Long baseline transceiver distributed multi-radar signal space-frequency code cooperative anti-jamming method

Abstract

The application discloses a long-baseline transceiver-displaced multi-radar signal space-frequency code cooperative anti-jamming method, which comprises the following steps: firstly, according to the identification mechanism of the jammer to the intercepted signal and the interference generation mechanism, the space-frequency code domain cooperative anti-jamming strategy is researched; according to the anti-jamming strategy, the narrow-band detection signal model, the wide-band cover signal model and the optimization problem model are established; the optimized signal is obtained by solving the optimization problem; each station transmits the optimized signal; finally, the receiving station utilizes the matched filter to process the radar receiving echo signal. The method considers the dual functions of cover and decoy, that is, even if the interference energy is large, the jammer generates the parameter error interference signal through the deception of the decoy signal, the interference energy received by the detection signal is greatly reduced, the signal form is more complex, the signal recognition of the countermeasure jammer is more difficult, and the anti-jamming performance of the radar system is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar anti-jamming, and particularly relates to a long-baseline transceiver-separated multi-radar signal space-frequency code cooperative anti-suppression jamming method. BACKGROUND

[0002] Radar jamming refers to the general term of all strategies and technical measures that can destroy and disturb the normal work of radars and related equipment. According to the action mechanism of the jamming signal, radar jamming can be divided into suppression jamming and deception jamming. Suppression jamming mainly transmits a large-power noise signal to raise the noise floor in the radar received echo. The essence is to reduce the signal-to-noise ratio in target detection, reduce the target detection probability, and greatly reduce the working performance of the radar, or even make it unable to work normally. Therefore, in order to ensure the correct detection and tracking of the target by the radar in a complex electromagnetic environment, it is of great theoretical value and practical significance to improve the anti-suppression jamming capability of the radar.

[0003] The method for cognitive radar anti-suppression jamming mainly focuses on signal processing and waveform design. The signal processing anti-jamming mainly utilizes the difference between the target echo and the jamming signal in different dimensions, and uses adaptive filtering and other signal processing methods to achieve the purpose of anti-jamming. The document “Du Dongping, Tang Bin. Noise amplitude modulation jamming suppression algorithm based on frequency domain cancellation. Journal of Electronics & Information, 2007(03):557-559” estimates the carrier frequency and initial phase of the jamming signal through logarithmic transformation, demodulates the echo signal with the estimated jamming carrier frequency, and finally suppresses the jamming through frequency domain cancellation. The waveform design anti-jamming mainly designs a frequency agile waveform, optimizes the waveform to improve the output signal-to-interference-and-noise ratio, and improves the performance of the radar in the jamming environment. The document “Zhang Jie, Chen Wanying, Wu Yue. Two-dimensional adaptive anti-jamming agile waveform design for cognitive radar. Radar Science and Technology, 2019, 17(04):415-420+425.” studies the optimization criteria and mathematical model for agile waveform design in a suppression jamming environment, and the obtained waveform can effectively suppress the noise amplitude modulation type suppression jamming. However, both the signal processing and waveform design anti-jamming methods have disadvantages. The anti-jamming method based on signal processing mostly needs to know the type or parameter of the jamming accurately, and when the jammer can cope with the agile waveform, the single waveform design method loses the effect of anti-jamming. The document “Yu Xianxiang, Lu Qinghui, Yang Jing, Sha Minghui, Cui Guolong, Kong Lingjiang. Short baseline transceiver-separated frequency domain cooperative waveform design method. Journal of Radar, 2022, 11(02):227-239.” considers the waveform design from the perspective of the frequency domain to study the cooperative anti-jamming, but the method proposed in the document uses the short baseline transceiver-separated station, and the frequency domain cooperative waveform design anti-jamming method proposed in the document only considers the angle of cover, and when the jamming energy is large, the detection signal will still be disturbed greatly. SUMMARY

[0004] To solve the above technical problems, the application provides a long baseline transceiver distributed multi-radar signal space-frequency code cooperative anti-jamming method.

[0005] The technical scheme adopted by the application is as follows: a long baseline transceiver distributed multi-radar signal space-frequency code cooperative anti-jamming method, and the specific steps are as follows:

[0006] Step S1, formulating a space-frequency code domain cooperative anti-jamming strategy;

[0007] Step S2, establishing a signal transmission model of each transmission station according to the space-frequency code domain cooperative anti-jamming strategy;

[0008] Step S3, establishing an optimization problem model based on the model established in step S2;

[0009] Step S4, solving the problem by using an optimization algorithm to obtain the signal transmitted by each transmission station;

[0010] Step S5, transmitting an optimized narrowband detection signal by the transmission station 1, transmitting an optimized wideband cover signal by the transmission station 2, and transmitting a narrowband decoy signal by the transmission station 3;

[0011] Step S6, processing the radar receiving echo signal by using a matched filter at the receiving station.

