Anti-Jamming Method for Multiple-Input Multiple-Output Synthetic Aperture Radar Based on APC and OFDM

Abstract

The present invention discloses an anti-jamming method for multiple-input multiple-output synthetic aperture radar based on APC and OFDM. By comprehensively utilizing APC and OFDM technologies, the two are combined to form an APC and OFDM dual-modulation waveform; the channel array is designed as a 2×2 square matrix; a space-time two-dimensional signal reception model is constructed, and at the same time, a repeater interference is added, and the echo is sampled to obtain range-azimuth-array three-dimensional echo data; OFDM demodulation and pulse compression are performed; the beam pointing angle corresponding to each azimuth channel is calculated to form a steering vector matrix, and the weighted vector matrix is calculated using the steering vector matrix and multiplied by the three-dimensional echo data to complete APC waveform separation and single-channel repeater interference suppression; imaging is performed on the echo data after anti-jamming processing, and finally a range-azimuth real target SAR image is formed. The present invention effectively utilizes the information resources in the time domain, frequency domain and spatial domain between the airborne radar and the target, making the anti-jamming algorithm more convenient, concise, accurate and effective.

Description

Technical Field

[0001] The present invention belongs to the fields of radar imaging technology and radar anti-jamming, and relates to airborne multi-input multi-output synthetic aperture radar imaging signal processing technology, and particularly relates to a multi-input multi-output synthetic aperture radar anti-jamming method based on APC and OFDM. Background Art

[0002] Synthetic Aperture Radar (SAR) is a powerful remote sensing technology that can provide all-weather and all-day long-distance surface radar images. With the increasingly urgent demand for radar applications, the performance of traditional SAR can no longer meet the current observation requirements. As a new type of radar system, Multi-Input Multi-Output Synthetic Aperture Radar (MIMO-SAR) has attracted extensive attention due to its unique performance. Compared with traditional synthetic aperture radar, MIMO-SAR can obtain far more degrees of freedom than the actual number of antennas through waveform and spatial diversity. By different combinations of transmitting antennas and receiving antennas, multiple equivalent phase centers are formed. The Digital Beam Forming (DBF) technology at the receiving end also makes it possible to form multiple beams. At the same time, spatial filtering technologies such as digital beam forming also have important applications in radar anti-jamming. Therefore, MIMO-SAR also has great potential in radar anti-jamming. Due to these system advantages, MIMO-SAR has become an important research direction for current and next-generation radar technologies. The current main research work on MIMO-SAR lies in the design and separation of orthogonal waveforms. Currently, several waveform diversity schemes with promising applications include Short-Time Shifted Orthogonal waveform (STSO), Orthogonal Frequency Division Multiplexing Chirp waveform (OFDM-chirp), stepped-frequency waveform, Azimuth Phase Coding (APC) waveform, etc.

[0003] Repeater deception jamming is a typical pulsed radar jamming measure based on Digital Radio Frequency Memory (DRFM) technology. A deception jammer using DRFM technology can, according to pre-set virtual targets, intercept, store and retransmit the radar emission signal, and perform time-delay and phase modulation on the intercepted radar signal to realize the formation of multiple realistic deceptive false targets in front of and behind the real target in the SAR image. Since such jammers usually aim at the main lobe of the radar beam, the false targets are very similar to the real targets in time-domain, frequency-domain and space-domain characteristics, and the deception jamming requires lower jamming power than traditional noise jamming. This makes it difficult for the anti-jamming methods of traditional radar systems against false targets to work effectively. Therefore, main-lobe repeater false target jamming has become an important threat to modern radars. Since the repeater jammer is a causal and realizable system, if multiple false targets are to be generated in front of and behind the real target, the jammer needs to delay one or more pulse periods after sampling the current pulse and then retransmit it.

