Energy accumulation-oriented multi-sub-pulse structure broadband waveform generation and processing method

Abstract

The invention discloses an energy accumulation-oriented multi-sub-pulse structure broadband waveform generation and processing method, which comprises the following steps of: firstly, constructing a broadband waveform based on a multi-sub-pulse structure by using a random phase coded signal as a narrow-band sub-pulse waveform; separating sub-pulses in broadband echoes of a multi-sub-pulse structure by using a multi-branch pulse compression method, and then designing an inter-pulse coherent accumulation filter matrix by discretizing echo signals into a fast and slow time dimension matrix by using a range gate alignment operation and a frequency spectrum shift operation; inter-pulse coherent accumulation of the sub-pulse waveforms and peak alignment of inter-pulse coherent accumulation results in the Doppler dimension are achieved, and finally phase compensation and coherent accumulation between the sub-pulse processing results are achieved through a maximum contrast method. According to the method, the final result reduces the range resolution of the broadband waveform, energy dispersed on a plurality of scattering points of the extended target can be effectively accumulated, and the output signal-to-noise ratio of the broadband waveform is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a method for generating and processing a broadband waveform of a multi-sub-pulse structure oriented to energy accumulation. Background Art

[0002] With the rapid development of electronic countermeasure technology, modern radar systems have encountered many challenges and threats, such as electronic interference on radar systems. When the radar waveform is easily intercepted and used by the adversary, it will face the risk of interference equipment such as noise interference, deception interference and power suppression by the adversary, which will seriously weaken its detection and survivability. Therefore, in order to ensure the survival and combat capability of the radar system in electronic countermeasures, it is urgent to design a radar transmission waveform with low intercept performance. The large time-width bandwidth waveform is a typical low intercept waveform. Since the waveform energy is dispersed over a large time and bandwidth range, it is difficult to be received by the adversary's reconnaissance aircraft and has good low intercept performance. However, the high range resolution of the broadband waveform causes the energy to be dispersed at various scattering points of the extended target, affecting the detection capability of the waveform.

[0003] At present, there are many studies on wideband low-acquisition waveforms that focus on the design of the transmit waveform and the echo processing method. The literature "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" designed a wideband cognitive radar waveform for detecting extended targets by maximizing the worst-case signal-to-interference-noise ratio based on the assumed random model of the target impulse response. However, this design method has a high dependence on the prior knowledge of the target and poor practicality. The document "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, the echo signal is processed by mismatch filtering to reduce the distance resolution of the broadband waveform, thereby achieving the purpose of accumulating the energy of the extended target scattered at each scattering point. However, due to the degree of freedom of waveform design, this method can only expand the mainlobe width within a limited range. Summary of the invention

[0004] To solve the above technical problems, the present invention provides a method for generating and processing a broadband waveform with a multi-sub-pulse structure for energy accumulation, thereby reducing the distance resolution of the broadband waveform and realizing the accumulation of energy dispersed at various scattering points of the extended target.

[0005] The technical solution adopted by the present invention is: a method for generating and processing a broadband waveform of a multi-sub-pulse structure for energy accumulation, and the specific steps are as follows:

[0006] S1, using random phase coded signals as narrowband sub-pulse waveforms to construct broadband waveforms based on multi-sub-pulse structures;

[0007] S2, based on step S1, using a multi-branch pulse compression method to separate the broadband echo neutron pulses of the multi-sub-pulse structure;

[0008] S3, based on step S2, using the range gate alignment operation to achieve peak alignment of each sub-pulse waveform in the range dimension, and using 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, discretize the echo signal into fast and slow time dimension matrices, design an inter-pulse coherent accumulation filter matrix, 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, a maximum contrast method is used to achieve phase compensation and coherent accumulation between the processing results of each sub-pulse.

