Radar anti-jamming waveform generation method based on multi-time-scale coupled network

Abstract

The present invention relates to the technical field of radar signal processing, and discloses a method for generating a radar anti-jamming waveform for a multi-time-scale coupled network. Its main contents include the generation of a transmitted waveform and the processing of an echo signal. First, a method for designing an orthogonal waveform for a MIMO radar is given. Then, the transmitted waveform of the MIMO radar for each channel is used as the input of the multi-time-scale coupled network, so as to generate a set of reference signal groups for broadband signal matched filtering. Finally, a method for processing the echo signal of the designed waveform is given. The purpose of the present invention is to design a MIMO radar waveform with good orthogonality and anti-jamming ability, generate a reference signal for broadband matched filtering using a multi-time-scale coupled network, and give a method for processing the echo; the transmitted waveforms between the sub-arrays of the MIMO radar should satisfy orthogonality so that the transmitted waveforms between the sub-arrays can be distinguished by matched filtering at the receiving end.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and specifically to a method for generating a radar anti-jamming waveform based on a multi-time-scale coupled network. Background Art

[0002] Waveform design is a very fundamental task in the process of radar development, which includes both the selection of signal waveforms and the optimization of related parameters, as well as the optimization of matching processing weights. There are significant differences in different types of waveform design methods, but for MIMO radars, sidelobe suppression and waveform orthogonality are always the focus of waveform design.

[0003] The orthogonal waveforms of MIMO radars are divided into frequency-division orthogonal waveforms and coding orthogonal waveforms. If only frequency-division orthogonal waveforms or coding orthogonal waveforms are considered, when the number of subarrays of the MIMO radar is large, the orthogonality between subarrays will decrease, affecting the target detection of the MIMO radar. At the same time, if the frequency-division orthogonal waveform is to obtain a lower autocorrelation sidelobe, a larger number of pulses are required, so the coherent processing period is relatively long, which is not conducive to the measurement of high-speed targets.

[0004] According to the interference principle of a repeater jammer, the intercept receiver needs to accurately extract the frequency, phase, amplitude, and pulse position information of the radar transmitted signal to be able to interfere with the radar. The parameters of the transmitted waveform of the MIMO radar of the present invention have a high degree of freedom, and the radiated power of the signal space is low, which brings great difficulties to the jammer to accurately extract the frequency, phase, and pulse position information of the radar signal. The waveform design of the present invention combines the orthogonality and anti-jamming ability of the waveform. Based on a linear frequency modulation pulse train, phase coding with a coding length of M is performed within a single pulse, and frequency and pulse position random agility are performed between pulses. After optimizing the waveform through a genetic algorithm, the frequency, phase, and pulse position of the waveform are random, making the waveform have the ability to resist repeater jamming while ensuring the orthogonality of the waveform.

[0005] In the processing of echo signals, traditional signal processing treats the echo signal as a narrowband signal, performs matched filtering on the echo pulses of each subarray at the same moment, and then obtains the range and velocity information of the target through coherent integration and constant false alarm rate processing. The traditional narrowband signal processing method requires complex phase compensation between pulses for the processing of the echo of a broadband modulated signal. In addition, when the target is in a high-speed motion state and the displacement exceeds one range resolution cell within the coherent processing period, the error of the traditional narrowband echo processing is relatively large. To address the problem of large errors in the narrowband processing algorithm, the present invention adopts a broadband signal ambiguity function matching algorithm based on multiple time scales to improve the measurement accuracy of target range and velocity. Summary of the Invention

[0006] The present invention provides a method for generating radar anti-jamming waveforms based on a multi-time scale coupled network. Aiming at the disadvantages in the above background technology, considering the orthogonality and anti-jamming performance of waveforms comprehensively, a method for generating radar anti-jamming waveforms based on a multi-time scale coupled network is given. The present invention optimizes the parameters of the waveforms using a genetic algorithm, obtaining better orthogonality and anti-jamming capabilities.

