A millimeter wave MIMO array two-dimensional far field fast imaging method

Abstract

The application provides a kind of millimeter wave MIMO array two-dimensional far field fast imaging method, comprising: step 1, mathematical modeling of echo signal is carried out;Step 2, reference point phase correction is carried out to signal, and phase is unfolded using far field approximation to received signal;Step 3, the image reconstruction process is converted into matrix multiplication;Step 4, the imaging area is divided into multiple sub-regions, reference point phase correction and image reconstruction are carried out to sub-regions respectively, and the overall imaging result is obtained by splicing sub-region image.The application simplifies processing steps, and improves imaging speed, which provides a method reference for MIMO array real-time imaging.

Description

Technical Field

[0001] This invention belongs to the field of millimeter-wave imaging, specifically relating to a two-dimensional far-field fast imaging method for millimeter-wave MIMO arrays. Background Technology

[0002] In the field of millimeter-wave imaging, MIMO arrays have been widely used in far-field imaging scenarios. Compared with near-field imaging, far-field imaging has lower resolution but greater flexibility because it has a limited impact on image quality due to errors caused by phase operations. Therefore, far-field imaging has a greater potential for real-time imaging compared to near-field imaging. However, most current imaging methods remain at the level of generalized, universal fast imaging methods, without fully and effectively utilizing the special properties of far-field imaging to further accelerate the imaging speed. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a two-dimensional far-field fast imaging method for millimeter-wave MIMO arrays, which is a two-dimensional fast polar coordinate imaging algorithm for millimeter-wave far-field arrays, and can greatly improve the imaging speed of millimeter-wave MIMO arrays.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for fast two-dimensional far-field imaging using a millimeter-wave MIMO array includes the following steps:

[0006] Step 1: Perform mathematical modeling of the echo signal;

[0007] Step 2: Perform reference point phase correction on the echo signal and use the far-field approximation to perform phase expansion on the received signal;

[0008] Step 3: Convert the image reconstruction process into matrix multiplication;

[0009] Step 4: Divide the imaging area into multiple sub-regions, perform reference point phase correction and image reconstruction on each sub-region, and stitch the sub-region images together to obtain the overall imaging result.

[0010] Further, step 1 includes: establishing the model of the echo signal as follows:

[0011]

[0012]

[0013] Where σ(x, z) is the target reflection coefficient, and x and z represent the target position; x t It is the location of the transmitting antenna, x r This refers to the location of the receiving antenna. exp[] is the exponential function, j is the imaginary unit, and R is the number of elements in the array. tR represents the distance from the transmitting antenna to the target. r This indicates the distance from the receiving antenna to the target; k0 represents the center wavenumber, and k represents the baseband wavenumber;

[0014] w t (x t ) and w r (x r ) is the antenna aperture window function, expressed as:

[0015]

[0016]

[0017] w kc (k) is the wavenumber window function, expressed as:

[0018]

[0019] L t and L r These represent the lengths of the transmitting and receiving arrays, respectively; B is the signal bandwidth, where B... k = 2πB / c, where c is the speed of light.

[0020] Further, step 2 includes:

[0021] When the array aperture is relative to the target distance The value is very small, at which point |x t |,|x r |< <R;

[0022] Distance Journey R t and R r The first-order approximation is:

[0023]

[0024]

[0025] The received echo signal is multiplied by the reference signal and approximated using a narrowband method. The received signal is further expressed as:

[0026]

[0027]

[0028] w a (x a The position of the equivalent array is represented as:

[0029]

[0030] x a =(xt +x r ) / 2

[0031] Where, x0, R0 and The coordinates of the reference point are represented; σ(sinθ,R) represents the target reflection coefficient in polar coordinates.

[0032] The narrowband approximation formula is:

[0033]

[0034] The subsequent step is to reconstruct the target reflectance coefficient image.

