Multi-sub-pulse structure-based multifunctional integrated waveform design method

Abstract

The invention provides a multifunctional integrated waveform design method based on a multi-sub-pulse structure, and belongs to the field of radar detection communication anti-interference integration. Specifically, an information transmission modulation method based on joint modulation of partial phase modulation in sub-pulses and waveform position arrangement modulation between sub-pulses is proposed, and the communication rate is remarkably improved; intermittent sampling forwarding interference is effectively suppressed by using the orthogonal characteristic of waveforms between sub-pulses. A signal processing method based on monopulse multifunctional integrated echoes is provided, and Doppler tolerance is enhanced; according to the invention, the integration of detection, communication and anti-interference functions is realized, the detection and communication requirements of a high-speed moving target are met, and the engineering application value is high.

Description

Technical Field

[0001] This invention belongs to the field of radar detection, communication and anti-interference integration, and particularly relates to a multi-functional integrated waveform design method based on a multi-sub-pulse structure. Background Technology

[0002] Against the backdrop of rapid development in modern electronic technology, the Dual Function Radar and Communication (DFRC) system, as an advanced architecture integrating radar detection and communication functions, places higher demands on signal waveform design. However, the shortcomings of DFRC waveform design, which is primarily for detection, are often manifested in its low communication rate and lack of consideration for the detection of high-speed moving targets. For example, combining Differential Phase Shift Keying (DPSK) modulation with Linear Frequency Modulation (LFM) radar waveforms to form an LFM-DPSK integrated waveform has a single modulation method, low communication rate, and poor Doppler tolerance.

[0003] In terms of anti-interference, research on anti-interference measures against intermittent sampling and forwarding interference mainly focuses on waveform design and signal processing. Existing anti-interference methods based on intra-pulse waveform design include intra-pulse stepped LFM waveforms, intra-pulse orthogonal waveforms, frequency agility combined with intra-pulse frequency coding, and intra-pulse frequency-delay agility waveforms. These methods suppress interference through waveform orthogonality, frequency orthogonality, or frequency-delay agility between sub-pulses. Although the above anti-interference techniques can suppress intermittent sampling and forwarding interference, they have not yet considered the important function of communication.

[0004] Currently, research on integrated waveforms capable of simultaneously achieving detection, communication, and anti-interference functions is still in its early stages, with a lack of relevant results. Only a few researchers have proposed some conceptual design schemes, but no practical technologies have yet been developed. The difficulty in designing multifunctional integrated waveforms lies in simultaneously meeting the three mutually restrictive requirements of detection performance, communication rate, and anti-interference capability. How to effectively combat complex electronic interference environments while ensuring high-precision detection and high-efficiency communication is a technical challenge that urgently needs to be overcome. Summary of the Invention

[0005] To address the above problems, this invention provides a multifunctional integrated waveform design method based on multi-sub-pulse signals.

[0006] The present invention provides a multi-functional integrated waveform design method based on multi-sub-pulse signals, comprising the following steps:

[0007] Step 1: Multifunctional integrated waveform application scenarios based on multi-sub-pulse structure.

[0008] Step 2: Propose an information transmission modulation method based on the joint modulation of partial phase modulation within sub-pulses and waveform position arrangement modulation between sub-pulses.

[0009] Step 3: Propose a method to resist intermittent sampling and forwarding interference based on the orthogonality of waveforms between sub-pulses.

[0010] Step 4: Establish and solve a multi-functional integrated waveform optimization model based on a multi-sub-pulse structure.

[0011] Step 5: A signal processing method based on single-pulse multi-functional integrated echo is proposed.

[0012] Step 6: Propose a communication information demodulation method.

[0013] Step 1: Multifunctional integrated waveform application scenarios based on multi-sub-pulse structure

[0014] This invention considers a scenario consisting of a multi-functional integrated phased array system with co-located transmit and receive terminals, a communication receiver equipped with a phased array, a jammer, and a target. Taking the normal to the phased array of the multi-functional integrated system as 0°, the angle between the target and the jammer and the normal to the phased array radar of the multi-functional integrated system is θ. t The angle between the normal to the phased array radar of the communication receiver and the multi-functional integrated system is θ. c3 If the normal to the phased array of the communication receiver is 0°, then the angle between the normal to the phased array radar of the multi-functional integrated system and the normal to the communication receiver is θ. c1 The angle between the normals of the jammer and the phased array radar of the communication receiver is θ. c2 .

[0015] The multi-functional integrated system uses transmitted beamforming to direct beams towards the main lobe directions θ of the target and the jammer, respectively. t and the sidelobe direction θ of the communication receiver c3 A multi-functional integrated signal is transmitted. The jammer intercepts and forwards the transmitted multi-functional integrated signal, forming an intermittent sampling and forwarding jamming signal. After being scattered by the target, the signal and the intermittent sampling and forwarding jamming signal are along θ. t The main lobe direction is received by the multi-functional integrated system; the communication receiver receives θ. c1 Multifunctional integrated signal in the main lobe direction and θ c2 Interference signals in the sidelobe direction; the communication receiver suppresses interference signals by receiving beamforming energy, enhances the energy of multi-functional integrated signals, and maximizes the energy of sidelobe transmission of communication information, thereby achieving effective reception of communication information.

[0016] Step 2: Information transmission modulation method based on combined modulation of intra-subpulse partial phase modulation and inter-subpulse waveform position arrangement modulation

[0017] 1) Multifunctional integrated signal model

[0018] Orthogonal waveform set of multi-functional integrated transmission signal Composed of M orthogonal waveforms, it is a set of orthogonal waveforms from a multi-functional integrated transmission signal. A multi-functional integrated transmission signal x(t) is formed by randomly selecting an arrangement of x1(t), x2(t), ..., x M If the signals are arranged in order (t), then the multi-functional integrated transmission signal x(t) can be expressed as:

[0019]

[0020] Where T0 is the sub-pulse width, T = MT0 is the long pulse width, and rect(t) is the rectangular window function, expressed as follows:

[0021]

[0022] The sub-pulse waveform is a phase-coded waveform. Each sub-pulse is divided into N sub-chips. Based on the requirements of communication and detection performance, the first sub-chip is designated as the reference sub-chip for information transmission, and N sub-chips are selected from the N sub-chips. c The first sub-chip is used as the information transmission sub-chip (including the first sub-chip), and the remaining chips N R =NN c To optimize and ensure the detection performance of the designed waveform, then x l (t) can be represented as:

[0023]

[0024] Among them, t b For the duration of the sub-slice, It is the amplitude of the i-th communication sub-chip of the l-th phase-coded waveform. This represents the amplitude of the q-th sub-chip used for optimization in the l-th phase-coded waveform. This represents the i-th phase in the set of communication sub-chips for the l-th phase-coded waveform. This represents the q-th phase of the subchip set used for optimization of the l-th phase encoded waveform.

[0025] 2) Information transmission method based on partial phase modulation and waveform arrangement modulation

[0026] The modulation method in the multi-functional integrated system uses partial phase modulation within sub-pulses and waveform arrangement modulation between sub-pulses to embed communication information.

