A synthetic aperture imaging method based on back projection of orthogonal frequency division multiplexing signals

Abstract

This invention discloses a synthetic aperture imaging method based on back projection orthogonal frequency division multiplexing (OFDM) signals, belonging to the field of radar imaging technology. In the process of synthetic aperture imaging using OFDM signals, the method first performs range compression using matched filtering, followed by range interpolation using zero-padding in the frequency domain. Then, the imaging region is divided, the distance to the radar grid points at each azimuth time is calculated, and the corresponding data is found. Finally, phase compensation and coherent superposition are performed on the data at each azimuth time, reconstructing the spatial position of targets in the imaging region point by point. This method can accurately calculate the spatial position of every pixel in the imaging region and reconstruct the spatial position of all targets in the imaging region, improving imaging accuracy and image quality, and exhibiting excellent imaging performance even under near-field conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar imaging, and particularly relates to a synthetic aperture imaging method of an orthogonal frequency division multiplexing signal based on back projection. BACKGROUND

[0002] Synthetic aperture radar (SAR) is a technology that uses radar systems to obtain high-resolution images, and is widely used in fields such as earth observation, military reconnaissance, weather monitoring and disaster warning. Its core principle is to synthesize a larger "virtual antenna" than the actual antenna by moving the radar antenna relative to the target, thereby improving the resolution of the radar. It can realize all-weather and all-time regional monitoring imaging. In recent years, with the development of information technology, wireless communication and radar detection in frequency band use, hardware architecture and signal processing tend to be similar. In consideration of spectrum efficiency and cost effectiveness, the demand for radar communication integration technology continues to grow.

[0003] Orthogonal frequency division multiplexing (OFDM) transmits data by decomposing a wideband signal into multiple mutually orthogonal narrowband subcarriers, has strong anti-multipath interference capability, high spectrum utilization, anti-symbol interference (ISI), and is easy to combine with multiple-input multiple-output (MIMO) systems. This makes OFDM provide efficient and reliable transmission in complex wireless channel environments, and is widely used in wireless communication technology. Therefore, OFDM signals have become one of the best candidate signals for radar communication integration. When using OFDM signals for synthetic aperture imaging, the range Doppler algorithm (RDA) is generally used to achieve it. The imaging accuracy and resolution of RDA are not enough in some application scenarios that require higher imaging accuracy and higher resolution. RDA is based on the far-field assumption, and the distance transformation between the target and the radar can be represented by a linear model. In near-field imaging, the distance variation rate of the target is large, and the RDA assumption is not established under the near-field condition, which is not suitable for near-field imaging. SUMMARY

[0004] The purpose of the present application is to overcome the defects of the prior art, and to provide a synthetic aperture imaging method of an orthogonal frequency division multiplexing signal based on back projection, which is a high-precision and high-resolution imaging method based on back projection, and has good imaging effect under near-field conditions. In the process of using OFDM signals for synthetic aperture imaging, first, distance compression is performed, distance compression is performed using the idea of matched filtering, then distance interpolation is performed, distance interpolation is performed through the idea of frequency domain zero padding, and then the imaging area is divided, the distance from each azimuth time to the radar grid point is calculated, the corresponding data is found, and finally the data of each azimuth time is phase compensated and coherently superimposed. The spatial position of the target in the imaging area is reconstructed point by point, which is an accurate synthetic aperture imaging method using OFDM signals.

[0005] The technical problem proposed by the present application is solved in this way:

[0006] A synthetic aperture imaging method of an orthogonal frequency division multiplexing signal based on back projection, comprising the following steps:

[0007] Step 1, after removing the central carrier frequency of echo data of SAR imaging based on an OFDM signal, performing a distance Fourier transform; performing a Fourier transform on a distance reference signal s0(τ); and performing conjugate multiplication on the two Fourier transform signals to obtain a distance compression frequency domain signal S r (f τ , t);

[0008] Step 2, performing distance interpolation and inverse Fourier transform on the signal S r (f τ , t) to obtain a time domain signal s r (τ, t) after distance interpolation;