[0035] Further, step 3 includes: converting equation (6) into matrix multiplication form:

[0036]

[0037] Among them, S o The received signal, representing the product of the corresponding reference signal, is an M×N matrix, indicating the positions x of M equivalent antennas. a A two-dimensional matrix consisting of N frequency points k;

[0038] σ represents the discretized target region, which is a P×Q matrix representing P azimuth angles θ and Q distance cells R. A θ and A R There are two guide vectors, (*) H This represents the conjugate transpose operation;

[0039] Array guide vector A θ The element in the m-th row and p-th column represents A. R The element in the nth row and qth column is represented as:

[0040] (A θ ) mp =exp[j2k0x am (sinθ p -sinθ0)]

[0041] (A R ) nq =exp[j2k n (R q -R0)]

[0042] x am Indicates the position of the m-th antenna, k n θ represents the nth frequency point. p R represents the p-th target angle. q This represents the q-th distance cell;

[0043] Both guide vector matrices are orthogonal matrices, therefore the final target reflection coefficient reconstruction is expressed as:

[0044]

[0045] Further, step 4 includes: dividing the imaging area into several sub-regions, selecting the center point of different sub-regions as reference points for reference point phase correction, reconstructing the reflection coefficient image of each sub-region, and stitching the final sub-region imaging results together;

[0046] The matrix formula for imaging the i-th sub-region is:

[0047]

[0048] Where M represents the number of sub-regions. This represents the echo signal after phase correction at the reference point of the i-th sub-region. Array steering vector A θi The element in the m-th row and p-th column represents A. Ri The element in the nth row and qth column is represented as:

[0049] (A θi ) mp =exp[j2k0x am (sinθ p -sinθ i )]

[0050] (A Ri ) nq =exp[j2k n (R q -R i )]

[0051] x i R i and This represents the position coordinates of the reference point selected in the i-th sub-region.

[0052] Furthermore, the image reconstruction selection and The order of operations is used to save time, while selecting shallower imaging regions where the target exists saves computation.

[0053] Beneficial effects:

[0054] This invention proposes an extremely fast sub-region matched filtering method for image reconstruction using matrix multiplication, utilizing signal approximation methods in the far-field case. This method transforms traditional Fourier transform-based image reconstruction operations into merely a few matrix multiplications, simplifying the processing steps and improving imaging speed, thus providing a methodological reference for real-time imaging with MIMO arrays. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of a MIMO linear array imaging scenario;

[0056] Figure 2 A diagram illustrating the sub-region imaging method;

[0057] Figure 3 This is a schematic diagram of a simulated linear array;

[0058] Figure 4a , Figure 4b , Figure 4c This is an image of the point target imaging result; where Figure 4a This is a schematic diagram of a point target. Figure 4b This is a single-reference point matched filter image. Figure 4c The sub-region matched filter imaging map;

[0059] Figure 5 This is a schematic diagram of a linear MIMO array for an experimental scenario.

[0060] Figure 6 Image of the human target;

[0061] Figure 7 This is an image showing the results of imaging a target at an angle. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0063] For traditional MIMO arrays, this invention first performs reference point phase correction on the signal, then uses a far-field approximation to perform phase expansion on the received signal, and subsequently transforms the image reconstruction process into matrix multiplication. To obtain a larger imaging range, this method divides the imaging space into multiple subspaces, each selecting a different reference point, and reconstructs the image from the referenced signals separately. This method ensures the quality of the reconstructed image without increasing the computational load.

[0064] like Figure 1The diagram illustrates the imaging of a MIMO array in the far field. The target point within the imaging area is a generalized point, representing any target point. Both the receiving and transmitting antennas are located on the x-axis, which represents the azimuth direction, and the z-axis represents the range direction. The influence of the antenna radiation pattern and signal amplitude loss due to signal propagation can be ignored, as the signal amplitude loss within the target scene is approximately the same in the far field. Simultaneously, the half-power beamwidth of the antennas in the array will cover the target scene, and the radiated power of a single antenna to all objects in the target scene is approximately the same.

[0065] Therefore, the echo signal is modeled as:

[0066]

[0067]

[0068] Where σ(x, z) is the target reflection coefficient, and x and z represent the target position. t It is the location of the transmitting antenna, x r This refers to the location of the receiving antenna. exp[] is the exponential function, j is the imaginary number, and R... t R represents the distance from the transmitting antenna to the target. r This indicates the distance from the receiving antenna to the target. k0 represents the center wavenumber, and k represents the baseband wavenumber.

