CN116502477B - Method for realizing nonlinear frequency scanning SAR based on nonlinear frequency modulation signal - Google Patents

Abstract

The invention discloses a method for realizing nonlinear frequency scanning SAR based on nonlinear frequency modulation signals, which comprises the following steps: step 1, acquiring a nonlinear frequency scanning response model, and acquiring a scanning coefficient vector by solving the nonlinear frequency scanning response model; step 2, obtaining a group delay function model by a polynomial fitting method; step 3, solving a group delay function of the nonlinear frequency modulation signal through a scanning coefficient vector; step 4, solving a time-frequency function of the nonlinear frequency modulation signal through a piecewise linear function method; and step 5, acquiring a nonlinear frequency modulation signal template through the solved time-frequency function. The invention can effectively realize specific nonlinear frequency scanning response and has stronger engineering realizability.

Description

Method for realizing nonlinear frequency scanning SAR based on nonlinear frequency modulation signal

Technical Field

The invention relates to the technical field of high-resolution wide-amplitude (High Resolution Wide Swath, HRWS) satellite-borne synthetic aperture radars (Synthetic Aperture Radar, SAR), in particular to a method for realizing nonlinear frequency scanning SAR based on nonlinear frequency modulation signals.

Background

The high-resolution wide-amplitude (High Resolution Wide Swath, HRWS) spaceborne synthetic aperture radar (Synthetic Aperture Radar, SAR) plays an important role in the field of remote sensing observation. The high resolution is helpful to accurately extract the information and characteristics of the target, and the wide swath can improve the revisiting frequency of the specific area, so that the high-resolution wide-range SAR becomes an important direction of future development of the spaceborne SAR.

However, for conventional spaceborne SAR systems, azimuth resolution and range imaging breadth are constrained by the principle of minimum antenna area. In order to alleviate or even break through the contradiction between high resolution and wide swaths, several effective methods and techniques have been proposed successively, such as azimuthal multichannel techniques, quad-array techniques, variable repetition frequency techniques, etc. Although these techniques can perform wide-range imaging without losing resolution, the problem of low reception gain in wide-range mapping cannot be solved. Specifically, wide-range imaging requires a wide beam to illuminate the swath, but this tends to result in reduced transmit-receive gain and limited system sensitivity. The gain of a narrow beam is high, however, a static narrow beam cannot directly cover a wide swath, and thus insufficient signal reception gain in wide-format imaging becomes a problem that must be faced. The (Digital Beamforming, DBF) pitching multichannel SAR system (DBF-SAR) with the digital beam forming capability can improve the receiving gain by forming a high-gain pencil beam in real time, thereby effectively relieving the contradiction between wide-range imaging and insufficient gain. It should be noted that the use of DBF technology causes a multiple increase in system cost and complexity, and the huge amount of calculation places a great burden on digital hardware, and in addition, the consistency of the amplitude and phase between channels is difficult to ensure. For the above reasons, the DBF technology is not practically applied to the on-orbit SAR observation task at present.

Recently, DLR scholars have proposed a SAR system (Frequency Scan SAR, F-SAR) that employs Frequency Scan (FS) techniques. The system utilizes the dispersion principle of the antenna, generates a dynamic wave beam in a frequency scanning mode, realizes irradiation and imaging of a swath, and easily discovers that the FS technology and the DBF technology have the advantage of 'different and same work', and can be realized by only needing a single channel, so that the FS technology has more competitive power compared with the DBF technology. However, this mode has a problem in that the distance resolution and the imaging width are mutually limited, and in a large swath, the distance resolution is very limited, and the ground distance resolution is also limited. To alleviate the above problems, AIR and university of ocean in china have proposed a nonlinear frequency scanning response (Nonlinear Frequency Scan Response, NFSR) that allows for more balanced ground range resolution by rational design of the scanning coefficients at the same emission bandwidth. However, there is little to do with how to embody the method of nonlinear frequency scanning response.

Disclosure of Invention

In order to solve the above technical problems, a main object of the present invention is to provide a method for implementing a nonlinear frequency scanning SAR based on a nonlinear frequency modulated signal, which can effectively implement a specific nonlinear frequency scanning response, and is a method for implementing a nonlinear frequency scanning response based on a nonlinear frequency modulated signal (Nonlinear Frequency Modulated, NLFM), and the method has higher precision and engineering feasibility.

