Generation and processing method of multi-sub-pulse structure wideband waveform for energy accumulation

Abstract

The application discloses a kind of energy accumulation-oriented multi-sub-pulse structure wideband waveform generation and processing method, first utilize random phase coding signal as narrowband sub-pulse waveform construction to obtain the wideband waveform based on multi-sub-pulse structure, then utilize multi-branch pulse compression method to realize the separation of sub-pulse in the wideband echo of multi-sub-pulse structure, then utilize distance gate alignment operation, spectrum shift operation, by the echo signal is dispersed into fast time dimension matrix, design inter-pulse coherent accumulation filter matrix, realize the inter-pulse coherent accumulation of each sub-pulse waveform and the peak value alignment of each inter-pulse coherent accumulation result in Doppler dimension, finally utilize maximum contrast method to realize the phase compensation and coherent accumulation between each sub-pulse processing result.The final result of the method of the application reduces the range resolution of wideband waveform, can effectively accumulate the energy dispersed on multiple scattering points of extended target, improves the output signal-to-noise ratio of wideband waveform.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a method for generating and processing broadband waveforms with multi-subpulse structures oriented towards energy accumulation. Background Technology

[0002] With the rapid development of electronic warfare technology, modern radar systems face numerous challenges and threats, such as electronic jamming. When radar waveforms are easily intercepted and exploited by the adversary, they risk being subjected to noise jamming, deception jamming, and power suppression, severely weakening their detection and survivability. Therefore, to ensure the survivability and operational capability of radar systems in electronic warfare, it is urgent to design radar transmission waveforms with low intercept performance. Wide bandwidth waveforms are a typical example of low intercept waveforms. Because the waveform energy is dispersed over a large time and bandwidth range, it is difficult for adversary reconnaissance aircraft to receive, exhibiting excellent low intercept performance. However, the high range resolution of broadband waveforms causes energy to be dispersed across various scattering points of the extended target, affecting the waveform's detection capability.

[0003] Current research on wideband low intercept waveforms focuses on the design of transmitted waveforms and echo processing methods. The paper "B. Tang and J. Tang, Robust waveform design of wideband cognitive radar for extended target detection, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China, 2016, pp. 3096-3100" designs a wideband cognitive radar waveform for detecting extended targets by maximizing the worst-case signal-to-interference-plus-noise ratio based on a stochastic model of the assumed target impulse response. However, this design method is highly dependent on prior knowledge of the target and has poor practicality. The paper “Yuanhao Wu, Tao Fan, Peijie Zhu, Rui Tan, Xianxiang Yu, Guolong Cui, An extended target signal integration method via mainlobe broadening, SignalProcessing, Volume 216, 2024” proposes a design method for a mismatch filter based on mainlobe broadening. Without relying on prior information, this method reduces the range resolution of the broadband waveform by performing mismatch filtering on the echo signal, thereby achieving the goal of accumulating and extending the energy of the target dispersed at each scattering point. However, due to the limited freedom of waveform design, this method can only extend the mainlobe width within a limited range. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for generating and processing broadband waveforms with multi-subpulse structures for energy accumulation, thereby reducing the range resolution of the broadband waveforms and enabling the accumulation of energy at various scattering points of the extended target.

[0005] The technical solution adopted in this invention is: a method for generating and processing broadband waveforms of multi-subpulse structures oriented towards energy accumulation, the specific steps of which are as follows:

[0006] S1. A broadband waveform based on a multi-subpulse structure is constructed by using a random phase-coded signal as a narrowband subpulse waveform.

[0007] S2. Based on step S1, the separation of broadband echo neutron pulses in a multi-sub-pulse structure is achieved using a multi-branch pulse compression method.

[0008] S3. Based on step S2, use the distance gate alignment operation to achieve peak alignment of each sub-pulse waveform in the distance dimension, and use the spectrum shifting operation to compensate for the difference in frequency modulation terms between the processing results of each branch.

[0009] S4. Based on step S3, the echo signal is discretized into fast and slow time-dimensional matrices, and an inter-pulse coherent accumulation filter matrix is ​​designed to realize the inter-pulse coherent accumulation of each sub-pulse waveform and the peak alignment of each inter-pulse coherent accumulation result in the Doppler dimension.