[0007] The present invention provides the following technical solution: A method for generating radar anti-jamming waveforms based on a multi-time scale coupled network, the main content of which includes the generation of transmitted waveforms and the processing of echo signals, and includes the following steps:

[0008] Step 1: Construct a mathematical model of the transmitted waveform of a MIMO radar, give the time-frequency relationship diagram of the array transmitted signal, and obtain the coding parameters that need to be optimized for waveform design;

[0009] Step 2: Construct a waveform optimization cost function according to the orthogonality principle of MIMO radar waveform design, optimize the coding parameters using a genetic algorithm, and construct the transmitted waveform of the MIMO radar;

[0010] Step 3: Combine the principle of broadband signal matched filtering to give the beamforming and target range-velocity information extraction and processing process of the MIMO radar of the present invention;

[0011] Step 4: According to the broadband signal ambiguity function theory, generate a set of matched filtering reference signals while generating the transmitted waveform of the MIMO radar, design a multi-time scale coupled network hardware system, and generate a corresponding set of matched filtering reference signals while generating the radar transmitted signal.

[0012] Preferably, the main modeling process of the MIMO radar anti-jamming composite modulation signal is as follows:

[0013] Suppose a MIMO radar has L sub-arrays, the number of pulses within one CPI is N, and phase coding with a code length of M is adopted within each pulse. Now, the mathematical model of the transmitted signal of the l-th sub-array is given:

[0014]

[0015] In the above formula, T r is the average pulse period of the sub-pulse, ΔT r is the minimum pulse position hopping interval, t p is the pulse width, t s is the phase coding symbol width, is the carrier of the n-th sub-pulse, μ is the frequency modulation slope, is the m-th symbol of the n-th sub-pulse. From the mathematical model of the transmitted signal, it can be seen that the waveform optimization parameters are ξ n 、 Denoted by a vector as Ω = [ξ 1 , ξ 2 , …, ξ N ,

[0016] Among the waveform parameters, the number of phase encoding bits within each pulse is M bits, and each symbol is a four-phase code; the minimum range of inter-pulse frequency hopping is Δf = 1 / t p , ensuring the orthogonality between pulses; the inter-pulse interval of each pulse also randomly hops within a range, enhancing the anti-jamming performance of the signal.

[0017] Preferably, for the MIMO radar anti-jamming waveform optimization method, the method of constructing the waveform optimization cost function is specifically as follows:

[0018] The orthogonality of the MIMO radar is reflected in the auto-correlation and cross-correlation performances of the transmitted signals between sub-arrays. In the present invention, it is required that the transmitted signals have low auto-correlation sidelobe peaks and cross-correlation peaks. Therefore, the peak sidelobe level criterion (PSL) is adopted for orthogonal waveform design:

[0019]

[0020] In the above formula, s p (t) and s q (t) are the transmitted signals of different sub-arrays. When p = q, c pq (τ) is the auto-correlation function of the transmitted signal; when p ≠ q, c pq (τ) is the cross-correlation function of the transmitted signal. In the present invention, the phase encoding matrix of the transmitted waveform, the frequency encoding sequence of the carrier, and the pulse position agile sequence are used as optimization variables, and the peak sidelobe ratio of the transmitted signal is used as the cost function to establish the following optimization model:

[0021]

[0022] The optimization parameters of this model are discrete phase, frequency, and pulse position encoding. The genetic algorithm can be used to optimize the model to obtain the MIMO orthogonal waveform that meets the conditions.

[0023] Preferably, the waveform separation and beamforming results of the MIMO radar wideband ambiguity function:

[0024] Considering a co-located MIMO radar system, the number of transmitting antenna elements and receiving antenna elements are P and Q respectively. Both the transmitting and receiving are uniform linear arrays, and the element spacings of the transmitting antenna and the receiving antenna are d t and d r , and the direction of arrival of the target is

[0025] Define s k (t) represents the transmission signal of the m-th transmitting antenna element, and s = [s 1 (t), s 2 (t), …, s P (t)] represents the transmission signal vector. After the M transmission signals propagate through space, the combined signal reaching the target located at the slant range R (corresponding to the r-th range cell) and azimuth θ is:

[0026]

[0027] In the formula, ξ 1 is the propagation attenuation factor. Assuming that the transmission signals for each sub-array are the same, ω = (c - v) / (c + v) is the scale parameter, and τ k is the time delay difference of the signal transmitted by the k-th (k = 1, 2, …, M) element relative to the reference element, which can be expressed as:

[0028]

[0029] In the above formula, τ k only depends on the antenna layout and is independent of the target's motion state. The fixed time delay τ k can be represented by . Therefore, the combined signal at the target is:

[0030]

[0031] In the above formula is the transmission signal steering vector, and s is the received signal vector at the target, which can be expressed as where τ 0 = 2R 0 / (c - v);

[0032] After the signal r(t) is reflected by a target with a certain RCS, the signal received by the q-th receiving antenna is:

[0033]

[0034] In the formula, is the phase difference of the q-th antenna. Let ξ 1 ξ 2 = ξ, and substitute formula (1) into formula (8), then the echo of the q-th receiving antenna is:

[0035]

[0036] The received signal vector is x(t) = [x 1 (t), x 2 (t), …, x Q (t)]. The matrix form of formula (9) is as follows:

[0037] x(t) = ξb(θ r )α T (θ t )s[ω(t - τ 0 )](10)

[0038] In equation (10), b(θ r ) is the receiving antenna steering vector, Now consider the wideband matching processing of the received echo of the q-th receiving antenna. From equation (10), the echo signal of the q-th receiving channel can be obtained as:

[0039]

[0040] Now perform wideband matching filtering on the echo signal of the q-th receiving antenna. According to the wideband ambiguity function theory, the reference signal of the p-th transmitting channel is:

[0041]

[0042] The matched output of the q-th receiving channel receiving the signal of the p-th transmitting channel is:

[0043]

[0044] In the above equation, T is the pulse train duration. Due to the orthogonality of the transmitted signals, only the signal of the p-th transmitting channel in the transmitted signal vector has an output. The matched output can be simplified as:

[0045]

[0046] From the above equation, when ω = η m , τ 0 = ξ m , the matched filter has the maximum output. The maximum output of the matched filtering is denoted as

[0047] The range-velocity information of the target can be obtained after the echo signal passes through the wideband matching network, and the azimuth angle of the target can be obtained through beamforming. The output of beamforming is:

[0048]

[0049] In equation (15), is the output of the wideband matching filtering, τ 0 and ω are the time delay and Doppler frequency of the target. When , the above equation has the maximum value. At this time, the target direction is:

[0050]

[0051] Preferably, a broadband echo matching signal is generated simultaneously with the radar transmission signal. The output of the orthogonal waveform is generated by a DDS waveform generator according to the frequency and phase coding sequence to obtain the amplitude value of the waveform at each corresponding phase. These amplitude values generate a series of sub-pulses, and the duration of each is determined by the bandwidth of the radar; the pulse timing control module changes the pulse period between pulses to achieve waveform pulse position agile modulation; after passing through a multi-channel DDS circuit, an MIMO radar orthogonal waveform can be generated. After generating the MIMO radar orthogonal waveform, one signal is sent to the MIMO radar transmitting antenna, and the other is used as the input of the multi-time scale coupling network circuit to generate a reference signal for broadband matching filtering of the echo signal;

[0052] The broadband matching network essentially finds the maximum value of the two-dimensional ambiguity function of the echo signal. A reference signal for the broadband matching network is generated simultaneously with the transmission signal at the transmitting end. The purpose of the multi-time scale coupling network is to generate a set of signals in which the transmitted signals of each subarray are jointly shifted in time and frequency for broadband matching filtering of the echo signal; in the multi-time scale coupling circuit part, assume that the transmission signal of each subarray is delayed by τ k is the received signal of the k-th range gate, and then all Doppler frequencies are matched and filtered within the k-th range gate to achieve broadband pulse compression processing of the echo signal of the k-th range gate.

[0053] The present invention has the following beneficial effects:

[0054] The purpose of the present invention is to design an MIMO radar waveform with good orthogonality and anti-interference ability, generate a reference signal for broadband matching filtering using a multi-time scale coupling network, and give a processing method for the echo; the transmission waveforms between the subarrays of the MIMO radar should satisfy orthogonality so that the transmission waveforms between the subarrays can be distinguished by matched filtering at the receiving end.

[0055] Based on linear frequency modulation, the waveform of the present invention performs intra-pulse phase coding on the pulse train, and jointly performs frequency and pulse position agility between pulses, making the waveform have good orthogonality and anti-interference performance. The echo signal uses the broadband signal matching filtering theory to perform matched filtering on the echo signal to distinguish the echo signals of each transmission channel, and finally combines digital beamforming to obtain the distance, speed, and angle information of the target.