[0009] Step 3, selecting an imaging area, setting an imaging area center, an imaging distance width and an imaging azimuth width, and dividing the imaging area into a grid;

[0010] Step 4, for each azimuth time, calculating a distance R ij between the radar platform and the i-th row and j-th column grid point, and calculating a two-way time delay The values of i and j can traverse all grids in the imaging area; for the i-th row and j-th column grid, data with a time delay of t ij is searched in the time domain signal s r (τ, t) collected at the current azimuth time;

[0011] Step 5, for each grid, the searched data at the current azimuth time is phase compensated, and the phase compensation amount is Then, coherent superposition is performed, and the result is taken as an imaging result.

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

[0013] The distance reference signal s0(τ) is expressed as:

[0014]

[0015] where w r is a distance window function, τ is a fast time variable, R min is the shortest distance from the imaging area to the radar, c is the speed of light, N is the number of OFDM signal subcarriers, 0≤k≤N-1, S k is information transmitted by the k-th subcarrier, and j is an imaginary part symbol. T is the radar pulse width;

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

[0017]

[0018] Among them, w a Here, g is the azimuth envelope window function, t is the slow time variable, and g is the azimuth envelope window function. m f is the target reflection coefficient. c For carrier frequency, v is the speed of the radar platform, R0 is the shortest distance between the radar and the target, and t c This refers to the beam center deviation time.

[0019] After removing the center carrier frequency, s r (τ, t) becomes:

[0020]

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

[0022]

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

[0024] Furthermore, the specific implementation process of step 2 is as follows:

[0025] For the frequency domain signal S after distance compression r (f τ Zero-padding is performed on t), followed by inverse Fourier transform to obtain the time-domain signal s after range interpolation. r (τ,t);

[0026] S k Encoding is done using 1 and -1, in S r (f τ ,t) Let s be a constant, and let s be the interpolated time-domain signal. r (τ, t) is represented as:

[0027]

[0028] wherein, p r is the distance-to-impact response amplitude function, and is a sinc function.

[0029] Further, in step 5, for any grid point position (x0, y0) in the imaging area, the imaging result after coherent superposition is represented as I(x0, y0):

[0030]

[0031] wherein, M is the number of pulses transmitted in the SAR imaging process.

[0032] The present application has the following beneficial effects:

[0033] The method of the present application can accurately calculate each pixel point in the imaging area, reconstruct the spatial positions of all targets in the imaging area, improve the imaging accuracy, improve the image quality, and obtain an image with higher accuracy and higher resolution, which also has good imaging effect under near-field conditions. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a flowchart of the method of the present application;

[0035] Figure 2 is a single-point target imaging graph when the distance interpolation is 32 times in the method of the embodiment;

[0036] Figure 3 is a single-point target distance slice graph when the distance interpolation is 32 times in the method of the embodiment;

[0037] Figure 4 is a single-point target azimuth slice graph when the distance interpolation is 32 times in the method of the embodiment;

[0038] Figure 5 is a multi-point target distribution graph in the method of the embodiment;

[0039] Figure 6 is a multi-point target imaging graph when the distance interpolation is 32 times in the method of the embodiment. DETAILED DESCRIPTION

[0040] The present application will be further described below in combination with the drawings and embodiments.

[0041] The present embodiment provides a synthetic aperture imaging method of an OFDM signal based on backward projection, a flowchart of which is shown in Figure 1 , including the following steps:

[0042] Step 1, SAR imaging echo data s based on OFDM signal r (τ,η) After removing the central carrier frequency, the distance Fourier transform is performed; the distance reference signal s0(τ) is Fourier transformed, and the conjugate multiplication can obtain the range-compressed signal S r (f τ , t).

