An Omega-K algorithm-based synthetic aperture imaging method for orthogonal frequency division multiplexing signals

Abstract

This invention discloses a synthetic aperture imaging method based on the Omega-K algorithm using orthogonal frequency division multiplexing (OFDM) signals, belonging to the field of radar imaging technology. The method described in this invention fully considers the high range resolution advantage of OFDM signals during synthetic aperture imaging. It performs range-direction Fourier transform on the echo signal, range-direction matched filtering in the range-frequency domain and azimuth-time domain, followed by azimuth-direction Fourier transform to transform the data to the two-dimensional frequency domain. Azimuth-direction matched filtering is then performed in the two-dimensional frequency domain, and Stolt interpolation is used to correct the phase of higher-order coupling in the range and azimuth directions. Finally, an inverse two-dimensional Fourier transform is performed to obtain the imaging result. This is a highly efficient synthetic aperture imaging method based on OFDM signals, achieving good focusing effects even at large oblique angles, and enabling high-precision, high-resolution imaging.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to a synthetic aperture imaging method based on the Omega-K algorithm for orthogonal frequency division multiplexing signals. Background Technology

[0002] Synthetic Aperture Radar (SAR) is an all-weather, high-resolution imaging technology that operates around the clock. By moving the radar antenna relative to the target, it creates a virtual antenna that is longer than the actual antenna, significantly improving resolution and achieving high-precision imaging. It is widely used in Earth observation, military reconnaissance, meteorological monitoring, and disaster early warning. In recent years, as radar and communication frequency bands have become increasingly similar, the demand for integrated radar and communication technologies has continued to grow, taking into full account spectrum and hardware resources. Integrated radar and communication technologies combine radar detection and communication functions, enabling simultaneous target detection and information transmission by sharing hardware and spectrum resources.

[0003] OFDM (Orthogonal Frequency Division Multiplexing) divides the spectrum into multiple orthogonal subcarriers for data transmission, reducing inter-symbol interference and exhibiting strong resistance to multipath interference. Furthermore, it utilizes cyclic prefixes to further mitigate multipath effects. Using OFDM signals for communication signal transmission not only enables rapid information transmission but also significantly improves spectrum utilization efficiency, making OFDM signals one of the optimal candidate signals for integrated radar and communication. For synthetic aperture imaging using OFDM signals, existing algorithms generally employ Range Doppler (RDA). RDA is typically used for low-angle or side-view imaging. In the range-Doppler domain, RDA decouples the range and azimuth directions through interpolation. However, this can lead to geometric distortion at large angles of view, and the accuracy of RDA imaging may be insufficient in certain high-precision applications. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a synthetic aperture imaging method based on the Omega-K algorithm using orthogonal frequency division multiplexing (OFDM) signals. In the process of synthetic aperture imaging using OFDM signals, the high range resolution advantage of OFDM signals is fully considered. Range Fourier transform is performed on the echo signal, followed by range-matched filtering in the range-frequency and azimuth-time domains. Then, azimuth Fourier transform is performed to transform the data to the two-dimensional frequency domain. Azimuth-matched filtering is performed in the two-dimensional frequency domain, and Stolt interpolation is used to correct the phase of higher-order coupling in the range and azimuth directions. Finally, an inverse two-dimensional Fourier transform is performed to obtain the imaging result. This is an efficient synthetic aperture imaging method based on OFDM signals, achieving good focusing effects even at large oblique angles, and enabling high-precision, high-resolution imaging.

