A Method for Establishing a Surface Target SAR Echo Model Based on Doppler Frequency Shift

Abstract

The present invention belongs to the technical field of radar imaging, and particularly relates to a method for establishing a surface target SAR echo model based on Doppler frequency offset. Combining with the ortho-view airborne SAR imaging scenario, the present invention analyzes the problem that the current popular CP-OFDM SAR imaging method generates Doppler frequency offset under the high-speed movement of the platform, resulting in the degradation of imaging performance, and analyzes and models the echo for the Doppler frequency offset caused by the surface target in the scenario. The proposal of the present invention is beneficial to the subsequent research on Doppler frequency offset compensation for surface targets in this background. In addition, the echo model proposed by the present invention does not involve complex mathematical expressions and is relatively simple and easy to understand.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar imaging, and particularly relates to a method for establishing a surface target SAR echo model based on Doppler frequency offset. Background Art

[0002] With the research upsurge of radar-communication integration, more and more research begins to apply communication signals to radar. One of the research hotspots is to combine Orthogonal Frequency Division Multiplexing (OFDM) signals with Synthetic Aperture Radar (SAR). Due to the strict orthogonality requirement between subcarriers of OFDM signals, their tolerance to Doppler frequency offset is poor. And SAR platforms are usually high-speed moving spaceborne or airborne platforms. Therefore, the problem of Doppler frequency offset cannot be ignored in SAR systems using OFDM signals for radar imaging, otherwise it will affect the imaging performance of the SAR system.

[0003] Currently, CP-OFDM SAR imaging combined with Cyclic Prefix (CP) has attracted extensive research because it can eliminate Inter-Range-Cell Interference (IRCI). The IRCI-free brought by this algorithm can achieve zero sidelobes in the range dimension, thus further improving the imaging performance of OFDM signals. However, since this algorithm realizes the range compression step by estimating the weighted Radar Cross Section (RCS) coefficients, which depends on the correspondence between the echo and the transmitted signal, the influence of Doppler frequency offset on the imaging performance of this algorithm will be more prominent. Summary of the Invention

[0004] The purpose of the present invention is to model the Doppler frequency offset problem not considered in IRCI-free CP-OFDM SAR. Due to the existence of CP, although it can bring better imaging performance and application prospects for radar-communication integration, its length will limit the imaging range. For the convenience of analyzing and modeling subsequent problems, the present invention mainly considers a small imaging scenario with an imaging range of hundreds of meters. In addition, the present invention mainly conducts two-dimensional analysis in the range and azimuth directions for the Doppler frequency offset caused by distributed targets, and gives a surface target CP-OFDM SAR echo model based on Doppler frequency offset. To introduce the content of the present invention and the specific model construction in detail, first, a simple introduction to the basic echo model of CP-OFDM SAR without considering Doppler frequency offset is given:

[0005] Consider the single-static squint SAR imaging scenario. Assume that the number of subcarriers of the OFDM signal is N and the bandwidth is B. Assume that the frequency-domain vector of the signal is S = [S0, S1,..., S N-1 T , the duration of the signal without adding CP is T, and the length of CP is T GI . Suppose the imaging scenario can be divided into M range cells, then the received signal from the m-th range cell can be written as:

[0006]

[0007] where t and η are the fast-time variable and slow-time variable respectively. ε a (η) represents the azimuth envelope, g m represents the RCS coefficient, R m (η) represents the instantaneous slant range, and ω(t, η) represents the noise. In the IRCI-free CP-OFDM SAR echo algorithm, its range compression step is realized by Equation (2):

[0008]

[0009] where is the estimated value after the weighted RCS coefficient Fourier transform (Fast Fourier Transform, FFT), U k is the FFT of the received signal, S k ' = S k exp{j2πk(M - 1) / N}.

[0010] It can be seen from Equation (2) that when there is a Doppler frequency offset in the echo signal, then the value of U k will also change correspondingly, and the estimated value ​There will be a deviation from the true value, affecting the accuracy of range - dimension pulse compression, thus leading to a decline in the final imaging performance. To avoid the above - mentioned situation, we need to model the Doppler frequency shift caused by the relative motion between the target (plane target in this invention) and the SAR platform in the radar imaging scenario. The modeling of this invention is mainly completed through a detailed analysis of the range dimension and azimuth dimension. Since the distance difference △R between each range cell in the same azimuth direction within a small imaging scenario and the airborne platform is small, we use the frequency - shift value of the central range cell in the same azimuth direction as an approximation of the Doppler frequency shift of different range cells. For the beam emitted at a certain azimuth - time moment, since it uniformly illuminates multiple cells at different azimuth positions within the beam range, and the echoes reflected by different cells correspond to different Doppler frequency shifts and become a Doppler frequency spread with a certain width at the receiving end, different cells in the azimuth direction can be analogized to different paths in a communication scenario to perform echo modeling related to the Doppler frequency shift.