[0069] w t (x t ) and w r (x r ) is the antenna aperture window function, expressed as:

[0070]

[0071]

[0072] w kc (k) is the wavenumber window function, expressed as:

[0073]

[0074] L t and L r These represent the lengths of the transmitting and receiving arrays, respectively. B is the signal bandwidth, where B... k = 2πB / c, where c is the speed of light.

[0075] The following is a fast imaging method in polar coordinates for far-field conditions:

[0076] When the array aperture is relative to the target distance The value is very small, at which point |x t |,|xr |<<R. Distance历程R t and R r The first - order approximation of is expressed as:

[0077]

[0078]

[0079] The received echo signal is multiplied by the reference signal and a narrow - band approximation is performed. The received signal is further expressed as:

[0080]

[0081]

[0082] w a (x a ) represents the position of the equivalent array and can be expressed as:

[0083]

[0084] x a =(x t +x r ) / 2

[0085] where, x0, R0 and represent the position coordinates of the reference point. σ(sinθ, R) represents the target reflection coefficient in polar coordinate form. The narrow - band approximation formula is:

[0086]

[0087] Equation (8) is applicable to a relatively small bandwidth. As can be seen from Equation (6), the received signal is the two - dimensional FFT Fourier transform of the target distribution function. Therefore, image reconstruction can be performed using two - dimensional IFFT inverse Fourier transform. However, for the flexibility of subsequent processing, the present invention uses matched filtering instead of FFT to achieve reconstruction.

[0088] First, convert Equation (6) into the form of matrix multiplication:

[0089]

[0090] where, S o represents the received signal multiplied by the corresponding reference signal, which is an M×N matrix, representing a two - dimensional matrix composed of M equivalent antenna positions x a and N frequency points k.

[0091] σ represents the reconstructed target area after discretization, which is a P×Q matrix, representing P azimuth angles θ and Q range cells R. A θ and AR There are two guide vectors, (*) H This indicates the conjugate transpose operation.

[0092] Array guide vector A θ The element in the m-th row and p-th column can be represented as A. R The element in the nth row and qth column can be represented as:

[0093] (A θ ) mp =exp[j2k0x am (sinθ p -sinθ0)]

[0094] (A R ) nq =exp[j2k n (R q -R0)]

[0095] x am Indicates the position of the m-th antenna, k n θ represents the nth frequency point. p R represents the p-th target angle. q This represents the q-th distance unit.

[0096] Both steering vector matrices are orthogonal. Therefore, the final target reflection coefficient reconstruction can be expressed as:

[0097]

[0098] To improve the overall imaging effect, this invention divides the imaging area into several sub-regions, such as... Figure 2 As shown, the center points of different sub-regions are selected as reference points for reference point phase correction, and matched filtering imaging is performed separately. The imaging results of the sub-regions are then stitched together. The matrix formula for the imaging of the i-th sub-region is:

[0099]

[0100] Where M represents the number of sub-regions. This represents the echo signal after phase correction at the reference point of the i-th sub-region. Array steering vector A θi The element in the m-th row and p-th column represents A. Ri The element in the nth row and qth column is represented as:

[0101]

[0102] x i R i and This represents the position coordinates of the reference point selected in the i-th sub-region.

[0103] Image reconstruction can be selected and The order of operations can be optimized to save time. Additionally, selecting a shallower imaging region where the target exists can further reduce computational cost. Since matched filtering is performed separately in the azimuth sub-regions, it does not increase computational complexity.

[0104] (2) The results of the polar coordinate fast imaging method are as follows:

[0105] use Figure 3 A linear array was simulated and verified, consisting of 81 transmitting antennas and 21 receiving antennas, with a total of 1701 virtual antenna centers. The frequency range was 90-100 GHz, with 128 frequency points. The spacing between the transmitting antennas was 5.2 mm, and the spacing between the receiving antennas was 20.8 mm. The imaging results were as follows: Figure 4a , Figure 4b , Figure 4c As shown, where Figure 4a This is a schematic diagram of a point target. Figure 4b This is a single-reference point matched filter image. Figure 4c The image shows a sub-region matched filter image. The imaging results indicate that the target reconstruction at a single reference point exhibits defocusing at the edges, while the sub-region-based method effectively focuses the target. Furthermore, the reconstruction time is only 0.05 seconds, making real-time imaging possible.

