Radar anti-jamming beam forming method based on analog-digital hybrid MIMO array

Abstract

The application provides a radar anti-jamming beam forming method based on an analog-digital hybrid MIMO array, comprising: constructing an array model and estimating array errors according to array element arrangement and target observation angle; generating a transmitting and receiving calibration matrix by using a least square-based transmitting-receiving separation calibration method; dividing the transmitting array into multiple sub-arrays and making the multiple sub-arrays transmit orthogonal waveforms; calibrating the phases of the array elements in the multiple sub-arrays according to the transmitting calibration matrix, and realizing beam forming by transmitting coherent signals; separating and extracting echo signals of each sub-array from the received signals by using a waveform decoding technology, and calibrating the amplitudes and phases of the echo signals by using the receiving calibration matrix; controlling the echo sidelobe level of the calibrated receiving array by using a window function, and adjusting the beam pointing direction by using the receiving end beam forming. The application can enhance the adaptability and anti-jamming capability of the radar in a complex environment, improve the radar detection probability and reduce the false alarm probability.

Description

Technical Field

[0001] This invention relates to the field of traffic radar anti-jamming technology, and in particular to a radar anti-jamming beamforming method based on a hybrid analog-digital MIMO array. Background Technology

[0002] Traffic radar is typically fixed on roads and is primarily used to monitor traffic conditions. These radar devices receive echo signals reflected from vehicles, pedestrians, and the surrounding environment. However, because traffic radar operates in a relatively complex environment, it is susceptible to interference from weather, ground clutter, and other electronic devices, which affects the radar's sensing sensitivity, detection range, and accuracy.

[0003] Therefore, there is an urgent need for a beamforming method that can effectively resist interference and ensure radar performance and accuracy. Summary of the Invention

[0004] Therefore, it is necessary to provide a radar anti-jamming beamforming method based on a hybrid analog-digital MIMO array to address the aforementioned technical problems.

[0005] A radar anti-jamming beamforming method based on a hybrid analog-digital (MIMO) array includes the following steps: constructing an array model and estimating array errors based on the array element arrangement and target observation angle; generating a transmit calibration matrix and a receive calibration matrix using a least-squares-based transmit-receive separation calibration method; dividing the transmit array into multiple subarrays and using phase modulation to transmit orthogonal waveforms between the subarrays; calibrating the phases of the array elements within the subarrays according to the transmit calibration matrix; after calibration, each subarray transmits a coherent signal to achieve transmit-end beamforming; using waveform decoding technology to separate and extract echo signals from each subarray from the received signal, and calibrating the amplitude and phase of the echo signals using the receive calibration matrix; controlling the echo sidelobe level of the calibrated receive array using a windowing function, and adjusting the beam pointing through receive-end beamforming.

[0006] In one embodiment, the step of constructing an array model and estimating array errors based on the array element arrangement and target observation angle, and generating transmit and receive calibration matrices using a least-squares-based transmit-receive separation calibration method, includes: obtaining the actual array response based on the target observation angle θ. for:

[0007]

[0008] Where M is the number of transmitting antennas and N is the number of receiving antennas. arrive This indicates the range of the transmitting antennas TX1 to TX at the observation angle θ. M The response of the first receiving antenna RX1 arrive Indicates the transmission antenna TX1 to TX M The response of the second receiving antenna RX2 arrive Indicates the transmission antenna TX1 to TX M With the Nth receiving antenna RX N The response of the array is represented by the transmit antenna array response vector and the receive antenna array response vector, as follows:

[0009]

[0010] In the formula, in the formula, Let represent the transmit antenna array response of the x-th transmit antenna when the target observation angle is θ. Let represent the transpose of the receiving antenna array response of the x-th receiving antenna at the target observation angle θ; for H observation angles, obtain the corresponding actual array responses and reconstruct them into M×N matrices respectively. Then, decompose these into separate transmit and receive antenna array responses, as follows:

[0011]

[0012] The actual transmit antenna array response matrix under H observation angles is:

[0013]

[0014] The actual receiving antenna array response matrix under H observation angles is:

[0015]

[0016] The actual transmit antenna array response matrix and the actual receive antenna array response matrix are calibrated as follows:

[0017]

[0018] In the formula, C t For the transmit antenna calibration matrix, Z tx To adjust the matrix for the transmitting antenna, C r For the receiving antenna calibration matrix, Z rx To adjust the receiving antenna matrix, A tx =[a tx (θ1), a tx (θ2), ..., a tx (θ H [)] represents the theoretical steering vector of the transmission array under H observation angles, A rx =[a rx (θ1), a rx (θ2), ..., arx (θ H [H] represents the theoretical steering vector of the receiving array at H observation angles; each transmission vector is compared with the ideal steering vector at its corresponding angle, and the optimal transmission calibration matrix is ​​found by minimizing the transmission objective function, which is:

[0019]

[0020] In the formula, U=[u(θ1),u(θ2),...,u(θ K [)] is the set of emission vectors collected from K angles, || || F Let Frobenius norm represent the matrix; for the receiving vector, the optimal receiving calibration matrix is ​​found by minimizing the receiving objective function, which is:

[0021]

[0022] In the formula, V * =[v * (θ1), v * (θ2), ..., v * (θ K [)] is the set of conjugate transposes of the received vectors collected from K angles; for each observation matrix The singular value decomposition formula is as follows:

[0023]

[0024] Will It is approximately a rank-1 matrix, represented as:

[0025]

[0026] In the formula, σ1 is the maximum singular value, and u1 is the left singular value vector corresponding to σ1, representing the transmit component of the MIMO antenna array system. It is the right singular value vector corresponding to σ1, representing the received component of the MIMO antenna array system, [·] H Represents the transpose of a matrix; for H observation angles, the array response matrix X real Perform singular value decomposition:

[0027] U=[u1(θ1),u1(θ2),...,u1(θ H (11)

[0028] In the formula, U represents the left singular vector matrix corresponding to the maximum singular value;

[0029]

[0030] In the formula, V represents the conjugate transpose of the right singular vector corresponding to the maximum singular value; the search for the optimal calibration matrix is ​​transformed into solving for the minimum norm, as shown in the formula:

[0031]

[0032] The minimum norm is solved by least squares iteration to obtain the transmit calibration matrix and receive calibration matrix that satisfy the norm threshold.

[0033] In one embodiment, dividing the transmit array into multiple subarrays and using phase modulation to transmit orthogonal waveforms between the multiple subarrays includes: dividing M transmit channels into K subarrays, each subarray containing N... t There are several transmission channels. An M×K dimensional matrix T0 reflects the subarray division. For the k-th column, if the m-th element belongs to the k-th subarray, its value is 1; otherwise, it is 0.

[0034]

[0035] Where m = 1, 2, ..., M, k = 1, 2, ..., K, N t • K = M; Assuming the signal transmitted by each element antenna is represented as s(t), the uncalibrated transmit array response at the observation angle θ is expressed as:

[0036]

[0037] In the formula, x1, x2, ... x M Let a represent the transmit array response of M transmit antennas. T (θ) represents the transmitted steering vector at the observation angle θ, the coefficient α1 is the signal scaling factor, representing the gain or attenuation coefficient of the entire array, and N(t) = [n1(t), n2(t), ..., n M (t)] T Let K represent the noise vectors of M transmitted signals; after dividing into subarrays, the K subarrays are represented as follows:

[0038]

[0039] In the formula, [·] T The transpose of the matrix is ​​used to perform phase modulation on the transmitted signals between subarrays, so that the transmitted waveforms between subarrays are orthogonal.

[0040] In one embodiment, the step of calibrating the phase of the array elements within the plurality of subarrays according to the transmission calibration matrix, and forming the transmitted coherent waveform within each subarray through the transmitting beam after calibration, includes: obtaining the transmission calibration matrix C according to equation (13). t Represented as:

[0041]

[0042] The diagonal elements represent amplitude and phase compensation for antenna amplitude and phase errors, while the off-diagonal elements represent amplitude and phase compensation for antenna coupling effects. The array is divided into K N subarrays according to the order of subarray partitioning. t ×N t Sub-calibration matrices c1, c2, ..., c K The elements in the sub-calibration matrix are:

[0043]

[0044] In a hybrid analog-to-digital architecture, the transmitter uses a phase shifter to control the signal phase. Phase calibration is performed using the phase shifter, and the calculated phase calibration matrix for the transmitting antenna is as follows:

[0045]

[0046] In the formula, arg(c1) represents the calibration of the sub-calibration matrix c1 using the rotation vector method; at the observation angle θ, the calibrated response of the uncalibrated transmit array is expressed as:

[0047]

[0048] Within the subarray, a coherent transmitted signal is formed through beamforming. The subarray-level transmit array response is expressed as:

[0049]

[0050] The calibrated subarray stage transmit array steering vector is then expressed as:

[0051]

[0052] Where a(θ) represents the emission guide vector at the observation angle θ. θ0 represents the conjugate transpose of the array partitioning matrix, diag(w) represents the diagonal matrix formed by using the elements of vector w as diagonal elements, and θ0 represents the element-level phase shift, making the direction point to the target angle.

[0053] In one embodiment, the use of waveform decoding technology to separate and extract echo signals from each subarray from the received signal, and to calibrate the amplitude and phase of the echo signals using a receive calibration matrix, includes: using waveform decoding technology to decode the echoes to obtain KN sets of echo data, and obtaining the actual array response under the mixed-signal structure.

[0054]

[0055] In the formula, V(t) = [v1(t), v2(t), ..., vKN (t)] T This represents the noise vector of the received echo. Let b(θ) represent the Kronecker product, and b(θ) represent the steering vector of the receiver array; the receiver calibration matrix C is obtained by iterative calculation using the least squares method. r Then, the calibrated expression for the receiver array response is obtained:

[0056]

[0057] In the formula, α = α1α2, and U(t) is the noise vector of the calibrated received signal.