[0004] Currently, there are mainly two types of methods for SAR to counter deception jamming. One type of method uses complex multi-channel or multi-static SAR imaging systems, making there be significant differences between the real echoes received indirectly by different channels and the deception jamming, so as to use these differences for effective interference suppression. On the other hand, starting from the limitations of the jammer itself, corresponding methods can be designed at the front end of the SAR imaging system for countermeasures. The strategy of waveform agility can be adopted, and the main methods include pulse phase perturbation, random initial phase, orthogonal frequency division multiplexing (OFDM), etc. Comprehensively using multi-domain information such as time domain, frequency domain, spatial domain, and polarization domain and various technical means is expected to become an effective means to counter repeat-back false target jamming. Summary of the Invention

[0005] Object of the Invention: The present invention provides an anti-jamming method for multiple-input multiple-output synthetic aperture radar based on APC and OFDM, which does not rely on a large number of complex SAR data processing processes, and separates waveforms and suppresses interference through the orthogonality of the MIMO-SAR transmitted waveforms and the DBF technology of multi-channel echo data.

[0006] Technical Solution: An anti-jamming method for multiple-input multiple-output synthetic aperture radar based on APC and OFDM dual-modulation waveforms according to the present invention includes the following steps:

[0007] (1) Waveform design: Comprehensively utilize APC and OFDM technologies, combine the two to form APC and OFDM dual-modulation waveforms, and form four or two groups of transmitted waveforms;

[0008] (2) Multi-channel design: Design the channel array as a 2×2 square matrix;

[0009] (3) Construct a space-time two-dimensional signal reception model: Use an airborne side-looking synthetic aperture radar to obtain multi-channel echoes. The radar operates in the spotlight mode, alternately transmits two groups of waveforms to the same scatterer target every other pulse interval, and at the same time adds repeat-back interference, and samples the echoes to obtain range-azimuth-array three-dimensional echo data;

[0010] (4) OFDM demodulation and pulse compression: Convert the echo data to the range frequency domain, separate the odd and even frequency point components, and can separate the multi-channel repeat-back interference delayed by one pulse interval while performing OFDM demodulation, and then multiply by the matched filtering function for pulse compression;

[0011] (5) Azimuth DBF: Calculate the beam pointing angle corresponding to each azimuth channel to form a steering vector matrix; Use the steering vector matrix to calculate the weighted vector matrix, and multiply it with the three-dimensional echo data to complete APC waveform separation and single-channel repeat-back interference suppression;

[0012] (6) Image the processed echo data according to the motion speed of the carrier platform and the antenna scanning parameters, and finally form a real target SAR image in range and azimuth.

[0013] Further, the implementation process of step (1) is as follows:

[0014] Adopt OFDM-chirp waveform modulation, insert 0 alternately in the frequency domain for the original linear frequency modulation signal (LFM) to double its spectrum and form the first OFDM-chirp signal, then shift the spectrum of this OFDM-chirp signal to obtain the second OFDM-chirp signal; perform double modulation of APC and OFDM on the original LFM signal to form four groups of transmitted signals and alternately transmit two groups of transmitted signals; the time-domain expressions of the four different transmitted signals are respectively:

[0015]

[0016] s 21 (t r ,t a )=s 11 (t r ,t a )phase(t a )

[0017]

[0018]

[0019] Among them, s 11 and s 21 are the first group of MIMO-SAR transmission waveforms, s 12 and s 22 are the second group, t r is the range time, t a is the azimuth time, T p is the pulse width, k r is the frequency modulation slope, n r is the length of the original LFM signal sequence, T s is the sampling interval, f s is the sampling frequency, phase(t a ) is the azimuth modulation phase.

[0020] Further, the implementation process of step (2) is as follows:

[0021] According to the number of transmitted waveforms and the modulation and demodulation methods, a 2×2 four-channel radar array is designed. Among them, two channels in the same column form a group to transmit signals, forming a total of two groups of transmitting channels; the four channels simultaneously receive all target echoes, interference echoes, and environmental noise; two channels in the same row in the azimuth direction are grouped together for azimuth DBF to separately separate two different APC waveforms and simultaneously suppress the repeater interference acting on a single channel.