[0005] The technical problem addressed by this invention is solved as follows:

[0006] A synthetic aperture imaging method based on the Omega-K algorithm for orthogonal frequency division multiplexing signals includes the following steps:

[0007] Step 1: Process the echo data s from SAR imaging based on OFDM signals. r After removing the center carrier frequency (τ, η), a range-directed Fourier transform is performed; a Fourier transform is then performed on the range-directed reference signal s0(τ); the range-compressed frequency domain signal S is obtained by multiplying the two Fourier transform signals by their conjugates. ic (f τ ,η);

[0008] Step 2, for signal S ic (f τ Perform an azimuth-to-Fourier transform on η) to obtain the two-dimensional frequency domain signal S. ic (f τ f η );

[0009] Step 3, Two-dimensional frequency domain signal S ic (f τ f η ) and two-dimensional frequency domain filter H(f τ f η Multiplying these two signals yields the uncorrected range-azimuth higher-order coupled phase two-dimensional frequency domain signal S. b (f τ f η );

[0010] Step 4: Use Stolt interpolation to correct the higher-order coupling phase between the range and azimuth directions, obtaining the two-dimensional frequency domain signal S of the corrected higher-order coupling phase in the range and azimuth directions. l (f τ ′, f η );

[0011] Step 5: For signal S l (f τ ′, f η Perform a two-dimensional inverse Fourier transform to obtain the time-domain data s. out (τ′,η) is used as the imaging result.

[0012] Furthermore, the specific process of step 1 is as follows:

[0013] The range-oriented radar reference signal s0(τ) is expressed as:

[0014]

[0015] Where τ is the fast-time variable, w rLet R0 be the range window function, where R0 is the shortest distance between the radar and the target, c is the speed of light, N is the number of OFDM signal subcarriers, and 0 ≤ k ≤ N-1. k The information transmitted for the k-th subcarrier; T represents the radar pulse width, and j represents the imaginary part.

[0016] SAR imaging echo data based on OFDM signals r (τ, η) is represented as:

[0017]

[0018] in, v is the velocity of the radar platform, η is the slow-time variable; w a For the azimuth envelope window function, η c g is the beam center deviation time; m f is the target reflection coefficient. c For carrier frequency,

[0019] After removing the center carrier frequency, s r (τ, η) is represented as:

[0020]

[0021] For s respectively r Perform a range-to-Fourier transform on (τ, η) and s0(τ) and multiply them by their conjugates to obtain the range-compressed frequency domain signal S. ic (f τ ,η):

[0022]

[0023] Among them, f τ For fast time-frequency domain variables, sinc is the sigma function, 0≤n≤N-1, S n For the information transmitted by the nth subcarrier, W r This is the frequency domain representation of the distance window function.

[0024] Furthermore, in step 2, the two-dimensional frequency domain signal S is obtained through the principle of stationary phase. ic (f τ f η Specifically:

[0025]

[0026] In the above formula, S ic (f τ f η The phase of ) is According to the principle of stationary phase Then S ic (f τ f η ) is represented as:

[0027]

[0028]

[0029] Among them, f η W is a slow-time frequency domain variable. a This is the frequency domain representation of the azimuth envelope window function; The center of the Doppler frequency is t0, which is the zero Doppler time.

[0030] Furthermore, in step 3, the two-dimensional frequency domain filter H(f) τ f η )for:

[0031]

[0032] Among them, R ref For reference distance;

[0033] The two-dimensional frequency domain signal S after azimuth pulse compression b (f τ f η )for:

[0034]

[0035] Furthermore, the specific process of step 4 is as follows:

[0036] The following correction is achieved using the Stolt interpolation mapping method:

[0037] For S b (f τ f η Perform the above operations to obtain S l (f τ ′, f η The expression for ) is:

[0038]

[0039] Among them, f τ ′ represents the fast time frequency domain variable after Stolt interpolation.

[0040] Furthermore, the specific process of step 5 is as follows:

[0041] In S l (f τ ′, f ηLieutenant General Let S be a constant. k Encoding with 1 and -1, then the time-domain data s out The expression for (τ′,η) is:

[0042]

[0043] Where τ′ is the fast time variable after Stolt interpolation.