[0056] The feature of the present invention is that while the transmitter generates a composite modulation transmission signal, a reference signal group for broadband signal matching filtering is generated through a multi-time scale coupling network, which can perform broadband matching filtering on the signals of each receiving channel to obtain the speed and distance of the target. Compared with the traditional echo signal processing method, the processing complexity of the echo signal is greatly reduced, and the target detection accuracy is relatively high. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Schematic diagram of the transmitted signal of the first sub-array of the present invention;

[0058] Figure 2 Time-frequency relationship diagram of the transmitted waveform of the MIMO radar of the present invention;

[0059] Figure 3 Flow chart of the echo signal processing of the present invention;

[0060] Figure 4 System diagram of the multi-time scale coupled network waveform generation of the present invention. Detailed implementation manners

[0061] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0062] Please refer to Figure 1 , a radar anti-jamming waveform generation method based on a multi-time scale coupled network, a radar anti-jamming waveform generation method based on a multi-time scale coupled network, the main contents of which include the generation of the transmitted waveform and the processing of the echo signal, and include the following steps:

[0063] Step 1: Construct a mathematical model of the MIMO radar transmitted waveform, give the time-frequency relationship diagram of the array transmitted signal, and obtain the coding parameters that need to be optimized for waveform design;

[0064] Step 2: Construct a waveform optimization cost function according to the orthogonality principle of the MIMO radar waveform design, optimize the coding parameters using a genetic algorithm, and construct the MIMO radar transmitted waveform;

[0065] Step 3: Combine the broadband signal matched filtering principle to give the beamforming and target range-velocity information extraction processing process of the MIMO radar of the present invention;

[0066] Step 4: According to the broadband signal ambiguity function theory, generate a group of matched filtering reference signals while generating the MIMO radar transmitted waveform, design a multi-time scale coupled network hardware system, and generate a corresponding group of matched filtering reference signals while generating the radar transmitted signal.

[0067] The anti-jamming composite modulation signal of the MIMO radar, the main modeling process is as follows:

[0068] Suppose the MIMO radar has L subarrays, the number of pulses within one CPI is N, and phase coding with a code length of M is adopted within each pulse. Now, the mathematical model of the transmitted signal of the l-th subarray is given as follows:

[0069]

[0070] In the above formula, T r is the average pulse period of the sub-pulse, ΔT r is the minimum pulse position jump interval, t p is the pulse width, t s is the phase coding symbol width, is the carrier of the n-th sub-pulse, μ is the frequency modulation slope, is the m-th symbol of the n-th sub-pulse. From the mathematical model of the transmitted signal, it can be seen that the waveform optimization parameters are ξ n , Denoted in vector form as Ω = [ξ 1 , ξ 2 , …, ξ N ,

[0071] Among the waveform parameters, the number of phase coding bits within each pulse is M bits, and each symbol is a four-phase code; the minimum range of inter-pulse frequency hopping is Δf = 1 / t p to ensure the orthogonality between pulses; the inter-pulse interval of each pulse also randomly jumps within a certain range to enhance the anti-jamming performance of the signal.

[0072] For the MIMO radar anti-jamming waveform optimization method, the method of constructing the waveform optimization cost function is specifically as follows:

[0073] The orthogonality of the MIMO radar is reflected in the autocorrelation and cross-correlation performances of the transmitted signals between subarrays. In the present invention, it is required that the transmitted signals have low autocorrelation sidelobe peaks and cross-correlation peaks. Therefore, the peak sidelobe level criterion (PSL) is adopted for orthogonal waveform design:

[0074]

[0075] In the above formula, s p (t) and s q (t) are the transmitted signals of different subarrays. When p = q, c pq (τ) is the autocorrelation function of the transmitted signal; when p ≠ q, c pq (τ) is the cross-correlation function of the transmitted signal. In the present invention, the phase coding matrix of the transmitted waveform, the frequency coding sequence of the carrier, and the pulse position agility sequence are used as optimization variables, and the peak sidelobe ratio of the transmitted signal is used as the cost function to establish the following optimization model:

[0076]

[0077] The optimized parameters of the model are discrete phase, frequency, and pulse position encoding. The genetic algorithm can be used to optimize the model to obtain the MIMO orthogonal waveform that meets the conditions.

