Inverse synthetic aperture radar image modulation method based on two-dimensional periodic phase coding

Abstract

The invention provides an inverse synthetic aperture radar image modulation method based on two-dimensional periodic phase coding, and the technical scheme is as follows: step 1, an image modulation device detects and receives an ISAR signal, and measures and obtains a radar signal parameter; 2, periodic phase coding modulation parameters such as a phase coding modulation period, a coding code element width and a coding sequence are set according to radar signal parameters, and modulation pulses are generated; and step 3, carrying out amplitude modulation on the radar signal by using the set target scattering template to generate an ISAR imaging signal containing two-dimensional image features. And step 4, performing phase modulation on the signals containing the two-dimensional image features in the fast and slow time domains through the generated periodic phase coding modulation pulses in the range direction and the azimuth direction, and forwarding the signals to an ISAR system needing to be tested. And 5, after the ISAR receives the modulation signal and the target echo and carries out imaging processing, a modulated image is generated.

Description

Technical Field

[0001] The present invention belongs to the fields of target electromagnetic scattering characteristic simulation and inverse synthetic aperture radar (ISAR) image processing, and specifically relates to ISAR image modulation technology. More specifically, an image modulation method based on two-dimensional periodic phase coding is proposed for simulating the ISAR imaging effect of target non-ideal scattering characteristics. According to the generated periodic sequence, the radar signal is modulated intra-pulse and inter-pulse and then forwarded, forming multiple two-dimensional target local feature images in the range and azimuth directions of the ISAR image.

Background Art

[0002] ISAR image modulation is an image processing technology for ISAR, which mainly changes the actual target characteristics reflected by ISAR imaging by modulating the amplitude, frequency or phase of the radar imaging signal. Intermittent sampling and forwarding uses a digital radio frequency memory (DRFM) and a direct digital synthesizer (DDS) to store and partially forward the radar signal with high fidelity. Due to its simple implementation method and good performance, this technology has also been widely used in radar image modulation. A 2024 literature (Q.W, Z.X, X.L, et al. Synthetic Aperture Radar Image Transform Using Periodic-Coded Phase Modulation[J]. IEEE Geoscience and Remote Sensing Letters, 2024, 21: 1-5.) proposed introducing intra-pulse periodic phase modulation on the basis of intermittent sampling and forwarding, and using the partial correlation characteristics of the signal to generate multiple two-dimensional target feature images in the range direction of the synthetic aperture radar image to reduce the energy loss of intra-pulse intermittent modulation. However, the targets generated by this method are limited to the range dimension, and the number of targets generated in the imaging area is limited, and there is still room for improvement in the consumption of radar detection resources.

[0003] By two-dimensional periodic phase coding modulation of the radar signal, while avoiding the loss of signal energy in inter-pulse intermittent modulation, the modulation dimension of the target scattering imaging characteristics is extended from a single range direction to a two-dimensional "range-azimuth" direction. Through the phase modulation and forwarding of the signal intra-pulse and inter-pulse by the periodic pseudo-random code, it can effectively form multiple target image feature extension effects with adjustable positions, amplitudes, and two-dimensional image features simultaneously along the range and azimuth directions within a specific range in the ISAR image, realizing low-cost imaging signal simulation of target non-ideal scattering characteristics, having a certain degree of flexibility in parameter regulation, and can be applied to the test and acceptance test of the ISAR system.

Summary of the Invention

[0004] The object of the present invention is to design an ISAR image modulation method for linear frequency modulation (LFM) signals by using the basic principle of intermittent sampling and forwarding. By using the "±1" periodic random phase coding within and between pulses, the energy loss of the intermittent sampling and forwarding signal is reduced, and two-dimensional target local features extended along the range and azimuth directions are formed in specific regions of the ISAR image, so as to realize the imaging signal simulation of the non-ideal scattering characteristics of the target.

[0005] To achieve the above object, the present invention proposes an inverse synthetic aperture radar image modulation method based on two-dimensional periodic phase coding, and the technical solutions adopted are as follows:

[0006] Step 1: The image modulation device scouts and receives the ISAR signal, and measures and obtains the radar signal parameters.

[0007] The image modulation device receives the radar signal through the antenna, and measures the pulse width, bandwidth, frequency modulation slope, and pulse repetition interval of the inverse synthetic aperture radar signal, which are used as the constraint conditions for designing the phase coding modulation period and coding element width parameters and the prior information for modulating the image features.

[0008] Step 2: Set the periodic phase coding modulation parameters such as the phase coding modulation period, coding element width, and coding sequence according to the radar signal parameters, and generate modulation pulses.

[0009] Design the periodic phase coding modulation parameters according to the range and azimuth dimensions of the target to be modulated, meet the requirements of non-overlapping target features and concentrated imaging energy, and generate a random phase coding sequence that meets the conditions as the in-pulse and inter-pulse modulation pulses.

[0010] Step 3: Modulate the amplitude of the radar signal with the set target scattering template to generate an ISAR imaging signal containing two-dimensional image features.