[0012] Further, in step S1, the space-frequency code domain cooperative anti-jamming strategy is as follows:

[0013] The three distributed transmission stations are controlled to cooperatively transmit simultaneously and in the same direction, and a receiving station receives the echo signal reflected by the target, and the transmission station and the receiving station belong to long baseline distribution.

[0014] Among them, the transmission station 1 transmits a narrowband detection signal, the transmission station 2 transmits a wideband cover signal, and the transmission station 3 transmits a narrowband decoy signal.

[0015] Further, step S2 is as follows:

[0016] Step S21, establishing a narrowband detection signal model;

[0017] Let the single-pulse narrowband detection signal transmitted by the transmission station 1 be represented as:

[0018] (1)

[0019] wherein, f represents the carrier frequency of the signal, f represents the frequency offset of the signal, t represents time, ​This refers to the narrowband probe phase-coded baseband signal, specifically:

[0020] (2)

[0021] in, Indicates the narrowband detection baseband signal of the first Phase of each chip, Indicates the number of chips in the narrowband detection baseband signal. This indicates the time width of one chip of the narrowband detection baseband signal. This indicates the pulse width of the single-pulse narrowband detection signal transmitted by the transmitting site. Represents a rectangle function.

[0022] Step S22: Establish a broadband cover signal model;

[0023] Assume that the single-pulse broadband cover signal transmitted from transmitting site 2 is... Represented as:

[0024] (3)

[0025] in, Indicates the carrier frequency of the signal. This refers to the broadband masking phase-coded baseband signal, specifically:

[0026] (4)

[0027] in, Indicates the broadband cover baseband signal. Phase of each chip, Indicates the number of baseband signal chips for broadband protection. This represents the time width of one chip of the broadband shielding baseband signal.

[0028] Step S23: Establish a narrowband decoy signal model;

[0029] Suppose that the single-pulse narrowband decoy signal is transmitted from transmitting site 3. Represented as:

[0030] (5)

[0031] in, Indicates the carrier frequency of the signal. Indicates the frequency offset of the signal. This refers to the broadband masking phase-coded baseband signal, specifically:

[0032] (6)

[0033] The narrow-band deception signal bandwidth is selected to be consistent with the narrow-band detection signal bandwidth and pulse width, and the number of chips and chip width are consistent. represents the phase of the th chip of the narrow-band deception baseband signal.

[0034] Further, the step S3 is specifically as follows:

[0035] Step S31, establishing a narrow-band detection signal optimization model;

[0036] The narrow-band detection phase encoding baseband signal is discretely represented as:

[0037] (7)

[0038] wherein, represents the th point of the discrete narrow-band detection phase encoding baseband signal , and represents the transposition operation of a vector, considering minimizing the autocorrelation peak sidelobe level, adding a constant modulus constraint, the narrow-band detection signal optimization model is specifically represented as:

[0039] (8)

[0040] wherein, represents a modulo operation, represents a maximum value operation, represents a minimum value operation, represents a peak restriction range of an autocorrelation function, represents the th point of the non-periodic autocorrelation function of , and is represented as:

[0041] (9)

[0042] wherein, represents the th point of , and represents the th point of , and represents the conjugate of a complex number.

[0043] According to the peak amplitude transformation principle, the objective function of the optimization problem is represented as -norm problem:

[0044] (10)

[0045] wherein, represents the - norm. The narrowband probing signal optimization model can be approximated as:

[0046] (11)

[0047] Step S32, establishing a wideband mask signal optimization model;

[0048] Wideband mask phase-coded baseband signal is discretely represented as:

[0049] (12)

[0050] wherein, represents the i-th point of the discretized wideband mask phase-coded baseband signal , the i-th point of the wideband mask phase-coded baseband signal is represented as:

[0051] (13)

[0052] wherein, , represents a complex vector of dimension , represents the number of Fourier transform points, represents a conjugate transpose operation of a matrix, represents an inverse Fourier transform matrix, represents the i-th column vector of the inverse Fourier transform matrix, represents a zero-padded signal of the discretized wideband mask phase-coded baseband signal , represents a 0 vector of dimension .

[0053] Considering the constant modulus constraint, the wideband mask signal optimization problem model is represented as:

[0054] (14)

[0055] wherein, represents a spectrum range that needs to be limited to ensure the frequency domain coordination performance, represents an auxiliary variable vector, represents the i-th point of the auxiliary variable vector , represents a desired spectrum shape of the wideband mask signal, represents a 2-norm.