[0043] Radar reference signal s0(τ):

[0044]

[0045] Where w r is the distance window function, τ is the fast time variable, R min is the shortest distance from the imaging area to the radar, c is the speed of light, N is the number of subcarriers of the OFDM signal, 0≤k≤N-1, S k is the information transmitted by the kth subcarrier, j is the imaginary symbol, T is the radar pulse width;

[0046] Echo data s of SAR imaging based on OFDM signal r (τ, t) is expressed as:

[0047]

[0048] Where w a is the azimuth envelope window function, t is the slow time variable, g m is the target reflection coefficient, f c is the carrier frequency, v is the motion speed of the radar platform, R0 is the shortest distance from the radar to the target, t c is the beam center deviation time;

[0049] After removing the central carrier frequency, s r (τ, t) becomes:

[0050]

[0051] The distance Fourier transform is performed on s r (τ, t) and s0(τ) respectively, and the conjugate multiplication is performed to obtain the range-compressed frequency domain signal S r (f τ , t):

[0052]

[0053] Where W r (f τ ) is the frequency domain expression form of the distance window function, fτ is the fast time-frequency variable, sinc is the sinc function, 0≤n≤N-1, S n is the information transmitted by the nth sub-carrier.

[0054] Step 2, distance direction interpolation is performed on the frequency domain signal S r (f τ , t).

[0055] Step 2 is specifically implemented as:

[0056] Step 3, zero padding is performed on the distance compressed frequency domain signal S r (f τ , t), and then inverse Fourier transform is performed to obtain the time domain signal s r (τ, t) after distance direction interpolation.

[0057] S k is encoded by 1 and -1, and can be approximated as a constant, and the time domain signal s r (τ, t) after distance direction interpolation is expressed as:

[0058]

[0059] where p r is a distance direction impulse response amplitude function, and is a sinc function.

[0060] Step 3, an imaging region is selected, a center of the imaging region, an imaging distance direction width, and an imaging azimuth direction width are set, the imaging region is divided into grids, and each grid corresponds to a pixel in a SAR image;

[0061] Step 4, for each azimuth time, a distance R ij between the radar platform and the grid point in the ith row and the jth column is calculated, and a two-way time delay is calculated. The values of i and j can traverse all grids in the imaging region; for the grid in the ith row and the jth column, data with a time delay of t ij is searched in the time domain signal s r (τ, t) collected at the current azimuth time; due to the limitation of the sampling rate, corresponding data with a time delay of t ij may not be found, and only a critical value can be approximated, and the critical value is estimated by interpolation on the time domain signal s r (τ, t) to improve the accuracy.

[0062] Step 5, for each grid, the searched data at the current azimuth time is phase compensated, and the phase compensation amount is then coherently superimposed as an imaging result.

[0063] For any grid point (x0, y0) in the imaging area, the imaging result after coherent superposition is represented as I(x0, y0):

[0064]

[0065] Wherein, M is the number of pulses transmitted in the SAR imaging process.

[0066] The method of the present application reconstructs the spatial positions of all targets in the imaging area by distance compression, distance interpolation, dividing the grid points of the imaging area, calculating the distance between each azimuth time and the pixel point, calculating the two-way time delay, finding the data corresponding to the distance in the current azimuth time data, then performing phase compensation and coherent superposition.

[0067] In the method of the present embodiment, the specific settings of the simulation parameters are as follows: the near-field imaging mode of linear OFDM SAR is adopted, the distance of the radar from the scene center is 100 m, the radar movement speed is 20 m / s, the center carrier frequency of the transmitted signal is 26 GHz, the distance interpolation multiple is 32 times, and the signal bandwidth is 250 MHz.

[0068] Figure 2 The single-point target imaging graph when the distance interpolation multiple in the method of the present embodiment is 32 times is shown in FIG. 6, the distance interpolation multiple is 32 times, the data found in the back projection has high precision, and the spatial position of the point target is accurately reconstructed, the scene center slant range is 100 m, and the imaging effect is good under the near-field condition.