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

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

[0013] Set up a broadband waveform model based on a multi-sub-pulse structure composed of K narrowband sub-pulses, and the expression is as follows:

[0014]

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

[0016]

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

[0018] Assuming that a total of M pulses are transmitted in one coherent processing cycle, the broadband LPI waveform baseband signal based on a multi-narrowband structure transmitted by the radar system is expressed as follows:

[0019]

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

[0021] S12, broadband 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 seen as a point target in the narrowband radar system. When the radar line of sight direction is specified, the broadband radar target response h(t) is expressed as follows:

[0023]

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

[0025] Suppose a rigid body target flies at a constant speed V towards the radar. The relative distance between the position of the target's lth scattering point and the radar is R. l , then we know that the round-trip propagation delay of the target's lth scattering point 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] Assume that there is a rigid body target flying at a constant speed V towards the radar, and the relative distance between the target's lth scattering point and the radar is R l , then 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 down conversion;

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

[0032]

[0033] Among them, f k =f c +kB,f dk =f k (2V) / c represents the Doppler frequency shift of the target detected by the kth sub-pulse waveform. Represents the noise after down-conversion. When the target speed is small, that is, V<<c, the simplified expression of the echo waveform is as follows:

[0034]

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

[0036] Let the matched filter bank be represented by w 0 (t),w 1 (t),…,w K-1 (t), the specific expression is as follows:

[0037]

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

[0039]

[0040] in, represents the kth matched filter w k (t) Output noise, τ′ represents the time variable of the 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 kth sub-pulse in the pulse, and the spectrum orthogonality between the sub-pulses, w k (t) has a very low level of cross-correlation with the rest of the sub-pulses and can be ignored, then r k (t) The specific expression is as follows:

[0041]

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

[0043] S31, range gate alignment;

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

[0045]

[0046] in,

[0047] S32, spectrum migration;

[0048] The output result y for the kth branch k (t) Compensation frequency modulation term Get the output result of the kth branch after spectrum shifting The expression is as follows:

[0049]

[0050] in,

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

[0052] Discrete the echo signal into fast and slow time dimension matrices, then the fast and slow time dimensions The expression is as follows:

[0053]

[0054] in, Indicates fast time.

[0055] Set the sampling time interval to ΔT = T p / Q, sampling is performed in the fast time tq=(q-1)ΔT,q=1,2,…,Q dimension, the expression is 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 represents the transpose operator, Represents a complex number domain.

[0059] make For the unambiguous velocity frequency range (-v max ,v max ) uniformly select J points, and J ≥ M, let Δv = 2v max / J, then we get v = [v 1 ,…,v J ].

[0060] Among them, v i =-v max +(i-1)2v max / J,i=1,2,…,J. Based on speed unit v i Designed filter The expression is as follows:

[0061]

[0062] Then construct the kth fast and slow time dimension matrix Y kThe inter-pulse coherent accumulation filter matrix is ​​expressed as follows:

[0063]

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

[0065]

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

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

[0068]

[0069] Among them, θ k represents the phase term of the kth branch compensation, (·) Η represents the conjugation operation.

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

[0071] The output result of the broadband waveform processing method for multi-sub-pulse structure oriented to energy accumulation is Y, which is expressed as follows:

[0072]

[0073] Beneficial effects of the present invention: The method of the present invention first uses a random phase-coded signal as a narrowband sub-pulse waveform to construct a broadband waveform based on a multi-sub-pulse structure, and then uses a multi-branch pulse compression method to achieve the separation of sub-pulses in the broadband echo of the multi-sub-pulse structure, and then uses a range gate alignment operation to achieve peak alignment of each sub-pulse waveform in the distance dimension, and uses a spectrum shifting operation to compensate for the difference in frequency modulation terms between the processing results of each branch. By discretizing the echo signal into fast and slow time dimension 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 each inter-pulse coherent accumulation result in the Doppler dimension, and finally uses a maximum contrast method to achieve phase compensation and coherent accumulation between the processing results of each sub-pulse. The method of the present invention generates a broadband waveform based on a multi-sub-pulse structure with a large time-width-bandwidth product and processes it. The final result reduces the distance resolution of the broadband waveform, can effectively accumulate energy dispersed on multiple scattering points of the extended target, and improves the output signal-to-noise ratio of the broadband waveform. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 The present invention is a flow chart of a method for generating and processing a broadband waveform with a multi-sub-pulse structure for energy accumulation.