[0056] Further, the step S4 is specifically as follows:

[0057] ​​Step S41, solve the narrowband probing signal optimization problem by using the proximal multiplier algorithm based on optimization minimization;

[0058] The formula (11) is decomposed into sub-optimization problems which are easy to solve by using the proximal multiplier algorithm based on optimization minimization, and parallel iteration calculation is carried out. By using the optimization minimization approximation principle, the norm problem is converted into a quadratic function optimization problem for solving.

[0059] The autocorrelation function is expressed by using fast Fourier transform and inverse fast Fourier transform as:

[0060] (15)

[0061] wherein, denotes the autocorrelation function of the sequence, denotes the discrete narrowband probing phase encoding baseband signal zero-padded signal, denotes a 0 vector of dimension, denotes Hadamard product, and the formula (11) is expressed as:

[0062] (16)

[0063] wherein, the proximal augmented Lagrangian function is expressed as:

[0064] (17)

[0065] wherein, denotes the proximal augmented Lagrangian function, denotes the proximal parameter, denotes the penalty parameter, denotes the extended dual variable, denotes the result of the sequence obtained in the th iteration.

[0066] The proximal multiplier algorithm based on optimization minimization is used to solve the process as follows by introducing an auxiliary variable:

[0067] Step S411, let , and initialize ;

[0068] wherein, denotes the sequence of the th iteration, denotes the autocorrelation function of the th iteration, denotes the sequence spectrum of the th iteration., denotes the th iteration of the extended dual variable . When , the above parameters are initialized.

[0069] Step S412, fix ;

[0070] Step S413, fix , solve ;

[0071] (18)

[0072] where arg denotes the value that satisfies , and the value of is taken as the value of when the minimum value is taken, that is:

[0073] (19)

[0074] Step S414, fix , solve ;

[0075] Convert into an upper bound optimization problem of a quadratic function about :

[0076] (20)

[0077] where , , , .

[0078] Step S415, fix , solve ;

[0079] The sub-optimization problem about is simplified as:

[0080] (21)

[0081] where

[0082] (22)

[0083] (23)

[0084] where denotes a vector with all elements being 1, denotes the real part operation on the elements of a vector, denotes a phase angle operation, denotes the first iteration result.

[0085] Step S416, fixing , solving ;

[0086] (24)

[0087] (25)

[0088] Step S417, determining whether to stop settlement;

[0089] The stop condition is:

[0090] (26)

[0091] wherein, denotes a residual error of stopping calculation, denotes a residual error of the first iteration, and is expressed as:

[0092] (27)

[0093] (28)

[0094] wherein, denotes an infinite norm. denotes the maximum number of iterations based on the proximal multiplier algorithm for optimization minimization.

[0095] If the current calculation value satisfies the condition, the calculation of the narrowband probe signal is stopped, otherwise, the step S412 is returned.

[0096] Step S42, solving the wideband cover signal optimization problem by using a spectral shaping algorithm;

[0097] The formula (14) is a spectral shaping algorithm problem model under the constant modulus constraint. In the case of only optimizing the intra-pulse spectral shape, the spectral shaping algorithm can be used to solve. The following minimization problem is introduced:

[0098] (29)

[0099] wherein, denotes a scalar factor to interpret the sequence and the spectral shape between any possible energy mismatch and / or phase constant offset. denotes an envelope constraint on the time domain sequence, and denote the upper and lower boundary functions of the spectrum. denote the auxiliary variables the first element of the first element of the envelope constraint, the first element of the upper boundary function, the first element of the lower boundary function.

[0100] The auxiliary variables are introduced, and the solving process of the spectrum shaping algorithm is as follows:

[0101] Step S421, let , initialize , satisfy , initialize temporary variables and ;

[0102] wherein denotes the value of obtained in the th iteration, denotes the value of the discrete wideband mask baseband signal obtained in the th iteration, denotes the value of the auxiliary variable obtained in the th iteration.

[0103] Step S422, let ;

[0104] Step S423, fix , solve ;

[0105] Let , regard it as a loop:

[0106] If , let ; if , let ; in other cases, . denotes the th element of the temporary variable

[0107] Step S424, fix , solve ;

[0108] (30)

[0109] Step S425, fixing , solving ;

[0110] Let , as a cycle:

[0111] Introduce as an intermediate calculation variable, if , then , otherwise . Indicate the first Element of the intermediate calculation variable .

[0112] Step S426, updating ;

[0113] Step S427, judging whether to stop calculation or not;

[0114] The stop condition is:

[0115] (31)

[0116] Wherein, Indicates the maximum number of iterations set by the spectral shaping algorithm. If the current calculation value satisfies the condition, stop calculating the wideband cover signal , otherwise return to step S422.

