A millimeter wave MIMO radar array amplitude and phase error calibration method based on least square criterion

Abstract

This invention relates to a method for calibrating the amplitude and phase errors of a millimeter-wave MIMO radar array based on the least squares criterion, belonging to the field of millimeter-wave radar technology. The method includes: first, initializing the amplitude and phase error matrix G and setting a convergence threshold; second, fixing G, scanning the angle of the incoming wave direction, and obtaining the desired target azimuth angle θ when the cost function J is minimized. D Then θ D With the value fixed, find the matrix G that minimizes the cost function J'; given the currently determined G and θ D Calculate the estimation error and determine if the convergence condition is met; if not, repeat the iterative optimization of G and θ. D Until the convergence condition is met; finally, output the final estimated G and θ. D It is used for real-time steering vector compensation to complete calibration. This invention requires no auxiliary source and utilizes iterative optimization techniques to effectively calibrate the amplitude and phase errors of the sensor, reducing the impact of rotational uncertainty on the final amplitude and phase error matrix estimation, and improving the accuracy of beam pointing and the robustness of the error calibration system.

Description

Technical Field

[0001] This invention relates to the field of array radar beamforming technology, and in particular to a method for calibrating the amplitude and phase errors of a millimeter-wave MIMO radar array based on the least squares criterion. Background Technology

[0002] Millimeter-wave radar has been widely used in autonomous driving and advanced driver assistance systems due to its advantages such as small size, light weight, and ability to operate normally in extreme weather conditions. However, traditional array radar requires more array elements to improve angular resolution, leading to increased computational complexity and cost. In contrast, multiple-input multiple-output (MIMO) radar uses fewer antennas to synthesize a virtual array, providing higher measurement accuracy and reducing costs, and is therefore widely used in autonomous driving.

[0003] Modern automotive radar utilizes antenna arrays and beamforming algorithms to achieve large-angle scanning, a technology that plays a crucial role in autonomous driving and advanced driver assistance systems (ADAS). However, this technology is extremely sensitive to array errors. When there are element errors in the transmit and receive arrays of a MIMO radar, a model mismatch occurs between the ideal array manifold and the actual array manifold, leading to a sharp decline in the performance of traditional algorithms. The beamformer will produce high sidelobes, and in severe cases, it may even alter the direction of the main beam.

[0004] High sidelobes introduce additional interference signals, making it difficult for radar to accurately detect and locate targets, posing a significant threat to the safety of autonomous vehicles. Furthermore, changes in the main beam direction can cause the radar to fail to correctly identify the distance and direction of objects ahead, affecting vehicle decision-making and control. Therefore, accurate error calibration is crucial for automotive millimeter-wave MIMO radar.

[0005] To address amplitude and phase errors, researchers have proposed various calibration algorithms, which can be categorized into two types based on whether an azimuth-accurate calibration source is required: active calibration algorithms and self-calibration algorithms. Active calibration algorithms calibrate amplitude and phase errors by setting an auxiliary source at a known azimuth. However, the estimation accuracy is affected by the accuracy of the auxiliary source's azimuth; higher accuracy results in higher estimation accuracy, and vice versa. Furthermore, active calibration algorithms are limited when it's inconvenient to set up an auxiliary source in practical environments. Self-calibration algorithms, on the other hand, do not require an auxiliary source at a known azimuth. Instead, they use an optimization function to jointly estimate the error parameters and the source azimuth. Traditional self-calibration methods, such as the one proposed by Paulraj that utilizes the ideal covariance matrix of a uniform linear array with a Toeplitz structure for estimating array channel amplitude and phase errors, suffer from rotational uncertainty in the estimation results, requiring additional information to resolve. Summary of the Invention

[0006] To address the problems existing in the self-calibration algorithms of the prior art, this invention provides a millimeter-wave MIMO radar array amplitude and phase error calibration method based on the least squares criterion. It utilizes iterative optimization technology to gradually approach the global optimal solution by alternately minimizing the cost function, thereby reducing the impact of rotation uncertainty on the final amplitude and phase error matrix estimation and improving the accuracy of beam pointing and the robustness of the error calibration algorithm.

[0007] This invention provides a method for calibrating the amplitude and phase errors of a millimeter-wave MIMO radar array based on the least squares criterion, comprising:

[0008] Step 1: Initialize the number of iterations n = 0 and the estimated amplitude and phase error matrix. Convergence threshold ε; where I is the identity matrix, M t M represents the number of transmitting antennas in the radar array. r This represents the number of receiving antennas in the radar array. Each iteration includes steps 2 through 5.