In order to achieve the above purpose, the technical scheme of the invention is realized as follows:

a method for implementing nonlinear frequency sweep SAR based on a nonlinear frequency modulated signal, comprising the steps of:

step 1, acquiring a nonlinear frequency scanning response model, and acquiring a scanning coefficient vector by solving the nonlinear frequency scanning response model;

step 2, obtaining a group delay function model by a polynomial fitting method;

step 3, solving a time-frequency function of the nonlinear frequency modulation signal through a series inverse solution method;

step 4, obtaining an approximate time-frequency function meeting the precision requirement by a piecewise linear function method;

and step 5, acquiring a nonlinear frequency modulation signal template through the solved approximate time-frequency function.

Further, the step 1 includes:

and acquiring a nonlinear frequency scanning response model according to the scanning constraint, the scene constraint and the expected nonlinear frequency scanning constraint, and then solving a scanning coefficient vector through an optimization method.

Further, the step 2 includes:

and solving a linear equation of a scanning angle and scanning time according to initial conditions, then acquiring a group delay function model of the nonlinear frequency modulation signal by adopting a polynomial fitting method, and finally solving polynomial coefficients of the group delay function model by combining a scanning coefficient vector.

Further, the step 3 includes:

and obtaining a group delay matrix based on the solved group delay function model, obtaining discrete frequency vectors according to prior information, solving polynomial coefficients of a time-frequency function in a generalized matrix inversion mode, and finally obtaining the time-frequency function of the nonlinear frequency modulation signal by a polynomial fitting method.

Further, the step 4 includes:

and (3) primarily determining the number of segments of the piecewise linear function according to the sampling points of the nonlinear frequency modulation signal, calculating the slope and intercept of each segment of the linear function, determining an approximate time-frequency function, and finally calculating a nonlinear frequency scanning response error based on the approximate time-frequency function, and if the nonlinear frequency scanning response error does not meet the requirement, modifying the number of segments of the piecewise linear function until the nonlinear frequency scanning response error meets the requirement.

The beneficial effects are that:

the invention fills the blank of the research in the aspect by providing a method for realizing nonlinear frequency scanning SAR based on nonlinear frequency modulation signals. In addition, the method not only can realize the expected nonlinear frequency scanning response, but also adopts a piecewise linear approximation nonlinear frequency modulation signal generation method, thereby greatly reducing algorithm complexity and being beneficial to the engineering of the whole technology.

Drawings

FIG. 1 is a flow chart of a method for implementing a nonlinear frequency scanning SAR based on a nonlinear frequency modulation signal in accordance with the present invention;

FIG. 2 is a schematic diagram of the principle of obtaining an approximate time-frequency function based on a piecewise linear function method;

FIG. 3 beam pointing versus instantaneous frequency;

FIG. 4a is a graph of a group delay function of a non-chirped signal;

FIG. 4b is a time-frequency function of a non-chirped signal;

fig. 5a is a graph of the real part of a chirp signal;

fig. 5b is a graph of the real part of a non-chirped signal;

FIG. 5c is a graph of a frequency spectrum of a chirp signal;

FIG. 5d is a graph of a non-chirped signal;

FIG. 6a, FIG. 6b, and FIG. 6c are graphs of simulation results for various parameters based on nonlinear frequency scanning response; wherein fig. 6a is a graph of dwell pulse width at each of the lower viewing angles, fig. 6b is a graph of dwell bandwidth at each of the lower viewing angles, and fig. 6c is a graph of ground range resolution at each of the lower viewing angles;

fig. 7a, fig. 7b, fig. 7c, fig. 7d, fig. 7e, fig. 7f are graphs of simulation results of the performance of the piecewise linear function to approximately describe the nonlinear frequency scanning response, wherein fig. 7a-7e show the results of the piecewise numbers 1, 10, 100, 1000, 15000, respectively, and fig. 7f shows the variation of the ground distance resolution average error with the piecewise numbers.

Detailed Description

The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by those skilled in the art without the inventive effort based on the embodiments of the present invention are within the scope of protection of the present invention.

According to an embodiment of the present invention, as shown in fig. 1, a method for implementing a nonlinear frequency scanning SAR based on a nonlinear frequency modulation signal according to the present invention includes the following steps:

step 101: and acquiring a nonlinear frequency scanning response model, and acquiring a scanning coefficient vector by solving the nonlinear frequency scanning response model.