[0011] According to the scene requirements, modulate the target scattering characteristics into the radar imaging signal so that it has the image features of ISAR imaging. The signal generated in this step will be the modulation object of the phase modulation pulse and is the basis for adjusting multiple target images in the ISAR image.

[0012] Step 4: Through the generated range and azimuth periodic phase coding modulation pulses, phase-modulate the signal containing two-dimensional image features in the fast and slow time domains and forward it to the ISAR system to be tested.

[0013] By means of the time-domain multiplication form, use the phase modulation pulse generated in Step 2 to modulate the ISAR imaging signal containing two-dimensional image features generated in Step 3 to realize the modulation of a single target image to multiple target images.

[0014] Step 5: After the ISAR receives the modulated signal and the target echo and performs imaging processing, a modulated image is generated.

[0015] The ISAR receives the modulated signal and performs ISAR imaging using the range-Doppler algorithm to obtain a radar image containing multiple targets with amplitude fluctuations and controllable positions.

[0016] The beneficial effects of the present invention mainly include:

[0017] First, expand the regulation dimension and increase the regulation effect. Based on the in-pulse binary modulation, this method adds inter-pulse phase modulation. Subsequently, the regulation expands from a single one-dimensional range to a two-dimensional range-azimuth, expanding the dimension of the regulated target and enabling a two-dimensional target group array. Based on this method, the misguidance effect on ISAR imaging under non-ideal scattering conditions on the target surface can be efficiently simulated.

[0018] Second, high hardware reuse rate and reduced system structure complexity. In this method, the periodic phase modulation in the range and azimuth directions both adopt "±1" rectangular envelope modulation. In implementation, only by digitally storing radar signals and modulating target characteristics, and changing the signal positive and negative in segments according to a specific strategy before forwarding, the hardware system of two-dimensional phase modulation can reuse the one-dimensional phase modulation system without the need to additionally implement the frequency shift function, avoiding additional system hardware costs. The system implementation structure is simple and has good energy use efficiency, facilitating the installation on a small test platform.

[0019] Third, the periodic phase-coded modulation signal combines the advantages of the intermittent sampling signal and the random coding modulation. The modulated signal has both partial correlation and randomness. The interval distances of multiple target images generated along the range and azimuth directions in the two-dimensional ISAR image are controllable, and the amplitude changes have no obvious pattern. The modulation parameters can be flexibly regulated to simulate the imaging effects of targets with different scattering characteristics. The duty cycle setting not equal to 50% avoids the modulation target amplitude being 0 in the azimuth and range directions where the real target is located, reducing the formation of guiding indication features for two-dimensional extended targets.

Description of the Drawings

[0020] Figure 1 It is the overall flowchart of the inverse synthetic aperture radar image modulation based on two-dimensional periodic cyclic phase coding proposed by the present invention.

[0021] Figure 2(a) shows the positional relationship among the inverse synthetic aperture radar, the radar target of interest, and the image modulation device in a typical inverse synthetic aperture radar imaging test scenario.

[0022] Figure 2(b) is a simplified inverse synthetic aperture radar turntable model during the imaging process of Figure 2(a).

[0023] Figure 3It is the corresponding relationship between the range-direction and azimuth-direction periodic cyclic phase-coded pulse time-domain waveform for modulating the radar imaging signal and the segmented coding modulation of the signal.

[0024] Figure 4 It is the multi-scattering point modulation template of the Yak-42 airliner set in the simulation experiment.

[0025] Figure 5 It is the original ISAR image of the Yak-42 airliner simulation data in the simulation experiment.

[0026] Figures 6(a), 6(b), 6(c), and 6(d) are the result images of the periodic phase modulation of this method using different phase modulation coding periods, code element widths, and duty cycles under Figure 4 the data.

[0027] Figure 7(a) is the range slice at r a = 0 m in the azimuth direction under the condition of Parameter Set 1.

[0028] Figure 7(b) is the azimuth slice at r = 0 m in the range direction under the condition of Parameter Set 1.

Specific Embodiment

[0029] The present invention is applicable to the ISAR imaging image modulation using LFM signals. Figure 1 It is the brief flow chart of the present invention. The method proposed by the present invention will be further explained below with reference to the accompanying drawings. The specific steps and effects of this method are as follows:

[0030] Step 1: The image modulation device receives the ISAR signal and measures and obtains the radar signal parameters.

[0031] A typical ISAR imaging test scenario is shown in Figure 2(a). In Step 1, the image modulation device receives the ISAR signal and measures and obtains the radar signal parameters. The specific method is as follows:

[0032] ① The image modulation device receives the radar signal through the antenna;

[0033] ② Measure the pulse width T p of the inverse synthetic aperture radar signal, the bandwidth B, the frequency modulation slope k, and the pulse repetition interval T r , and use them as the constraint conditions for designing the phase coding modulation period T c and the prior information of the coding code element width τ parameter and the modulation image characteristics.

[0034] Step 2: Set the phase coding modulation period, coding code element width, coding sequence and other periodic phase coding modulation parameters according to the radar signal parameters, and generate modulation pulses.