[0011] The technical solution of this invention is: A plane - target CP - OFDM SAR echo model based on Doppler frequency shift, including the following steps:

[0012] Step 1: Take the beam center point as the reference point, and the line connecting the beam center point and the radar platform as the reference line. Assume the number of azimuth cells covered by the radar beam is K. Since the distance differences of each cell in the range direction are ignored, the frequency - shift magnitude only depends on the azimuth - direction distance between the beam center and the scene cells it illuminates. Therefore, the values of the Doppler frequency shifts within its coverage are selected from a fixed set f d . Since it is a squint - side imaging scenario, the angle between the reference line and the velocity is π / 2, and the corresponding Doppler frequency shift is 0. Therefore, the set f d can be written as:

[0013]

[0014] Step 2: Assume the platform's moving speed is v, the carrier frequency is f c , and the slant range between the beam center point and the radar is R0. Combining the characteristics of the frequency shifts on both sides of the beam center point, take (K - 1) / 2 cells on the side where the Doppler frequency shift is positive for analysis. According to the distance from the reference point from near to far, assume the azimuth - direction distance between the i - th (i = 1, 2,..., (K - 1) / 2) cell and the reference point is △R ai , then its corresponding Doppler frequency shift is: where θ i = arctan(△R ai / R0).

[0015] Step 3: Due to the motion characteristics of the SAR platform, except for the process when the beam just enters and flies away from the scene edge, the beams emitted at other times can completely illuminate the entire scene. As described above, the entire flight process can be divided into 2K azimuth time nodes. The possible Doppler frequency offset values during the entire process are written into the 2K×K matrix F according to the azimuth sampling moments. D :

[0016]

[0017] Step 4: Assume that the number of subcarriers of the OFDM signal is N, the bandwidth is B, and the frequency-domain vector of the OFDM signal is S = [S0, S1,..., S N-1 T , the duration of the signal without adding CP is T, and the length of the CP is T GI , then the OFDM time-domain signal can be expressed as: When the SAR platform is at the j-th (j = 1, 2,..., 2K) azimuth moment, the frequency offset values of each unit within its illumination range correspond to the elements in the j-th row of the matrix F D . The elements in the j-th row are arranged from left to right according to the change of Doppler frequency offset from negative, frequency offset of 0 to positive frequency offset. Assume that the imaging scene can be divided into M range cells. When the SAR platform is at the j-th (j = 1, 2,..., 2K) azimuth moment, then the i-th (i = 1, 2,..., K) echo component from the m-th range cell considering the Doppler frequency offset can be written as:

[0018]

[0019] Then, for the beam emitted at the j-th azimuth moment, the echo within its illumination range is the sum of K components.

[0020] The present invention takes into account the Doppler frequency offset generated by the relative motion between the high-speed airborne SAR platform and the surface target. Since the range compression step in the current CP-OFDM SAR algorithm depends on the correspondence between the echo signal and the original transmitted signal, the existence of the Doppler frequency offset will affect the range compression effect and the final imaging. The present invention solves this problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is the imaging scene diagram corresponding to the present invention;

[0022] Figure 2 is the range-Doppler frequency offset analysis of the scene corresponding to the present invention;

[0023] Figure 3 is the azimuth-Doppler frequency offset analysis of the scene corresponding to the present invention; DETAILED DESCRIPTION OF THE INVENTION​

[0024] The echo model proposed by the present invention will be described in detail below in conjunction with the accompanying drawings to prove the practicability of the present invention.

[0025] As shown in the attached Figure 1 figures, the forward-looking airborne SAR imaging scenario considered by the present invention targets are surface targets. Assume that the radar synthetic aperture time is T s , and the length of the surface target area is one synthetic aperture length. Then the radar needs to fly over for 2T s time to irradiate the entire scene completely. Let 2T s correspond to 2K moments in the azimuth direction.