[0010] S5. Based on step S4, phase compensation and coherent accumulation between the processing results of each sub-pulse are achieved by using the maximum contrast method.

[0011] Furthermore, step S1 is specifically as follows:

[0012] S11. Broadband waveform modeling based on multi-sub-pulse structure;

[0013] A broadband waveform model based on a multi-sub-pulse structure, consisting of K narrowband sub-pulses, is defined as follows:

[0014]

[0015] Where τ and B represent the pulse width and bandwidth of the sub-pulse waveform, respectively, and t represents time, s. k (t) represents the waveform of the k-th sub-pulse, which is set as a random phase-coded signal, and its expression is as follows:

[0016]

[0017] Where rect(t) represents a rectangular signal, N represents the number of codewords in the k-th sub-pulse waveform, and T s φ represents the length of each codeword. k (n) represents the nth phase codeword of the kth sub-pulse waveform, then τ = NT. s .

[0018] If a coherent processing cycle is defined to transmit a total of M pulses, then the expression for the broadband LPI waveform baseband signal transmitted by the radar system based on a multi-narrowband structure is as follows:

[0019]

[0020] Among them, T p f represents the pulse repetition period. c Indicates the carrier frequency.

[0021] S12, Wideband Radar Target Response Modeling;

[0022] Ideally, the broadband radar target response can be composed of the responses of several scattering points, and each scattering point can be considered a point target in a narrowband radar system. Therefore, when the radar line-of-sight is specified, the expression for the broadband radar target response h(t) is as follows:

[0023]

[0024] Where δ(t) represents the impact function, L represents the total number of scattering points of the target, and A l and t l These represent the complex scattering amplitude and the two-way delay relative to the radar at the l-th scattering point, respectively.

[0025] Imagine a rigid target moving at a constant velocity V toward the radar. The relative distance between the location of the l-th scattering point of the target and the radar is R. l Therefore, the two-way propagation time delay of the reflection from the l-th scattering point of the target is t. l =(2R) l -2Vt) / c, where c represents the speed of light.

[0026] S13. Broadband echo modeling based on multi-sub-pulse structure;

[0027] Suppose there exists a rigid target moving at a constant velocity V toward the radar, and the relative distance between the location of the l-th scattering point of the target and the radar is R. l The echo signal expression is as follows:

[0028]

[0029] Where n(t) represents Gaussian additive white noise, b l =2R l / c.

[0030] S14, echo downconversion;

[0031] After downconversion, the broadband baseband echo waveform expression based on the multi-sub-pulse structure is as follows:

[0032]

[0033] Among them, f k =f c +kB, f dk =f k (2V) / c represents the Doppler frequency shift of the k-th sub-pulse waveform when detecting the target. This represents the noise after down-conversion. When the target speed is relatively low, i.e., V << c, the simplified expression for the echo waveform is as follows:

[0034]

[0035] Furthermore, step S2 is specifically as follows:

[0036] Let the matched filter bank be represented as w0(t), w1(t), ..., w K-1 (t), the specific expression is as follows:

[0037]

[0038] in, s k The conjugate form of (t). Then the expression for the compression result of the k-th pulse is as follows:

[0039]

[0040] in, Represents the k-th matched filter w k (t) Output noise, τ′ represents the time variable of the integral, z k (t,m) represents the matched filter w k (t) The sum of the outputs of other sub-pulses after filtering out the k-th sub-pulse within the pulse, and the orthogonality of the spectra between the sub-pulses, w k The cross-correlation level between (t) and the other sub-pulses is very low and can be ignored, then r k The specific expression for (t) is as follows:

[0041]

[0042] Furthermore, step S3 is specifically as follows:

[0043] S31, Align the distance gate;

[0044] Shift the pulse compression result of the k-th branch to the left by kτ to obtain the output result y of the k-th branch. k (t), the expression is as follows:

[0045]

[0046] in,

[0047] S32, Spectrum shifting;

[0048] The output result y of the kth branch k (t) Compensation frequency modulation term The output of the k-th branch after spectrum shifting processing is obtained. The expression is as follows:

[0049]

[0050] in,

[0051] Furthermore, step S4 is specifically as follows:

[0052] Discretizing the echo signal into a fast and slow time-dimensional matrix, then the fast and slow time dimensions... The expression is as follows:

[0053]

[0054] in, It indicates a fast time.