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

[0076] Figure 3 Schematic diagram of the amplitude distribution of each scattering point of a broadband radar target in an embodiment of the present invention.

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

[0078] Figure 5 This is a range-Doppler (RD) plane result diagram obtained by processing a broadband echo based on a multi-sub-pulse structure through the method of the present invention in an embodiment of the present invention.

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

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

[0081] Figure 8 It is a comparison diagram of the distance dimension tangent plane of the RD plane after three processing results in the embodiment of the present invention. DETAILED DESCRIPTION

[0082] The method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0083] like Figure 1 As shown, a flow chart of a method for generating and processing a broadband waveform of a multi-sub-pulse structure for energy accumulation of the present invention is shown, and the specific steps are as follows:

[0084] S1, using random phase coded signals as narrowband sub-pulse waveforms to construct broadband waveforms based on multi-sub-pulse structures;

[0085] S2, based on step S1, using a multi-branch pulse compression method to separate the broadband echo neutron pulses of the multi-sub-pulse structure;

[0086] S3, based on step S2, using the range gate alignment operation to achieve peak alignment of each sub-pulse waveform in the range dimension, and using 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, discretize the echo signal into fast and slow time dimension matrices, design an inter-pulse coherent accumulation filter matrix, 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, a maximum contrast method is used to achieve phase compensation and coherent accumulation between the processing results of each sub-pulse.

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

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

[0091] Set up a broadband waveform model based on a multi-sub-pulse structure composed of K narrowband sub-pulses, and the expression is as follows:

[0092]

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

[0094]

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

[0096] Assuming that a total of M pulses are transmitted in one coherent processing cycle, the broadband LPI waveform baseband signal based on a multi-narrowband structure transmitted by the radar system is expressed as follows:

[0097]

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

[0099] S12, broadband 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 seen as a point target in the narrowband radar system. When the radar line of sight direction is specified, the broadband radar target response h(t) is expressed as follows:

[0101]

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

[0103] Suppose a rigid body target flies at a constant speed V towards the radar. The relative distance between the position of the target's lth scattering point and the radar is R. l , then we know that the round-trip propagation delay of the target's lth scattering point 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] Assume that there is a rigid body target flying at a constant speed V towards the radar, and the relative distance between the target's lth scattering point and the radar is R l , then 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 down conversion;

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

[0110]

[0111] Among them, f k =f c +kB,f dk =f k (2V) / c represents the Doppler frequency shift of the target detected by the kth sub-pulse waveform. Represents the noise after down-conversion. When the target speed is small, that is, V<<c, the simplified expression of the echo waveform is as follows:

[0112]

[0113] This embodiment is based on a broadband waveform of a multi-sub-pulse structure such as Figure 2 As shown in the figure, t k represents the emission time of the kth sub-pulse, and t k =kτ,Δf k represents the frequency offset of the kth sub-pulse, and Δf k =kB.

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

[0115] Let the matched filter bank be represented by w 0 (t),w 1 (t),…,w K-1 (t), the specific expression is as follows:

[0116]

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

[0118]

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

[0120]

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

[0122] S31, range gate alignment;

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

[0124]

[0125] in,

[0126] S32, spectrum migration;

[0127] The output result y for the kth branch k (t) Compensation frequency modulation term Get the output result of the kth branch after spectrum shifting The expression is as follows:

[0128]

[0129] in,

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

[0131] Discrete the echo signal into fast and slow time dimension matrices, then the fast and slow time dimensions The expression is as follows:

[0132]

[0133] in, Indicates fast time.

[0134] Set the sampling time interval to ΔT = T p / Q, sampling is performed in the fast time tq=(q-1)ΔT,q=1,2,…,Q dimension, the expression is 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,[] Trepresents the transpose operator, Represents a complex number domain.

[0138] make For the unambiguous velocity frequency range (-v max ,v max ) uniformly select J points, and J ≥ M, let Δv = 2v max / J, then we get v = [v 1 ,…,v J ].