[0027] a) Partial phase modulation

[0028] The mathematical expression of the partial phase modulation method has been given in the multi-functional integrated signal model. By selecting the communication chip phase of each sub-pulse signal to embed different communication information, and by using the remaining chip phase to optimize the detection performance of signal transmission, partial phase modulation is achieved to improve communication performance.

[0029] The total number of possible combinations of information transmission sub-chip positions is .

[0030]

[0031] Based on the above formula, it can be deduced that, within each Pulse Repetition Interval (PRI), the maximum number of bits available for transmission, selected by combining the positions of the information transmission sub-chips, is:

[0032]

[0033] To distinguish between communication sub-chips and sub-chips used for optimization, let N... c -1 communication sub-chips s(m) i ), i = 2, 3, ... N c The phase difference between the reference sub-chip s(m1) and the reference sub-chip s(m1) belongs to a specific set, which is constrained as follows:

[0034]

[0035] in W is a set The number of elements in the middle. Then the number of information bits transmitted within one sub-pulse via phase difference modulation is...

[0036]

[0037] Therefore, the total information transmission rate is

[0038]

[0039] Where T r This is the pulse repetition interval.

[0040] b) Waveform arrangement modulation

[0041] Waveform arrangement modulation between sub-pulses involves constructing orthogonal waveforms from multiple sub-pulse signals, based on the orthogonal waveform set of the multi-functional integrated transmission signal. Choosing any arrangement to construct a multi-functional integrated transmission signal, the waveform position arrangement modulation between sub-pulses transmits information by utilizing different waveform arrangement positions. The modulation process involves randomly arranging M waveforms from a set of orthogonal waveforms, resulting in a total of [number missing] possible arrangements. One method is to randomly select a sequence of sub-pulse combinations as the transmitted signal.

[0042] Therefore, the transmission rate of waveform position arrangement modulation between sub-pulses is

[0043]

[0044] Therefore, the total information transmission rate of the combined modulation within and between subpulses is:

[0045]

[0046] Step 3: Anti-intermittent sampling and forwarding interference method based on the orthogonality of waveforms between sub-pulses

[0047] Considering that the phased array in the multifunctional integrated signal system is a uniform linear array composed of Z array elements, and the distance between two adjacent array elements is d = λ / 2, where λ is the wavelength of the electromagnetic wave, the weight vector of the beamformer can be expressed as w = [w0 w1 … w Z-1 ] T If a signal is incident on a phased array at an angle θ, then the steering vector of the uniform linear array can be expressed as α(θ) = [1e -jφ … e -j(Z-1)φ ] T Where φ=2πdsinθ / λ. The jammer samples the multi-subpulse signal T emitted by the multi-function integrated system. L The duration is calculated, and then the sampled signal is repeatedly forwarded. When the integrated system transmits signal x(t), with the normal of the phased array radar of the integrated system as 0°, the target and the jammer are located at θ, which is the normal of the phased array radar of the integrated system. t At the azimuth position, the interference signal can be represented as:

[0048]

[0049] in, For the number of reposts, among which This indicates rounding down, where T is the pulse width of the multi-functional integrated signal.

[0050] During the sampling process, the sampling time T L Shorter, assuming the jammer captures I sub-pulses. Partial signal relay, after pulse compression, interference signal and sub-pulse The matched filtering result can be expressed as:

[0051]

[0052] Interference signals and unsampled sub-pulses The matched filtering result can be expressed as:

[0053]

[0054] In the above formula, the matched filter result p i Multiple peak results will appear in (t), and the matched filter result p of the unsampled sub-pulses. o (t) peak value is much lower than p l The peak value of the matched filtering result in (t) is because the waveforms between the multi-functional integrated signal sub-pulses are pairwise orthogonal. The interference signal only has the correlation segment of the first I sub-pulse signal. Therefore, when performing matched filtering, the interference signal only has a partial correlation with the first I sub-pulses and no correlation with the unsampled sub-pulses. When performing moving target detection (MTD), under the gain of the pulse compression result of M sub-pulses, since only the first I sub-pulses are correlated with the interference signal, the correlation gain of the interference signal cannot accumulate, so it has a certain ability to resist intermittent sampling and forwarding interference.

[0055] Step 4: Solve the multi-functional integrated waveform optimization model based on the multi-sub-pulse structure.

[0056] Based on the above methods for communication information modulation and anti-interference, it is evident that an optimized design of the orthogonal waveform set is required. Discretize x l (t) gives x l (n), n=1,2,…,N. Based on minimizing the C / A-PSL of orthogonal signal families, the following orthogonal waveform family optimization design problem is constructed:

[0057]

[0058] in when At that time, weight c l,l It is the autocorrelation function of the waveform. Otherwise, It is the cross-correlation function of the waveform, with weights x = [x1, x2, ..., x M ], m c and These are the communication sub-chip and the set of phase differences used for information transmission, respectively. q and N RThese are the sub-chips used for optimization and the total number of sub-chips used for optimization, respectively. ε is the phase protection interval, which is a small positive number.

[0059] To solve the above non-convex high-dimensional multi-constraint optimization problem By constructing an upper bound function for the objective function, iterative optimization is performed until this upper bound function monotonically decreases to convergence. In each iteration, Fourier transform and inverse Fourier transform are used to accelerate the algorithm's convergence.

[0060] First use L p The norm approximates the objective function, and by performing an equivalent transformation, we can obtain...

[0061]

[0062] At the t-th iteration, its upper bound function is

[0063]

[0064] in

[0065]

[0066] In each iteration, the Fourier transform operation is used to represent the waveform autocorrelation function, accelerating the algorithm. The autocorrelation function of an aperiodic sequence can be expressed using the Fourier transform and inverse Fourier transform as follows:

[0067]

[0068] in It is the Fourier transform matrix.

[0069] Perform a Fourier transform on the autocorrelation function and combine it with FF. H =I, the above formula can be written as

[0070]

[0071] in

[0072] Let g l =F H [x l ;0],the objective function is approximately:

[0073]

[0074] The above formula can be approximated as

[0075]

[0076] make and as well as The above formula is equivalent to

[0077]

[0078] make The original optimization problem is approximated as follows:

[0079]

[0080] Case 1: When n = 1, this sub-chip is the reference sub-chip in the communication chip. Case 2: n = m i And when n≠1, The modulus is 1, and the phase is determined by the transmitted information; Case 3: n≠m i That is, n = y q season The required solution is the following optimization problem.

[0081]

[0082] Its closed-form solution is:

[0083]

[0084] in yes The set of all endpoints of the sub-intervals in the set.

[0085] Step 5: Signal processing method based on monopulse multi-functional integrated echo

[0086] After the multi-functional integrated signal is scattered by the target echo and sampled and relayed by the jammer, the signal received by the integrated system through beamforming can be expressed as:

[0087]

[0088] Where ξ1 represents the amplitude coefficient of the target echo signal, ξ2 represents the amplitude coefficient of the interference signal, the radial distance of the target is r, the radial velocity is v (defined as positive when moving towards the radar), R(t) = r - vt, f c This represents the carrier frequency of the signal. n(t) represents the noise component.

[0089] use Indicates the amplitude of the target echo signal. The amplitude of the interference signal can be represented by R(t) = r - vt in the above equation, which gives the result.