[0009] Step 2: Fix G, scan the incoming wave direction θ, and update the target azimuth angle θ by minimizing the cost function J according to formula (1). D :

[0010]

[0011] In the formula, w is the steering vector of the actual radar array, the superscript H denotes the conjugate transpose, A(θ) is the array manifold matrix, and a(θ) is the vector of the array. D ) is the steering vector of the target signal.

[0012] Step 3: θ obtained from Step 2 D Fixed a(θ D According to formula (2), minimize the cost function J′ and update G as follows:

[0013] J′=min||w H Ga H (θ D (2)

[0014] Step 4: Calculate the estimation error J in the current iteration from the updated G. n as follows:

[0015] J n =Gw-a(θ) D (3)

[0016] Step 5: When J is satisfied n-1 -J n If n > ε, increment n by 1 and return to step 2 to continue iteration; otherwise, end the iteration.

[0017] Step 6: Use the estimated value of the amplitude and phase error matrix G obtained from the final iteration to perform error calibration on the signal received by the millimeter-wave MIMO radar.

[0018] Furthermore, step 2 includes:

[0019] Step 2-1: When a monostatic MIMO radar detects a single stationary target, the steering vector of the target signal is equal to the steering vector a of the transmitting array. t (θ D ) and receiver array steering vector a r (θ D The Kronecker product is...

[0020] Step 2-2: Collect the radar antenna array received signal X(t) at time t, and then calculate the covariance matrix R of the received signal X(t). x For the covariance matrix R x Perform eigenvalue decomposition to obtain the largest eigenvalue. The corresponding eigenvector is the steering vector w of the actual array.

[0021] Steps 2-3: According to formula (4), scan the incoming wave direction θ to obtain the corresponding minimum J1 value. The corresponding angle is the calibrated desired signal θ. D ;

[0022]

[0023] Where a(θ) is the guide vector corresponding to the scanning angle.

[0024] Furthermore, step 3 includes:

[0025] Step 3-1: Based on the target signal value θ obtained in Step 2-3 D Substitute the guiding vector a(θ) D ), calculate formula (2), and determine G.

[0026] Step 3-2: To avoid the phase and amplitude error matrix G being non-invertible, it is transformed into the least squares form to obtain formula (5).

[0027] G = diag(w H w) -1 w H a(θ D (5)

[0028] The superscript -1 indicates that the inverse matrix is ​​being sought.

[0029] The present invention adopts the above-mentioned technical solution and has the following beneficial effects: The millimeter-wave MIMO radar array amplitude and phase error calibration method based on the least squares criterion provided by the present invention does not require an auxiliary source. Through iterative optimization technology, it effectively calibrates the amplitude and phase errors of the sensor, significantly improves the accuracy of DBF (digital beamforming) beam pointing and the robustness of the error calibration system, and reduces the impact of rotational uncertainty on the final amplitude and phase error matrix estimation. It is particularly suitable for autonomous driving and advanced driver assistance systems, and significantly improves the reliability and safety of radar in these applications. Attached Figure Description

[0030] Figure 1 This is a schematic flowchart of the millimeter-wave MIMO radar array amplitude and phase error calibration method of the present invention;

[0031] Figure 2 This is a schematic diagram of a monostatic MIMO radar transmission and reception provided in an embodiment of the present invention;

[0032] Figure 3 This is a simulation pattern before and after calibration using the self-calibration method of this invention in an embodiment of the invention;

[0033] Figure 4 This is a test scenario diagram provided in an embodiment of the present invention;

[0034] Figure 5 This is a measured radiation pattern before and after calibration using the self-calibration method of this invention in an embodiment of the invention. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Traditional self-calibration methods use an ideal covariance matrix with a Toeplitz structure. The symmetry of the Toeplitz structure leads to a relative rotation in the estimated array amplitude and phase errors. This means that while the relative magnitude and phase of the amplitude and phase errors can be determined, their absolute values ​​or actual directions cannot be determined, as this rotation cannot be uniquely determined solely by the existing covariance matrix. To address this problem, this invention provides a millimeter-wave MIMO radar array amplitude and phase error calibration method based on the least squares criterion. It avoids using the properties of the Toeplitz structure for amplitude and phase error calibration by iteratively minimizing the cost function to gradually approach the global optimum, progressively reducing the amplitude and phase errors and eliminating rotational uncertainty.