[0044] The beneficial effects of this invention are:

[0045] The method described in this invention can accurately compress the reference distance and remove the higher-order coupling phase of the range and azimuth directions through Stolt interpolation for non-reference distances, thereby achieving high-precision and high-resolution imaging. It also has good imaging effects when the oblique angle is large, and the implementation process does not involve complex calculations. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the method described in this invention;

[0047] Figure 2 This is a single-point target imaging image in the method described in the embodiment;

[0048] Figure 3 This is a row slice map showing the distance to the point target in the method described in the embodiment;

[0049] Figure 4 This is a directional slice of the point target in the method described in the embodiment;

[0050] Figure 5 This is a single-point target imaging image from the existing RDA algorithm.

[0051] Figure 6 A multi-point target distribution map configured for the method described in the embodiments;

[0052] Figure 7 This is an image showing the multi-point target imaging result from the method described in the embodiment;

[0053] Figure 8 This is an image showing the imaging result of the method described in the embodiment at an oblique angle of 10 degrees. Detailed Implementation

[0054] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0055] This embodiment provides a synthetic aperture imaging method based on the Omega-K algorithm for orthogonal frequency division multiplexing signals, and its flowchart is shown below. Figure 1As shown, the raw echo of the input OFDM-based SAR imaging is processed to obtain a two-dimensional image of the OFDM-based SAR imaging. The specific steps include:

[0056] Step 1: Process the echo data s from SAR imaging based on OFDM signals. r After removing the center carrier frequency (τ, η), a range-directed Fourier transform is performed. Then, a Fourier transform is performed on the range-directed reference signal s0(τ), and the range compression signal S is obtained by conjugate multiplication. ic (f τ ,η);

[0057] Radar reference signal s0(τ):

[0058]

[0059] Where τ is the fast time variable, j is the imaginary part sign, c is the speed of light; N is the number of OFDM signal subcarriers; 0≤k≤N-1, S k The information transmitted for the k-th subcarrier; T is the radar pulse width, R0 is the shortest distance between the radar and the target, and w r (τ) is the distance window function.

[0060] SAR imaging echo data based on OFDM signals r (τ, η) are:

[0061]

[0062] Among them, g m f is the target reflection coefficient. c Let η be the carrier frequency and η be the slow time variable. v represents the speed of the radar platform. w a (η) is the azimuth envelope window function, η c This represents the beam center deviation time.

[0063] After removing the center carrier frequency, s r (τ, η) becomes:

[0064]

[0065] For s respectively r Perform a range-to-Fourier transform on (τ, η) and s0(τ) and multiply them by their conjugates to obtain the range-compressed frequency domain signal S. ic (f τ ,η):

[0066]

[0067] Among them, f τ For fast time-frequency domain variables, sinc is the sigma function, 0≤n≤N-1, S n For the information transmitted by the nth subcarrier, W r (f τ ) for w r The frequency domain representation of (τ).

[0068] Step 2, for S ic (f τ The η signal undergoes an azimuth-to-Fourier transform, which is converted to a two-dimensional frequency domain to obtain S. ic (f τ f η );

[0069] In step 2, the two-dimensional frequency domain signal S is obtained through the stationary phase principle. ic (f τ f η Specifically:

[0070]

[0071] S ic (f τ f η The phase of ) is According to the principle of stationary phase Then S ic (f τ f η ) is represented as:

[0072]

[0073] Among them, f η For slow time frequency domain variables, Antenna radiation pattern w a (η-η c The frequency domain form of the two is largely the same in form. The center of the Doppler frequency is t0, which is the zero Doppler time.

[0074] Step 3: Perform azimuth pulse compression in the two-dimensional frequency domain;

[0075] The specific implementation process of step 3 is as follows:

[0076] The two-dimensional frequency domain signal S ic (f τ f η ) and two-dimensional frequency domain filter H(f τ f η Multiplying these yields the uncorrected range-azimuth higher-order coupled phase two-dimensional frequency domain signal S.b (f τ f η );

[0077] Among them, the two-dimensional frequency domain filter H(f) τ f η )for:

[0078]

[0079] Among them, R ref For reference distance.