[0090]

[0091] Assuming the range resolution unit is ΔR, when the velocity v is small, 2vT0 / c ≤ ΔR, that is, the target's movement distance within one pulse repetition interval PRT is less than the range resolution unit. In this case, the second term 2vt / c in the above formula can be ignored. When the target velocity v is large, 2vT0 / c > ΔR, in which case the target exhibits the phenomenon of crossing range units. In this case, the second term 2vt / c in the above formula cannot be ignored.

[0092] Here, we consider that 2vT0 / c≤ΔR always holds true, so the above equation can be approximated as:

[0093]

[0094] Substituting x(t) into the equation, we get

[0095]

[0096] By downconverting the target echo, we can obtain...

[0097]

[0098] Where n′(t) is the noise component after down-conversion. Target echo y r (t) is composed of target echoes, interference signals, and noise from multiple sub-pulses. Match filtering is performed on the echo signals and the transmitted sub-pulse signals respectively. The result of pulse compression with the i-th, i=1,…,M-th sub-pulse is expressed as:

[0099]

[0100] Where n″(t) is the noise component after pulse compression, substituted into Then we can get:

[0101]

[0102] Observing the above formula, we can obtain M pulse compression results. Under the premise of ensuring good orthogonality of each sub-pulse, due to the sampling time T of the interference machine... LThe pulse compression is relatively short. Assuming the jammer samples and forwards I sub-pulses, during pulse compression, the interference signal is only partially correlated with the first I sub-pulses and not correlated with the unsampled sub-pulses. Therefore, only the pulse compression results of the first I sub-pulses contain multiple interference signal peaks. These M pulse compression results are then shifted and their range gates aligned. Finally, during MTD (Mean Time Difference), the target's range and velocity information are estimated using Fast Fourier Transform (FFT). Since MTD involves the accumulation gain of M pulse compression results, and each sub-pulse pulse compression result contains a target signal peak, these M peaks accumulate after MTD. However, the interference signal's pulse compression result only has peaks in the first I sub-pulses, not the remaining sub-pulses. Therefore, the interference signal's peaks do not accumulate after MTD. Thus, the interference signal is suppressed after MTD, and the result only contains the target's range and velocity information.

[0103] Step 6: Communication Information Demodulation Method

[0104] The signal received by the communication receiver can be represented as:

[0105]

[0106] Where ξ3 represents the amplitude coefficient of the transmitted signal from the integrated system to the communication receiver, ξ4 represents the amplitude coefficient of the jamming signal from the jammer to the communication receiver, and n c (t) represents the noise component. Substituting x(t) into the equation, we get:

[0107]

[0108] Assume the communication user has a differential phase set And the total number N of communication sub-chips c Given the known state, and since the partial phase demodulation of each sub-pulse signal is relatively independent, we will take one sub-pulse as an example. The specific steps for partial phase demodulation are as follows:

[0109] 1) The communication user can discretize the received sub-pulses to obtain y. c (n), n=1,2,...,N;

[0110] 2) Detect y c Phase φ of each sub-chip of (n) n =arg{(y c (n))}, n=1,2,…,N;

[0111] 3) Calculate the phase difference between the phase of each sub-chip (starting from the second sub-chip) and the first reference sub-chip within the sub-pulse.

[0112] 4) Calculate the phase difference with all elements of the phase set.

[0113] 5) Let U c :={U c2 U c3 ,…,U cN}, determine U c The smallest N c The sub-chip corresponding to each element is the communication sub-chip, from which its position and phase information can be further extracted.

[0114] The waveform position arrangement demodulation between sub-pulses is achieved by matching each waveform in the orthogonal waveform set with each sub-pulse, selecting the waveform with the largest peak value as the current sub-pulse transmission waveform, and then demodulating the arrangement of the sub-pulse waveforms.

[0115] The beneficial technical effects of this invention are as follows:

[0116] This invention proposes a multi-functional integrated waveform design method based on a multi-sub-pulse structure. By optimizing the design of the multi-sub-pulse signal and combining it with communication information modulation methods, it achieves high-speed communication while also possessing excellent detection performance and anti-interference capabilities. Compared with existing integrated detection and communication waveform design techniques, this waveform exhibits high Doppler tolerance, reduces signal-to-noise ratio attenuation during high-speed target detection, and significantly improves communication speed through information modulation. The inter-pulse orthogonal waveform cluster design reduces the correlation between the intercepted and forwarded signal and the matched filter, achieving suppression of intermittent sampling and forwarding interference. This innovative waveform design, integrating detection, communication, and anti-interference functions, provides an efficient and reliable solution for multi-functional radio frequency systems in complex electromagnetic environments. Attached Figure Description

[0117] Figure 1 Application scenarios for multi-functional integrated waveforms with multi-sub-pulse signal structures;

[0118] Figure 2 A schematic diagram of the phased array transmitting and receiving beams for a multi-functional integrated system;

[0119] Figure 3 A schematic diagram of the null receiving beam of a communication receiver;

[0120] Figure 4 A multi-functional integrated signal model with a multi-sub-pulse structure;

[0121] Figure 5 This is an example of partial phase modulation within a sub-pulse;

[0122] Figure 6 This is an example of a partial phase modulation information mapping relationship;

[0123] Figure 7 To resist intermittent sampling and forwarding interference;

[0124] Figure 8 This is a schematic diagram of a multi-functional integrated echo processing flow based on a single pulse.

[0125] Figure 9 This describes the phase demodulation process within a sub-pulse.

[0126] Figure 10 A schematic diagram of waveform position arrangement demodulation between sub-pulses;

[0127] Figure 11 This is a time-domain diagram of the jamming signal and the radar transmitted signal;

[0128] Figure 12 The symbol error rate of the phase demodulation section of the communication receiver;

[0129] Figure 13 The symbol error rate of waveform demodulation in a communication receiver;

[0130] Figure 14 The pulse compression result of the first sub-pulse and echo;

[0131] Figure 15 The pulse compression result after distance shift alignment for the remaining sub-pulses;

[0132] Figure 16 A 3D plot of pulse compression results before all sub-pulse distance gates are aligned;

[0133] Figure 17 A 3D plot of the pulse compression results after all sub-pulses are aligned with the distance gates.

[0134] Figure 18 This is a distance-Doppler plane diagram of the majority pulse signal and the received echo signal;

[0135] Figure 19 The MTD of the multi-subpulse signal and the received echo signal; Detailed Implementation

[0136] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0137] The present invention provides an integrated anti-interference waveform design method for detection and communication based on multi-sub-pulse signals, comprising the following steps:

[0138] 1. Multifunctional integrated waveform application scenarios based on multi-sub-pulse structure.

[0139] like Figure 1As shown, this invention considers a scenario consisting of a multi-functional integrated phased array radar system with co-located transmit and receive terminals, a communication receiver equipped with a phased array radar, a jammer, and a target. Taking the normal to the phased array radar of the multi-functional integrated system as 0°, the angle between the target and the jammer and the normal to the phased array radar of the multi-functional integrated system is θ. t The angle between the normal to the phased array radar of the communication receiver and the multi-functional integrated system is θ. c3 If the normal to the phased array of the communication receiver is 0°, then the angle between the normal to the phased array radar of the multi-functional integrated system and the normal to the communication receiver is θ. c1 The angle between the normals of the jammer and the phased array radar of the communication receiver is θ. c2 .