[0035] Among them, the specific implementation process of Step 2 is as follows:

[0036] The periodic cyclic phase - coded modulation pulse is a bipolar rectangular pulse train that remains unchanged along the slow - time domain. Figure 3 The time - domain waveform of the two - dimensional periodic phase - coded pulse is shown. Let the range - direction coding element width be τ and the range - direction coding period be T. c , and the modulation pulse is denoted as Then:

[0037]

[0038] Among them, represents the convolution operation, δ(·) is the impulse function, is the fast - time variable, T p is the signal pulse width, a n represents the coding sequence of the range - direction modulation pulse, which is composed of elements in {+1, - 1}. Among them, the +1 code represents positive - phase modulation, and the - 1 code represents anti - phase modulation. n is the coding - element number of the range - direction modulation pulse.

[0039] The number of elements during one range - direction coding period is:

[0040] N c = T c / τ (2)

[0041] The coding sequence within one range - direction coding period is expressed as where l r = 0, 1, …, N c - 1 represents the serial number of the coding pulse within one coding period. The modulation pulse in formula (1) can be expressed as a rectangular pulse train modulated by the coding sequence:

[0042]

[0043] Among them, represents the convolution operation, and δ(·) is the impulse function.

[0044] According to the properties of the Fourier transform, the spectrum representation of the modulation pulse is obtained as:

[0045]

[0046] where f s is the phase - coding frequency, and its calculation formula is f s = 1 / T c , f is the signal frequency, and j represents the imaginary unit.

[0047] In formula (4), the spectrum of the periodic phase - modulation pulse is a discrete comb - like spectrum. The adjacent - interval phase - coding frequency is f s, the amplitude envelope is the discrete sampling of a sinc(·)-shaped function determined by the coding sequence . The order of the peak of the sampling points corresponds to the coding symbol number n of the range modulation pulse. The amplitude of the nth-order peak is:

[0048]

[0049] In particular, when n = 0, the output amplitude of the 0th-order peak is:

[0050]

[0051] where η represents the proportion of +1 coding in

[0052] Similarly, denote the azimuth coding symbol width as τ a , the azimuth coding period as T ca , and the modulation sequence as q(t m ), then:

[0053]

[0054] where b m represents the {+1, -1} azimuth coding sequence, t m = mT r is the slow time variable, and m is the coding symbol number of the azimuth modulation pulse.

[0055] The number of symbols within one azimuth coding period is:

[0056] M c = T ca / τ a (8)

[0057] The coding sequence within one azimuth coding period is expressed as where l a = 0, 1, …, M c - 1 represents the serial number of the coding pulse within one coding period. The azimuth modulation pulse in formula (7) can be expressed as a rectangular pulse train modulated by the coding sequence:

[0058]

[0059] According to the properties of Fourier transform, let the azimuth Doppler frequency be f d , then the spectrum of the azimuth modulation pulse is expressed as:

[0060]

[0061] where f sa is the azimuth phase modulation frequency, and the calculation formula is fsa = 1 / T ca 。

[0062] The order of the peak at the sampling point corresponds to the coding symbol number m of the azimuth modulation pulse. The amplitude of the m-th order peak is:

[0063]

[0064] The following gives the design criteria and methods for modulation parameters:

[0065] The modulation period and coding width of phase modulation determine the range, azimuth range of the generated target, and the coverage range of the generated target. To achieve the effect of two-dimensional multi-target groups, the design of the coding width of periodic phase modulation needs to be considered from the following three aspects, namely: avoiding the overlap of the generated targets, the generated targets appearing in the radar imaging interval, and the energy being concentrated in the imaging area.

[0066] ① Modulation period design

[0067] Assume that the length of the radar target of interest TOI in the range direction is L r , and the length in the azimuth direction is L a . To avoid overlapping of the generated targets, the range and azimuth intervals should be no less than the size of the target in that direction, that is, the range interval ΔR r satisfies:

[0068] ΔR r ≥ L r (12)

[0069] The azimuth interval ΔR a satisfies:

[0070] ΔR a ≥ L a (13)

[0071] Therefore, the range coding period should satisfy:

[0072]

[0073] where c represents the speed of light and k represents the chirp rate of the LFM signal.

[0074] The azimuth coding period should satisfy:

[0075]

[0076] On the other hand, to ensure that the generated target is within the imaging area, the first-order generated target must be within the inverse synthetic aperture radar imaging range, that is, the target spacing in the range direction should not be greater than the range imaging range R r , and the target spacing in the azimuth direction should not be greater than the azimuth imaging range Ra 。

[0077] ② Design of the coding element width

[0078] After determining the coding period, since the targets generated by modulation are mainly distributed in the main lobe region [-1 / τ, 1 / τ] of P(f) and Q(f d ). To further concentrate the energy within the ISAR imaging region, the range-direction coding element width should satisfy:

[0079]

[0080] The azimuth-direction coding element width should satisfy:

[0081]

[0082] Meanwhile, since the coding period is an integer multiple of the element width, the first-order generated targets with coding parameters satisfying the above conditions can also appear within the imaging range. At this time, the numbers of generated targets of the main target group in the ISAR image in the range direction and the azimuth direction are respectively:

[0083]

[0084] Among them, N false_r represents the number of range-direction targets generated by the modulation signal within the imaging main lobe, and N false_a represents the number of azimuth-direction targets generated by the modulation signal within the imaging main lobe.