[0080] The two-dimensional frequency domain signal S after azimuth pulse compression b (f τ f η )for:

[0081]

[0082] Step 4: Use stolt interpolation to correct the higher-order coupling phase between the range and azimuth directions, obtaining the two-dimensional frequency domain signal S of the corrected higher-order coupling phase in the range and azimuth directions. l (f τ ′, f η );

[0083] The following correction is achieved using the Stolt interpolation mapping method:

[0084] For S b (f τ f η Perform the above operations to obtain S l (f τ ′, f η The expression for ) is:

[0085]

[0086] Among them, f τ ′ represents the fast time frequency domain variable after Stolt interpolation.

[0087] Step 5, for S l (f τ ′, f η Perform a two-dimensional inverse Fourier transform to obtain the time-domain data s. out (τ′,η) is used as the imaging result.

[0088] In S l (f τ ′, f η )middle It can be approximated as a constant, S k Encoding 1 and -1, then s outThe expression for (τ′,η) is:

[0089]

[0090] Where τ′ is the fast time variable after Stolt interpolation.

[0091] In the method described in this embodiment, the specific settings of the simulation parameters are as follows: a linear OFDM-based SAR imaging mode is adopted, the distance between the radar and the center of the scene is 12,000 meters, the center carrier frequency of the transmitted signal is 16 GHz, the movement speed of the radar platform is 20 m / s, the number of subcarriers is 400, the bandwidth is 400 MHz, and the synthetic aperture time is 20 s.

[0092] Figure 2 Single-point target imaging is presented, and it can be seen that the echo data of SAR imaging based on OFDM signals is compressed into a single point after imaging processing.

[0093] Figure 3 The range slice of the point target is given. It can be seen that its sidelobes are relatively low, with the first sidelobe being less than -20dB, indicating high range resolution. Figure 4 Azimuth slices of point targets are provided, with low side lobes and good imaging results.

[0094] right Figure 2 The midpoint target range slice and azimuth slice PSLR and ISLR are shown in Table 1:

[0095] Table 1 shows the point target range slices and azimuth slices PSLR and ISLR in the methods described in the embodiments.

[0096]

[0097] The data in Table 1 show that this imaging method has good resolution.

[0098] Figure 5 The image shows the point target imaging results under the same conditions using traditional RDA. The point target can be focused into a single point, but the effect is not as good as the method described in the example.

[0099] right Figure 5 The midpoint target range slice and azimuth slice PSLR and ISLR are shown in Table 2:

[0100] Table 2 shows the PSLR and ISLR data obtained using RDA point target range and azimuth slices.

[0101]

[0102] A comparison of Tables 1 and 2 shows that the PSLR of the point target slices obtained by the method described in the embodiments is superior to that obtained by using the commonly used RDA. This demonstrates that the method described in the embodiments possesses high-resolution characteristics.

[0103] Figure 6 A multi-point target distribution map configured by the method described in this embodiment is given, showing the distribution of the nine point targets at the center of the scene; Figure 7 The method described in the embodiments is for Figure 6 The imaging result after oversampling of the multi-point target. From Figure 7 It can be seen that the imaging results are consistent with Figure 6 The configured multi-point target distribution map is highly consistent, with good imaging effect and high imaging accuracy.

[0104] Figure 8 Imaging results of the method described in the embodiment are given at an oblique viewing angle of 10 degrees. In standard frontal side-view imaging, the range sidelobe and azimuth sidelobe are arranged orthogonally to the range and azimuth directions, respectively. Figure 8 For a midpoint target, the orthogonality changes due to the oblique angle, causing the range and azimuth side lobes to no longer maintain their original alignment, but still maintaining good focusing effect. Therefore, it can be seen that the method described in the embodiment has a relatively good focusing effect even at a large oblique angle.

[0105] In conclusion, the method described in this invention has practical value based on the processing results.