[0140] The multi-functional integrated system uses transmitted beamforming to direct beams towards the main lobe directions θ of the target and the jammer, respectively. t and the sidelobe direction θ of the communication receiver c3 A multi-functional integrated signal is transmitted. The jammer intercepts and forwards the transmitted multi-functional integrated signal, forming an intermittent sampling and forwarding jamming signal. After being scattered by the target, the signal and the intermittent sampling and forwarding jamming signal are along θ. t The main lobe direction is received by the multi-functional integrated system; the communication receiver receives θ. c1 Multifunctional integrated signal in the main lobe direction and θ c2 Interference signals in the sidelobe direction; the communication receiver suppresses interference signals by using the receiving beamforming energy, enhances the energy of the multi-functional integrated signal, and maximizes the energy of sidelobe-transmitted communication information, thus achieving effective reception of communication information. The transmitting and receiving beams of the multi-functional integrated system are the same, such as... Figure 2 As shown. The receiving beam of the communication receiver, designed to suppress interference signals and enhance multi-functional integrated signals, employs a null receiving beam, such as... Figure 3 As shown.

[0141] 2. An information transmission modulation method based on the combined modulation of partial phase modulation within sub-pulses and waveform position arrangement modulation between sub-pulses.

[0142] 1) Multifunctional integrated signal model

[0143] Orthogonal waveform set of multi-functional integrated transmission signal Composed of M orthogonal waveforms, it is a set of orthogonal waveforms from a multi-functional integrated transmission signal. A multi-functional integrated transmission signal x(t) is formed by randomly selecting an arrangement of x1(t), x2(t), ..., x M (t) sequential arrangement, multi-functional integrated signal model such as Figure 4 As shown, the multi-functional integrated transmission signal x(t) can be expressed as:

[0144]

[0145] Where T0 is the sub-pulse width, T = MT0 is the long pulse width, and rect(t) is the rectangular window function, expressed as follows:

[0146]

[0147] The sub-pulse waveform is a phase-coded waveform. Each sub-pulse is divided into N sub-chips. Based on the requirements of communication and detection performance, the first sub-chip is designated as the reference sub-chip for information transmission, and N sub-chips are selected from the N sub-chips. c The first sub-chip is used as the information transmission sub-chip (including the first sub-chip), and the remaining chips N R =NN c To optimize and ensure the detection performance of the designed waveform, then x l (t) can be represented as:

[0148]

[0149] Among them, t b For the duration of the sub-slice, It is the amplitude of the i-th communication sub-chip of the l-th phase-coded waveform. This represents the amplitude of the q-th sub-chip used for optimization in the l-th phase-coded waveform. This represents the i-th phase in the set of communication sub-chips for the l-th phase-coded waveform. This represents the q-th phase of the subchip set used for optimization of the l-th phase encoded waveform.

[0150] 2) Information transmission method based on partial phase modulation and waveform arrangement modulation

[0151] The modulation method in the multi-functional integrated system uses partial phase modulation within sub-pulses and waveform arrangement modulation between sub-pulses to embed communication information.

[0152] a) Partial phase modulation

[0153] The mathematical formula for partial phase modulation has been given in the multi-functional integrated signal model. By selecting the communication chip phase of each sub-pulse signal to embed different communication information, and by using the remaining chip phase to optimize the detection performance of signal transmission, partial phase modulation is achieved to improve communication performance.

[0154] The total number of possible combinations of information transmission sub-chip positions is .

[0155]

[0156] Based on the above formula, it can be deduced that, within each Pulse Repetition Interval (PRI), the maximum number of bits available for transmission, selected by combining the positions of the information transmission sub-chips, is:

[0157]

[0158] The following example shows how to select N from N available sub-chips. c One sub-chip is used as the information transmission sub-chip. The remaining N R Each sub-chip is used to minimize the PSL of the integrated signal autocorrelation function, ensuring weak target detection performance under strong target masking. The total number of sub-chip position combinations and the maximum number of bits transmitted are respectively... and

[0159] Figure 5 Describes all possible combinations of communication sub-chip positions. Because the number of bits of information transmitted is Therefore, the choice should be made. Different combinations of communication sub-chip positions transmit information. For example, when N=5, N c When = 2, D1 = 2, so choose Different combinations of communication sub-chip positions The transmitted information sequence is “00”, “01”, “10”, “11”. Table 1 shows the mapping relationship between the communication sub-chip position combinations and the transmitted information sequence.

[0160] Table 1. Mapping relationship of position index modulation

[0161]

[0162] To distinguish between communication sub-chips and sub-chips used for optimization, let N... c -1 communication sub-chips s(m) i ), i = 2, 3, ... N c The phase difference between the reference sub-chip s(m1) and the reference sub-chip s(m1) belongs to a specific set, which is constrained as follows:

[0163]

[0164] in W is a set The number of elements in the middle. Then the number of information bits transmitted within one sub-pulse via phase difference modulation is...

[0165]

[0166] Figure 6An example of PIP modulation information mapping relationship using phase sets of 0 and π is given.

[0167] Therefore, the total information transmission rate is

[0168]

[0169] Where T r This is the pulse repetition interval.

[0170] b) Waveform arrangement modulation

[0171] Waveform arrangement modulation between sub-pulses involves constructing orthogonal waveforms from multiple sub-pulse signals, based on the orthogonal waveform set of the multi-functional integrated transmission signal. Choosing any arrangement to construct a multi-functional integrated transmission signal, the waveform position arrangement modulation between sub-pulses transmits information by utilizing different waveform arrangement positions. The modulation process involves randomly arranging M waveforms from a set of orthogonal waveforms, resulting in a total of [number missing] possible arrangements. One method is to randomly select a sequence of sub-pulse combinations as the transmitted signal.

[0172] Therefore, the transmission rate of waveform position arrangement modulation between sub-pulses is

[0173]

[0174] Therefore, the total information transmission rate of the combined modulation within and between subpulses is:

[0175]

[0176] 3. Anti-intermittent sampling and forwarding interference method based on the orthogonality of waveforms between sub-pulses

[0177] Considering that the phased array in the multifunctional integrated signal system is a uniform linear array composed of Z array elements, and the distance between two adjacent array elements is d = λ / 2, where λ is the wavelength of the electromagnetic wave, the weight vector of the beamformer can be expressed as w = [w0 w1 … w Z-1 ] T If a signal is incident on a phased array at an angle θ, then the steering vector of the uniform linear array can be expressed as α(θ) = [1e -jφ … e -j(Z-1)φ ] T Where φ=2πdsinθ / λ. The jammer samples the multi-subpulse signal T emitted by the multi-function integrated system. L The duration is calculated, and then the sampled signal is repeatedly forwarded. When the integrated system transmits signal x(t), with the normal of the phased array radar of the integrated system as 0°, the target and the jammer are located at θ, which is the normal of the phased array radar of the integrated system. tAt the azimuth position, the interference signal can be represented as:

[0178]

[0179] in, For the number of reposts, among which This indicates rounding down, where T is the pulse width of the multi-functional integrated signal.