[0055] Set the sampling time interval to ΔT = T p / Q is sampled in the fast time dimension tq=(q-1)ΔT, q=1,2,…,Q, and is expressed as follows:

[0056]

[0057] Let y k,q =[y k (t q ,0),y k (t q ,1),…,y k (t q [M-1] Τ Then the fast and slow time dimension matrix can be expressed as

[0058] in,[] T This represents the transpose operator. Represents the complex field.

[0059] make For the unambiguous velocity frequency range (-v) max ,v max If points J are uniformly sampled, and J ≥ M, let Δv = 2v max / J, then we get v=[v1,…,v J ].

[0060] Among them, v i =-v max +(i-1)2v max / J,i=1,2,…,J. Based on velocity element v i The filter was designed and obtained. The expression is as follows:

[0061]

[0062] Then construct the k-th fast and slow time dimension matrix Y k The expression for the inter-pulse coherent accumulation filter matrix is ​​as follows:

[0063]

[0064] The RD plane obtained by processing the echo of the k-th branch through inter-pulse coherent accumulation. The expression is as follows:

[0065]

[0066] Furthermore, step S5 is specifically as follows:

[0067] The phase difference between the RD planes of each sub-pulse is compensated using the maximum contrast method, and the output results of each branch are set. The phase vector that needs to be compensated is The phase compensation problem for each sub-pulse is then transformed and solved as follows:

[0068]

[0069] Where, θ k This represents the phase term for compensation in the k-th branch. (·) Η This indicates a conjugate operation.

[0070] Then, using the idea of ​​coordinate descent algorithm, the high-dimensional optimization problem is transformed into a series of subproblems that are easy to solve, and solved using gradient descent methods such as the Newton-Horner algorithm until the algorithm converges and the optimal compensation phase value is obtained.

[0071] The output of the broadband waveform processing method for multi-subpulse structures oriented towards energy accumulation is Y, expressed as follows:

[0072]

[0073] The beneficial effects of this invention are as follows: First, the method of this invention utilizes a random phase-coded signal as a narrowband sub-pulse waveform to construct a broadband waveform based on a multi-sub-pulse structure. Then, a multi-branch pulse compression method is used to separate the sub-pulses in the broadband echo of the multi-sub-pulse structure. Next, a range gate alignment operation is used to align the peak values ​​of each sub-pulse waveform in the range dimension. A spectrum shifting operation is used to compensate for the differences in frequency modulation terms between the processing results of each branch. By discretizing the echo signal into fast and slow time-dimensional matrices, an inter-pulse coherent accumulation filter matrix is ​​designed to achieve inter-pulse coherent accumulation of each sub-pulse waveform and peak alignment of the inter-pulse coherent accumulation results in the Doppler dimension. Finally, a maximum contrast method is used to achieve phase compensation and coherent accumulation between the processing results of each sub-pulse. This invention generates and processes a broadband waveform based on a multi-sub-pulse structure with a large time-bandwidth product. The final result reduces the range resolution of the broadband waveform, effectively accumulates energy dispersed across multiple scattering points of the extended target, and improves the output signal-to-noise ratio of the broadband waveform. Attached Figure Description

[0074] Figure 1 This is a flowchart of a method for generating and processing broadband waveforms of a multi-subpulse structure oriented towards energy accumulation, according to the present invention.

[0075] Figure 2 This is a schematic diagram of a broadband waveform based on a multi-sub-pulse structure in an embodiment of the present invention.

[0076] Figure 3 This is a schematic diagram of the amplitude distribution of various scattering points of a broadband radar target in an embodiment of the present invention.

[0077] Figure 4 This is a schematic diagram of the phase distribution of each scattering point of a broadband radar target in an embodiment of the present invention.

[0078] Figure 5 This is a distance-Doppler (RD) plane result obtained by processing a broadband echo based on a multi-subpulse structure using the method of this invention in an embodiment of the invention.

[0079] Figure 6 This is an RD plane result diagram obtained by processing the broadband echo based on the multi-sub-pulse structure in an embodiment of the present invention using a matched filtering and moving target detection (MTD) method.

[0080] Figure 7 This is an RD plane result diagram obtained by processing the narrowband signal echo through a method based on matched filtering and moving target detection (MTD) in an embodiment of the present invention.