[0058] In one embodiment, controlling the echo sidelobe level of the calibrated receiving array through a windowing function and adjusting the beam pointing through receiver beamforming includes:

[0059] Assuming a beam is formed in the θ0 direction, and a low sidelobe window function win is added to the receiver pattern, the weight vector that maintains a low sidelobe level in the receiver pattern is obtained:

[0060]

[0061] Where b(θ0) represents the steering vector of the receiving array in the θ0 direction. Represents the Hadmard product;

[0062] The received signal, obtained by beamforming and weighted by weight vector, is as follows:

[0063] Y(t) = b win (θ0)·y cal (t); (26)

[0064] The joint weight vector of the hybrid analog-digital MIMO radar array is obtained as follows:

[0065]

[0066] Compared with existing technologies, the advantages and beneficial effects of this invention are as follows: Based on the array element arrangement and target observation angle, an array model is constructed and array errors are estimated. A least-squares-based transmit-receive separation calibration method is used to generate transmit calibration matrices and receive calibration matrices. The transmit array is divided into multiple subarrays, and phase modulation is used to transmit orthogonal waveforms between the multiple subarrays. Based on the transmit calibration matrix, the phases of the array elements within the multiple subarrays are calibrated. After calibration, coherent waveforms are transmitted within each subarray to achieve beamforming. Combining the high degree of freedom of MIMO radar and the high gain of phased array radar, high gain can be effectively maintained, while the overall array retains the MIMO characteristics. MO radar offers advantages in high angular resolution and target detection. It employs waveform decoding technology to separate and extract echo signals from each subarray from the received signal. Using a receiver calibration matrix, it calibrates the amplitude and phase of the echo signals. A windowing function controls the echo sidelobe level of the calibrated receiver array, and beam pointing is adjusted through receiver beamforming. By using amplitude and phase calibration and beamforming, and with antenna coupling, it achieves enhanced reception in specific areas and effective suppression of potential interference areas. This enhances the radar system's adaptability and anti-interference capabilities in complex environments, increases radar detection probability, and reduces false alarm probability. Attached Figure Description

[0067] Figure 1 This is a flowchart illustrating a radar anti-jamming beamforming method based on a hybrid analog-digital MIMO array in one embodiment.

[0068] Figure 2 This is a calibration procedure for a transceiver separation calibration method in one embodiment;

[0069] Figure 3 Here is a comparison diagram of the subarray before and after calibration in one embodiment, where (1) is the beamforming before calibration and (2) is the beamforming after calibration;

[0070] Figure 4 This is an anti-interference pattern of a hybrid analog-digital MIMO in one embodiment. Detailed Implementation

[0071] Before describing the specific embodiments of the present invention, the overall concept of the present invention will be explained as follows:

[0072] This invention is mainly based on the beamforming process of traffic radar. Currently, traffic radar is easily interfered with by various factors in complex environments, making it difficult to guarantee radar performance and accuracy.

[0073] Therefore, this invention proposes a radar anti-jamming beamforming method based on a hybrid analog-digital (MIMO) array. Based on the array element arrangement and target observation angle, an array model is constructed and array errors are estimated. A least-squares-based transmit-receive separation calibration method is used to generate transmit and receive calibration matrices. The transmit array is divided into multiple subarrays, and phase modulation is applied to ensure orthogonal waveforms are transmitted between the subarrays. Based on the transmit calibration matrices, the phases of the array elements within each subarray are calibrated. After calibration, coherent waveforms are transmitted within the subarrays to achieve beamforming, effectively maintaining the advantages of high gain and MIMO radar in terms of high angle resolution and target detection. Waveform decoding is employed. The technology separates and extracts the transmitted signals from each subarray from the received signal, and uses a receive calibration matrix to calibrate the amplitude and phase of the echo data. This enhances reception in specific areas and effectively suppresses potential interference areas, thereby improving the radar's adaptability and anti-jamming capabilities in complex environments. By controlling the echo sidelobe level of the calibrated receive array through a windowing function and adjusting the beam pointing through receiver beamforming, the calibration of the echo sidelobe level in the receive array further reduces interference signals from non-main lobe directions, effectively suppressing noise and interference from non-target directions, ensuring main lobe gain, and ensuring radar performance and accuracy.

[0074] Hybrid MIMO (Multiple-Input Multiple-Output) array radar combines the advantages of analog phased array radar and digital MIMO radar. It divides the array into subarrays at the transmitter end, transmits orthogonal waveforms between subarrays, and transmits the same waveform within subarrays. This allows it to retain the coherent processing gain of the phased array mode while also having the high system freedom of MIMO.

[0075] Having introduced the overall concept of the present invention, to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below through specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0076] In one embodiment, such as Figure 1 As shown, a radar anti-jamming beamforming method based on a hybrid analog-digital MIMO array is provided, including the following steps:

[0077] Step S101: Based on the array element arrangement and target observation angle, construct an array model and estimate array error. Use a least squares-based transmit / receive separation calibration method to generate transmit calibration matrix and receive calibration matrix.