[0085] In addition, according to formulas (2) and (8), the coding element width should satisfy dividing the coding period evenly.

[0086] ③ Design of the modulation coding sequence

[0087] The duty cycles η r and η a of the coding modulation in the range direction and the azimuth direction respectively determine the amplitudes of the generated targets in the range direction and the azimuth direction. Since the image modulation device is placed at the center of the radar target of interest (TOI), the 0th-order extended generated target is synchronized with the TOI in the time domain. To avoid the amplitudes of the generated targets in the range direction and the azimuth direction where the TOI is located being both 0, thus forming an obvious TOI indication effect, the coding modulation duty cycle should satisfy:

[0088]

[0089] Use the randerr function in MATLAB to generate a coding sequence with the specified number of elements and the duty cycle within one coding period and

[0090] Step 3: Modulate the radar signal amplitude with the set target scattering template to generate an ISAR imaging signal containing two-dimensional imaging features.

[0091] Assume that the inverse synthetic aperture radar emits a linear frequency modulation (LFM) signal, expressed as:

[0092]

[0093] where is the fast time variable, T p is the signal pulse width, and f0 is the center frequency of the LFM signal. t m = mT r is the slow time variable, where T r is the pulse repetition interval, m is the encoding symbol number of the azimuth modulation pulse, and the value satisfies 1 ≤ m ≤ M and is an integer, and M is the ISAR imaging pulse accumulation number. T L = MT r is the imaging accumulation time. The signal bandwidth is B = kT p .

[0094] Design a scattering point modulation template according to the electromagnetic scattering characteristics of the TOI, which consists of multiple ideal scattering points. Figure 4 is a schematic diagram of the scattering point modulation template. Let the coordinates of the i-th scattering point be (x i , y i ), and the scattering intensity be σ i .

[0095] Combined with the equivalent model of actual inverse synthetic aperture radar imaging, convert the image modulation action scenario in Figure 2(a) into the turntable model in Figure 2(b). Taking the rotation center point of the TOI as the origin, the radar pointing direction to the TOI as the X-axis, and the vertical direction as the Y-axis. When the radar performs imaging, the target rotation angle within one slow time is a small rotation angle, and no scattering point undergoes cross-range cell migration. The radar has achieved translational compensation for the target. Let the distance between the radar and the TOI center be R0. Then the radar imaging signal containing the target scattering characteristics is:

[0096]

[0097] where τ i (t m ) = 2R i (t m ) / c, R i (t m ) ≈ R0 + x i sin(ωt m ) + y i cos(ωt m ), indicating t mThe slant range of the i-th scatterer at a certain moment from the ISAR, and ω represents the rotational angular velocity of the target during the imaging process.

[0098] According to the principle of inverse synthetic aperture radar imaging, the ISAR image of this signal is the superposition of the scatterer responses of each scatterer in the range-azimuth plane:

[0099]

[0100] Among them, T L represents the imaging accumulation time, x and y respectively represent the range variables in the azimuth and range directions of the ISAR image, represents the range resolution, represents the azimuth resolution.

[0101] Step 4: Through the generated range and azimuth periodic phase-encoding modulation pulses, phase-modulate the signal containing two-dimensional image features in the fast and slow time domains and forward it to the ISAR system to be tested.

[0102] Phase-modulate the signal containing two-dimensional image features in the fast time domain through the generated periodic cyclic phase-encoding modulation pulses and forward it to the ISAR system to be tested.

[0103] Figure 3 It is a schematic diagram of segmented coding modulation for the two-dimensional periodic phase modulation method. Multiply the radar imaging signal containing the target scattering characteristics by the range and azimuth modulation pulses to obtain the modulation signal That is;

[0104]

[0105] Discuss the modulation effects from the range and azimuth directions respectively:

[0106] Range modulation:

[0107] According to the linear property of the Fourier transform, the spectrum of the radar imaging signal containing the target scattering characteristics in the fast time domain can be expressed as the sum of the spectra corresponding to each scatterer:

[0108] S r (f) = ∑ i S i (f) (25)

[0109] Among them, S i (f) represents the radar echo spectrum of the i-th modulated scatterer.

[0110] According to the properties of the Fourier transform, the spectrum of the signal after range modulation is expressed as:

[0111]

[0112] Among them, A n is the amplitude of the nth peak in the range direction, and S i (f) represents the spectrum of the radar echo of the ith simulated scatterer.

[0113] If the ISAR uses matched filtering, the high-resolution range profile (HRRP) obtained after the radar scattering wave signal containing the target characteristics is subjected to range-direction phase modulation can be expressed as:

[0114]

[0115] Among them, represents the autocorrelation function of the echo of the ith modulated scatterer, and the subscript "0" represents the signal without the carrier frequency after down-conversion. S0 * (f) represents the conjugate of the radar baseband signal.