[0037] like Figure 1 As shown, the overall process of the millimeter-wave MIMO radar array amplitude and phase error calibration method based on the least squares criterion of the present invention includes: first, initializing the amplitude and phase error matrix and setting the number of iterations and the convergence threshold; second, fixing the amplitude and phase error matrix, minimizing the cost function through iterative optimization, and obtaining the target azimuth angle; then, fixing the obtained target azimuth angle, minimizing the cost function through iterative optimization, and obtaining the updated amplitude and phase error matrix; then calculating the cost function value of the current iteration and checking whether the convergence condition is met; if not, repeating the above iterative optimization process until the convergence condition is met; finally, outputting the final estimated amplitude and phase error matrix and the desired angle, and compensating them into the true steering vector to complete the calibration. The following is combined with... Figure 1 The implementation steps of the millimeter-wave MIMO radar array amplitude and phase error calibration method based on the least squares criterion described in this invention are explained in detail.

[0038] Step 1: Initialize the number of iterations n = 0, and estimate the amplitude and phase error matrix. Convergence threshold ε = 10 -6 Where I is the identity matrix, M t M r These represent the number of transmitting antennas and the number of receiving antennas, respectively.

[0039] Step 2: Fix G, scan the angle of the incoming wave direction, and update the target azimuth angle θ by minimizing the cost function J according to the following formula. D .

[0040]

[0041] In the formula, w is the steering vector of the actual radar array, A(θ) is the array manifold matrix, and a(θ) is the steering vector of the actual radar array. D ) is the steering vector of the target signal, and the superscript H indicates the conjugate transpose; θ is the direction of the incoming signal wave, and the scanning angle range is -90° to 90°.

[0042] Step 2-1: Calculate the signal steering vector. When the target is stationary, for a single target signal, a monostatic MIMO radar, such as... Figure 2 As shown, its steering vector is equal to the Kronecker product of the steering vectors of the transmitting and receiving arrays, i.e. Transmitter array steering vector a t (θ D ) and receiver array steering vector a r (θ D Specifically, it is expressed as:

[0043]

[0044] Among them, M t For the number of transmitting antennas, M r The number of receiving antennas is d, and both the transmitting and receiving antennas are uniformly linearly arranged with element spacing of d. t and d r The superscript T indicates transpose, and λ indicates the signal wavelength.

[0045] Step 2-2: Calculate the steering vector w of the actual array.

[0046] The collected radar antenna array received signal is obtained according to the following formula:

[0047] X(t)=Γ(a(θ D )s(t)+n(t))

[0048] In the formula, X(t) is the received signal acquired at time t; n(t) is the array noise vector at time t; and s(t) is the incident signal vector at time t. Let ΓG represent the joint amplitude and phase error matrix of the equivalent arrays of the transmitting and receiving arrays. In the case of full calibration, ΓG = I.

[0049] The covariance matrix R of the array received signal is calculated according to the following formula. x :

[0050] R x =E[X(t)X H [(t)]=σ S 2 Γa(θ D )a H (θ D )Γ H +σ n 2 I

[0051] Where, σ S It is the target signal power, σ n It is noise power.

[0052] For the above covariance matrix R x Perform eigenvalue decomposition to obtain the largest eigenvalue. The corresponding eigenvector is the steering vector w of the actual array.

[0053] Steps 2-3: According to the following formula, iterate through θ to obtain the value when the cost function J1 is at its minimum, and use it as the calibrated expected signal θ. D .

[0054]

[0055] Step 3: Fix the calculated target azimuth angle θ D Substitute the target signal steering vector a(θ) D ), and update G by minimizing the cost function J′ according to the following formula.

[0056] J′=min||w H Ga H (θ D )||

[0057] Step 3-1: Substitute the target azimuth angle obtained in Step 2-3 into the guidance vector a(θ) D Then, minimize the cost function J′ to calculate G.

[0058] Step 3-2: To avoid the amplitude and phase error matrix G being non-invertible, it is transformed into a least squares form, as follows:

[0059] G = diag(w H w) -1 w H a(θ D )

[0060] The superscript -1 indicates that the inverse matrix is ​​being sought.

[0061] Step 4: Determine if convergence has occurred. Calculate the estimation error J for the current nth iteration. n as follows:

[0062] J n =Gw-a(θ) D )

[0063] Step 5: If J is satisfied n-1 -J n If the result is greater than ε, continue iterating until n = n + 1, then return to step 2; otherwise, end the iteration and output the final G and θ. D .

[0064] Step 6: Using the estimated value G of the obtained error matrix, perform error calibration on the data received by the millimeter-wave MIMO radar in practical applications.