[0078] Specifically, based on the array element arrangement and target observation angle, an array model is constructed, and the array error is estimated. A least-squares-based transmit-receive separation calibration method can be used to split the overall array into independent transmit and receive antenna arrays, and the transmit calibration matrix and receive calibration matrix are obtained to improve radar performance.

[0079] Step S101 includes: obtaining the actual array response based on the target observation angle θ. for:

[0080]

[0081] Where M is the number of transmitting antennas and N is the number of receiving antennas. arrive This indicates the range of the transmitting antennas TX1 to TX at the observation angle θ. M The response of the first receiving antenna RX1 arrive Indicates the transmission antenna TX1 to TX M The response of the second receiving antenna RX2 arrive Indicates the transmission antenna TX1 to TX M With the Nth receiving antenna RX N The response;

[0082] The actual array response is represented using the transmit antenna array response vector and the receive antenna array response vector, as follows:

[0083]

[0084] In the formula, Let represent the transmit antenna array response of the x-th transmit antenna when the target observation angle is θ. This represents the transpose of the receiving antenna array response of the x-th receiving antenna when the target observation angle is θ.

[0085] For H observation angles, the corresponding actual array responses are obtained and reconstructed into M×N matrices. These matrices are then split to obtain the individual transmit antenna array responses and receive antenna array responses, as follows:

[0086]

[0087] The actual transmit antenna array response matrix under H observation angles is:

[0088]

[0089] The actual receiving antenna array response matrix under H observation angles is:

[0090]

[0091] The actual transmit antenna array response matrix and the actual receive antenna array response matrix are calibrated as follows:

[0092]

[0093] In the formula, C t For the transmit antenna calibration matrix, Z tx To adjust the matrix for the transmitting antenna, C r For the receiving antenna calibration matrix, Z rx To adjust the receiving antenna matrix, A tx =[a tx (θ1), a tx (θ2), ..., a tx (θ H [)] represents the theoretical steering vector of the transmission array under H observation angles, where a tx (θ1) is the theoretical steering vector of the transmission array under the observation angle θ1, A rx =[a rx (θ1), a rx (θ2), ..., a rx (θ H [)] represents the theoretical steering vector of the receiving array under H observation angles, where a rx (θ1) is the theoretical steering vector of the receiving array at the observation angle θ1;

[0094] Each launch vector is compared with its corresponding ideal steering vector at its angle. The optimal launch calibration matrix is ​​found by minimizing the launch objective function, which is:

[0095]

[0096] In the formula, U=[u(θ1),u(θ2),...,u(θ K [)] is the set of emission vectors collected from K different angles, || || F Denotes the Frobenius norm of a matrix;

[0097] For the received vector, the optimal received calibration matrix is ​​found by minimizing the received objective function, which is:

[0098]

[0099] In the formula, V * =[v * (θ1), v * (θ2), ..., v * (θ K[)] is the set of conjugate transposes of the received vectors collected from K different angles;

[0100] For each observation matrix The singular value decomposition formula is as follows:

[0101]

[0102] Will It is approximately a rank-1 matrix, represented as:

[0103]

[0104] In the formula, σ1 is the maximum singular value, and u1 is the left singular value vector corresponding to σ1, representing the transmit component of the MIMO antenna array system. It is the right singular value vector corresponding to σ1, representing the received component of the MIMO antenna array system, [·] H Represents the transpose of a matrix;

[0105] Under H observation angles, the array response matrix X real Perform singular value decomposition:

[0106] U=[u1(θ1),u1(θ2),...,u1(θ H (11)

[0107] In the formula, U represents the left singular vector matrix corresponding to the maximum singular value;

[0108]

[0109] In the formula, V represents the conjugate transpose of the right singular vector corresponding to the maximum singular value;

[0110] Finding the optimal calibration matrix is ​​transformed into solving for the minimum norm, as shown in the formula:

[0111]

[0112] The minimum norm is solved by least squares iteration to obtain the transmit calibration matrix and receive calibration matrix that satisfy the norm threshold.

[0113] Specifically, an array model with an observation angle of θ and an array element arrangement of M×N is constructed, as shown in Equation (1). In a MIMO system where the transmit and receive antennas are independent, the overall array response vector can be split into separate transmit and receive antenna array response vectors. The array response matrices under multiple observation angles are split and reconstructed into independent transmit and receive antenna array response vectors. In order to calibrate the system, each transmit vector is compared with the ideal steering vector of its corresponding angle, and the optimal transmit calibration matrix is ​​found by minimizing the objective function. Similarly, the receive vector is processed to find the optimal receive calibration matrix, thereby calibrating the transmit and receive vectors. The array response matrix under each observation angle is decomposed by singular value decomposition to simplify matrix operations. Based on the simplified matrix, the minimum range is solved by least squares iteration, and finally the transmit antenna calibration matrix and receive antenna calibration matrix that satisfy the norm threshold are obtained.