[0022] Further, the implementation process of step (3) is as follows:

[0023] The actual received echo at the receiving end within each pulse repetition interval consists of two parts. One part is the target echo generated by the current group of transmitted signals, and the other part is the repeater interference echo brought about by the previous group of transmitted signals being intercepted by the jammer; the expression of the echo signal received by a single receiving channel is as follows:

[0024]

[0025] where r represents the single-channel echo, s1 represents the current group of signals in the current transmission period, s2 represents the previous group of signals in the previous transmission period, t r is the range time, t is the echo delay of the real target, c is the speed of light, λ is the wavelength, t j is the interference echo delay;

[0026] When only a single transmitted signal is intercepted by the jammer, the jammer can forward the interference echo back within the current pulse interval. At this time, the received echo at the receiving end has one part as the target echo generated by the current transmitted signal group and the other part as the interference echo generated by a certain transmitted signal in the current transmitted signal group; when N waveforms are transmitted simultaneously and the Nth transmitted waveform is intercepted and forwarded, the expression of the two-dimensional echo signal of a single receiving channel is:

[0027]

[0028] where s ij represents the mixed echo received by the receiving channel Tx ij , s n represents the transmitted waveform, n = 1, 2,..., N, s N represents the Nth transmitted waveform, t ij is the delay of the interference echo arriving at the receiving channel Tx ij , R n,ij is the total distance traveled by the nth transmitted waveform from transmission to being received by the receiving channel Tx ij , t r is the range time, t a is the azimuth time, c is the speed of light, and λ is the wavelength.

[0029] Further, the implementation process of step (4) is as follows:

[0030] Perform range FFT transformation on the echo data received by each channel to the range frequency domain, and its expression is as follows:

[0031]

[0032] where, R[p] represents the frequency domain sequence of the echo signal, S1[p] and S2[p] respectively represent the frequency domain sequences of two groups of OFDM signals, t is the echo delay of the real target, c is the speed of light, λ is the wavelength, and t j is the interference echo delay; it can be seen from the frequency domain expression of the echo that the odd and even components of the spectrum are the echo of the real target and the interference echo respectively; separate the odd and even frequency point components to form two groups of discrete spectrum sequences, which are the echo spectrum of the real target and the echo spectrum of the repeater interference respectively; then multiply the echo data of the real target after interference suppression by the matched filtering function for pulse compression.

[0033] Further, the implementation process of step (5) is as follows:

[0034] Calculate the beam pointing angle corresponding to each azimuth channel, and the calculation formula is as follows:

[0035]

[0036] where, f a is the azimuth frequency, PRF is the pulse repetition frequency, is the Doppler frequency offset, is the ambiguity number of the k-th Doppler sub-band of the transmitted waveform, n = 1, 2,..., N, k = 1, 2,..., N, and then generate the corresponding steering vector matrix using the beam pointing angle, and the calculation formula is as follows:

[0037] A = [a1, a2,..., a N

[0038] where, the n-th steering vector a n is given by the following formula:

[0039]

[0040] where, w rs is the channel interval, θ n is the beam pointing angle, and λ is the wavelength; calculate the corresponding weighted vector matrix, and the calculation formula is as follows:

[0041] W = [w1, w2,..., w N T =(A H A) -1 A H ​​

[0042] The echo data after pulse compression are transformed to range time domain and azimuth frequency domain through azimuth FFT and range IFFT. Finally, the weighted vector matrix is multiplied by the range-azimuth-space three-dimensional echo data matrix to obtain two sets of echo data. One set is the true target echo data generated by the un-intercepted and un-forwarded transmitted signal, and the other set is the target echo plus interference generated by the intercepted and forwarded transmitted signal. The mathematical expressions are as follows:

[0043] w n S i T = S n (t r - R n,i1 / c, f a - Δf d,n )

[0044]

[0045] where S i = [S i1 (f a ), S i2 (f a ), …, S iN (f a )] T is the three-dimensional echo matrix, S n is the transmitted waveform in the range-Doppler domain, n = 1, 2, …, N, S N is the Nth transmitted waveform in the range-Doppler domain, w n is the weighted vector, w N is the Nth weighted vector, t r is the range time, f a is the azimuth frequency, R n,i1 is the total distance that the transmitted waveform travels from transmission to reception by the receiving channel Tx i1 , R N,N1 is the total distance that the Nth transmitted waveform travels from transmission to reception by the receiving channel Tx N1 , t N1 is the time delay for the interference echo to reach the receiving channel Tx N1 , is the Doppler frequency offset.