[0117] Advantages of the present application: the method of the present application first studies the space-frequency code domain cooperative jamming strategy according to the recognition mechanism of the jammer to the intercepted signal and the interference generation mechanism, establishes a narrowband detection signal model, a wideband cover signal model and an optimization problem model according to the anti-jamming strategy, obtains an optimized signal by solving the optimization problem, transmits the optimized signal at each site, and finally the receiving station uses a matched filter to process the radar received echo signal. The method of the present application considers the dual functions of cover and deception, that is, even if the interference energy is large, through the deception of the deception signal, the jammer generates a parameter error interference signal, greatly reduces the interference energy received by the detection signal, and the signal form is more complex, causing greater difficulty in signal recognition for the counterparty jammer, and improving the anti-jamming performance of the radar system. BRIEF DESCRIPTION OF DRAWINGS

[0118] Figure 1 It is a flow chart of a long baseline transceiver distributed multi-radar signal space-frequency code cooperative anti-suppression jamming method of the present application.

[0119] Figure 2 It is a space-frequency code domain cooperative anti-jamming system model diagram in the embodiment of the present application.

[0120] Figure 3This is a flowchart of the proximal multiplier algorithm based on optimization minimization in an embodiment of the present invention.

[0121] Figure 4 This is a flowchart of the spectrum shaping algorithm solution in an embodiment of the present invention.

[0122] Figure 5 This is a diagram illustrating the signal transmission method in an embodiment of the present invention.

[0123] Figure 6 This is a diagram illustrating the radar echo signal processing procedure in an embodiment of the present invention.

[0124] Figure 7 The images show the autocorrelation function graph of the detection signal and the spectrum of the cooperative signal in this embodiment of the invention.

[0125] Figure 8 The figure shows the RD results of the simulated single-transmit single-receive mode and MIMO mode under suppressed interference in the embodiments of the present invention.

[0126] Figure 9 The figures show the RD and detection results under suppressed interference in the simulation collaborative mode in this embodiment of the invention. Specific implementation methods

[0127] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0128] like Figure 1 The flowchart of a long-baseline transceiver-multiple radar signal space-frequency code cooperative anti-suppression interference method of the present invention is shown below. The specific steps are as follows:

[0129] Step S1: Formulate a space-frequency code domain collaborative anti-interference strategy;

[0130] Step S2: Establish the transmission signal model of each transmitting site according to the space-frequency code domain collaborative anti-interference strategy;

[0131] Step S3: Based on the model established in step S2, establish an optimization problem model;

[0132] Step S4: Solve the problem using an optimization algorithm to obtain the transmitted signals from each transmitting station;

[0133] Step S5: Transmitting station 1 transmits an optimized narrowband detection signal, transmitting station 2 transmits an optimized broadband cover signal, and transmitting station 3 transmits a narrowband decoy signal.

[0134] Step S6: Process the radar received echo signal at the receiving station using a matched filter.

[0135] like Figure 2As shown, the space-frequency code domain collaborative anti-jamming system model, in this embodiment, in the step S1, the frequency domain of the transmission signal of each sub-site of the distributed radar is used to form a collaborative transmission signal actively, mislead the interference guidance of the opponent, so that it cannot quickly identify the real threat signal, and it is difficult to effectively interfere, thereby protecting the normal operation of our radar system, achieving the interference suppression effect of active anti-jamming, and the space-frequency code domain collaborative anti-jamming strategy is as follows:

[0136] The three distributed transmission sites are controlled to transmit collaboratively in the same direction at the same time, and a receiving site receives the echo signal reflected by the target. The transmission sites and the receiving site belong to a long baseline distribution.

[0137] Among them, the transmission site 1 transmits a narrowband detection signal, the transmission site 2 transmits a wideband cover signal, and the transmission site 3 transmits a narrowband decoy signal. The spectrum of the wideband cover signal is designed to reserve a matching groove for the spectrum of the narrowband detection signal, so that when transmitting collaboratively, the wideband cover signal can cover the narrowband detection signal in its spectrum. For the spectrum of the narrowband decoy signal, it can be superimposed with the wideband signal in a certain specific frequency band region of the wideband cover signal to form a narrowband decoy frequency band with high amplitude as a deception information to interfere with the judgment of the jammer of the opponent. In the decision process of the channelized receiver, the narrowband detection signal is covered by the wideband cover signal in the frequency domain, and the narrowband decoy signal and the wideband cover signal are superimposed to form a deceptive effect of a convex narrowband spectrum in the frequency spectrum. The analysis of the channelized receiver is wrong, and the jamming signal with the wrong aiming frequency is transmitted. With the dual effects of deception and cover, the anti-jamming performance of the radar system is finally improved.

[0138] In this embodiment, the step 2 is as follows:

[0139] Step S21, establish a narrowband detection signal model;

[0140] Let the single-pulse narrowband detection signal transmitted by the transmission site 1 be represented as:

[0141] (1)

[0142] wherein, f represents the carrier frequency of the signal, f represents the frequency offset of the signal, , t represents time, represents a narrowband detection phase encoding baseband signal, and is specifically:

[0143] (2)

[0144] wherein, represents the first pulse of the narrowband detection baseband signal phase of the chip, denotes the number of chips of the narrowband probe baseband signal, denotes the time width of one chip of the narrowband probe baseband signal, denotes the pulse width of the single-pulse narrowband probe signal transmitted by the transmitting station, denotes a rectangular function.