[0081] Figure 8 This is a comparison diagram of the distance dimension tangent of the RD plane after three processing results in an embodiment of the present invention. Detailed Implementation

[0082] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0083] like Figure 1 The flowchart shown is a method for generating and processing broadband waveforms of multi-subpulse structures for energy accumulation according to the present invention. The specific steps are as follows:

[0084] S1. A broadband waveform based on a multi-subpulse structure is constructed by using a random phase-coded signal as a narrowband subpulse waveform.

[0085] S2. Based on step S1, the separation of broadband echo neutron pulses in a multi-sub-pulse structure is achieved using a multi-branch pulse compression method.

[0086] S3. Based on step S2, use the distance gate alignment operation to achieve peak alignment of each sub-pulse waveform in the distance dimension, and use the spectrum shifting operation to compensate for the difference in frequency modulation terms between the processing results of each branch.

[0087] S4. Based on step S3, the echo signal is discretized into fast and slow time-dimensional matrices, and an inter-pulse coherent accumulation filter matrix is ​​designed to realize the inter-pulse coherent accumulation of each sub-pulse waveform and the peak alignment of each inter-pulse coherent accumulation result in the Doppler dimension.

[0088] S5. Based on step S4, phase compensation and coherent accumulation between the processing results of each sub-pulse are achieved by using the maximum contrast method.

[0089] In this embodiment, step S1 is specifically as follows:

[0090] S11. Broadband waveform modeling based on multi-sub-pulse structure;

[0091] A broadband waveform model based on a multi-sub-pulse structure, consisting of K narrowband sub-pulses, is defined as follows:

[0092]

[0093] Where τ and B represent the pulse width and bandwidth of the sub-pulse waveform, respectively, and t represents time, s. k (t) represents the waveform of the k-th sub-pulse, which is set as a random phase-coded signal, and its expression is as follows:

[0094]

[0095] Where rect(t) represents a rectangular signal, N represents the number of codewords in the k-th sub-pulse waveform, and T s φ represents the length of each codeword. k (n) represents the nth phase codeword of the kth sub-pulse waveform, then τ = NT. s .

[0096] If a coherent processing cycle is defined to transmit a total of M pulses, then the expression for the broadband LPI waveform baseband signal transmitted by the radar system based on a multi-narrowband structure is as follows:

[0097]

[0098] Among them, T p f represents the pulse repetition period. c Indicates the carrier frequency.

[0099] S12, Wideband Radar Target Response Modeling;

[0100] Ideally, the broadband radar target response can be composed of the responses of several scattering points, and each scattering point can be considered a point target in a narrowband radar system. Therefore, when the radar line-of-sight direction is specified, the expression for the broadband radar target response h(t) is as follows:

[0101]

[0102] Where δ(t) represents the impact function, L represents the total number of scattering points of the target, and A l and t l These represent the complex scattering amplitude and the two-way delay relative to the radar at the l-th scattering point, respectively.

[0103] Imagine a rigid target moving at a constant velocity V toward the radar. The relative distance between the location of the l-th scattering point of the target and the radar is R. l Therefore, the two-way propagation time delay of the reflection from the l-th scattering point of the target is t. l =(2R) l -2Vt) / c, where c represents the speed of light.

[0104] S13. Broadband echo modeling based on multi-sub-pulse structure;

[0105] Suppose there exists a rigid target moving at a constant velocity V toward the radar, and the relative distance between the l-th scattering point of the target and the radar is R. l The echo signal expression is as follows:

[0106]

[0107] Where n(t) represents Gaussian additive white noise, b l =2R l / c.

[0108] S14, echo downconversion;

[0109] After downconversion, the broadband baseband echo waveform expression based on the multi-sub-pulse structure is as follows:

[0110]

[0111] Among them, f k =f c +kB, f dk =f k (2V) / c represents the Doppler frequency shift of the k-th sub-pulse waveform when detecting the target. This represents the noise after down-conversion. When the target speed is relatively low, i.e., V << c, the simplified expression for the echo waveform is as follows:

[0112]

[0113] This embodiment uses a broadband waveform based on a multi-sub-pulse structure, as shown below. Figure 2 As shown in the figure, t k Let t represent the transmission time of the k-th sub-pulse, and t k =kτ,Δf k Let Δf represent the frequency offset of the k-th sub-pulse, and Δf k =kB.