[0046] Advantages: Compared with the prior art, the advantages of the present invention are as follows: The present invention designs an APC and OFDM dual modulation waveform with anti-interference potential, establishes a scene model and an echo model for airborne MIMO-SAR anti-interference, obtains the spatio-temporal two-dimensional sampling information of the echo, and uses the frequency-domain orthogonality of OFDM modulation and DBF spatial domain filtering to solve the problem of repeater deception interference in a single or multiple channels in the actual battlefield, and the anti-interference and imaging results are more concise, accurate and stable; while adopting multi-channel technology, the information resources in the three dimensions of time domain, frequency domain and spatial domain between the airborne radar and the target are effectively utilized, making the anti-interference algorithm more convenient, concise, accurate and effective. Description of the Drawings

[0047] Figure 1 is the flowchart of the present invention;

[0048] Figure 2 is a schematic diagram of the APC waveform MIMO-SAR imaging geometric model;

[0049] Figure 3 is the time-domain image of the OFDM modulation waveform;

[0050] Figure 4 is a schematic diagram of the transmitting and receiving antenna arrays of MIMO-SAR;

[0051] Figure 5 is a schematic diagram of the principle of repeater deception interference;

[0052] Figure 6 is the simulation result diagram of the full-channel interference of one-dimensional point targets;

[0053] Figure 7 is the simulation result diagram of the single-channel single-waveform interference of one-dimensional point targets;

[0054] Figure 8 is the imaging result diagram of the surface target scene affected by single-channel single-waveform interference;

[0055] Figure 9 is the imaging result diagram of the single-channel surface target scene after anti-interference;

[0056] Figure 10 is the imaging result diagram of the surface target scene with full-channel repeater false target interference;

[0057] Figure 11 is the imaging result diagram of the full-channel surface target scene after anti-interference. Detailed Embodiment

[0058] The present invention will be further described in detail below with reference to the drawings.

[0059] The present invention provides a multi-input multi-output synthetic aperture radar anti-jamming method based on APC and OFDM, and its processing flow is as follows Figure 1 shown, including the following steps:

[0060] Step 1: Comprehensively utilize APC and OFDM technologies, combine the two to design and form an APC and OFDM dual-modulation waveform, and form four or two groups of transmitted waveforms.

[0061] The azimuth phase coding (APC) waveform modulates an additional azimuth phase to the transmitted waveform by every other pulse repetition frequency (PRF) or pulse repetition interval (PRI), so that the multi-beams have obvious differences in the Doppler domain. Using this different characteristic of different echoes and interferences, they can be separated by using the DBF technology. Orthogonal frequency division multiplexing (OFDM) technology has an important application in the field of radar anti-jamming. Alternately transmitting OFDM signals can effectively suppress the repeater interference delayed by one period. Here, the OFDM-chirp waveform modulation is adopted. This modulation scheme inserts 0 in the frequency domain alternately for the original linear frequency modulation signal (LFM), so that its spectrum is doubled to form the first OFDM-chirp signal, and then the spectrum of this OFDM-chirp signal is frequency-shifted to obtain the second OFDM-chirp signal. Finally, the original LFM signal is subjected to double modulation of APC and OFDM to form four or two groups of transmitted signals and alternately transmit the two groups of transmitted signals. The time-domain expressions of the four different transmitted signals are respectively:

[0062]

[0063] s 21 (t r ,t a )=s 11 (t r ,t a )phase(t a )

[0064]

[0065]

[0066] Among them, s 11 and s 21 are the first group of MIMO-SAR transmitted waveforms, s 12 and s 22 are the second group, t r is the range time, t a is the azimuth time, T p is the pulse width, k r is the frequency modulation slope, n r is the length of the original LFM signal sequence, T sis the sampling interval, and f s is the sampling frequency, and phase(t a ) is the azimuth modulation phase.

[0067] The time-domain images of two OFDM-modulated waveforms in the range direction are as Figure 3 shown. Compared with the original LFM waveform, OFDM waveform 1 repeats one period; on the basis of OFDM waveform 1 repeating the LFM waveform once, OFDM waveform 2 adds an additional phase, making them orthogonal to each other in the frequency domain. The specific airborne MIMO-SAR imaging geometric model using the APC waveform is as Figure 2 shown. The multi-channel forward-looking airborne radar flies at a constant speed v. Every other pulse repetition period, on the basis of OFDM modulation, an additional phase that changes with azimuth time is modulated to the signal to achieve APC modulation. Finally, the dual modulation of OFDM and APC for the LFM waveform is completed.