[0106] Experimental data were obtained using a real-aperture scanning system with a linear MIMO array operating at 90-100 GHz. The antenna array configuration is as follows: Figure 5 As shown, there are 8 transmitting antennas and 8 receiving antennas. This invention images 10 corner reflectors and a human target. The target is 7.4 meters away from the antenna. The raw data is an 8×8×128×35 matrix. This invention also selects three sub-regions. (See attached image.) Figure 6 and Figure 7 The two imaging results shown are synthesized by stitching together multiple two-dimensional images in the azimuth direction. Both images employ a sub-region imaging method in the azimuth direction. It can be observed that all methods can recover the target well. The image reconstruction time is 0.075 s, reflecting the speed of the proposed method.

[0107] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A two-dimensional far-field fast imaging method for millimeter-wave MIMO arrays, characterized in that, Includes the following steps: Step 1: Perform mathematical modeling of the echo signal; the established model of the echo signal is as follows: in, This is the target reflection coefficient, where x and z represent the target position; It is the location of the transmitting antenna. Here, exp[] represents the location of the receiving antenna, exp[] is the exponential function, and j is the imaginary unit. This indicates the distance from the transmitting antenna to the target. This indicates the distance from the receiving antenna to the target; k0 represents the center wavenumber, and k represents the baseband wavenumber; and It is the antenna aperture window function, expressed as: ； It is a wavenumber window function, expressed as: and represents the lengths of the transmitting and receiving arrays, respectively; B is the signal bandwidth, where c is the speed of light; Step 2: Perform reference point phase correction on the echo signal and use the far-field approximation to perform phase expansion on the received signal; When the array aperture is relative to the target distance It is very small, and at this time it satisfies ; Distance and Journey and The first-order approximation is: ； ； The received echo signal is multiplied by the reference signal and approximated using a narrowband method. The received signal is further expressed as: The position of the equivalent array is represented as: ； in, , and Indicates the position coordinates of the reference point; Represents the target reflection coefficient in polar coordinates; The narrowband approximation formula is: The next step is to reconstruct the target reflectance coefficient image; Step 3: Convert the image reconstruction process into matrix multiplication; Step 4: Divide the imaging area into multiple sub-regions, perform reference point phase correction and image reconstruction on each sub-region, and stitch the sub-region images together to obtain the overall imaging result.

2. The two-dimensional far-field fast imaging method for millimeter-wave MIMO arrays according to claim 1, characterized in that, Step 3 includes: converting equation (6) into matrix multiplication form: in, The received signal, representing the corresponding reference signal, is a Matrix, representing One equivalent antenna position and frequency points A two-dimensional matrix composed of; The target region for reconstruction after discretization is a A matrix representing P azimuth angles. and Q distance units ; and There are two guide vectors. This represents the conjugate transpose operation; Array guide vector The element in the m-th row and p-th column represents the sum. The element in the nth row and qth column is represented as: ； ； This indicates the position of the m-th equivalent antenna. This represents the wave number at the nth frequency point; This represents the p-th target angle. This represents the q-th distance cell; Both guide vector matrices are orthogonal matrices, therefore the final target reflection coefficient reconstruction is expressed as: 。 3. The two-dimensional far-field fast imaging method for millimeter-wave MIMO arrays according to claim 2, characterized in that, Step 4 includes: dividing the imaging area into several sub-regions, selecting the center point of different sub-regions as reference points for reference signal multiplication, and reconstructing the reflection coefficient image of each sub-region; and stitching the final sub-region imaging results together. The matrix formula for imaging the i-th sub-region is: ； Where M represents the number of sub-regions. The array steering vector represents the echo signal after phase correction at the reference point of the i-th sub-region. The element in the m-th row and p-th column represents the sum. The element in the nth row and qth column is represented as: ； ； , and This represents the position coordinates of the reference point selected in the i-th sub-region.

4. The two-dimensional far-field fast imaging method for millimeter-wave MIMO arrays according to claim 3, characterized in that, The image reconstruction selection and The order of operations is used to save time, while selecting shallower imaging regions where the target exists saves computation.

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