[0078] The results of MIMO radar wideband ambiguity function waveform separation and beamforming are as follows:

[0079] Considering a co-located MIMO radar system, the number of transmit antenna elements and receive antenna elements are P and Q respectively. Both the transmit and receive are uniform linear arrays, and the element spacings of the transmit antenna and receive antenna are d t and d r , and the direction of arrival of the target is

[0080] Define s k (t) to represent the transmit signal of the m-th transmit antenna element, and s = [s 1 (t), s 2 (t), …, s P (t)] to represent the transmit signal vector. After the M transmit signals propagate through space, the combined signal reaching the target located at the slant range R (corresponding to the r-th range cell) and azimuth θ is:

[0081]

[0082] In the formula, ξ 1 is the propagation attenuation factor. Assuming that the transmit signals of each subarray are the same, ω = (c - v) / (c + v) is the scale parameter, and τ k is the time delay difference of the signal transmitted by the k-th (k = 1, 2, …, M) element relative to the reference element, which can be expressed as:

[0083]

[0084] In the above formula, τ k only depends on the antenna layout and has nothing to do with the motion state of the target. The fixed time delay τ k can be represented by , so the combined signal at the target is:

[0085]

[0086] In the above formula, is the transmit signal steering vector, and s is the receive signal vector at the target, which can be expressed as where τ 0 = 2R 0 / (c - v);

[0087] The signal r(t) is reflected by a target with a certain RCS, and the signal received by the q-th receiving antenna is:

[0088]

[0089] In the formula, is the phase difference of the q-th antenna. Let ξ in the formula 1 ξ 2 = ξ. Substitute formula (1) into formula (8), then the echo of the q-th receiving antenna is:

[0090]

[0091] The received signal vector is x(t) = [x 1 (t), x 2 (t), …, x Q (t)]. The matrix form of formula (9) is as follows:

[0092] x(t) = ξb(θ r )α T (θ t )s[ω(t - τ 0 )](10)

[0093] b(θ r ) in formula (10) is the receiving antenna steering vector, Now consider the wideband matching processing of the received echo of the q-th receiving antenna. From formula (10), the echo signal of the q-th receiving channel can be obtained as:

[0094]

[0095] Now perform wideband matching filtering on the echo signal of the q-th receiving antenna. According to the wideband ambiguity function theory, the reference signal of the p-th transmitting channel is:

[0096]

[0097] The matching output of the q-th receiving channel receiving the signal of the p-th transmitting channel is:

[0098]

[0099] In the above formula, T is the pulse train duration. Due to the orthogonality of the transmitted signals, only the signal of the p-th transmitting channel in the transmitted signal vector has an output. The matching output can be simplified as:

[0100]

[0101] In the above formula, when ω = η m , τ 0 = ξ mWhen the matching filter has the maximum output, the maximum output of the matched filtering is denoted as

[0102] After the echo signal passes through the broadband matching network, the range-velocity information of the target can be obtained. Then, through beamforming, the azimuth angle of the target can be obtained. The output of beamforming is:

[0103]

[0104] In Equation (15), is the output of the broadband matched filtering, τ 0 and ω are the time delay and Doppler frequency of the target. When the above formula has a maximum value. At this time, the target direction is:

[0105]

[0106] While generating the radar transmit signal, a broadband echo matching signal is generated simultaneously. The output of the orthogonal waveform is the amplitude value of the waveform at each corresponding phase generated by the DDS waveform generator according to the frequency and phase coding sequence. These amplitude values generate a series of sub-pulses, and the duration of each is determined by the bandwidth of the radar; the pulse timing control module changes the pulse period between pulses to achieve waveform pulse position agile modulation; after passing through the multi-channel DDS circuit, the MIMO radar orthogonal waveform can be generated. After generating the MIMO radar orthogonal waveform, one signal is given to the MIMO radar transmit antenna, and the other is used as the input of the multi-time scale coupling network circuit to generate the reference signal for the broadband matched filtering of the echo signal; The broadband matching network essentially finds the maximum value of the two-dimensional ambiguity function of the echo signal. While generating the transmit signal at the transmit end, the reference signal of the broadband matching network is also generated. The purpose of the multi-time scale coupling network is to generate a set of signals in which the transmit signals of each subarray are jointly shifted in time and frequency for the broadband matched filtering of the echo signal; in the multi-time scale coupling circuit part, let the transmit signal delay of each subarray be τ

[0107] is the received signal of the k-th range gate. Then, within the k-th range gate, matched filtering is performed on all Doppler frequencies to achieve broadband pulse compression processing of the echo signal of the k-th range gate. k is the received signal of the k-th range gate. Then, within the k-th range gate, matched filtering is performed on all Doppler frequencies to achieve broadband pulse compression processing of the echo signal of the k-th range gate.