[0068] Step 2: Design the radar antenna array according to the transmitted signal. According to the number of transmitted waveforms and the modulation and demodulation methods, a 2×2 four-channel radar array is designed. Among them, two channels in the same column are a group of transmitted signals, forming a total of two groups of transmitting channels. At the same time, these four channels also receive all target echoes, interference echoes, and environmental noises simultaneously. Since there are two different APC modulation waveforms, two channels in the same row in the azimuth direction are a group, which is used for azimuth DBF to separately separate the two different APC waveforms and simultaneously suppress the repeater interference acting on a single channel.

[0069] The transmitting and receiving antenna arrays of MIMO-SAR are as Figure 4 shown. Transmitting channels Tx11 and Tx21 are the first group, transmitting the first group of MIMO-SAR waveforms. Transmitting channels Tx12 and Tx22 are the first group, transmitting the second group of MIMO-SAR waveforms. The first group of transmitting channels and the second group of transmitting channels alternately transmit two groups of MIMO-SAR waveforms. The array antenna system is fixed on the airborne mobile platform along the direction perpendicular to the flight track. The array antennas are evenly distributed at equal intervals, constituting four receiving channels. The total size of the antenna is L, and the channel interval is W rs .

[0070] Step 3: Construct a space-time two-dimensional signal reception model: Use an airborne forward-looking synthetic aperture radar to obtain multi-channel echoes. The radar operates in the spotlight mode. Every other pulse interval, two groups of waveforms are alternately transmitted to the same scatterer target, and at the same time, repeater interference is added. The distance-azimuth-array three-dimensional echo data is obtained by sampling the echoes.

[0071] Assume there is a single-point scatterer target in the scenario, and an airborne side-looking synthetic aperture radar is used to obtain multi-channel echoes. The radar operates in the spotlight mode. The schematic diagram of the echo simulation principle of the repeater deception jamming is as shown in Figure 5 Figure []. After all the transmitted signals are intercepted by the jammer, it takes a certain amount of time to extract the parameters and use the pre-set false target to modulate and form the jamming echo. Assume that this process needs to generate jamming after intercepting the current radar signal in the next pulse repetition interval. Therefore, the actual received echo at the receiving end within each pulse repetition interval consists of two parts. One part is the target echo generated by the current set of transmitted signals, and the other part is the repeater jamming echo brought about by the interception of the previous set of transmitted signals by the jammer. The expression of the echo signal received by a single receiving channel is as follows:

[0072]

[0073] where \(r\) represents the single-channel echo, \(s_1\) represents the current set of signals in the current transmission period, \(s_2\) represents the previous set of signals in the previous transmission period, \(t\) r is the range time, \(t_d\) is the echo delay of the real target, \(c\) is the speed of light, \(\lambda\) is the wavelength, and \(t_{j}\) j is the jamming echo delay.

[0074] When only a single transmitted signal is intercepted by the jammer, the jammer may forward the jamming echo back within the current pulse interval. In this case, a part of the received echo at the receiving end is the target echo generated by the current transmitted signal group, and the other part is the jamming echo generated by a certain transmitted signal in the current transmitted signal group. Assume that the \(N\)th transmitted waveform is intercepted and forwarded. In this case, the expression of the echo signal of a single receiving channel is:

[0075]

[0076] where \(s\) ij represents the mixed echo received by the receiving channel \(Tx\) ij , \(s_n\) n represents the transmitted waveform, \(n = 1, 2, \ldots, N\), \(s_N\) N represents the \(N\)th transmitted waveform, \(t_{j}\) ij is the delay of the jamming echo arriving at the receiving channel \(Tx\) ij , \(R_n\) n,ij is the total distance traveled by the \(n\)th transmitted waveform from transmission to being received by the receiving channel \(Tx\) ij , \(t\) r is the range time, \(t_a\) a is the azimuth time, \(c\) is the speed of light, and \(\lambda\) is the wavelength.

[0077] Step 4: OFDM Demodulation and Pulse Compression: Convert the echo data to the range frequency domain, separate the even and odd frequency components, and be able to separate multi-channel repeater jamming delayed by one pulse interval while performing OFDM demodulation, and then multiply by the matched filtering function for pulse compression.