[0069] Figure 3 The single-point target distance slice when the distance interpolation multiple is 32 times is shown in FIG. 7, the distance interpolation multiple is 32 times, and the precision of finding the corresponding data in the back projection is high; Figure 4 The single-point target azimuth slice when the distance interpolation multiple in the method of the present embodiment is 32 times is shown in FIG. 8. The point target distance slice and the azimuth slice PSLR and ISLR are shown in Table 1:

[0070] Table 1: Point target distance slice and azimuth slice PSLR and ISLR table

[0071]

[0072] From the data in the table, it can be seen that the imaging method has good resolution.

[0073] Figure 5 The multi-point target distribution graph is shown in FIG. 9, which shows the distribution of 9 point targets at the scene center.

[0074] Figure 6For the multi-point target imaging graph of 32 times distance interpolation, the scene center slant distance is 100 m, the spatial position of each point is accurately reconstructed, the data accuracy is increased by using distance interpolation, the scene center slant distance is 100 m, and high-precision and high-resolution imaging can be realized under near-field conditions.

[0075] In summary, the method provided by the application has practical value from the results of processing.

Claims

1. A method of synthetic aperture imaging of an orthogonal frequency division multiplexed signal based on back-projection, characterized by, The method comprises the following steps: Step 1, after removing the center carrier frequency from the echo data of SAR imaging based on OFDM signal, distance Fourier transform is performed; the distance reference signal s0(τ) is subjected to Fourier transform; the two Fourier transform signals are multiplied by conjugate to obtain the range-compressed range-frequency azimuth-time domain signal S r (f τ ,t). Step 2, distance direction interpolation and inverse Fourier transform are performed on the signal S(τ, t) to obtain a time domain signal s(τ, t) after distance direction interpolation r (f τ r (τ, t)​ Step 3, selecting an imaging area, setting the imaging area center, the imaging distance direction width and the imaging azimuth direction width, and dividing the imaging area into a grid; Step 4, for each azimuth time, calculate the distance R between the radar platform and the grid point in the ith row and jth column ij , calculate the two-way time delay The values of i and j can traverse all grids in the imaging area; for the grid in the ith row and jth column, find the data with time delay t ij in the time domain signal s r (τ, t) collected at the current azimuth time Step 5, for each grid, phase compensation is performed on the data found at the current position instant, the phase compensation amount Coherent stacking is then performed as the imaging result; The specific process of step 1 is as follows: The distance direction reference signal s0(τ) is expressed as: wherein w r is a distance window function, and τ is a fast time variable, R min is the shortest distance of the imaging area from the radar, c is the speed of light, N is the number of subcarriers of the OFDM signal, 0≤k≤N-1, S k is the information transmitted by the kth subcarrier, j is the imaginary unit, T is the radar pulse width; Echo data s for SAR imaging based on OFDM signals r (τ, t) is expressed as: where w a is an azimuthal envelope window function, t is a slow time variable, g m is a target reflectivity, f c is a carrier frequency, v is the speed of the radar platform, R0 is the shortest distance of the radar from the target, t c is the beam center offset time; After removing the central carrier frequency, s r (τ,t) becomes s r (τ,t): For s respectively r Perform a range-to-Fourier transform on (τ,t) and s0(τ) and multiply them by their conjugates to obtain the range-compressed frequency domain signal S. r (f τ ,t): wherein W r (f τ ) is a frequency domain representation of the distance window function, f τ is a fast time frequency domain variable, sinc is a sinc function, 0≤n≤N-1, S n is information transmitted by the nth subcarrier; The specific implementation process of step 2 is as follows: The distance-compressed frequency-domain signal S r (f τ (t) is zero-padded and inverse Fourier-transformed to obtain the distance-interpolated time-domain signal s r (τ,t). S k Encoding is performed using 1 and -1 in S r (f τ ,t) is expressed as: The distance between the interpolated time-domain signal s r (τ,t) is expressed as: where p r is the distance-dependent impact response amplitude function, and is a sinc function.

2. The back-projection based synthetic aperture imaging method of orthogonal frequency division multiplexed signals according to claim 1, characterized in that, In step 5, for any grid point position (x0, y0) of the imaging area, the imaging result after coherent superposition is expressed as I(x0, y0): Wherein, M is the number of pulses transmitted in the SAR imaging process.

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