[0108] It should be noted that, in this document, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variation thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device.

[0109] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for generating radar anti-jamming waveforms based on a multi-time scale coupled network, the main content of which includes the generation of transmitted waveforms and the processing of echo signals, Characterized in that: It includes the following steps: Step 1: Construct a mathematical model of the MIMO radar transmitted waveform, give the time-frequency relationship diagram of the array transmitted signal, and obtain the coding parameters that need to be optimized for waveform design; Step 2: Construct a waveform optimization cost function according to the orthogonality principle of MIMO radar waveform design, optimize the coding parameters with a genetic algorithm, and construct the MIMO radar transmitted waveform; Step 3: Combine the broadband signal matched filtering principle to give the beamforming of the MIMO radar and the processing process for extracting target range and velocity information; Step 4: According to the broadband signal ambiguity function theory, generate a set of matched filtering reference signals while generating the MIMO radar transmitted waveform, design a multi-time scale coupled network hardware system, and generate a corresponding set of matched filtering reference signals while generating the radar transmitted signal.

2. The method for generating radar anti-jamming waveforms based on a multi-time scale coupled network according to claim 1, Characterized in that: The main modeling process of the MIMO radar anti-jamming composite modulation signal is as follows: Suppose the MIMO radar has L sub-arrays, the number of pulses in one CPI is N, and phase coding with a code length of M is used in each pulse. Now, the mathematical model of the transmitted signal of the l-th sub-array is given: In the above formula, T r is the average pulse period of the sub-pulse, ΔT r is the minimum pulse position jump interval, t p is the pulse width, t s is the phase coding symbol width, is the carrier wave of the nth sub-pulse, μ is the frequency modulation slope, is the mth symbol of the nth sub-pulse. According to the mathematical model of the transmitted signal, the waveform optimization parameter is Denoted by a vector as Ω = [ξ 1 , ξ 2 , …, ξ N , Among the waveform parameters, the number of phase encoding bits within each pulse is M bits, and each symbol is a four-phase code; the minimum range of frequency hopping between pulses is Δf = 1 / t p , ensuring orthogonality between pulses; the inter-pulse interval of each pulse also randomly hops within a range, enhancing the anti-interference performance of the signal.

3. The method for generating radar anti-jamming waveforms based on a multi-time scale coupled network according to claim 2, Characterized in that: For the MIMO radar anti-jamming waveform optimization method, the method for constructing the waveform optimization cost function is specifically: The orthogonality of the MIMO radar is reflected in the autocorrelation and cross-correlation performance of the transmitted signals between sub-arrays. It is required that the transmitted signals have low autocorrelation sidelobe peaks and cross-correlation peaks. Therefore, the peak sidelobe level criterion (PSL) is used for orthogonal waveform design: In the above formula, s p (t) and s q (t) are the transmitted signals of different sub-arrays. When p = q, c pq (τ) is the autocorrelation function of the transmitted signal; when p ≠ q, c pq (τ) is the cross-correlation function of the transmitted signals. Taking the phase encoding matrix of the transmitted waveform, the frequency encoding sequence of the carrier wave, and the pulse position agile sequence as optimization variables, and taking the peak sidelobe ratio of the transmitted signal as the cost function, the following optimization model is established: The optimization parameters of this model are discrete phase, frequency, and pulse position coding. The genetic algorithm is used to optimize the model to obtain the MIMO orthogonal waveform that meets the conditions.