[0180] like Figure 7 As shown, the principle of resisting intermittent sampling and forwarding interference is presented. During the sampling process, the sampling time T... L Shorter, assuming the jammer captures I sub-pulses. Partial signal relay, after pulse compression, interference signal and sub-pulse The matched filtering result can be expressed as:

[0181]

[0182] Interference signals and unsampled sub-pulses The matched filtering result can be expressed as:

[0183]

[0184] In the above formula, the matched filter result p i Multiple peak results will appear in (t), and the matched filter result p of the unsampled sub-pulses. o (t) peak value is much lower than p l The peak value of the matched filtering result in (t) is because the waveforms between the multi-functional integrated signal sub-pulses are pairwise orthogonal. The interference signal only has a correlation segment with the first I sub-pulse signals. Therefore, when performing matched filtering, the interference signal only has a partial correlation with the first I sub-pulses and no correlation with the unsampled sub-pulses. When performing MTD, under the gain of the pulse compression result of M sub-pulses, since only the first I sub-pulses are correlated with the interference signal, the correlation gain of the interference signal cannot accumulate, so it has a certain ability to resist intermittent sampling and forwarding interference.

[0185] 4. Solving a multi-functional integrated waveform optimization model based on a multi-sub-pulse structure.

[0186] Based on the above methods for communication information modulation and anti-interference, it is evident that an optimized design of the orthogonal waveform set is required. Discretize x l (t) gives x l (n), n=1,2,…,N. Based on minimizing the C / A-PSL of orthogonal signal families, the following orthogonal waveform family optimization design problem is constructed:

[0187]

[0188] in when At that time, weight c l,l It is the autocorrelation function of the waveform. Otherwise, It is the cross-correlation function of the waveform, with weights x = [x1, x2, ..., x M ], m c and These are the communication sub-chip and the set of phase differences used for information transmission, respectively. q and N R These are the sub-chips used for optimization and the total number of sub-chips used for optimization, respectively. ε is the phase protection interval, which is a small positive number.

[0189] To solve the above non-convex high-dimensional multi-constraint optimization problem By constructing an upper bound function for the objective function, iterative optimization is performed until this upper bound function monotonically decreases to convergence. In each iteration, Fourier transform and inverse Fourier transform are used to accelerate the algorithm's convergence.

[0190] First use L p The norm approximates the objective function, and by performing an equivalent transformation, we can obtain...

[0191]

[0192] At the t-th iteration, its upper bound function is

[0193]

[0194] in

[0195]

[0196]

[0197] In each iteration, the Fourier transform operation is used to represent the waveform autocorrelation function, accelerating the algorithm. The autocorrelation function of an aperiodic sequence can be expressed using the Fourier transform and inverse Fourier transform as follows:

[0198]

[0199] in It is the Fourier transform matrix.

[0200] Perform a Fourier transform on the autocorrelation function and combine it with FF. H =I, the above formula can be written as

[0201]

[0202] in

[0203] Let g l =F H [x l ;0],the objective function is approximately:

[0204]

[0205] The above formula can be approximated as

[0206]

[0207] make and as well as The above formula is equivalent to

[0208]

[0209] make The original optimization problem is approximated as follows:

[0210]

[0211] Case 1: When n = 1, this sub-chip is the reference sub-chip in the communication chip.

[0212] Case 2: n = m i And when n≠1, The magnitude is 1, and the phase is determined by the transmitted information;

[0213] Case 3: n≠m i That is, n = y q season The required solution is the following optimization problem.

[0214]

[0215] Its closed-form solution is:

[0216]

[0217] in yes The set of all endpoints of the sub-intervals in the set.

[0218] 5. Signal processing method based on monopulse multi-functional integrated echo

[0219] After the multi-functional integrated signal is scattered by the target echo and sampled and relayed by the jammer, the signal received by the integrated system through beamforming can be expressed as:

[0220]

[0221] Where ξ1 represents the attenuation factor of the target echo signal, ξ2 represents the attenuation factor of the interference signal, the radial distance of the target is r, the radial velocity is v (defined as positive when moving towards the radar), R(t) = r - vt, f c The carrier frequency of the signal is represented by n(t), and the noise component is represented by n(t).

[0222] use Indicates the amplitude of the target echo signal. The amplitude of the interference signal can be represented by R(t) = r - vt in the above equation, which gives the result.

[0223]

[0224] Assuming the range resolution unit is ΔR, when the velocity v is small, 2vT0 / c ≤ ΔR, that is, the target's movement distance within one pulse repetition interval PRT is less than the range resolution unit. In this case, the second term 2vt / c in the above formula can be ignored. When the target velocity v is large, 2vT0 / c > ΔR, in which case the target exhibits the phenomenon of crossing range units. In this case, the second term 2vt / c in the above formula cannot be ignored.

[0225] Here, we consider that 2vT0 / c≤ΔR always holds true, so the above equation can be approximated as:

[0226]

[0227] Substituting x(t) into the equation, we get

[0228]

[0229] By downconverting the target echo, we can obtain...

[0230]

[0231] Where n′(t) is the noise component after down-conversion. Target echo y r (t) is composed of target echoes, interference signals, and noise from multiple sub-pulses. Match filtering is performed on the echo signals and the transmitted sub-pulse signals respectively. The result of pulse compression with the i-th, i=1,…,M-th sub-pulse is expressed as:

[0232]

[0233] Where n″(t) is the noise component after pulse compression, substituted into Then we can get:

[0234]

[0235] Observing the above formula, we can obtain M pulse compression results. Under the premise of ensuring good orthogonality of each sub-pulse, due to the sampling time T of the interference machine... L The pulse compression is relatively short. Assuming the jammer acquires and forwards I sub-pulses, during pulse compression, the interference signal is only partially correlated with the first I sub-pulses and not correlated with the unsampled sub-pulses. Therefore, only the pulse compression results of the first I sub-pulses contain multiple interference signal peaks. These M pulse compression results are then shifted and their range gates aligned. Finally, during MTD (Mean Transform Dependency), the target's range and velocity information are estimated using FFT (Fast Fourier Transform). Since MTD involves the accumulation gain of M pulse compression results, and each sub-pulse pulse compression result contains a target signal peak, these M peaks accumulate after MTD. However, the interference signal's pulse compression result only has peaks in the first I sub-pulses, not the remaining sub-pulses. Therefore, the interference signal's peaks do not accumulate after MTD. Thus, the interference signal is suppressed after MTD, and the result only contains the target's range and velocity information. A detailed schematic diagram of the echo processing flow is shown below. Figure 8 As shown.

[0236] The specific processing steps are as follows:

[0237] Step 1: Use respectively For y r (t) is down-converted to obtain the corresponding baseband echo signal;

[0238] Step 2: Use x1(t) to x M (t) is pulse-compressed with the corresponding down-converted echo to obtain the corresponding pulse compression result y1′(t)~y′ M (t);

[0239] Step 3: Based on the position information of the sub-pulse in the transmitted waveform, and taking the pulse compression result of the first sub-pulse as the reference, shift the remaining pulse compression results so that the target distance cells of all pulse compression results are aligned.

