehensive objective function and the gradient of the comprehensive objective function with respect to the signal phase matrix based on the sub-objective function, the scaling coefficients of the multiple sub-objective functions, the time-varying radiation pattern pointed to by each main lobe, and the expected radiation pattern pointed to by each main lobe. The search module is used to perform gradient descent search using the conjugate gradient method based on the gradient, correction coefficient, and iteration termination threshold to determine the final waveform matrix and the final time-varying orientation pattern.

Images