[0114] like Figure 2 The diagram illustrates the calibration process for the transmit-receive separation calibration method. The array response matrices of L virtual array elements are collected under H observation angles. Matrix reconstruction and singular value decomposition are performed to obtain the left singular vector matrix U corresponding to the maximum singular value and the right singular vector matrix V corresponding to the maximum singular value. Based on the left singular vector matrix, the theoretical transmit array response matrix is ​​obtained with the known transmit element arrangement and observation angles, and the objective function is solved. Based on the right singular vector matrix, the theoretical receive array response matrix is ​​obtained with the known receive element arrangement and observation angles. The transmit calibration matrix and receive calibration matrix, which meet the optimization criteria, are output respectively, and the actual array response is calibrated based on the two calibration matrices.

[0115] Step S102: Divide the transmitting array into multiple subarrays and use phase modulation to transmit orthogonal waveforms between the multiple subarrays.

[0116] Specifically, the transmitting array is divided into multiple subarrays, and phase modulation is used to make the transmitting subarrays transmit orthogonal waveforms to reduce the cross-correlation between signals, which helps to improve signal quality and reliability. By dividing the transmitting array into subarrays, the high degree of freedom of MIMO radar and the high gain of phased array radar can be effectively combined.

[0117] Step S102 includes: dividing the M transmission channels into K subarrays, with N subarrays containing N channels. t There are several transmission channels. An M×K dimensional matrix T0 reflects the subarray division. For the k-th column, if the m-th element belongs to the k-th subarray, its value is 1; otherwise, it is 0.

[0118]

[0119] Where m = 1, 2, ..., M, k = 1, 2, ..., K, Nt K = M;

[0120] Assuming the signal transmitted by each element antenna is represented as s(t), the uncalibrated transmit array response at the observation angle θ is expressed as:

[0121]

[0122] In the formula, x1, x2, ... x M Let a represent the transmit array response of M transmit antennas. T (θ) represents the transpose of the transmitted steering vector at the observation angle θ, the coefficient α1 is the signal scaling factor, representing the gain or attenuation coefficient of the entire array, and N(t) = [n1(t), n2(t), ..., n M (t)] T This represents the noise vector of M transmitted signals;

[0123] After dividing into subarrays, the K subarrays are represented as:

[0124]

[0125] In the formula, [·] T The transpose of the matrix is ​​used to perform phase modulation on the transmitted signals between subarrays, so that the transmitted waveforms between subarrays are orthogonal.

[0126] Specifically, the M transmission channels are divided into K subarrays, each containing several transmission channels. The subarrays are represented, and the transmission signals between the subarrays are phase-modulated to ensure that the waveforms of different subarrays are orthogonal, thereby reducing cross-correlation between signals, improving signal quality and reliability, and ultimately improving the accuracy of target detection.

[0127] Step S103: According to the transmission calibration matrix, the phase of the array elements in multiple subarrays is calibrated. After calibration, the transmitted coherent waveform in each subarray is formed by the transmitting beam.

[0128] Specifically, after dividing the transmission array into subarrays, phase calibration is performed on the array elements within the subarrays according to the transmission calibration matrix. After calibration, the transmitted coherent waveforms within each subarray are formed by the transmitting beam, thus forming a phased array radar. This allows the beam to point in a specific direction in space, thereby achieving beam guidance and obtaining directional gain, which helps to enhance the radar's ability to detect and track weak targets.

[0129] Step S103 includes: obtaining the transmission calibration matrix C according to equation (13). t Represented as:

[0130]

[0131] Among them, the diagonal elements are the amplitude and phase compensation for antenna amplitude and phase errors, and the off-diagonal elements are the amplitude and phase compensation for antenna coupling effects.

[0132] Divide the matrix into K N subarrays according to the order of subarray partitioning. t ×N t Sub-calibration matrices c1, c2, ..., c K The elements in the sub-calibration matrix are:

[0133]

[0134] In a hybrid analog-to-digital architecture, the transmitter uses a phase shifter to control the signal phase. Phase calibration is performed using the phase shifter, and the calculated phase calibration matrix for the transmitting antenna is as follows:

[0135]

[0136] In the formula, arg(c1) represents the calibration of the sub-calibration matrix c1 using the rotation vector method. The rotation vector method is applied in far-field environments. It involves transmitting a signal from a probe antenna to a phased array antenna, and then rotating the phase of each element of the phased array antenna. The amplitude and phase difference of each element channel is calculated by the maximum and minimum amplitude difference and phase shift angle of the synthesized signal to calibrate and compensate the antenna.

[0137] At the observation angle θ, the calibrated response of the uncalibrated transmit array is expressed as:

[0138]

[0139] Within the subarray, a coherent transmitted signal is formed through beamforming. The subarray-level transmit array response is expressed as:

[0140]

[0141] The calibrated subarray stage transmit array steering vector is then expressed as:

[0142]

[0143] Where a(θ) represents the emission guide vector at the observation angle θ. θ0 represents the conjugate transpose of the array partitioning matrix, diag(w) represents the diagonal matrix formed by using the elements of vector w as diagonal elements, and θ0 represents the element-level phase shift, making the direction point to the target angle.