[0145] Step S22, establishing a wideband cover signal model;

[0146] Suppose that the single-pulse wideband cover signal transmitted by the transmitting station 2 is denoted as:

[0147] (3)

[0148] wherein, denotes the carrier frequency of the signal, denotes the wideband cover phase-coded baseband signal, specifically,

[0149] (4)

[0150] wherein, denotes the phase of the first chip of the wideband cover baseband signal, denotes the number of chips of the wideband cover baseband signal, denotes the time width of one chip of the wideband cover baseband signal. Step S23, establishing a narrowband decoy signal model;

[0151] Suppose that the single-pulse narrowband decoy signal transmitted by the transmitting station 3 is

[0152] denoted as:

[0153] (5)

[0154] wherein, denotes the carrier frequency of the signal, denotes the frequency offset of the signal, denotes the wideband cover phase-coded baseband signal, specifically,

[0155] (6)

[0156] wherein, the narrowband decoy signal bandwidth is selected to be consistent with the narrowband probe signal bandwidth and pulse width, and the number of chips and the chip width are consistent, denotes the phase of the first chip of the narrowband decoy baseband signal. The narrowband decoy signal only plays a decoy role and is not designed separately, and the spectral coordination characteristics are maintained.

[0157] ​​In the embodiment, the step S3 is specifically as follows:

[0158] The step S31 is to establish a narrow-band probe signal optimization model.

[0159] Considering that the narrow-band probe signal satisfies good autocorrelation characteristics, the narrow-band probe phase encoding baseband signal is discretely represented as:

[0160] (7)

[0161] wherein, represents the kth point of the discrete narrow-band probe phase encoding baseband signal , and represents a transposition operation of a vector. Considering that the autocorrelation peak side lobe level is minimized, a constant modulus constraint is added, and the narrow-band probe signal optimization model can be specifically represented as:

[0162] (8)

[0163] wherein, represents a modulo operation, represents a maximum value operation, represents a minimum value operation, represents a peak value limiting range of an autocorrelation function, represents the non-periodic autocorrelation function of the kth point of , and is represented as:

[0164] (9) wherein,

[0165] represents the kth point of , represents the kth point of , and represents a conjugate of a complex number. According to a peak amplitude transformation principle, the objective function of the optimization problem is represented as an -norm problem:

[0166] (10)

[0167] wherein, represents an -norm. The narrow-band probe signal optimization model can be approximated as:

[0168] (11)

[0169] (12)

[0170] ​​​Step S32, a wideband cover signal optimization model is established;

[0171] The wideband cover signal needs to design a spectrum template, and the wideband cover signal is obtained according to the set template. The wideband cover phase coding baseband signal The discrete representation is:

[0172] (12)

[0173] wherein, represents the kth point of the discrete wideband cover phase coding baseband signal , The point Fourier transform spectrum representation of is:

[0174] (13)

[0175] wherein, , represents a complex vector of dimension , represents the Fourier transform point number, represents the conjugate transpose operation of the matrix, represents the inverse Fourier transform matrix, represents the kth column vector of the inverse Fourier transform matrix, represents the zero-padded signal of the discrete wideband cover phase coding baseband signal, represents a 0 vector of dimension . Considering the constant modulus constraint, the wideband cover signal optimization problem model is represented as:

[0176]

[0177] (14) wherein,

[0178] represents the spectrum range that needs to be limited to ensure the frequency domain coordination performance, represents an auxiliary variable vector, represents the kth point of the auxiliary variable vector , represents the expected spectrum shape of the wideband cover signal, represents the 2-norm. In this embodiment, the step S4 is specifically as follows:

[0179] Step S41, a narrowband probe signal optimization problem is solved by using a proximal multiplier algorithm based on optimization minimization;

[0180] Step S41, a narrowband probe signal optimization problem is solved by using a proximal multiplier algorithm based on optimization minimization;

[0181] ​​Equation (11) is decomposed into easily solvable sub-optimization problems using the near-end multiplier algorithm based on optimization minimization, and then iteratively computed in parallel. The norm problem is transformed into a quadratic function optimization problem using the optimization minimization approximation principle.