[0065] The technical effects of the method of the present invention will be further explained below in conjunction with simulation experiments and actual measurements.

[0066] use Figure 2 A simulation experiment was conducted on the monostatic MIMO radar system shown, with the signal center frequency set at 77 GHz and the number of transmitting array elements M. t The number of receiving array elements Mr is 4, the antenna array is uniformly linearly arranged, the desired signal direction is 10°, the received noise is Gaussian white noise, the scanning step is 0.1°, the signal-to-noise ratio SNR = 0dB, the normalized amplitude error varies randomly within (0.5~1.5), and the phase error varies randomly within (-60°~60°).

[0067] like Figure 3 As shown in the simulation experiment using the method of this invention, a beam pattern before and after calibration is obtained. It can be seen that the main beam pointing of the beam pattern calibrated using the method of this invention is more accurate and consistent with the true direction. Furthermore, the sidelobe level is significantly reduced, and the performance of the beam pattern is significantly improved. Therefore, the method of this invention can accurately solve for the amplitude and phase error matrix and the desired angular direction, improving the reliability and security of millimeter-wave MIMO radar array applications.

[0068] To further verify the effectiveness of the method of the present invention, the following was adopted: Figure 4 The test scenario shown uses a two-transmitter, four-receiver radar, with the target positioned at 15°. (Example:) Figure 5 As shown, the method of the present invention is applied in... Figure 4 The measured radiation patterns before and after calibration in the test scenario show that the main beam pointing direction after calibration using the method of this invention is 14.4°, which is consistent with the expected direction. The sidelobe level is also significantly reduced, which can realize the calibration of amplitude and phase error of monostatic millimeter-wave MIMO radar system.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and all such modifications and transformations should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for calibrating the amplitude and phase errors of a millimeter-wave MIMO radar array based on the least squares criterion, characterized in that, The method continuously updates the radar array amplitude and phase error matrix by iteration and target azimuth angle , comprising the following steps: Step 1: initialize the amplitude and phase error matrix to be estimated , set the initial iteration number , set the convergence threshold ; wherein I is the unit matrix, is the number of radar array transmitting antennas, is the number of radar array receiving antennas; Update radar array amplitude and phase error matrix and target orientation angle joint cost function as follows: ; (1) in, This is the steering vector of the actual radar array, with the superscript H indicating the conjugate transpose. It is an array manifold matrix; The angle range is -90° to 90°; The steering vector of the target signal; Each iteration process includes steps 2 to 5; Step 2: Fix the amplitude and phase error matrix , joint cost function Transform into a cost function as follows: ; (2) in, It is the guide vector corresponding to the scanning angle; Scanning direction angle The scanning angle range is -90° to 90°, minimizing the cost function. ,renew ; The minimum corresponding For the calibrated desired signal ; Step 3: Calculate the target azimuth angle Fixed, joint cost function Transform into a cost function as follows: ; (3) Iterative optimization to minimize the cost function ,renew ; Step 4: Updated Calculate the estimation error in the current iteration as follows: ; (4) Step 5: If satisfied , Increment by 1, return to step 2 and continue iterating; otherwise, end the iteration. Step 6: Utilize the amplitude and phase error matrix output from the final iteration Error calibration is performed on the signals received by the millimeter-wave MIMO radar array.

2. The method for calibrating the amplitude and phase error of a millimeter-wave MIMO radar array based on the least squares criterion according to claim 1, characterized in that, Step 2 includes: Step 2-1: When a monostatic MIMO radar detects a single stationary target, the steering vector of the target signal... Equal to the transmission array steering vector and receiver array steering vector Make the Kronecker product; Step 2-2: Acquire the radar antenna array received signal at time t. Then calculate the received signal. covariance matrix For the covariance matrix Perform eigenvalue decomposition to obtain the largest eigenvalue; the corresponding eigenvector is then the steering vector of the actual array. ; Steps 2-3: Scan the direction of incoming wave According to formula (2), we get The angle corresponding to the minimum is the calibrated desired signal. .

3. A method for calibrating the amplitude and phase error of a millimeter-wave MIMO radar array based on the least squares criterion according to claim 1 or 2, characterized in that, Step 3 includes: Step 3-1: Substitute the target azimuth angle obtained in Step 2 into the guidance vector. Then minimize the cost function Calculate the amplitude and phase error matrix ; Step 3-2: To avoid amplitude and phase error matrix Irreversible, will Transformed into least squares form, as follows: The superscript -1 indicates that the inverse matrix is ​​being sought.

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