[0116] When n = 0, the amplitude of the 0th-order target of the matched filtering output is:

[0117]

[0118] Among them, represents the output of the matched filtering of the echo of the ith modulated scatterer.

[0119] Substituting the LFM signal, the output of the matched filtering is obtained as:

[0120]

[0121] Azimuth modulation:

[0122] Let the azimuth frequency be f d , then the modulation effect of the azimuth phase modulation on the Doppler frequency can be expressed as:

[0123]

[0124] Among them, S ra (f d ) represents the azimuth spectrum of the imaging signal, B m represents the amplitude of the mth peak, and S ia (f d ) represents the Doppler spectrum of the echo signal of the ith scatterer in the slow-time domain.

[0125] Based on formula (24), considering the propagation delay of the electromagnetic wave, the modulated signal received by the radar is:

[0126]

[0127] Step 5: After receiving the modulated signal and the target echo and performing imaging processing, ISAR generates a modulated image.

[0128] After down-converting the received modulated signal, ISAR uses the range-Doppler algorithm for imaging to obtain an image containing the set target scattering characteristics after modulation. Since the modulation phase of this method is 0-π, it is equivalent to ±1 modulation of the amplitude. The azimuth modulation only affects the sign of the amplitude coefficient of the HRRP output by the in-pulse compression in the range direction. Similarly, the range modulation only affects the amplitude of the output of the same azimuth unit. Therefore, the influence of two-dimensional phase modulation on ISAR imaging can be analyzed separately from two dimensions.

[0129] First, perform range-direction pulse compression on the received signal. Taking the dechirp method with a relatively low sampling rate requirement as an example, let the range-direction reference signal be:

[0130]

[0131] where T ref is the pulse width of the reference signal, and R ref is the imaging reference range, representing the distance from the range-direction reference point on the target to the radar.

[0132] After taking the phase compensation of the difference-frequency signal and performing Fourier transform along the slow time, the HRRP at each slow time is obtained. Taking single-scatter point imaging as an example, by replacing the fast-time variable with the range-direction distance variable r, the obtained HRRP is:

[0133]

[0134] Then, perform Fourier transform on the HRRP along the slow time domain (i.e., azimuth direction). Combining the principle of the ISAR imaging RD algorithm and the frequency-domain characteristics of periodic phase modulation, the theoretical imaging result is obtained.

[0135]

[0136] According to the two-dimensional resolution of ISAR imaging, the actual output image is:

[0137]

[0138] where n y represents the range-direction distance unit, and n y represents the azimuth-direction distance unit.

[0139] In formula (35), the range-direction periodic phase modulation extends the position of each scatter point to multiple range units. The nth peak of the ith scatter point is located in the range direction at:

[0140]

[0141] The range interval distance of the nth-order peak of the ith scattering point is:

[0142]

[0143] From formula (35), the azimuth periodic phase modulation will also extend the position of each scattering point to multiple azimuth range points. The position of the mth-order peak of the ith scattering point is:

[0144]

[0145] The azimuth interval distance of the mth-order peak of the ith scattering point is:

[0146]

[0147] For the two modulation dimensions of range and azimuth, the longer the period of the periodic coding, the smaller the range interval. The nth-order range and mth-order azimuth peaks of each scattering point jointly form an nth-order range and mth-order azimuth target. Considering the scattering intensity differences between scattering points, a certain scattering point of the target is selected to compare the relative amplitudes between the generated targets. Assume that in the target scattering template, the spacing between each scattering point is greater than the imaging resolution. Then, the amplitude at the ith scattering point of the nth-order range and mth-order azimuth target can be approximated as:

[0148]

[0149] Variable Numerical value <![CDATA[Center frequency (f0)]]> 10 GHz Bandwidth (B) 500 MHz <![CDATA[Pulse width (T p )]]> 100 μs Frame rate (k) <![CDATA[5×10 12 Hz / s]]> <![CDATA[Pulse Repetition Interval (T r )]]> 1 ms <![CDATA[Imaging accumulation time (T L )]]> 256 ms

[0150] Table 1

[0151] The following gives the simulation results of the modulation algorithm using Matlab. In the experiment, the scattering points are set along the contour of the Yak-42 airliner as the simulation modulation template for ISAR target characteristics. The LFM parameters used in ISAR imaging are shown in Table 1. The effectiveness of this method is verified through simulation experiments. Figure 4 The scattering point distribution of the set template is given. Figure 5 The ISAR imaging results of the characteristic modulation signal are given. The range length of the TOI is approximately L R = 35 m, and the azimuth length is approximately L A = 30 m. The angular velocity of the target rotation during imaging is ω = 0.16 rad / s. The imaging range is R r = 300 m, R a = 100 m. The image modulation device is fixed at the center of the aircraft, i.e., at the coordinate (0, 0). The image modulation method proposed above is verified using the parameter combinations listed in Table 2, and the transformation effects are shown in Figures 6(a), 6(b), 6(c), and 6(d).