When the SAR system based on the frequency scanning antenna works, a beam pointing direction is formed through the frequency scanning antenna by utilizing the dispersion effect of the antennaAnd signal frequency->And the narrow beams corresponding to the linearity realize scanning irradiation of the swath within the pulse transmitting time, and echo signals from different visual angles are received by adopting a frequency scanning mode at a receiving end. Unlike on-board SAR systems that employ phased arrays, the beam pointing and the instantaneous frequency of the transmitted signal satisfy the form of the following polynomial:

/>，

wherein, the order of the polynomial is represented,for the scan coefficients, the formula (1) may be rewritten as:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,representing the transpose of the matrix>In order to scan the coefficient vector,is a frequency progression vector. As can be seen from equation (1), when the scan coefficient changes, the beam is directed +.>And signal frequency->The relationship between these will also change, i.e. different scan coefficients will produce different frequency scan responses, referred to as nonlinear frequency scan responses when the higher order term coefficients in equation (1) are present. Considering constraints in terms of scenario, system performance, etc., the nonlinear frequency scanning response model can be expressed as:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,representing the error between the actual nonlinear sweep response and the desired nonlinear sweep response, in a form related to the desired nonlinear frequency sweep response,/a>Representing inequality constraints, ++>Represents->The number of constraints to be applied to the system,representing equality constraints +.>Representing the number of inequality constraints +.>Is the number of total constraints. The optimization model can be solved by genetic algorithm and other optimization methods, and then the scan coefficient vector is obtained>，/>Representing a given scan coefficient vectorDown (S)>Minimizing.

Step 102: and obtaining a group delay function model by a polynomial fitting method.

The present invention aims to achieve a non-linear frequency sweep response by transmitting a non-chirped signal. Assuming beam pointing angleAnd scanning time->The linear relationship is still satisfied as follows:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,is a constant term, related to breadth and beam width, +.>Is a primary item. To ensure the possibility of compression of the received echoIt should be satisfied that the beam is directed to the distal end of the swath when the signal is transmitted, and the beam is directed to the proximal end of the swath when the signal is transmitted, so +.>And->The method meets the following conditions:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,for the scanning angle range +.>For the time width of the transmitted signal, < >>For initiating the scan angle, wherein->For the far-end view down of the scene, +.>Beam width.

Unlike linear scanning, nonlinear frequency scanning response requires the generation of a nonlinear frequency modulated signal at the transmitting end, whose group delay function can be expressed in terms of a polynomial:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,is a coefficient of a polynomial. Substitution of formula (2) to formula (1) yields:

/>，

obviously, the beam direction and the frequency are nonlinear, i.e. the nonlinear frequency is scanning. The key is therefore to solve the group delay function of the transmitted signal. For ease of derivation, formula (7) is rewritten as:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,the coefficient vector, which is a group delay function, is a frequency progression vector, and equation (8) can be expressed as:

/>，

the beam pointing may be performed in the following manner:

/>，

the combination of formula (2) and formula (10) can be obtained:

/>，

if the above formula is established, the following two points must be satisfied: first, vectorAnd->Is the same length; second, the left of the equal sign is a constant, so there should be no non-constant term to the right of the equal sign. Let->Then the following is satisfied:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,as an intermediate variable, there is no special meaning, and it can be further deduced that:

/>，

thus, the group delay function of the nonlinear frequency modulation signal can be obtained.

Step 103: and solving a time-frequency function of the nonlinear frequency modulation signal by a series inverse solution method.

The NLFM signal cannot be solved directly by the group delay function, the inverse function, i.e. the time-frequency function, of the NLFM signal needs to be solved by the group delay function, and then the NLFM signal is solved based on the time-frequency function. For an NLFM signal with a sampling point of N, its time-frequency function can be written as:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,coefficient vector representing a time-frequency function, +.>Representing discrete frequency vectors, each discrete frequency point satisfying:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,for the distance sampling rate, +.>For the number of sampling points, +.>The group delay function matrix is as follows:

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,discrete value structure for group delay functionThe resulting vector can be solved by equation (8) and equation (13). Generally speaking,/->Therefore, the coefficient vector of the time-frequency function can be solved by a generalized inverse method:

/>，

step 104: obtaining an approximate time-frequency function meeting the precision requirement by a piecewise linear function method:

in general, the process of inversion consumes resources, which requires more computation and memory resources for operations such as matrix decomposition and matrix transposition, which is disadvantageous for real-time generation of non-chirp signals. The invention thus uses the idea of describing a time-frequency function with a piecewise linear function to approximately replace the exact time-frequency function. For an NLFM signal with a number of samples N, it can be described by M segments of piecewise linear functions, as shown in fig. 2, the slope and intercept of each segment of linear function are:

/>，

/>，

wherein, the liquid crystal display device comprises a liquid crystal display device,is->Segment lineThe starting and ending frequency values on the sexual function can be obtained according to the sequence number of the segment number and the discrete frequency vector, ">Is->The starting and ending time values on the segment linear function can also be obtained according to the sequence number of the segment number and the discrete frequency vector. The subscript "1" indicates the start value of the piecewise function and the subscript "2" indicates the end value of the piecewise function. Each piece of linear function can be expressed as:

/>，

thus far, the time-frequency function can be approximated to the piecewise linear function, however, it should be noted that the fewer the number of segments, the less the resource consumption, but the accuracy will be reduced accordingly, so that it is necessary to determine an appropriate M according to the error tolerance of the nonlinear scanning response.