[0139] Among them, v i =-v max +(i-1)2v max / J,i=1,2,…,J. Based on speed unit v i Designed filter The expression is as follows:

[0140]

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

[0142]

[0143] Then the RD plane obtained by the inter-pulse coherent accumulation of the k-th branch processed echo is 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 by the maximum contrast method, and the output results of each branch are set. The phase vector that needs to be compensated is Then the phase compensation problem of each sub-pulse is transformed and solved, and the expression is as follows:

[0147]

[0148] Among them, θ k represents the phase term of the kth branch compensation, (·) Η represents the conjugation operation.

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

[0150] The output result of the broadband waveform processing method for multi-sub-pulse structure oriented to energy accumulation is Y, which is expressed as follows:

[0151]

[0152] This embodiment further performs simulation verification, firstly setting simulation parameters, as follows:

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

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

[0155] The simulation results of this embodiment are as follows Figure 5-8 As shown, Figure 5 and Figure 6 The RD planes obtained by respectively processing the echoes using the method of the present invention and the processing method based on matched filtering and moving target detection (MTD) after the radar transmits a broadband waveform of a multi-sub-pulse structure and receives the echoes are shown. Figure 7 The RD plane of the narrowband LFM signal echo after matched filtering and moving target detection (MTD) method is shown. In order to intuitively show the accumulation effect of the extended target energy after sub-band processing, Figure 8The distance dimension sections of the three results are compared. It can be seen that the method of the present invention can synthesize the detection of single peaks of multiple scattering points of broadband radar targets. The output signal-to-noise ratio of the broadband waveform of the multi-sub-pulse structure is 27.46dB after being processed by the method proposed in the patent, and the output signal-to-noise ratio after being processed by the matched filter-MTD method is 22.67dB, while the output SNR of the narrowband LFM signal is 31.10dB. The designed echo processing method achieves a 4.79dB signal-to-noise ratio improvement, which is 3.64dB less than the narrowband signal SNR loss.

[0156] In summary, the method of the present 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 distance resolution of the broadband waveform, can effectively accumulate energy dispersed at 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 appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for generating and processing a broadband waveform of a multi-sub-pulse structure for energy accumulation, the specific steps are as follows: S1, using random phase coded signals as narrowband sub-pulse waveforms to construct broadband waveforms based on multi-sub-pulse structures; S2, based on step S1, using a multi-branch pulse compression method to separate the broadband echo neutron pulses of the multi-sub-pulse structure; S3, based on step S2, using the range gate alignment operation to achieve peak alignment of each sub-pulse waveform in the range dimension, and using 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, discretize the echo signal into fast and slow time dimension matrices, design an inter-pulse coherent accumulation filter matrix, 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, a maximum contrast method is used to achieve phase compensation and coherent accumulation between the processing results of each sub-pulse.

2. The method for generating and processing a broadband waveform with a multi-sub-pulse structure for energy accumulation according to claim 1, characterized in that: The step S1 is specifically as follows: S11. Broadband waveform modeling based on multi-sub-pulse structure; Set up a broadband waveform model based on a multi-sub-pulse structure composed of K narrowband sub-pulses, and the expression is as follows: Where τ and B represent the pulse width and bandwidth of the sub-pulse waveform, t represents time, and s k (t) represents the kth sub-pulse waveform, which is set as a random phase coded signal, and the expression is as follows: Where rect(t) represents a rectangular signal, N represents the number of codewords of the kth sub-pulse waveform, and T s represents the length of each codeword, φ k (n) represents the nth phase codeword of the kth sub-pulse waveform, then τ=NT s ; Assuming that a total of M pulses are transmitted in one coherent processing cycle, the broadband LPI waveform baseband signal based on a multi-narrowband structure transmitted by the radar system is expressed as follows: Among them, T p represents the pulse repetition period, f c Indicates the carrier frequency; S12, broadband radar target response modeling; Ideally, the broadband radar target response can be composed of the responses of several scattering points, and each scattering point can be seen as a point target in the narrowband radar system. When the radar line of sight direction is specified, the broadband radar target response h(t) is expressed as follows: Among them, δ(t) represents the impact function, L represents the total number of scattering points of the target, and A l and t l represent the complex scattering amplitude of the lth scattering point and the two-way delay relative to the radar respectively; Suppose a rigid body target flies at a constant speed V towards the radar. The relative distance between the position of the target's lth scattering point and the radar is R. l , then we know that the round-trip propagation delay of the target's lth scattering point is t l =(2R l -2Vt) / c, where c represents the speed of light; S13, broadband echo modeling based on multi-sub-pulse structure; Assume that there is a rigid body target flying at a constant speed V towards the radar, and the relative distance between the target's lth scattering point and the radar is R l , then the echo signal expression is as follows: Where n(t) represents Gaussian additive white noise, b l =2R l / c; S14, echo down conversion; After down-conversion, the broadband baseband echo waveform based on the multi-sub-pulse structure is expressed as follows: Among them, f k =f c +kB,f dk =f k (2V) / c represents the Doppler frequency shift of the target detected by the kth sub-pulse waveform. represents the noise after down-conversion; when the target speed is small, that is, V<<c, the simplified expression of the echo waveform is as follows:

3. The method for generating and processing a broadband waveform with a multi-sub-pulse structure for energy accumulation according to claim 1, characterized in that: The step S2 is specifically as follows: Let the matched filter bank be represented by w0(t),w1(t),…,w K-1 (t), the specific expression is as follows: in, Indicates k (t) is the conjugate form; then the k-th pulse compression result expression is as follows: in, represents the kth matched filter w k (t) Output noise, τ′ represents the time variable of the 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 kth sub-pulse in the pulse, and the spectrum orthogonality between the sub-pulses, w k (t) has a very low level of cross-correlation with the rest of the sub-pulses and can be ignored, then r k (t) The specific expression is as follows:

4. The method for generating and processing a broadband waveform with a multi-sub-pulse structure for energy accumulation according to claim 1, characterized in that: The step S3 is specifically as follows: S31, distance gate alignment; Shift the pulse compression result of the kth branch to the left by kτ to obtain the output result y of the kth branch k (t), the expression is as follows: in, S32, spectrum migration; The output result y for the kth branch k (t) Compensation frequency modulation term Get the output result of the kth branch after spectrum shifting The expression is as follows: in, 5. The method for generating and processing a broadband waveform with a multi-sub-pulse structure for energy accumulation according to claim 1, characterized in that: The step S4 is specifically as follows: Discrete the echo signal into fast and slow time dimension matrices, then the fast and slow time dimensions The expression is as follows: in, Indicates fast time; Set the sampling time interval to ΔT = T p / Q, at fast time t q =(q-1)ΔT, q=1,2,…,Q dimension for sampling, the expression is as follows: 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 in,[] T represents the transpose operator, represents a complex domain; make For the unambiguous velocity frequency range (-v max ,v max ) uniformly select J points, and J ≥ M, let Δv = 2v max / J, then we get v=[v1,…,v J ]; Among them, v i =-v max +(i-1)2v max / J,i=1,2,…,J;Based on speed unit v i Designed filter The expression is as follows: Then construct the kth fast and slow time dimension matrix Y k The inter-pulse coherent accumulation filter matrix is ​​expressed as follows: Then the RD plane obtained by the inter-pulse coherent accumulation of the k-th branch processed echo is The expression is as follows:

6. The method for generating and processing a broadband waveform with a multi-sub-pulse structure for energy accumulation according to claim 1, characterized in that: The step S5 is specifically as follows: The phase difference between the RD planes of each sub-pulse is compensated by the maximum contrast method, and the output results of each branch are set. The phase vector that needs to be compensated is Then the phase compensation problem of each sub-pulse is transformed and solved, and the expression is as follows: Among them, θ k represents the phase term of the kth branch compensation, (·) Η represents the conjugation operation; Then, using the idea of ​​coordinate descent algorithm, the high-dimensional optimization problem is converted into a series of easy-to-solve sub-problems, 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-sub-pulse structure oriented to energy accumulation is Y, which is expressed as follows:

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