[0078] First, perform range FFT on the echo data received by each channel to convert it to the range frequency domain. The expression is as follows:

[0079]

[0080] where R[p] represents the frequency domain sequence of the echo signal, S1[p] and S2[p] respectively represent the frequency domain sequences of two groups of OFDM signals, t is the echo delay of the real target, c is the speed of light, λ is the wavelength, and t j is the echo delay of the jamming.

[0081] Then separate the even and odd frequency components to form two groups of discrete spectrum sequences, which are the echo spectrum of the real target and the echo spectrum of the repeater jamming respectively. Then multiply the echo data of the real target after jamming suppression by the matched filtering function for pulse compression. Figure 6 Fig. is the simulation result diagram of using OFDM to resist all-channel jamming for one-dimensional point target echo.

[0082] Step 5: Azimuth DBF: Calculate the beam pointing angle corresponding to each azimuth channel to form a steering vector matrix; use the steering vector matrix to calculate the weighted vector matrix and multiply it with the three-dimensional echo data to complete APC waveform separation and single-channel repeater jamming suppression.

[0083] In the case where a single transmitted signal is intercepted and repeated by a jammer, OFDM cannot suppress the jamming. At this time, APC and azimuth DBF are needed to filter out the single-channel and single-waveform repeater jamming. The specific process of azimuth DBF is as follows:

[0084] First, calculate the beam pointing angle corresponding to each azimuth channel. The calculation formula is as follows:

[0085]

[0086] where f a is the azimuth frequency, PRF is the pulse repetition frequency, is the Doppler frequency offset, is the ambiguity number of the kth Doppler sub-band of the transmitted waveform, n = 1, 2, …, N, k = 1, 2, …, N. Then use the beam pointing angle to generate the corresponding steering vector matrix. The calculation formula is as follows:

[0087] A = [a1, a2, …, a N

[0088] ​Among them, the nth steering vector is given by the following formula:

[0089]

[0090] Among them, w rs is the channel spacing, θ n is the beam pointing angle, and λ is the wavelength. Next, calculate the corresponding weighted vector matrix, and the calculation formula is as follows:

[0091] W = [w1, w2, …, w N T = (A H A) -1 A H

[0092] Perform azimuth FFT and range IFFT on the echo data after pulse compression in step 4 to convert it to the range time domain and azimuth frequency domain. Finally, multiply the weighted vector matrix by the range-azimuth-space three-dimensional echo data matrix to obtain two sets of echo data respectively. One set is the true target echo data generated by the un-intercepted and un-forwarded transmitted signal, and the other set is the target echo plus interference generated by the intercepted and forwarded transmitted signal. The mathematical expression is as follows:

[0093] w n S i T = S n (t r - R n,i1 / c, f a - △f d,n )

[0094]

[0095] Among them, S i = [S i1 (f a ), S i2 (f a ), …, S iN (f a )] T is the three-dimensional echo matrix, S n is the transmitted waveform in the range-Doppler domain, n = 1, 2, …, N, S N is the Nth transmitted waveform in the range-Doppler domain, w n is the weighted vector, w N is the Nth weighted vector, t r is the range time, f a is the azimuth frequency, R n,i1 is the total distance traveled by the nth transmitted waveform from transmission to reception by the receiving channel Tx i1 R​N,N1 is the total distance that the Nth transmitted waveform travels from transmission to reception by the receiving channel Tx N1 , and t N1 is the time delay for the interfering echo to reach the receiving channel Tx N1 . is the Doppler frequency shift. It can be seen that after DBF, only channel N is interfered, and the other channels only have the real target echo of a single transmitted waveform. Figure 7 is the simulation result diagram of using azimuth DBF to resist single-channel single-waveform interference for one-dimensional point target echo.

[0096] Step 6: According to the motion speed of the carrier platform and the antenna scanning parameters, image the processed echo data to finally form a real target SAR image of range and azimuth.

[0097] First, perform range migration correction on the echo data processed in Step 5, and then perform azimuth compression to obtain a clear real target SAR image. Then, select a high-resolution SAR image as the ground simulation scene to simulate distributed scene surface scattering volume targets.