4. The method for generating radar anti-jamming waveforms based on a multi-time scale coupled network according to claim 3, Characterized in that: The results of MIMO radar broadband ambiguity function waveform separation and beamforming: Consider a monostatic MIMO radar system where the number of transmit and receive antenna elements are \(P\) and \(Q\) respectively. Both the transmit and receive arrays are uniform linear arrays, and the element spacings of the transmit and receive antennas are \(d\) t and \(d\) r , and the direction of arrival of the target is Define s k (t) represents the transmission signal of the m-th transmitting antenna element, and s = [s 1 (t), s 2 (t), …, s P (t)] represents the transmission signal vector. After the M transmission signals propagate through space, the combined signal reaching the target located at the slant range R and azimuth θ is: where the slant range \(R\) corresponds to the \(r\)th range bin, \(\xi\) 1 is the propagation attenuation factor. Assuming that the transmitted signals for each subarray are the same, \(\omega=(c - v) / (c + v)\) is the scaling parameter, and \(\tau\) k is the time delay difference of the signal transmitted by the \(k\)th array element relative to the reference array element, \(k = 1,2,\cdots,M\), and \(\tau\) k is expressed as: The above τ k is only related to the layout of the antenna and has nothing to do with the motion state of the target. The fixed time delay τ k is adopted to represent. Therefore, the composite signal at the target is: In the above formula is the steering vector of the transmitted signal, and s is the received signal vector at the target, expressed as where τ 0 = 2R 0 / (c - v); The signal r(t) is reflected by a target with a certain RCS, and the signal received by the q-th receiving antenna is: wherein is the q-th antenna phase difference. Let ξ in the formula 1 ξ 2 = ξ. Substitute Equation (1) into Equation (8), then the echo of the q-th receiving antenna is as follows: The received signal vector is x(t) = [x 1 (t), x 2 (t), …, x Q (t)], and the matrix form of Equation (9) is as follows: x(t) = ξb(θ r )α T (θ t )s[ω(t - τ 0 )] (10) The b(θ r ) in Equation (10) is the receiving antenna steering vector, Now consider the wideband matching processing of the received echo of the q-th receiving antenna. From Equation (10), the echo signal of the q-th receiving channel is obtained as follows: Now, perform broadband matched filtering on the echo signal of the q-th receiving antenna. According to the broadband ambiguity function theory, the reference signal of the p-th transmitting channel is: The matched output of the q-th receiving channel receiving the signal of the p-th transmitting channel is: In the above formula, T is the pulse train duration. According to the orthogonality of the transmitted signals, only the signal of the p-th transmitting channel in the transmitted signal vector has an output, and the matched output is simplified to: In the above equation, when ω = η m , τ 0 = ξ m , the matched filter has the maximum output, and the maximum output of the matched filtering is denoted as After the echo signal passes through the broadband matching network, the range and velocity information of the target is obtained, and then the azimuth angle of the target is obtained through beamforming. The output of beamforming is: In Equation (15), is the output of broadband matched filtering, τ 0 and ω are the time delay and Doppler frequency of the target. When the above equation has a maximum value, and the target direction at this time is:

5. The method for generating radar anti-jamming waveforms based on a multi-time scale coupled network according to claim 4, Characterized in that: While generating the radar transmission signal, a broadband echo matching signal is generated at the same time. The output of the orthogonal waveform is generated by the DDS waveform generator according to the frequency and phase coding sequence for each amplitude value of the waveform at the corresponding phase. These amplitude values generate a series of sub-pulses, each of which the duration is determined by the bandwidth of the radar; the pulse timing control module changes the pulse period between pulses to achieve waveform pulse position agile modulation; after passing through the multi-channel DDS circuit, the MIMO radar orthogonal waveform is generated. After generating the MIMO radar orthogonal waveform, one signal is sent to the MIMO radar transmitting antenna, and one signal is used as the input of the multi-time scale coupling network circuit to generate the reference signal for broadband matched filtering of the echo signal; The broadband matching network essentially aims to find the maximum value of the two-dimensional ambiguity function of the echo signal. While generating the transmitted signal at the transmitter, a reference signal for the broadband matching network is also generated. The purpose of the multi-time-scale coupling network is to generate a set of signals in which the transmitted signals of each subarray are jointly shifted in time and frequency for broadband matched filtering of the echo signal. In the multi-time-scale coupling circuit part, let the delay of the transmitted signal of each subarray be τ k be the received signal of the k-th range gate, and then perform matched filtering on all Doppler frequencies within the k-th range gate to achieve broadband pulse compression processing of the echo signal of the k-th range gate.

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