[0240] Step 4: Pad the pulse compression result after the shifting process in Step 3 with zeros to obtain y1″(t)~y″. M (t), so that each pulse pressure result is restored to the length of the result processed in step 1;

[0241] Step 5: Take the pulse compression result obtained in Step 4 and perform FFT (Fast Fourier Transform) processing to obtain information about the target's velocity and position.

[0242] 6. Communication information demodulation methods

[0243] The signal received by the communication receiver can be represented as:

[0244]

[0245] Where ξ3 represents the attenuation factor of the transmitted signal from the integrated system to the communication receiver, ξ4 represents the attenuation factor of the jammer's interference signal to the communication receiver, and n c x(t) represents the noise signal. Substituting x(t) into the equation, we get:

[0246]

[0247] Assume the communication user has a differential phase set And the total number N of communication sub-chips c This is a known state. Since the phase demodulation of each sub-pulse signal is relatively independent, we will take one sub-pulse as an example here. Figure 9 The demodulation process for a portion of the phase within a sub-pulse is presented, and the specific steps are as follows:

[0248] 1) The communication user can discretize the received sub-pulses to obtain y. c (n), n=1,2,...,N;

[0249] 2) Detect y c Phase φ of each sub-chip of (n) n =arg{(y c (n))}, n=1,2,…,N;

[0250] 3) Calculate the phase difference between the phase of each sub-chip (starting from the second sub-chip) and the first reference sub-chip within the sub-pulse.

[0251] 4) Calculate the phase difference with all elements of the phase set.

[0252] 5) Let U c :={U c2 U c3 ,…,U cN}, determine U c The smallest N c The sub-chip corresponding to each element is the communication sub-chip, from which its position and phase information can be further extracted.

[0253] Demodulation of the waveform position arrangement between sub-pulses involves matching each waveform in the orthogonal waveform set with each sub-pulse, selecting the waveform with the largest peak value as the current sub-pulse's transmitted waveform, and thus demodulating the arrangement of the sub-pulse waveforms. A demodulation diagram is shown below. Figure 10 As shown.

[0254] Parameter settings: Number of phased array elements Z = 20, number of multi-functional integrated sub-pulses M = 24, number of sub-pulse waveform chips N = 512, number of communication chips within a sub-pulse N c =16. Bandwidth is B=50MHz, baseband signal sampling rate is f s =100MHz, sub-chip width is t b =0.02μs, in the multi-functional integrated system, the target echo signal-to-noise ratio (SNR) is 0dB, the interference-to-signal ratio (JSR) is 10dB, and the carrier frequency is f. c =2GHz, target distance is r=100km, target speed is v=1000m / s, noise power P n =1, the azimuth of the integrated target and jammer range system is θ t = -5°, the azimuth of the integrated system from the communication receiver is θ c1 =20°, the azimuth of the target and the jammer relative to the communication receiver is θ. c2 = -70°, the communication receiver is located at the azimuth of the phased array radar of the integrated system at θ. c3 = -60°. The input signal-to-noise ratio (SNR) for the communication receiver is... c =20dB, interference-to-signal ratio is JSR c =10dB.

[0255] Example 1:

[0256] If a combined modulation method of intra-subpulse partial phase modulation and inter-subpulse waveform position arrangement modulation is used, the communication performance results can be compared and analyzed. The communication rate can be significantly improved, as shown in Table 2.

[0257] Table 2 Communication rates (per PRT time) under typical parameters

[0258]

[0259] Table 2 shows the communication rates of the integrated waveform of LFM-DPSK based on Frequency Nulling Modulation (FNM) and the multi-functional integrated waveform presented in this paper. FNM16 and FNM256 represent the selection of 16 and 256 sub-bands for information transmission, respectively. Table 2 shows that the combined modulation of intra-sub-pulse partial phase modulation and inter-sub-pulse waveform position arrangement modulation used in this paper varies with the number of communication chips N. c With the increase of the value of M, the number of sub-pulses increases, and the communication rate is significantly improved.

[0260] Example 2:

[0261] If the multi-sub-pulse structure and multi-functional integrated waveform design method designed in this paper are adopted, Figure 11 Time-domain plots of the jamming signal and the radar transmitted signal are given. The plots show that the jammer samples the radar transmitted signal and then repeatedly forwards the sampled signal segments until the last forwarding signal has a pulse width insufficient to completely reproduce the sampled segment, at which point forwarding stops. Furthermore, Figure 3 The null receiver beamform of the design is given. The figure shows that the gain varies with distance θ from the communication receiver. c1 The gain is greatest at θ = 20°, with a gain of about 8dB, at a distance of θ from the communication receiver. c2 It has a gain of approximately -114 dB in the direction of -70°. Figure 12 The communication performance of partial phase demodulation of the communication receiver under null receive beam gain is presented. Under null receive beam gain, when SNR c After reaching 20dB, the Symbol Error Rate (SER) increases with the SNR. c As SNR increases, it gradually decreases. c After reaching 27dB, SER decreases to 0. It exhibits good communication performance. Similarly, Figure 13 The communication performance of the receiver waveform arrangement demodulation under the gain of the null-received beam is presented. Similar to the above, under the null-received beam gain, the SNR is... c After being reduced to -18dB, the SER during waveform arrangement demodulation changes with the SNR. c The increase gradually decreases in SNR. c After a signal-to-noise ratio of -12dB, SER decreases to 0. This demonstrates that waveform arrangement demodulation exhibits good communication performance even at very low signal-to-noise ratios.

[0262] Example 3:

[0263] If the multi-functional integrated waveform design method of the multi-sub-pulse structure designed in this paper is adopted, after the phased array beamforming gain is obtained, the echo signal is converted into a baseband signal according to the processing steps; the echo is processed by the matched filter corresponding to the sub-pulse waveform to obtain the distance information; the target peak value of each sub-pulse filtering result is aligned; the Doppler frequency is extracted by Fourier transform to calculate the target velocity; Figure 2 The phased array receiving beam diagram of the integrated system is given. It can be seen that at a distance θ from the integrated system... t The gain is greatest in the direction of -5, with a gain of about 26dB, at a distance of θ from the integrated system. c3 The gain is approximately -3.6 dB in the direction of -60°. Since the target's azimuth distance from the integrated system is θ... t = -5°, and the jammer sampling time T L =4μs, so after processing the echo, the result can be obtained as follows. Figures 14-19 As shown, Figure 14 The pulse compression results of the first sub-pulse and the echo (including the target echo + interference signal + noise) are given, and it can be seen that the distance between the target and the first interference peak is the sampling time T. L The corresponding distance, and the distance between every two interference peaks is also T. L The corresponding distance is consistent with the theoretical derivation. Figure 15 The pulse compression results of the remaining sub-pulses after distance shift alignment are given. It can be seen that there is only the peak value corresponding to the target in the figure, and no peak value of the interference signal. This is because under the parameters in this paper, the jammer only sampled a part of the first sub-pulse signal and then repeatedly forwarded it. Therefore, only the pulse compression result of the first sub-pulse has the pulse compression peak value of the interference signal, and the pulse compression results of the remaining sub-pulses do not have the interference signal. Figures 16-17 Three-dimensional plots of pulse compression results before and after distance gate alignment for all sub-pulses are presented. It can be seen from the plots that only the pulse compression result of the first sub-pulse has a pulse compression peak of interference signal. Figures 18-19 The MTD (Mean Time Tolerance) for multi-subpulse signals and echo signals (including target echo + interference signal + noise) is presented. The figure shows that only the target is present, with no interference. This is because the multi-subpulse echo processing method is used. Since the interference signal only consists of the first subpulse signal segment, the pulse compression peak of the interference cannot accumulate during MTD, resulting in only the target and no interference. The figure also demonstrates its excellent detection performance, accurately detecting the target's distance and velocity.