[0098] Figure 8 is the imaging result diagram of the surface target scene affected by single-channel single-waveform interference. The figure shows that the jammer brings a retransmitted suppression surface interference; Figure 9 is the imaging result diagram of the single-channel surface target scene after anti-interference; Figure 10 is the imaging result diagram of the surface target scene where all channels are affected by retransmitted false targets. It can be seen that the jammer brings several ship false targets; Figure 11 is the imaging result diagram of the all-channel surface target scene after anti-interference. It can be seen from the imaging results that the retransmitted interference and false targets can be effectively suppressed and filtered, proving the effectiveness of the algorithm. It is proved that while adopting multi-channel technology, effectively utilizing time-domain, frequency-domain, and space-domain information resources can more effectively resist interference and more accurately image real targets.

Claims

1. A multi-input multi-output synthetic aperture radar anti-jamming method based on APC and OFDM, characterized in that It includes the following steps: (1) Waveform design: By comprehensively utilizing APC and OFDM technologies and combining the two to form an APC and OFDM dual-modulation waveform, four and two groups of transmitted waveforms are formed; (2) Multi-channel design: The channel array is designed as a 2×2 square matrix; (3) Constructing a space-time two-dimensional signal reception model: Using an airborne side-looking synthetic aperture radar to obtain multi-channel echoes. The radar operates in the spotlight mode. Every other pulse interval, two groups of waveforms are alternately transmitted to the same scatterer target, and at the same time, repeater jamming is added. Sampling the echoes to obtain range-azimuth-array three-dimensional echo data; (4) OFDM demodulation and pulse compression: Convert the echo data to the range frequency domain, separate the odd and even frequency point components. While performing OFDM demodulation, the multi-channel repeater jamming delayed by one pulse interval can be separated, and then multiplied by the matched filtering function for pulse compression; (5) Azimuth DBF: Calculate the beam pointing angle corresponding to each azimuth channel to form a steering vector matrix; Use the steering vector matrix to calculate the weighted vector matrix and multiply it with the three-dimensional echo data to complete APC waveform separation and single-channel repeater jamming suppression; (6) According to the motion speed of the carrier platform and the antenna scanning parameters, image the processed echo data to finally form a range-azimuth real target SAR image; The implementation process of step (1) is as follows: Adopt OFDM-chirp waveform modulation. Insert 0 alternately in the frequency domain for the original linear frequency modulation signal (LFM) to double its spectrum and form the first OFDM-chirp signal. Then shift the spectrum of this OFDM-chirp signal to obtain the second OFDM-chirp signal; Perform dual modulation of APC and OFDM on the original LFM signal to form four and two groups of transmitted signals and alternately transmit the two groups of transmitted signals; The time-domain expressions of the four different transmitted signals are respectively: s 21 (t r ,t a ) = s 11 (t r ,t a )phase(t a ) Among them, s 11 and s 21 are the first group of MIMO - SAR transmission waveforms, s 12 and s 22 are the second group, t r is the range time, t a is the azimuth time, T p is the pulse width, k r is the frequency modulation slope, n r is the length of the original LFM signal sequence, T s is the sampling interval, f s is the sampling frequency, phase(t a ) is the azimuth modulation phase.

2. The anti-jamming method for multiple-input multiple-output synthetic aperture radar based on APC and OFDM according to claim 1, wherein The implementation process of step (2) is as follows: According to the number of transmitted waveforms and the modulation and demodulation methods, design a 2×2 four-channel radar array. Among them, the two channels in the same column are a group of transmitted signals, forming a total of two groups of transmission channels; The four channels simultaneously receive all target echoes, interference echoes and environmental noises; The two channels in the same row in the azimuth direction are a group, which is used for azimuth DBF to separately separate two different APC waveforms and at the same time suppress the repeater jamming acting on a single channel.