[0182] The autocorrelation function is expressed using the Fast Fourier Transform (FFT) and the Inverse Fast Fourier Transform (IFFT):

[0183] (15)

[0184] in, The autocorrelation function of a sequence. This represents the discrete narrowband probe phase-coded baseband signal. The signal to fill in zeros, express A zero-dimensional vector If the Hadamard product is represented, then equation (11) can be expressed as:

[0185] (16)

[0186] The proximal augmented Lagrangian function is expressed as:

[0187] (17)

[0188] in, Denotes the proximal augmented Lagrangian function. Indicates the proximal parameter, Indicates the penalty parameter. Represents the extended dual variable. Indicates the first The iteration yielded The result.

[0189] like Figure 3 As shown, the solution process based on the proximal multiplier algorithm with auxiliary variables and optimization minimization is as follows:

[0190] Step S411, let and initialize ;

[0191] in, Indicates the first The sequence of iterations , Indicates the first The autocorrelation function of the next iteration , Indicates the first Sequence spectrum of the next iteration , denotes the extension dual variable of the next iteration . When , the above parameters are initialized.

[0192] Step S412, let ;

[0193] Step S413, fix , solve ;

[0194] (18)

[0195] where arg denotes the value of at the minimum, i.e.:

[0196] (19)

[0197] Let , , then the above formula can be expressed as:

[0198] (20)

[0199] where is a calculation auxiliary variable defined for solving formula (19), denotes taking the real part of the elements of the vector, and for the first added item, the equivalent problem is obtained:

[0200] (21)

[0201] where denotes the element of in the iteration, denotes the element of in the iteration, denotes the column vector of the inverse Fourier transform matrix, denotes the conjugate transpose of , and simultaneously denotes the column vector of the Fourier transform matrix.

[0202] Because:

[0203] (22) ​​

[0204] get:

[0205] (twenty three)

[0206] in, The auxiliary variables for calculation defined in the simplified formula (22), To express the phase angle calculation operation, equation (20) is optimized as follows:

[0207] (twenty four)

[0208] in, Expanding and deleting irrelevant items yields:

[0209] (25)

[0210] The sum of the first and second additions is:

[0211] (26)

[0212] in, The auxiliary variables defined for solving equation (24) This refers to a vector whose elements are all 1s. The third and fourth added terms are:

[0213] (27)

[0214] make Then equation (25) can be expressed as:

[0215] (28)

[0216] Adding a constant does not affect the optimization result, resulting in:

[0217] (29)

[0218] Equation (19) can be rewritten as:

[0219] (30)

[0220] The above equation is equivalent to:

[0221] (31)

[0222] in,

[0223] (32)

[0224] And because , To represent the identity matrix, therefore:

[0225] (33)

[0226] get :

[0227] (34)

[0228] Step S414, Fix Solve ;

[0229] At this point, the Lagrange function is:

[0230] (35)

[0231] Combining the principle of optimization and minimization, Convert to about The optimization problem of the upper bound of a quadratic function:

[0232] (36)

[0233] in, , , , ,about The sub-optimization problem is simplified to:

[0234] (37)

[0235] in,

[0236] (38)

[0237] (39)

[0238] (40)

[0239] in, To solve Defined auxiliary variables, They represent the first In the next iteration The Each element.

[0240] get :

[0241] (41)

[0242] Step S415, Fix Solve ;

[0243] about The sub-optimization problem can be simplified to:

[0244] (42)

[0245] in,

[0246] (43)

[0247] (44)

[0248] get :

[0249] (45)

[0250] Step S416, Fix Solve ;

[0251] (46)

[0252] (47)

[0253] Step S417: Determine whether to stop settlement;

[0254] The stopping condition is:

[0255] (48)

[0256] in, This indicates the residual at which calculations cease. Indicates the first The residual from this calculation is expressed as:

[0257] (49)

[0258] (50)

[0259] in, It represents the infinite norm. This represents the maximum number of iterations for the proximal multiplier algorithm based on optimization minimization.

[0260] If the current calculated value meets the condition, then stop the calculation to obtain the narrowband detection signal. Otherwise, return to step S412.

[0261] Step S42: Solve the broadband cover signal optimization problem using the spectrum shaping algorithm;

[0262] Equation (14) is the problem model of the spectrum shaping algorithm under constant modulus constraint. When only the intrapulse spectrum shape needs to be optimized, the spectrum shaping algorithm can be used to solve it. The following minimization problem is introduced:

[0263] (51)

[0264] in, Represents the scalar factor interpretation sequence Any possible energy mismatch and / or constant phase shift between the spectrum and the target spectrum. Represents the envelope constraint on a time-domain sequence. and This represents the upper and lower boundary functions for sampling on the spectrum. Representing auxiliary variables The One element, The first envelope constraint represents the first... One element, Denotes the first boundary function of the upper boundary. One element, Describes the first boundary function of the lower boundary. Each element.