Claims

1. A synthetic aperture imaging method based on the Omega-K algorithm for orthogonal frequency division multiplexing signals, characterized in that, Includes the following steps: Step 1: Process the echo data s from SAR imaging based on OFDM signals. r After removing the center carrier frequency (τ, η), a range-directed Fourier transform is performed; a Fourier transform is then performed on the range-directed reference signal s0(τ); the range-compressed frequency domain signal S is obtained by multiplying the two Fourier transform signals by their conjugates. ic (f τ ,η); Step 2, for signal S ic (f τ Perform an azimuth-to-Fourier transform on η) to obtain the two-dimensional frequency domain signal S. ic (f τ f η ); Step 3, Two-dimensional frequency domain signal S ic (f τ f η ) and two-dimensional frequency domain filter H(f τ f η Multiplying these two signals yields the uncorrected two-dimensional frequency domain signal S, which is a higher-order coupled phase signal in the range and azimuth directions. b (f τ f η ); Step 4: Use Stolt interpolation to correct the higher-order coupling phase between the range and azimuth directions, obtaining the two-dimensional frequency domain signal S of the corrected higher-order coupling phase in the range and azimuth directions. l (f τ ′, f η ); Step 5: For signal S l (f τ ′, f η Perform a two-dimensional inverse Fourier transform to obtain the time-domain data s. out (τ′,η) is used as the imaging result.

2. The synthetic aperture imaging method based on the Omega-K algorithm for orthogonal frequency division multiplexing signals according to claim 1, characterized in that, The specific process of step 1 is as follows: The range-oriented radar reference signal s0(τ) is expressed as: Where τ is the fast-time variable, w r Let R0 be the range window function, where R0 is the shortest distance between the radar and the target, c is the speed of light, N is the number of OFDM signal subcarriers, and 0 ≤ k ≤ N-1. k The information transmitted for the k-th subcarrier; T represents the radar pulse width, and j represents the imaginary part. SAR imaging echo data based on OFDM signals r (τ, η) is represented as: in, v is the velocity of the radar platform, η is the slow-time variable; w a For the azimuth envelope window function, η c For beam center deviation time; g m f is the target reflection coefficient. c For carrier frequency, After removing the center carrier frequency, s r (τ, η) is represented as: For s respectively r Perform a range-to-Fourier transform on (τ, η) and s0(τ) and multiply them by their conjugates to obtain the range-compressed frequency domain signal S. ic (f τ ,η): Among them, f τ For fast time-frequency domain variables, sinc is the sigma function, 0≤n≤N-1, S n For the information transmitted by the nth subcarrier, W r This is the frequency domain representation of the distance window function.

3. The synthetic aperture imaging method based on the Omega-K algorithm for orthogonal frequency division multiplexing signals according to claim 2, characterized in that, In step 2, the two-dimensional frequency domain signal S is obtained through the stationary phase principle. ic (f τ f η Specifically: In the above formula, S ic (f τ f η The phase of ) is According to the principle of stationary phase Then S ic (f τ f η ) is represented as: Among them, f η For slow-time frequency domain variables, Wa 为 The frequency domain representation of the azimuth envelope window function; The center of the Doppler frequency is t0, which is the zero Doppler time.

4. The synthetic aperture imaging method for orthogonal frequency division multiplexing signals based on the Omega-K algorithm according to claim 3, characterized in that, In step 3, the two-dimensional frequency domain filter H(f) τ f η )for: Among them, R ref For reference distance; The two-dimensional frequency domain signal S after azimuth pulse compression b (f τ f η )for:

5. The synthetic aperture imaging method for orthogonal frequency division multiplexing signals based on the Omega-K algorithm according to claim 4, characterized in that, The specific process of step 4 is as follows: The following correction is achieved using the Stolt interpolation mapping method: For S b (f τ f η Perform the above operations to obtain S l (f τ ′, f η The expression for ) is: Among them, f τ ′ represents the fast time frequency domain variable after Stolt interpolation.

6. The synthetic aperture imaging method for orthogonal frequency division multiplexing signals based on the Omega-K algorithm according to claim 5, characterized in that, The specific process of step 5 is as follows: In S l (f τ ′, f η Lieutenant General Let S be a constant. k Encoding with 1 and -1, then the time-domain data s out The expression for (τ′,η) is: Where τ′ is the fast time variable after Stolt interpolation.

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