Claims

1. A multifunctional integrated waveform design method based on a multi-sub-pulse structure, characterized in that, Includes the following steps: Step 1: Multifunctional integrated waveform application scenarios based on multi-sub-pulse structure. Step 2: Propose an information transmission modulation method based on the joint modulation of partial phase modulation within sub-pulses and waveform position arrangement modulation between sub-pulses. Step 3: Propose a method to resist intermittent sampling and forwarding interference based on the orthogonality of waveforms between sub-pulses. Step 4: Establish and solve a multi-functional integrated waveform optimization model based on a multi-sub-pulse structure. Step 5: A signal processing method based on single-pulse multi-functional integrated echo is proposed. Step 6: Propose a communication information demodulation method.

2. The multifunctional integrated waveform design method based on a multi-sub-pulse structure according to claim 1, characterized in that, The multi-functional integrated waveform application scenario based on a multi-subpulse structure in step 1 consists of a phased array multi-functional integrated system with co-located transmit and receive terminals, a communication receiver equipped with a phased array, a jammer, and a target. Taking the normal of the phased array of the multi-functional integrated system as 0°, the angle between the target and the jammer and the normal of the phased array radar of the multi-functional integrated system is θ. t The angle between the normal to the phased array radar of the communication receiver and the multi-functional integrated system is θ. c3 If the normal to the phased array of the communication receiver is 0°, then the angle between the normal to the phased array radar of the multi-functional integrated system and the normal to the communication receiver is θ. c1 The angle between the normals of the jammer and the phased array radar of the communication receiver is θ. c2 . The multi-functional integrated system uses transmitted beamforming to direct beams towards the main lobe directions θ of the target and the jammer, respectively. t and the sidelobe direction θ of the communication receiver c3 A multi-functional integrated signal is transmitted. The jammer intercepts and forwards the transmitted multi-functional integrated signal, forming an intermittent sampling and forwarding jamming signal. After being scattered by the target, the signal and the intermittent sampling and forwarding jamming signal are along θ. t The main lobe direction is received by the multi-functional integrated system; the communication receiver receives θ. c1 Multifunctional integrated signal in the main lobe direction and θ c2 Interference signals in the sidelobe direction; in The communication receiver achieves effective reception of communication information by receiving the energy of the beamforming signal to suppress interference, enhancing the energy of the multi-functional integrated signal, and maximizing the energy of the sidelobe transmission of communication information.

3. The multifunctional integrated waveform design method based on a multi-sub-pulse structure according to claim 2, characterized in that, The information transmission modulation method in step 2, based on the joint modulation of intra-subpulse partial phase modulation and inter-subpulse waveform position arrangement modulation, provides a set of orthogonal waveforms for the multi-functional integrated transmission signal. Composed of M orthogonal waveforms, it is a set of orthogonal waveforms from a multi-functional integrated transmission signal. A multi-functional integrated transmission signal x(t) is formed by randomly selecting an arrangement of x1(t), x2(t), ..., x M If the signals are arranged in order (t), then the multi-functional integrated transmission signal x(t) can be expressed as: Where T0 is the sub-pulse width, T = MT0 is the long pulse width, and rect(t) is the rectangular window function, expressed as follows: The modulation method in the multi-functional integrated system employs partial phase modulation within sub-pulses. The sub-pulse waveform is a partially phase-coded waveform, and each sub-pulse is divided into N sub-chips. Based on the requirements of communication and detection performance, the first sub-chip is designated as the reference sub-chip for information transmission, and N sub-chips are selected from the N sub-chips. c The first sub-chip is used as the information transmission sub-chip (including the first sub-chip), and the remaining chips N R =NN c To optimize and ensure the detection performance of the designed waveform, the partial phase-coded sub-pulse x l (t) can be represented as: Among them, t b For the duration of the sub-slice, It is the amplitude of the i-th communication sub-chip of the l-th phase-coded waveform. This represents the amplitude of the q-th sub-chip used for optimization in the l-th phase-coded waveform. This represents the i-th phase in the set of communication sub-chips for the l-th phase-coded waveform. This represents the q-th phase of the subchip set used for optimization of the l-th phase encoded waveform. The total number of possible combinations of communication sub-chip positions is: Based on the above formula, it can be deduced that, within each Pulse Repetition Interval (PRI), the maximum number of bits available for transmission, selected by combining the positions of the information transmission sub-chips, is: To distinguish between communication sub-chips and sub-chips used for optimization, let N... c -1 communication sub-chips s(m) i ), i = 2, 3, ... N c The phase difference between the reference sub-chip s(m1) and the reference sub-chip s(m1) belongs to a specific set, which is constrained as follows: in W is a set The number of elements in the middle. Then the number of information bits transmitted within one sub-pulse via phase difference modulation is... Therefore, the total information transmission rate is Where T r This is the pulse repetition interval. Waveform arrangement modulation between sub-pulses involves constructing orthogonal waveforms from multiple sub-pulse signals, based on the orthogonal waveform set of the multi-functional integrated transmission signal. Choosing any arrangement to form a multi-functional integrated transmission signal, the waveform position arrangement modulation between sub-pulses transmits information by utilizing different waveform arrangement positions; its modulation process involves randomly arranging M waveforms from the orthogonal waveform set, thus there are a total of... One method is to randomly select a sequence of sub-pulse combinations as the transmitted signal. Therefore, the transmission rate of waveform position arrangement modulation between sub-pulses is Therefore, the total information transmission rate of the combined modulation within and between subpulses is:

4. The multifunctional integrated waveform design method based on a multi-sub-pulse structure according to claim 3, characterized in that, In step 3, considering that the phased array in the multifunctional integrated signal system is a uniform linear array composed of Z array elements, the distance between two adjacent array elements is d = λ / 2, where λ is the wavelength of the electromagnetic wave. The weight vector of the beamformer can be expressed as w = [w0 w1 … w Z-1 ] T If a signal is incident on a phased array at an angle θ, then the steering vector of the uniform linear array can be expressed as α(θ) = [1 e -jφ … e -j(Z-1)φ ] T Where φ=2πdsinθ / λ; the jammer samples the multi-subpulse signal T emitted by the multi-functional integrated system. L The duration is then calculated, and the sampled signal is repeatedly relayed. When the integrated system transmits signal x(t), with the normal of the phased array radar of the integrated system as 0°, the target and the jammer are located at θ, which is the normal of the phased array radar of the integrated system. t At the azimuth position, the interference signal can be represented as: in, For the number of reposts, among which This indicates rounding down, where T is the pulse width of the multi-functional integrated signal. During the sampling process, the sampling time T L Shorter, assuming the jammer captures I sub-pulses. Partial signal relay, after pulse compression, interference signal and sub-pulse The matched filtering result can be expressed as: Interference signals and unsampled sub-pulses The matched filtering result can be expressed as: In the above formula, the matched filter result p i Multiple peak results will appear in (t), and the matched filter result p of the unsampled sub-pulses. o (t) peak value is much lower than p l The peak value of the matched filtering result in (t) is because the waveforms between the multi-functional integrated signal sub-pulses are pairwise orthogonal. The interference signal only has the correlation segment of the first I sub-pulse signal. Therefore, when performing matched filtering, the interference signal only has a partial correlation with the first I sub-pulses and no correlation with the unsampled sub-pulses. When performing MTD, under the gain of the pulse compression result of M sub-pulses, since only the first I sub-pulses are correlated with the interference signal, the correlation gain of the interference signal cannot accumulate, so it has a certain ability to resist intermittent sampling and forwarding interference.