[0144] Specifically, after subarray division, the optimal transmitter calibration matrix is ​​found by solving for the minimum norm, and the corresponding subcalibration matrix is ​​obtained according to the order of subarray division. In the mixed analog-digital structure, the transmitter uses a phase shifter to control the phase signal. Therefore, phase calibration can be achieved using a phase shifter, thereby obtaining the phase calibration matrix of the transmitting antenna. Within the subarray, coherent signals are transmitted through beamforming. Beamforming, also known as spatial filtering, enhances the desired signal in a specific direction and suppresses interference by weighting the output signals of each element of the antenna array, thereby improving radar performance.

[0145] Step S104: Using waveform decoding technology, the echo signals from each subarray are separated and extracted from the received signal, and the amplitude and phase of the echo signals are calibrated using the receiving calibration matrix.

[0146] Specifically, waveform decoding technology is a method of recovering analog signals by decoding and filtering the received digital sequence, separating and extracting echo signals from each subarray from the received signal; at the same time, the amplitude and phase of the echo signal are calibrated by a receiving calibration matrix, which combines amplitude and phase calibration and beamforming to achieve enhanced reception in specific areas and effective suppression of potential interference areas. This spatial selectivity enhances the adaptability and anti-interference capability of the radar system in complex environments.

[0147] Step S104 includes: using waveform decoding technology to decode the echo to obtain KN sets of echo data y1(t), y2(t), ..., y KN (t), to obtain the actual array response under the hybrid modular structure:

[0148]

[0149] In the formula, V(t) = [v1(t), v2(t), ..., v KN (t)] T This represents the noise vector of the received echo. Let θ represent the Kronecker product, and b(θ) represent the steering vector of the receiver array;

[0150] The receiver calibration matrix C is obtained by iterative calculation using the least squares method. r Then, the calibrated expression for the receiver array response is obtained:

[0151]

[0152] In the formula, α = α1α2, and U(t) is the noise vector of the calibrated received signal.

[0153] Specifically, in order to calibrate the receiver signal, waveform decoding technology is used to decode the echo signal to obtain the actual array response under the analog-digital hybrid structure. Then, a receiver calibration matrix is ​​used to calibrate the amplitude and phase of the echo signal, thereby achieving enhanced reception in specific areas and effective suppression of potential interference areas, thus enhancing the radar system's adaptability and anti-interference capability in complex environments.

[0154] Step S105: The level of the recovered sidelobe of the calibrated receiving array is controlled by a windowing function, and the beam pointing is formed by the receiving end beam.

[0155] Specifically, the sidelobe level is a factor that directly affects the system's resolution and interference suppression capability. Therefore, a windowing function is needed to control the recovered sidelobe level of the calibrated receiving array to significantly reduce the sidelobe level and thus improve the radar's performance. Finally, by using the beam pointing of the receiver beamforming, anti-interference beamforming of the target angle is achieved, effectively improving the radar's anti-interference capability, making it suitable for complex environments, and ensuring radar performance and accuracy.

[0156] Step S105 includes: assuming a beam is formed in the θ0 direction, and adding a low sidelobe window function win to the receiving pattern, to obtain a weight vector that maintains a low sidelobe level in the receiving pattern:

[0157]

[0158] Where b(θ0) represents the steering vector of the receiving array in the θ0 direction. Represents the Hadmard product;

[0159] The received signal, obtained by beamforming and weighted by weight vector, is as follows:

[0160] Y(t) = b win (θ0)·y cal (t); (26)

[0161] The joint weight vector of the hybrid analog-digital MIMO radar array is obtained as follows:

[0162]

[0163] Specifically, the radar's observation angle is set, and in order to reduce the influence of sidelobe levels, a low sidelobe window function is added to the received pattern to obtain a weight vector that maintains low sidelobe levels in the received pattern. Finally, the received signal, which is beamformed and weighted by the weight vector, is obtained, resulting in the joint weight vector of the mixed analog-digital (MIMO) radar array.

[0164] In this embodiment, an array model is constructed and array errors are estimated based on the array element arrangement and target observation angle. A least-squares-based transmit-receive separation calibration method is used to generate transmit and receive calibration matrices. The transmit array is divided into multiple subarrays, and phase modulation is applied to ensure orthogonal waveforms are transmitted between the subarrays. Based on the transmit calibration matrices, the phases of the array elements within each subarray are calibrated. After calibration, coherent waveforms are transmitted within the subarrays to achieve beamforming. Combining the high degrees of freedom of MIMO radar with the high gain of phased array radar, high gain can be effectively maintained, while the overall array retains the high angular gain advantage of MIMO radar. Advantages in resolution and target detection; employing waveform decoding technology, the echo signals from each subarray are separated and extracted from the received signal. The amplitude and phase of the echo signals are calibrated using a receiver calibration matrix. The echo sidelobe level of the calibrated receiver array is controlled by a window function, and the beam pointing is adjusted by receiver beamforming. By employing amplitude and phase calibration and beamforming, under antenna coupling, enhanced reception in specific areas and effective suppression of potential interference areas are achieved. This enhances the radar system's adaptability and anti-interference capability in complex environments, increases radar detection probability, and reduces radar false alarm probability.