3. The anti-jamming method for multiple-input multiple-output synthetic aperture radar based on APC and OFDM according to claim 1, wherein The implementation process of step (3) is as follows: The actual received echo at each pulse repetition interval consists of two parts. One part is the target echo generated by the current group of transmitted signals, and the other part is the repeater interference echo brought by the previous group of transmitted signals being intercepted by the jammer; The expression of the echo signal received by a single receiving channel is as follows: where r represents the single-channel echo, s1 represents the current set of signals in the current transmission period, s2 represents the previous set of signals in the previous transmission period, and t r is the range time, t is the echo delay of the real target, c is the speed of light, λ is the wavelength, and t j is the interference echo delay; When only a single transmitted signal is intercepted by the jammer, the jammer can forward the interference echo back during the current pulse interval. At this time, part of the received echo at the receiving end is the target echo generated by the current transmitted signal group, and the other part is the interference echo generated by a certain transmitted signal in the current transmitted signal group. When N waveforms are transmitted simultaneously and the Nth transmitted waveform is intercepted and forwarded, the expression of the two-dimensional echo signal of a single receiving channel is as follows: Among them, s ij represents the received mixed echo of the receiving channel Tx ij received, s n represents the transmitted waveform, n = 1, 2, …, N, s N represents the Nth transmitted waveform, t ij is the time delay for the interference echo to reach the receiving channel Tx ij of, R n,ij is the total distance traveled by the nth transmitted waveform from transmission to reception by the receiving channel Tx ij received, t r is the range time, t a is the azimuth time, c is the speed of light, and λ is the wavelength.

4. The anti-jamming method for multi-input multi-output synthetic aperture radar based on APC and OFDM according to claim 1, characterized in that The implementation process of step (4) is as follows: Perform range FFT on the echo data received by each channel to convert it to the range frequency domain. The expression is as follows: Among them, R[p] represents the frequency-domain sequence of the echo signal, S1[p] and S2[p] respectively represent the frequency-domain sequences of two groups of OFDM signals, t is the echo delay of the real target, c is the speed of light, λ is the wavelength, and t j is the interference echo delay; it can be seen from the frequency-domain expression of the echo that the even and odd components of the spectrum are the echo of the real target and the interference echo respectively; the even and odd frequency components are separated to form two groups of discrete spectrum sequences, which are the echo spectrum of the real target and the echo spectrum of the repeater interference respectively; then the real target echo data after interference suppression is multiplied by the matched filtering function for pulse compression.

5. The anti-jamming method for multiple-input multiple-output synthetic aperture radar based on APC and OFDM according to claim 1, characterized in that The implementation process of step (5) is as follows: Calculate the beam pointing angle corresponding to each azimuth channel. The calculation formula is as follows: where f a is the azimuth frequency, PRF is the pulse repetition frequency, is the Doppler frequency offset, is the ambiguity number of the k-th Doppler sub-band of the transmitted waveform, n = 1, 2, …, N, k = 1, 2, …, N, and then the corresponding steering vector matrix is generated using the beam pointing angle, and the calculation formula is as follows: A = [a1, a2, …, a N ​ where the nth steering vector a n is given by: where, w rs is the channel interval, θ n is the beam pointing angle, λ is the wavelength; calculate the corresponding weighted vector matrix, and the calculation formula is as follows: W = [w1, w2, …, w N T = (A H A) -1 A H ​ Perform azimuth FFT and range IFFT on the echo data after pulse compression to convert it to the range time domain and azimuth frequency domain. Finally, multiply the weighting vector matrix by the range-azimuth-space three-dimensional echo data matrix to obtain two sets of echo data respectively. One set is the real target echo data generated by the transmitted signals that are not intercepted and forwarded, and the other set is the target echo plus interference generated by the transmitted signals that are intercepted and forwarded. The mathematical expression is as follows: w n S i T = S n (t r - R n,i1 / c,f a -Δf d,n ) Among them, S i = [S i1 (f a ), S i2 (f a ), …, S iN (f a )] T is a three-dimensional echo matrix, S n is the transmitted waveform in the range-Doppler domain, n = 1, 2, …, N, S N is the Nth transmitted waveform in the range-Doppler domain, w n is the weighting vector, w N is the Nth weighting vector, t r is the range time, f a is the azimuth frequency, R n,i1 is the total distance that the transmitted waveform travels from transmission to being received by the receiving channel Tx i1 R N,N1 is the total distance that the Nth transmitted waveform travels from transmission to being received by the receiving channel Tx N1 t N1 is the time delay for the interfering echo to reach the receiving channel Tx N1 . is the Doppler frequency offset.

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