5. The multifunctional integrated waveform design method based on a multi-sub-pulse structure according to claim 4, characterized in that, Step 4 requires optimizing the design of the orthogonal waveform set. Discretize x l (t) gives x l (n), n=1,2,…,N; Based on minimizing the C / A-PSL of orthogonal signal clusters, the following orthogonal waveform cluster optimization design problem is constructed: in when At that time, weight c l,l It is the autocorrelation function of the waveform; otherwise, It is the cross-correlation function of the waveform, with weights x = [x1, x2, ..., x M ], m c and These are the communication sub-chip and the set of phase differences used for information transmission, respectively. q and N R These are the sub-chips used for optimization and the total number of sub-chips used for optimization, respectively. m u =2π(u-1) / W+ε,y u =2πu / W-ε, where ε is the phase protection interval, which is a small positive number. To solve the above non-convex high-dimensional multi-constraint optimization problem By constructing an upper bound function for the objective function, iterative optimization makes the upper bound function monotonically decrease until convergence; In each iteration, Fourier transform and inverse Fourier transform are used to accelerate algorithm convergence. First use L p The norm approximates the objective function, and by performing an equivalent transformation, we can obtain... At the t-th iteration, its upper bound function is in In each iteration, Fourier transform is used to represent the waveform autocorrelation function to accelerate the algorithm; The autocorrelation function of an aperiodic sequence can be expressed using Fourier transform and inverse Fourier transform as follows: in It is the Fourier transform matrix. Perform a Fourier transform on the autocorrelation function and combine it with FF. H =I, the above formula can be written as in Let g l =F H [x l ;0],the objective function is approximately: The above formula can be approximated as make and as well as The above formula is equivalent to make The original optimization problem is approximated as follows: Case 1: When n = 1, this sub-chip is the reference sub-chip in the communication chip. Case 2: n = m i And when n≠1, The magnitude is 1, and the phase is determined by the transmitted information; Case 3: n≠m i That is, n = y q season The required solution is the following optimization problem. Its closed-form solution is: in yes The set of all endpoints of the sub-intervals in the set.

6. The multifunctional integrated waveform design method based on a multi-sub-pulse structure according to claim 5, characterized in that, In step 5, after the multi-functional integrated signal is scattered by the target echo and sampled and forwarded by the jammer, the signal received by the integrated system through beamforming can be expressed as: Where ξ1 represents the amplitude coefficient of the target echo signal, ξ2 represents the amplitude coefficient of the interference signal, the radial distance of the target is r, the radial velocity is v (defined as positive when moving towards the radar), R(t) = r - vt, f c The carrier frequency of the signal is represented by n(t), and the noise component is represented by n(t). use Indicates the amplitude of the target echo signal. The amplitude of the interference signal can be represented by R(t) = r - vt in the above equation, which gives the result. Assuming the range resolution unit is ΔR, when the velocity v is small, 2vT0 / c ≤ ΔR, that is, the target's movement distance within one pulse repetition interval PRT is less than the range resolution unit. In this case, the second term 2vt / c in the above formula can be ignored. When the target velocity v is large, 2vT0 / c > ΔR, in which case the target exhibits the phenomenon of crossing range units. In this case, the second term 2vt / c in the above formula cannot be ignored. Here, we consider that 2vT0 / c≤ΔR always holds true, so the above equation can be approximated as: Substituting x(t) into the equation, we get By downconverting the target echo, we can obtain... Where n′(t) is the noise component after down-conversion; target echo y r (t) is composed of the target echo, interference signal, and noise from multiple sub-pulses. The echo signal is matched and filtered with the transmitted sub-pulse signal, and the result of pulse compression with the i-th, i=1,…,M-th sub-pulse is expressed as: Where n″(t) is the noise component after pulse compression, substituted into Then we can get: Observing the above formula, we can obtain M pulse compression results. Under the premise of ensuring good orthogonality of each sub-pulse, due to the sampling time T of the interference machine... L The process is relatively short. Assuming the jammer samples and forwards I sub-pulses, during pulse compression, the interference signal is only partially correlated with the first I sub-pulses and not correlated with the unsampled sub-pulses. Therefore, only the pulse compression results of the first I sub-pulses contain multiple interference signal peaks. These M pulse compression results are then shifted and their range gates aligned. Finally, during MTD (Mean Time Difference), the target's range and velocity information are estimated using Fast Fourier Transform (FFT). Since MTD involves the cumulative gain of M pulse compression results, and each sub-pulse pulse compression result contains a target signal peak, these M peaks accumulate after MTD. However, the interference signal's pulse compression result only has peaks in the first I sub-pulses, not the remaining sub-pulses. Therefore, the interference signal's peaks cannot accumulate after MTD, resulting in suppressed interference signal information. The final result only contains the target's range and velocity information.

7. The multifunctional integrated waveform design method based on a multi-sub-pulse structure according to claim 6, characterized in that, The signal received by the communication receiver in step 6 can be represented as: Where ξ3 represents the amplitude coefficient of the transmitted signal from the integrated system to the communication receiver, ξ4 represents the amplitude coefficient of the jamming signal from the jammer to the communication receiver, and n c (t) represents the noise component. Substituting x(t) into the equation, we get: Assume the communication user has a differential phase set And the total number N of communication sub-chips c Given the known state, and since the partial phase demodulation of each sub-pulse signal is relatively independent, we will take one sub-pulse as an example. The specific steps for partial phase demodulation are as follows: 1) The communication user can discretize the received sub-pulses to obtain y. c (n), n = 1, 2, ..., N; 2) Detect y c Phase φ of each sub-chip of (n) n =arg{(y c (n))}, n=1,2,…,N; 3) Calculate the phase difference between the phase of each sub-chip (starting from the second sub-chip) and the first reference sub-chip within the sub-pulse. 4) Calculate the phase difference with all elements of the phase set. 5) Let U c :={U c2 U c3 ,…,U cN }, determine U c The smallest N c The sub-chip corresponding to each element is the communication sub-chip, from which its position and phase information can be further extracted. The waveform position arrangement demodulation between sub-pulses is achieved by matching each waveform in the orthogonal waveform set with each sub-pulse, selecting the waveform with the largest peak value as the current sub-pulse transmission waveform, and then demodulating the arrangement of the sub-pulse waveforms.

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