[0165] In one embodiment, the radar anti-jamming beamforming method based on the analog-digital hybrid MIMO array described above can be illustrated by the following experimental data.

[0166] Scenario Setup: For a transmit-receive MIMO radar system, all array elements are uniformly arranged at half wavelength, with 16 transmit elements and 16 receive elements. Assuming the beam pointing is 0°, the transmit array is uniformly divided into 4 subarrays, each containing 4 elements. The window function used at the receiver is a 40dB Chebyshev window. Parameter selections are shown in Table 1 below:

[0167] Table 1 Parameter Value Selection Table

[0168]

[0169]

[0170] Experimental results: such as Figure 3 As shown, the calibration effect after subarray division of the hybrid analog-digital MIMO array radar is demonstrated. It can be seen that phase calibration at the transmitter end can reduce beam sidelobes and improve beam pointing accuracy.

[0171] like Figure 4 As shown, the anti-jamming performance of the hybrid analog-digital MIMO array radar is demonstrated, where the desired target echo signal in the main lobe direction is significantly enhanced, while interference signals in other directions are effectively suppressed.

[0172] In summary, this application obtains the transmission and reception calibration matrices through a separate calibration method. The transmission matrix is ​​divided into subarrays, and the divided transmission array maintains the high degree of freedom of the MIMO radar. Furthermore, phase calibration is performed on the transmission array using the transmission calibration matrix to form a precise beam pointing. At the receiving end, the echo signal is decoded and separated, and the amplitude and phase errors of the echo signal are calibrated using the receiving calibration matrix. The receiving array effectively controls the sidelobe level through a windowing function, and beam pointing is completed using receiver beamforming, enabling the radar system to meet the requirements of high gain and anti-interference performance.

[0173] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0174] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a computer storage medium (ROM / RAM, magnetic disk, optical disk) for execution by the computing device. In some cases, the steps shown or described can be performed in a different order than those described herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Therefore, the present invention is not limited to any particular hardware and software combination.

[0175] The above description, in conjunction with specific embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered within the scope of protection of the present invention.

Claims

1. A radar anti-jamming beamforming method based on a hybrid analog-digital MIMO array, characterized in that, Includes the following steps: Based on the array element arrangement and target observation angle, an array model is constructed and the array error is estimated. A transmit and receive calibration matrix is ​​generated using a least squares-based transmit-receive separation calibration method. The transmitting array is divided into multiple subarrays, and phase modulation is applied to make the multiple subarrays transmit orthogonal waveforms; According to the transmission calibration matrix, the phases of the array elements within the plurality of subarrays are calibrated. After calibration, coherent signals are transmitted within the subarrays to achieve beamforming, including: transmit calibration matrix Represented as: ；（17） Among them, the diagonal elements are the amplitude and phase compensation for antenna amplitude and phase errors, and the off-diagonal elements are the amplitude and phase compensation for antenna coupling effects. Divide into K subarrays according to the order of subarray division. Subcalibration matrix The elements in the sub-calibration matrix are: ；（18） In a hybrid analog-to-digital architecture, the transmitter uses a phase shifter to control the signal phase. Phase calibration is performed using the phase shifter, and the calculated phase calibration matrix for the transmitting antenna is as follows: ；（19） In the formula, This indicates that the sub-calibration matrix is ​​adjusted using the rotating vector method. Perform calibration; From the perspective of observation The calibrated response of the uncalibrated transmit array is represented as follows: ；（20） Within the subarray, a coherent transmitted signal is formed through beamforming. The subarray-level transmit array response is expressed as: ；（21） The calibrated subarray stage transmit array steering vector is then expressed as: ；（22） in, Indicates the observation angle Lower launch guide vector, This represents the conjugate transpose of the array partitioning matrix. Represented by vector The elements of the matrix form a diagonal matrix with the elements on the diagonal. This indicates a phase shift at the array element level, causing the direction to point towards the target angle; Waveform decoding technology is used to separate and extract echo signals from each subarray from the received signal, and the amplitude and phase of the echo signals are calibrated using a receiving calibration matrix. The echo sidelobe level of the calibrated receiving array is controlled by a windowing function, and the beam pointing is adjusted by beamforming at the receiving end.