[0265] like Figure 4 As shown, with the introduction of auxiliary variables, the specific solution process of the spectrum shaping algorithm is as follows:

[0266] Step S421, let ,initialization , satisfy Initialize temporary variables and ;

[0267] in, Indicates the first The iteration yielded The value, Indicates the first The discrete broadband shielding baseband signal obtained in the second iteration The value, Indicates the first Auxiliary variables obtained in the next iteration The value of .

[0268] Step S422, let ;

[0269] Step S423, Fix Solve ;

[0270] make This is considered as one cycle:

[0271] like Then let If so, then let In other cases, . Temporary variables The Each element.

[0272] Step S424, Fix Solve ;

[0273] (52)

[0274] Step S425, Fix Solve ;

[0275] make This is considered as one cycle:

[0276] Introduction As an intermediate calculation variable, if ,but ,otherwise . Indicates intermediate calculation variables The Each element.

[0277] Step S426, Update ;

[0278] Step S427: Determine whether to stop the calculation;

[0279] The stopping condition is:

[0280] (53)

[0281] in, This represents the maximum number of iterations set by the spectrum shaping algorithm. If the current calculated value meets the condition, the calculation stops to obtain the broadband masking signal. Otherwise, return to step S422.

[0282] In this embodiment, in step S5, the number of pulses within a coherent processing interval (CPI) is known to be... Transmitting station 1 transmits an optimized narrowband detection signal, transmitting station 2 transmits an optimized broadband cover signal, and transmitting station 3 transmits a narrowband decoy signal. These signals are transmitted simultaneously and in the same direction via the control center. The specific signal transmission method is as follows: Figure 5 As shown, where, This indicates a narrowband detection signal transmitted from launch site 1. This indicates the broadband cover signal transmitted from transmission site 2. This indicates a narrowband decoy signal transmitted from launch site 3. This indicates that three transmitting sites are coordinating to transmit signals.

[0283] In this embodiment, in step S6, the receiving station filters the received echo signal through a matched filter of the narrowband probe signal, then performs coherent accumulation and outputs the result. The specific processing flow is as follows: Figure 6 As shown.

[0284] The present invention also provides another embodiment, which verifies and analyzes the method of the present invention through simulation:

[0285] The detection performance of conventional single-transmit single-receive mode and MIMO (Multiple-Input-Multiple-Output) mode is compared with that of the cooperative mode of the present invention under jamming suppression.

[0286] The number of chips designed is Narrowband radar signals, , , , , , , carrier frequency Pulse duration The pulse repetition time (PRT) is... The number of pulses within one coherent processing interval (CPI) is Narrowband detection signal amplitude Broadband shielding signal amplitude Narrowband decoy signal amplitude Narrowband detection signal bandwidth Broadband protection signal bandwidth Narrowband decoy signal bandwidth Sampling rate .

[0287] The coordinates of the three launch sites are The coordinates of the receiving station are The target coordinates in the environment are The target's horizontal speed is The signal-to-noise ratio of the narrowband detection signal at the receiving end The interference is randomly modulated FM noise, with an interference-to-noise ratio of [insert value here]. .

[0288] like Figure 7As shown, the autocorrelation function graph of the probe signal and the spectrum graph of the cooperative signal in this embodiment are obtained from... Figure 7 (a) The autocorrelation function results of the narrowband detection signal show that the normalized level of the autocorrelation sidelobe region of the optimized narrowband detection signal is very low, indicating good target detection performance; while from Figure 7 (b) The spectral results of the coordinated transmission signal show that the spectrum of the narrowband detection signal is masked within the groove of the broadband signal spectrum, while the coordinated signal is within the spectral range. The inner band is relatively flat and has low interception characteristics, which provides a protective effect. The narrowband decoy spectrum on the left side has a higher amplitude than the flat broadband spectrum, which attracts the attention of the adversary jammer and plays a deceptive role. This achieves the function of the broadband cover signal of the transmitting site effectively covering the narrowband detection signal and deceiving the adversary jammer.

[0289] like Figure 8 As shown in the figure, the RD results of the simulation of single-transmit single-receive mode and MIMO mode under suppressed interference in this embodiment are as follows: Figure 8 (a) RD (Range-Doppler) results for single-transmitter / single-receiver mode under suppressed interference and Figure 8 (b) The RD results for MIMO mode show that, under suppression and interference, both the conventional single-transmit / single-receive mode and MIMO mode fail to detect target information, resulting in severe interference; Figure 9 As shown in the figure, the RD results and detection results of the simulated cooperative mode under suppressed interference in this embodiment are displayed. Figure 9 (a) RD results of cooperative mode under suppressed interference and Figure 9 (b) The detection results of the cooperative mode indicate that the jammer's analysis of the cooperative signal characteristics is subject to our active interference. It cannot identify the frequency and bandwidth of the narrowband detection signal and is deceived by false narrowband spectra, resulting in erroneous interference. In this case, the echo, after signal processing, can still detect the target's state information, and the target information is synthesized as follows:

[0290] (54)

[0291] The results are largely consistent with the simulation results, verifying the effectiveness of the spatial frequency code domain signal in coordinating against suppression interference.