[0152]

[0153]

[0154] Table 2

[0155] To ensure that the generated target appears within the imaging range, according to the imaging range set by formulas (14) and (15), the range and azimuth encoding periods should satisfy T c ≥0.1 μs, T ca ≥0.95 ms, to ensure that ISAR can successfully obtain the modulated target scattering characteristics. On the other hand, to ensure that the energy of the modulated signal is concentrated in the imaging area and the generated targets after transformation do not overlap, according to the TOI size and formulas (16) and (17), the encoding symbol width should satisfy τ ≤ 0.86 μs, τ a ≤ 3 ms. As shown in Fig. 6(a), when the intrapulse and interpulse encoding period requirements are met, there is no overlap in both the range and azimuth directions. In Fig. 6(b), when the parameters used are greater than the appropriate range, adjacent-order generated targets will produce aliasing in the range and azimuth directions, making it difficult to reproduce the modulated target characteristics. At the same time, the modulation of the signal is easily recognized by the radar, and it is difficult to verify the detection and recognition efficiency of the radar in complex working conditions. Comparing Fig. 6(a) and Fig. 6(b), a wider modulation period will make the distance intervals of the targets closer in this dimension. Fig. 6(c) shows that when the duty cycles in both the range and azimuth directions are 0.5, the amplitudes of the generated targets in the azimuth and range directions where the real target is located are both 0, with obvious characteristics. The modulation period set in Fig. 6(d) can make the main lobe frequency domains in both the range and azimuth directions smaller than the imaging range. Since the phase modulation period is an integer multiple of the encoding symbol width, according to formulas (18) and (19), for any imaging dimension, the number of generated targets within the main lobe is respectively

[0156] N false_r = 2N c - 1 (41)

[0157] N false_a = 2N ca - 1 (42)

[0158] For combination 4, the number of encoding symbols within one modulation period in both the range and azimuth directions of the parameters used is 4, so the number of generated targets should be 7. In Fig. 6(d), the number of generated targets within the main lobe area is 7 × 7. The above simulation results are consistent with the theoretical analysis of the proposed method, supporting the analysis conclusion.

[0159] To specifically demonstrate the two-dimensional phase modulation effect, Fig. 7(a) and Fig. 7(b) respectively show the azimuth r under the parameter conditions of combination 1 aSlice at a range of r = 0m and a cross-range of 0m. In the experiment, the target echo signal and the modulation signal have the same power. As shown in Figs. 7(a) and 7(b), the adjacent generated targets obtained by modulation have an interval of 38m in the range direction and an interval of 24m in the cross-range direction, which is consistent with the theoretical analysis given by Eqs. (37) and (39). Under this scenario setting, the amplitude of the generated target in the range direction is approximately 10 - 18dB lower than that of the real target, and the amplitude in the cross-range direction is approximately 18dB lower. There are certain fluctuations in the amplitudes of the generated targets in both dimensions, thus realizing the simulation of the ISAR imaging signal and imaging effect for the non-ideal scattering characteristics of the target. Compared with single intra-pulse phase modulation, the cross-range control ability is increased, and the generated two-dimensional extended target has higher simulation fidelity.

Claims

1. An inverse synthetic aperture radar image modulation method based on two-dimensional periodic phase coding, characterized in that, The steps are as follows: Step 1: The image modulation device scouts and receives the ISAR signal, and measures and obtains the radar signal parameters; The image modulation device receives the radar signal through the antenna, and measures the pulse width, bandwidth, frequency modulation slope, and pulse repetition interval of the inverse synthetic aperture radar signal, which are used as the constraint conditions for designing the phase encoding modulation period and the encoding symbol width parameters, and the prior information for modulating the image features; Step 2: Set the phase encoding modulation period, encoding symbol width, and the periodic phase encoding modulation parameters of the encoding sequence according to the radar signal parameters to generate modulation pulses; Design the periodic phase encoding modulation parameters according to the range and azimuth dimensions of the target to be modulated, meet the requirements of non-overlapping target features and concentrated imaging energy, and generate a random phase encoding sequence that meets the conditions as the in-pulse and inter-pulse modulation pulses; Step 3: Modulate the amplitude of the radar signal with the set target scattering template to generate an ISAR imaging signal containing two-dimensional image features; According to the scene requirements, modulate the target scattering characteristics into the radar imaging signal to make it have the image features of ISAR imaging; the signal generated in this step will be the modulation object of the phase modulation pulse and is the basis for adjusting multiple target images in the ISAR image; Step 4: Through the generated range and azimuth periodic phase encoding modulation pulses, perform phase modulation on the signal containing two-dimensional image features in the fast and slow time domains and forward it to the ISAR system to be tested; By means of the time-domain product form, use the phase modulation pulse generated in Step 2 to modulate the ISAR imaging signal containing two-dimensional image features generated in Step 3 to achieve the modulation of expanding a single target image to multiple target images; Step 5: After the ISAR receives the modulated signal and the target echo and performs imaging processing, a modulated image is generated; The ISAR receives the modulated signal and performs ISAR imaging using the range-Doppler algorithm to obtain a radar image containing multiple targets with amplitude fluctuations and controllable positions.

2. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase coding according to claim 1, characterized in that: In Step 1, the image modulation device receives the ISAR signal and measures and obtains the radar signal parameters. The specific method is as follows: ① The image modulation device receives the radar signal through the antenna; ② Measure the pulse width T of the inverse synthetic aperture radar signal p , bandwidth B, frequency modulation slope k, and pulse repetition interval T r , which are used as the constraint conditions for designing the phase encoding modulation period T c and the prior information of the modulation image characteristics with respect to the parameter of the encoding symbol width τ.

3. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase encoding according to claim 1, characterized in that: In step two, the periodic cyclic phase-coded modulation pulse is a bipolar rectangular pulse train, which remains unchanged along the slow time domain; let the range-encoding symbol width be τ and the range-encoding period be T c , and the modulation pulse is denoted as Then: Among them, represents the convolution operation, and δ(·) is the impulse function. is the fast time variable, and T p is the signal pulse width, and a n represents the coding sequence of the range modulation pulse, which is composed of elements in {+1, -1}. Among them, the +1 code represents positive phase modulation, and the -1 code represents inverse phase modulation. n is the coding symbol number of the range modulation pulse. The number of symbols during one range encoding period is: N c = T c / τ The coding sequence within a range coding period is expressed as where l r = 0, 1, …, N c -1 represents the coding pulse serial number within a coding period; the modulation pulse is expressed as a rectangular pulse train modulated by the coding sequence: Among them, represents the convolution operation, and δ(·) is the impulse function; According to the properties of Fourier transform, the spectral representation of the modulation pulse is obtained as: Among them, f s is the phase encoding frequency, and the calculation formula is f s = 1 / T c , where f is the signal frequency and j represents the imaginary unit; The amplitude envelope is the discrete sampling of the sinc(·)-shaped function determined by the coding sequence and the order of the peak of the sampling point corresponds to the coding symbol number n of the range modulation pulse; the amplitude of the nth-order peak is: Denote the azimuth encoding symbol width as τ a , and the azimuth encoding period as T ca , and denote the modulation sequence as q(t m ). Then: Among them, b m represents the {+1, -1} azimuth encoding sequence, and t m = mT r is the slow time variable, and m is the encoding symbol number of the azimuth modulation pulse; The number of symbols within one azimuth encoding period is: M c = T ca / τ a The coding sequence within one azimuth encoding period is expressed as where l a = 0, 1, …, M c -1 represents the serial number of the coding pulse within one coding period; the azimuth modulation pulse is represented as a rectangular pulse train modulated by the coding sequence: According to the properties of Fourier transform, let the azimuth Doppler frequency be f d , then the spectrum of the azimuth modulation pulse is expressed as: where f sa is the azimuth phase modulation frequency, and the calculation formula is f sa = 1 / T ca ; The order of the sampling point peak corresponds to the encoding symbol number m of the azimuth modulation pulse; the amplitude of the m-th order peak is:

4. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase encoding according to claim 1 or 3, characterized in that: The modulation parameter design criteria and methods include: modulation period design: Let the length of the target of interest (TOI) of the radar in the range direction be L r , and the length in the azimuth direction be L a ; To avoid target overlap, the range and azimuth intervals should be no less than the target size in that direction, i.e., the range interval ΔR r satisfies: ΔR r ≥L r Azimuth interval ΔR a Satisfy: ΔR a ≥L a Therefore, the range encoding period should satisfy: where c represents the speed of light and k represents the frequency modulation slope of the LFM signal; The azimuth encoding period should satisfy: On the other hand, in order to ensure that the generated target is within the imaging region, the first-order generated target must be within the inverse synthetic aperture radar imaging range, that is, the target spacing in the range direction should not be greater than the imaging range R in the range direction r , and the target spacing in the azimuth direction should not be greater than the imaging range R in the azimuth direction a .

5. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase encoding according to claim 1 or 3, characterized in that: The modulation parameter design criteria and methods include: encoding symbol width design: After determining the coding period, the target generated by modulation is distributed within the main lobe region [-1 / τ, 1 / τ] of P(f) and Q(f d ); to further concentrate the energy within the ISAR imaging region, the range-encoding code element width should satisfy: The azimuth encoding symbol width should satisfy: At this time, the number of generated targets of the target group in the ISAR image in the range and azimuth directions are respectively: Among them, N false_r represents the number of range-direction targets generated by the modulation signal within the imaging main lobe, and N false_a represents the number of azimuth-direction targets generated by the modulation signal within the imaging main lobe.

6. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase coding according to claim 1 or 3, characterized in that: The modulation parameter design criteria and methods include: modulation encoding sequence design: Encoding modulation range and azimuth duty cycle η r and η a respectively determine the amplitudes of the generated targets in the range and azimuth directions; since the image modulation device is placed at the center of the radar target of interest (TOI), the 0th-order extended generated target is synchronized with the TOI in the time domain; to avoid the amplitudes of the generated targets in the range and azimuth directions where the TOI is located being both 0, thus forming an obvious TOI indication effect, the encoding modulation duty cycle should satisfy: Use the randerr function in MATLAB to generate a coding sequence with a specified number of code elements and duty cycle within one coding period and 7. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase encoding according to claim 1, characterized in that: In Step 3, assume that the inverse synthetic aperture radar emits a linear frequency modulation LFM signal, which is expressed as: Among them, is the fast time variable, T p is the signal pulse width, f0 is the center frequency of the LFM signal; t m = mT r is the slow time variable, where T r is the pulse repetition interval, m is the coding symbol number of the azimuth modulation pulse, and the value satisfies 1 ≤ m ≤ M and is an integer, M is the number of ISAR imaging pulse accumulations; T L = MT r is the imaging accumulation time; the signal bandwidth is B = kT p ; Design a scattering point modulation template according to the electromagnetic scattering characteristics of the TOI, which consists of multiple ideal scattering points. Let the coordinates of the i-th scattering point be (x i , y i ), and the scattering intensity be σ i ; Assume that the distance between the radar and the center of the TOI is R0; then the radar imaging signal containing the target scattering characteristics is: where τ i (t m ) = 2R i (t m ) / c, R i (t m ) ≈ R0 + x i sin(ωt m ) + y i cos(ωt m ), representing the slant range between the ith scattering point and the ISAR at time t m , ω represents the rotational angular velocity of the target during the imaging process; According to the inverse synthetic aperture radar (ISAR) imaging principle, the ISAR image of this signal is the superposition of the scattering point responses of each scattering point in the range-azimuth plane: Among them, T L represents the imaging accumulation time, x and y respectively represent the range variables in the azimuth and range directions of the ISAR image, represents the range resolution, represents the azimuth resolution.

8. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase coding according to claim 1, characterized in that: In step four, range modulation: According to the linear property of Fourier transform, the frequency spectrum of the radar imaging signal containing the target scattering characteristics in the fast time domain is expressed as the sum of the frequency spectra corresponding to each scattering point: S r (f) = ∑ i S i (f) Among them, S i (f) represents the radar echo spectrum of the i-th modulated scattering point; According to the properties of Fourier transform, the frequency spectrum of the signal after range modulation is expressed as: Among them, A n is the amplitude of the nth peak in the range direction, and S i (f) represents the spectrum of the radar echo of the ith simulated scattering point; If ISAR uses matched filtering, the high-resolution range profile (HRRP) obtained after range-phase modulation of the radar scattering wave signal containing target characteristics is expressed as: Among them, represents the autocorrelation function of the echo of the i-th modulation scattering point. The subscript "0" represents the signal without the carrier frequency after downconversion, S0 * (f) represents the conjugate of the radar baseband signal; Substituting the LFM signal, the output of the matched filtering is obtained as:

9. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase encoding according to claim 1, characterized in that: In step four, azimuth modulation: Let the azimuth frequency be f d , then the modulation effect of the azimuth phase modulation on the Doppler frequency is expressed as: Among them, S ra (f d ) represents the azimuth spectrum of the imaging signal, B m represents the peak amplitude of the m-th order, and S ia (f d ) represents the Doppler spectrum of the echo signal of the i-th scattering point in the slow-time domain; If the electromagnetic wave propagation delay is considered, the modulated signal received by the radar is:

10. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase encoding according to claim 1, characterized in that: In step five, after the ISAR down-converts the received modulated signal, the range-Doppler algorithm is used for imaging to obtain an image containing the set target scattering characteristics after modulation; Since the modulation phase is 0 - π, it is equivalent to the amplitude modulation of ±1; the azimuth modulation only affects the sign of the amplitude coefficient of the HRRP output by the in-pulse compression in the range direction; similarly, the range modulation only affects the amplitude of the output of the same azimuth unit; therefore, the imaging effect of the two-dimensional phase modulation on ISAR is analyzed separately from two dimensions; Perform range pulse compression on the received signal; assume the range reference signal is: Among them, T ref is the reference signal pulse width, and R ref is the imaging reference distance, representing the distance from the range-direction reference point on the target to the radar; After taking the phase compensation of the difference frequency signal and performing Fourier transform along the slow time, the HRRP of each slow time is obtained; by replacing the fast time variable with the range variable r in the range direction, the obtained HRRP is:

11. A method for inverse synthetic aperture radar image modulation based on two-dimensional periodic phase encoding according to claim 10, characterized in that: Perform Fourier transform on the HRRP along the slow time domain, i.e., the azimuth direction; combining the principle of the ISAR imaging RD algorithm and the frequency domain characteristics of the periodic phase modulation, the theoretical imaging result is obtained; According to the two-dimensional resolution of ISAR imaging, the actual output image is: where n y represents the range bin in the range direction, and n y represents the range bin in the azimuth direction; For the two modulation dimensions of the range direction and the azimuth direction, the longer the period of the periodic coding, the smaller the range interval; The nth-order range and mth-order azimuth peaks of each scattering point jointly form an nth-order range and mth-order azimuth target; considering the scattering intensity difference between scattering points, a certain scattering point of the target is selected to compare the relative amplitude between the generated targets; assume that in the target scattering template, the spacing between each scattering point is greater than the imaging resolution, then the amplitude at the ith scattering point of the nth-order range and mth-order azimuth target is:

Images