[0026] Step 1: Take the beam center point as the reference point, and the line connecting the position of the beam center point and the radar platform as the reference line. From the Figure 2 analysis, it can be seen that in a small imaging scenario, the distance difference △R values of each unit in the range direction are relatively small. Even if △R max (△R max = R max - R min ) is much smaller than the height H, so its influence on the calculation of the angle between the echo component of a single range unit and the velocity is relatively small. Therefore, we neglect the distance difference between each unit in the range direction and the radar. From Figure 3 it can be known that for the K azimuth units covered by the radar beam, the angles between the lines connecting the units on both sides symmetric to the reference line l and the radar and the velocity direction satisfy the relationship: θ1 + θ2 = p. Therefore, the frequency offset values on both sides are opposite to each other. In addition, at each azimuth moment, the line connecting the unit irradiated by the radar on the ground and the radar is fixed, and the angle with the velocity will change from the angle between l1 and v to the angle between l k and v. Since the Doppler frequency offset is only related to the radial velocity, a fixed set f d can be used to represent the possible Doppler frequency offset values within the beam coverage.

[0027]

[0028] Step 2: Taking advantage of the characteristics that the frequency offset values on the left and right sides of the beam center point are the same in magnitude and opposite in sign, take the (K - 1) / 2 units on the side where the Doppler frequency offset is positive for analysis. According to the distance from the reference point from near to far, when the azimuth distance of the i-th (i = 1, 2,..., (K - 1) / 2) unit from the reference point is △R ai , calculate its corresponding Doppler frequency offset according to Equation where θ i = arctan(△R ai / R0).

[0029] Step 3: Combining the motion characteristics of the SAR imaging platform, the entire flight process can be divided into 2K azimuth time nodes, and the possible Doppler frequency offset values during the entire process are written into the 2K×K matrix F according to the azimuth sampling moments. D :

[0030]

[0031] Step 4: When the SAR platform is at the j-th (j = 1, 2,..., 2K) azimuth moment, the frequency offset values of the cells within its illumination range correspond to the elements in the j-th row of the matrix F. D The elements in the j-th row are arranged from left to right according to the change of negative Doppler frequency offset, zero frequency offset, and then positive frequency offset. Therefore, the i-th (i = 1, 2,..., K) echo component from the m-th range cell considering the Doppler frequency offset can be written as:

[0032]

[0033] For the beam emitted at the j-th azimuth moment, the echo within its illumination range is the sum of K components.

Claims

1. A method for establishing a surface target SAR echo model based on Doppler frequency offset, characterized in that Including the following steps: S1. Take the beam center point as the reference point, and the line connecting the position where the beam center point is located and the radar platform as the reference line; for the K azimuth units covered by the radar beam, use f d to represent the set composed of the Doppler frequency offset values of each unit within the beam coverage range: S2. For the (K - 1) / 2 cells on the positive Doppler frequency shift side, when the azimuth distance of the i-th cell from the reference point is ΔR ai at this time, according to the formula calculate its corresponding Doppler frequency shift where i = 1, 2,..., (K - 1) / 2, v is the moving speed of the SAR platform, f c is the carrier frequency, θ i = arctan(ΔR ai / R0), and R0 is the slant range from the beam center point to the radar; S3. Divide the flight process of the SAR platform into 2K azimuth time nodes, and write the possible Doppler frequency offset values generated during the whole process into the 2K×K matrix F according to the azimuth sampling time D : S4. When the SAR platform is at the j-th azimuth time, where j = 1, 2, ..., 2K, the Doppler frequency offset values of the cells within its illumination range correspond to the elements of the j-th row in the matrix F D The elements in the j-th row are arranged from left to right according to the change of negative Doppler frequency offset, zero frequency offset, and then positive frequency offset; the i-th echo component of the m-th range cell considering the Doppler frequency offset is, where i = 1, 2, ..., K: where \(t\) and \(\eta\) are the fast time variable and the slow time variable respectively, and \(\varepsilon\) a \((\eta)\) represents the azimuth envelope, and \(g\) m represents the RCS coefficient, \(R\) m \((\eta)\) represents the instantaneous slant range, \(N\) is the number of subcarriers of the OFDM signal, and \(S\) k is the frequency-domain symbol of the signal, \(T\) is the duration of the signal without adding CP, and \(T\) GI is the CP length. \(\omega(t,\eta)\) represents the echo of the noise for the beam transmitted at the \(j\)-th azimuth time, and the illuminated range is the sum of \(K\) components.

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