Example 1

In the embodiment, part of system parameters of a certain satellite-borne task are selected for simulation, the system adopts a frequency scanning antenna, and more balanced ground range resolution is realized through set secondary nonlinear frequency scanning response, and the system parameters are shown in table 1.

TABLE 1

，

Based on scan coefficient vectors given in the tableThe group delay function polynomial coefficients for the corresponding non-chirped signal can be solved as shown in table 2.

TABLE 2

，

Fig. 3 shows the results of the nonlinear response described based on the parameters of table 1, it can be seen that the beam pointing and the frequency no longer satisfy a linear relationship but are characterized by a quadratic function. Fig. 4a shows the group delay function of the NLFM signal solved according to the scan coefficients; fig. 4b shows the time-frequency function of the NLFM signal obtained based on the inverse of the series, it is not difficult to find that the group delay function and the time-frequency function are inverse functions to each other. Fig. 5a shows the real part of the chirp signal with the same parameters as in table 1, fig. 5b shows the real part of the NLFM signal designed based on an exact time-frequency function, and fig. 5c and 5d show the spectra of both, respectively, it can be seen that the spectrum of the NLFM signal can be seen as a result of the windowing of the frequency spectrum of the chirp signal. Fig. 6a shows dwell pulse width in a nonlinear frequency scanning response, it can be seen that dwell bandwidth is substantially constant over the entire scan angle range, since beam pointing is a linear relationship with time, i.e., scan speed is constant, since the angular displacement produced by the beam is the beam width when a target is illuminated at any viewing angle, so is the time each target is illuminated; fig. 6b shows the bandwidth of the target at each view, and it can be seen that the overall signal emission bandwidth is characterized by a large near-end and a small far-end, i.e., the emission bandwidth is "allocated on demand", and such a bandwidth distribution can improve near-end ground-range resolution and can achieve a more uniform ground-range resolution, as shown in fig. 6 c. 7a, 7b, 7c, 7d, 7e, and 7f illustrate the performance of a piecewise linear function describing the nonlinear frequency sweep response, and FIGS. 7a-7e illustrate the results for a number of segments of 1, 10, 100, 1000, 15000, respectively, it being seen that when the number of segments is 1000, the error in the nonlinear frequency sweep response is substantially negligible, i.e., a 1000-segment linear function is sufficient to describe the nonlinear frequency sweep response signal to achieve the desired nonlinear frequency sweep response; FIG. 7f shows the variation of the ground range resolution average error with the number of segments, when the number of segments reaches a level of 1e3, it can be seen that the ground range resolution average error is substantially on the order of 1e-2, which is well below the resolution level; in a word, the NLFM signal is generated by adopting a piecewise linear function approximation method, so that the complexity is greatly reduced under the condition of ensuring the realization precision of nonlinear frequency scanning response, and the real-time generation of the NLFM signal is facilitated.

The foregoing is merely a few examples of the present invention, and the present invention is applicable in other situations and is not intended to limit the scope of the present invention.

Claims (1)

1. A method for implementing a nonlinear frequency sweep SAR based on a nonlinear frequency modulated signal, comprising the steps of:

step 1, acquiring a nonlinear frequency scanning response model according to scanning constraint, scene constraint and expected nonlinear frequency scanning constraint, and then solving a scanning coefficient vector through an optimization method;

step 2, solving a linear equation of a scanning angle and scanning time according to initial conditions, then obtaining a group delay function model of the nonlinear frequency modulation signal by adopting a polynomial fitting method, and finally solving polynomial coefficients of the group delay function model by combining a scanning coefficient vector;

step 3, obtaining a group delay matrix based on the solved group delay function model, obtaining a discrete frequency vector according to prior information, then solving polynomial coefficients of a time-frequency function in a generalized matrix inversion mode, and finally obtaining the time-frequency function of the nonlinear frequency modulation signal by a polynomial fitting method;

step 4, preliminarily determining the number of segments of the piecewise linear function according to the sampling points of the nonlinear frequency modulation signal, then calculating the slope and intercept of each segment of the linear function, determining an approximate time-frequency function, and finally calculating a nonlinear frequency scanning response error based on the approximate time-frequency function, and if the nonlinear frequency scanning response error does not meet the requirement, modifying the number of segments of the piecewise linear function until the nonlinear frequency scanning response error meets the requirement;

and step 5, acquiring a nonlinear frequency modulation signal template through the solved approximate time-frequency function.