2. The radar anti-jamming beamforming method based on a hybrid analog-digital MIMO array according to claim 1, characterized in that, The process involves constructing an array model based on the array element arrangement and target observation angle, estimating array errors, and generating transmit and receive calibration matrices using a least-squares-based transmit-receive separation calibration method. This includes: According to the target observation angle Obtain the actual array response for: ；（1） Where M is the number of transmitting antennas and N is the number of receiving antennas. arrive Indicates the observation angle Lower transmitting antenna arrive With the first receiving antenna The response arrive Indicates the transmitting antenna arrive With the second receiving antenna The response arrive Indicates transmitting antenna arrive With the One receiving antenna The response; The actual array response is represented using the transmit antenna array response vector and the receive antenna array response vector, as follows: ；（2） In the formula, Indicates the target observation angle Time x The transmit antenna array response of each transmit antenna Indicates the target observation angle Time x The transpose of the receiving antenna array response of each receiving antenna; For H observation angles, obtain the corresponding actual array response and reconstruct them respectively. The matrix, when decomposed into separate transmit and receive antenna array responses, yields: ；（3） The actual transmit antenna array response matrix under H observation angles is: ；（4） The actual receiving antenna array response matrix under H observation angles is: ；（5） The actual transmit antenna array response matrix and the actual receive antenna array response matrix are calibrated as follows: ；（6） In the formula, For the launch calibration matrix, Adjust the matrix for the transmitting antenna. To receive the calibration matrix, Adjust the matrix for the receiving antenna. Let H be the theoretical steering vectors of the transmitting array at H observation angles. The theoretical steering vector of the receiving array under H observation angles; Each launch vector is compared with its corresponding ideal steering vector at its angle. The optimal launch calibration matrix is ​​found by minimizing the launch objective function, which is: ； ， In the formula, From K The set of emission vectors collected from each angle. Denotes the Frobenius norm of a matrix; For the receiving vector, the optimal receiving calibration matrix is ​​found by minimizing the receiving objective function, which is: ；（8） In the formula, From K The set of conjugate transposes of the received vectors collected from each angle; For each observation matrix Singular value decomposition is performed using the following formula: ； ， Will It is approximately a rank-1 matrix, represented as: ； ， In the formula, For the maximum singular value, Is with The corresponding left singular value vector represents the transmit components of the MIMO antenna array system. Is with The corresponding right singular value vector represents the received component of the MIMO antenna array system. Represents the transpose of a matrix; Under H observation angles, the array response matrix Perform singular value decomposition: ；（11） In the formula, This represents the left singular vector matrix corresponding to the maximum singular value; ；（12） In the formula, The matrix representing the conjugate transpose of the right singular vector corresponding to the maximum singular value; Finding the optimal calibration matrix is ​​transformed into solving for the minimum norm, as shown in the formula: ；（13） The minimum norm is solved by least squares iteration to obtain the transmit calibration matrix and receive calibration matrix that satisfy the norm threshold.

3. The radar anti-jamming beamforming method based on a hybrid analog-to-digital MIMO array according to claim 2, characterized in that, The step of dividing the transmitting array into multiple subarrays and using phase modulation to transmit orthogonal waveforms between the multiple subarrays includes: The M transmission channels are divided into K subarrays, each subarray containing... One transmission channel, M×K dimensional matrix The value of the subarray is 1 if the m-th element belongs to the k-th subarray, and 0 otherwise. ；（14）， Where m = 1,2,…M, k = 1,2,…K, ; Assume the signals transmitted by each element antenna are represented as follows: From the perspective of observation Under these conditions, the uncalibrated transmit array response is represented as: ；（15） In the formula, This represents the transmit array response of M transmit antennas. Indicates the observation angle The transpose of the lower launch steering vector, coefficient It is the signal scaling factor, representing the gain or attenuation coefficient of the entire array. This represents the noise vector of M transmitted signals; After dividing into subarrays, the K subarrays are represented as: ；（16） In the formula, The transpose of the matrix is ​​used to perform phase modulation on the transmitted signals between subarrays, so that the transmitted waveforms between subarrays are orthogonal.

4. The radar anti-jamming beamforming method based on a hybrid analog-to-digital MIMO array according to claim 3, characterized in that, The method employs waveform decoding technology to separate and extract echo signals from each subarray from the received signal, and uses a receiving calibration matrix to calibrate the amplitude and phase of the echo signals, including: Waveform decoding technology is used to decode the echo waveform to obtain... The echo data was used to obtain the actual array response under the hybrid analog-digital structure: ；（23） In the formula, It is the scaling factor for the overall array signal. This represents the noise vector of the received echo. Represents the Kronecker product. This represents the steering vector of the receiving array; The receiver calibration matrix is ​​obtained by iterative calculation using the least squares method. Then, the calibrated expression for the receiver array response is obtained: ；（24） In the formula, , This is the noise vector of the received signal after calibration.

5. The radar anti-jamming beamforming method based on a hybrid analog-to-digital MIMO array according to claim 4, characterized in that, The method of controlling the echo sidelobe level of the calibrated receiving array through a windowing function and adjusting the beam pointing through receiver beamforming includes: Assuming in The direction forms a beam, and a low-sidelobe window function win is added to the received pattern to obtain a weight vector that maintains a low sidelobe level in the received pattern: ；（25） in, Indicates in The steering vector of the directional receiving array, Represents the Hadmard product; The received signal, obtained by beamforming and weighted by weight vector, is as follows: ；（26） The joint weight vector of the hybrid analog-digital MIMO radar array is obtained as follows: （27）。

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