[0114] In this embodiment, step S2 is specifically as follows:

[0115] Let the matched filter bank be represented as w0(t), w1(t), ..., w K-1 (t), the specific expression is as follows:

[0116]

[0117] in, s k The conjugate form of (t). Then the expression for the compression result of the k-th pulse is as follows:

[0118]

[0119] in, Represents the k-th matched filter w k (t) Output noise, τ′ represents the time variable of integration, z k (t,m) represents the matched filter w k (t) The sum of the outputs of other sub-pulses after filtering out the k-th sub-pulse within the pulse. Due to the spectral orthogonality between the sub-pulses, w k The cross-correlation level between (t) and the other sub-pulses is very low and can be ignored, then r k The specific expression for (t) is as follows:

[0120]

[0121] In this embodiment, step S3 is specifically as follows:

[0122] S31, Align with distance gates;

[0123] Shift the pulse compression result of the k-th branch to the left by kτ to obtain the output result y of the k-th branch. k (t), the expression is as follows:

[0124]

[0125] in,

[0126] S32, Spectrum shifting;

[0127] The output result y of the kth branch k (t) Compensation frequency modulation term The output of the k-th branch after spectrum shifting processing is obtained. The expression is as follows:

[0128]

[0129] in,

[0130] In this embodiment, step S4 is specifically as follows:

[0131] Discretizing the echo signal into a fast and slow time-dimensional matrix, then the fast and slow time dimensions... The expression is as follows:

[0132]

[0133] in, It indicates a fast time.

[0134] Set the sampling time interval to ΔT = T p / Q is sampled in the fast time dimension tq=(q-1)ΔT, q=1,2,…,Q, and is expressed as follows:

[0135]

[0136] Let y k,q =[y k (t q ,0),y k (t q ,1),…,y k (t q [M-1] Τ Then the fast and slow time dimension matrix can be expressed as

[0137] in,[] T This represents the transpose operator. Represents the complex field.

[0138] make For the unambiguous velocity frequency range (-v) max ,v max If points J are uniformly sampled, and J ≥ M, let Δv = 2v max / J, then we get v=[v1,…,v J ].

[0139] Among them, v i =-v max +(i-1)2v max / J,i=1,2,…,J. Based on velocity element v i The filter was designed and obtained. The expression is as follows:

[0140]

[0141] Then construct the k-th fast and slow time dimension matrix Y k The expression for the inter-pulse coherent accumulation filter matrix is ​​as follows:

[0142]

[0143] The RD plane obtained by processing the echo of the k-th branch through inter-pulse coherent accumulation. The expression is as follows:

[0144]

[0145] In this embodiment, step S5 is specifically as follows:

[0146] The phase difference between the RD planes of each sub-pulse is compensated using the maximum contrast method, and the output results of each branch are set. The phase vector that needs to be compensated is The phase compensation problem for each sub-pulse is then transformed and solved as follows:

[0147]

[0148] Where, θ k This represents the phase term for compensation in the k-th branch. (·) Η This indicates a conjugate operation.

[0149] Then, using the idea of ​​coordinate descent algorithm, the high-dimensional optimization problem is transformed into a series of subproblems that are easy to solve, and solved using gradient descent methods such as the Newton-Horner algorithm until the algorithm converges and the optimal compensation phase value is obtained.

[0150] The output of the broadband waveform processing method for multi-subpulse structures oriented towards energy accumulation is Y, expressed as follows:

[0151]

[0152] This embodiment further performs simulation verification. First, the simulation parameters are set as follows:

[0153] Radar parameters: Considering airborne radar, carrier frequency f c =9GHz, sampling frequency f s =400MHz, radar transmit pulse number M=64, pulse repetition period PRI=50μs. The noise is set to Gaussian white noise with mean of 0 and power of 1. For the same scenario, narrowband and wideband signals are transmitted separately, with the following parameters: For the wideband waveform based on a multi-sub-pulse structure, the number of sub-pulses K=20, the sub-pulses are random phase-coded waveforms with pulse width τ=1μs and bandwidth B=10MHz, resulting in a wideband waveform with a bandwidth of 200MHz and a pulse width of 20μs; the narrowband linear frequency modulation (LFM) signal has a pulse width of 20μs and a bandwidth of 10MHz. To ensure that the energy of the wideband and narrowband signals is the same, the power of the narrowband transmit signal is set to be 20 times that of the wideband transmit signal.

[0154] Target parameter: While ensuring that the energy of broadband and narrowband signals are the same, set the target echo signal-to-noise ratio (SNR) of the broadband waveform. r = -25dB, target length 15m, with 16 scattering points, each with different phases and amplitudes, and strong and weak scattering points are distributed alternately. The energy of both strong and weak scattering points follows a Rayleigh probability distribution model. The initial phase of the scattering points follows a Gaussian random distribution with mean 0 and variance 1. The scattering point distribution model is as follows. Figure 3 and Figure 4 As shown, the target's distance relative to the broadband radar is set to R = 50 km, and the relative speed between the target and the platform is V = 102 m / s.

[0155] The simulation results of this embodiment are as follows: Figure 5-8 As shown, Figure 5 and Figure 6 The diagrams show the RD planes obtained by processing the received echoes of the radar's multi-subpulse structure broadband waveform using the method of this invention and a processing method based on matched filtering and moving target detection (MTD), respectively. Figure 7 The RD plane of the narrowband LFM signal echo after processing with matched filtering and Moving Target Detection (MTD) is shown. To visually demonstrate the effect of extended target energy accumulation after subbanding, Figure 8Comparing the range dimension cross-sections of the three results, it can be seen that the method of this invention can synthesize multiple scattering points of a broadband radar target into a single detection peak. After processing the broadband waveform with the multi-subpulse structure using the method proposed in the patent, the output signal-to-noise ratio is 27.46 dB. After processing using the matched filter-MTD method, the output signal-to-noise ratio is 22.67 dB, while the output SNR of the narrowband LFM signal is 31.10 dB. The designed echo processing method achieves a signal-to-noise ratio improvement of 4.79 dB, compared to a narrowband signal SNR loss of 3.64 dB.

[0156] In summary, the method of this invention generates and processes a broadband waveform based on a multi-subpulse structure with a large time-bandwidth product. The final result reduces the range resolution of the broadband waveform, effectively accumulates the energy dispersed on multiple scattering points of the extended target, and improves the output signal-to-noise ratio of the broadband waveform.

[0157] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for generating and processing broadband waveforms of multi-subpulse structures oriented towards energy accumulation, the specific steps of which are as follows: S1. A broadband waveform based on a multi-subpulse structure is constructed by using a random phase-coded signal as a narrowband subpulse waveform. S2. Based on step S1, the separation of broadband echo neutron pulses in a multi-sub-pulse structure is achieved using a multi-branch pulse compression method. S3. Based on step S2, use the distance gate alignment operation to achieve peak alignment of each sub-pulse waveform in the distance dimension, and use the spectrum shifting operation to compensate for the difference in frequency modulation terms between the processing results of each branch. S4. Based on step S3, the echo signal is discretized into fast and slow time-dimensional matrices, and an inter-pulse coherent accumulation filter matrix is ​​designed to realize the inter-pulse coherent accumulation of each sub-pulse waveform and the peak alignment of each inter-pulse coherent accumulation result in the Doppler dimension. S5. Based on step S4, phase compensation and coherent accumulation between the processing results of each sub-pulse are achieved by using the maximum contrast method.

2. The method for generating and processing broadband waveforms of multi-subpulse structures oriented towards energy accumulation according to claim 1, characterized in that, The specific steps of S1 are as follows: S11. Broadband waveform modeling based on multi-sub-pulse structure; Settings by A broadband waveform model based on a multi-sub-pulse structure is composed of several narrow-band sub-pulses, and its expression is as follows: ； in, and These represent the pulse width and bandwidth of the sub-pulse waveform, respectively. Indicates time, Indicates the first The sub-pulse waveform, set as a random phase-coded signal, is expressed as follows: ； in, Represents a rectangular signal. Indicates the first Number of codewords in each sub-pulse waveform Indicates the length of each codeword. Indicates the first The first sub-pulse waveform If each phase codeword is given, then... ; Set a coherent processing cycle for a total of [number] emissions. Given a pulse, the expression for the broadband LPI waveform baseband signal transmitted by the radar system based on a multi-narrowband structure is as follows: ； in, Indicates the pulse repetition period. Indicates the carrier frequency; S12, Wideband Radar Target Response Modeling; Ideally, the target response of a broadband radar consists of the responses of several scattering points, and each scattering point is considered a point target in a narrowband radar system. Therefore, when the radar line-of-sight is specified, the broadband radar target response... The expression is as follows: ； in, Represents the impulse function. This represents the total number of scattering points from the target. and They represent the first The complex scattering amplitude at each scattering point and the two-way delay relative to the radar; Set a speed A rigid target flying at a constant speed toward the radar, the target's first... The relative distance between the location of each scattering point and the radar is Then we can know the target number. The two-way propagation delay of the reflections from each scattering point is ,and Represents the speed of light; S13. Broadband echo modeling based on multi-sub-pulse structure; Assume there exists a speed A rigid target flying at a constant speed toward the radar, the target's first... The relative distance between the location of each scattering point and the radar is The echo signal expression is as follows: ； in, This represents Gaussian additive white noise. ; S14, echo downconversion; After downconversion, the broadband baseband echo waveform expression based on the multi-sub-pulse structure is as follows: ； in, , Indicates the first Detecting the Doppler frequency shift of the target using sub-pulse waveforms This represents the noise after down-conversion; when the target speed is relatively low, i.e. The simplified expression for the echo waveform is as follows: 。 3. The method for generating and processing broadband waveforms of multi-subpulse structures oriented towards energy accumulation according to claim 2, characterized in that, Step S2 is as follows: The matched filter bank is set as follows: The specific expression is as follows: ； in, express The conjugate form; then the first The expression for the pulse compression result is as follows: ； in, Indicates the first Matched filters Output noise, , The time variable representing the integral, Represents a matched filter Filtering intravascular coagulation The sum of the outputs of the other sub-pulses after the first sub-pulse, and the orthogonality of the spectra between the sub-pulses. The cross-correlation level with the other sub-pulses is very low and can be ignored. The specific expression is as follows: 。 4. The method for generating and processing broadband waveforms of multi-sub-pulse structures oriented towards energy accumulation according to claim 3, characterized in that, Step S3 is as follows: S31, Align the distance gate; The first The pulse compression results of each branch are shifted to the left. , obtained the Output results of each branch The expression is as follows: ； in, ; S32, Spectrum shifting; For the Output results of each branch Compensation frequency modulation term After obtaining the spectrum shifting process, the first Output results of each branch The expression is as follows: ； in, .

5. The method for generating and processing broadband waveforms of multi-subpulse structures oriented towards energy accumulation according to claim 4, characterized in that, Step S4 is as follows: Discretizing the echo signal into a fast and slow time-dimensional matrix, then the fast and slow time dimensions... The expression is as follows: ； in, Indicates a fast time; Set the sampling time interval to In a fast time Sampling is performed on a dimension, as shown in the following expression: ； make Then the fast and slow time dimension matrix is ​​expressed as ; in, This represents the transpose operator. Represents the field of complex numbers; make For the unambiguous speed-frequency range Uniform sampling Point, and ,make Then we get ; in, Based on velocity unit The filter was designed and obtained. The expression is as follows: ； Then construct the first A fast and slow time dimension matrix The expression for the inter-pulse coherent accumulation filter matrix is ​​as follows: ； Then the first The RD plane is obtained by inter-pulse coherent accumulation of the echo processed by each branch. The expression is as follows: 。 6. The method for generating and processing broadband waveforms of multi-subpulse structures oriented towards energy accumulation according to claim 5, characterized in that, Step S5 is as follows: The phase difference between the RD planes of each sub-pulse is compensated using the maximum contrast method, and the output results of each branch are set. The phase vector that needs to be compensated is The phase compensation problem for each sub-pulse is then transformed and solved as follows: ； in, Indicates the first Phase term of branch compensation, , Indicates the conjugate operation; Then, using the idea of ​​coordinate descent algorithm, the high-dimensional optimization problem is transformed into a series of subproblems that are easy to solve, and solved using gradient descent methods such as Newton-Horner algorithm, until the algorithm converges and the optimal compensation phase value is obtained. The output result of the broadband waveform processing method for multi-subpulse structures oriented towards energy accumulation is: The expression is as follows: 。

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