[0292] In summary, the method of this invention considers a long-baseline, separately deployed transmission and reception stations. In this configuration, the adversary jammer targets the transmitted beam to transmit jamming signals. The energy of the jamming signal received by the receiving station is the sidelobe energy of the jamming beam, thus providing an initial reduction in jamming energy. This invention's method studies a space-frequency code domain cooperative anti-jamming strategy, establishes an optimization problem model, and utilizes the cooperative masking and deception effects of the optimized transmitted signals in the frequency domain to influence the form of jamming generated by the jammer, reducing the jamming energy received by the actual detection signal and thus achieving anti-suppression jamming. Furthermore, it incorporates constant modulus constraints beneficial to hardware compatibility, studies near-end multiplier algorithms and spectrum shaping algorithms based on optimization minimization to solve the optimization problem, obtains the transmitted signals of each station, and suppresses suppression jamming by controlling the transmitted signals of each station and the received signals of the separately deployed receiving stations.

Claims

1. A method for resisting suppression interference using space-frequency codes of multiple radar signals with separate long-baseline transceiver locations, the specific steps of which are as follows: Step S1: Formulate a space-frequency code domain collaborative anti-interference strategy; Step S2: Establish the transmission signal model of each transmitting site according to the space-frequency code domain collaborative anti-interference strategy; Step S3: Based on the model established in step S2, establish an optimization problem model; Step S4: Solve the problem using an optimization algorithm to obtain the transmitted signals from each transmitting station; Step S5: Transmitting station 1 transmits an optimized narrowband detection signal, transmitting station 2 transmits an optimized broadband cover signal, and transmitting station 3 transmits a narrowband decoy signal. Step S6: Process the radar received echo signal at the receiving station using a matched filter; In step S1, the specific anti-interference strategy of the space-frequency code domain is as follows: The system controls three separate transmitting stations to simultaneously transmit in the same direction, while a receiving station receives the echo signal reflected from the target. The transmitting and receiving stations are located on a long baseline. in, Transmitting station 1 transmits a narrowband detection signal, transmitting station 2 transmits a broadband cover signal, and transmitting station 3 transmits a narrowband decoy signal.

2. The method for resisting suppression interference by long-baseline transceiver-multiple radar signal space-frequency code coordination according to claim 1, characterized in that, Step S2 is as follows: Step S21: Establish a narrowband detection signal model; Suppose that the single-pulse narrowband detection signal is transmitted from transmitting site 1. Represented as: （1）； in, Indicates the carrier frequency of the signal. Indicates the frequency offset of the signal. , Indicates time, This refers to the narrowband probe phase-coded baseband signal, specifically: （2）； in, Indicates the narrowband detection baseband signal of the first Phase of each chip, Indicates the number of chips in the narrowband detection baseband signal. This indicates the time width of one chip of the narrowband detection baseband signal. This indicates the pulse width of the single-pulse narrowband detection signal transmitted by the transmitting site. Represents a rectangular function; Step S22: Establish a broadband cover signal model; Assume that the single-pulse broadband cover signal transmitted from transmitting site 2 is... Represented as: （3）； in, Indicates the carrier frequency of the signal. This refers to the broadband masking phase-coded baseband signal, specifically: （4）； in, Indicates the broadband cover baseband signal. Phase of each chip, Indicates the number of baseband signal chips for broadband protection. This represents the time width of one chip of the broadband shielding baseband signal; Step S23: Establish a narrowband decoy signal model; Suppose that the single-pulse narrowband decoy signal is transmitted from transmitting site 3. Represented as: （5）； in, Indicates the carrier frequency of the signal. Indicates the frequency offset of the signal. This refers to the broadband masking phase-coded baseband signal, specifically: （6）； The narrowband decoy signal bandwidth is selected to be consistent with the narrowband detection signal bandwidth and pulse width, and its number of chips and chip width are also consistent. This indicates the narrowband decoy baseband signal. The phase of each chip.

3. The method for resisting suppression interference by long-baseline transceiver-multiple radar signal space-frequency code coordination according to claim 2, characterized in that, Step S3 is as follows: Step S31: Establish a narrowband detection signal optimization model; Narrowband detection phase-coded baseband signal Discrete representation is: （7）； in, Represents discrete narrowband probe phase-coded baseband signal The One point, , The transpose operation of the vector is represented by the following: considering minimizing the autocorrelation peak sidelobe level and incorporating constant mode constraints, the narrowband detection signal optimization model is specifically expressed as follows: （8）； in, This indicates a modulo operation. This indicates the operation of retrieving the maximum value. This indicates the operation of finding the minimum value. This indicates the peak limit range of the autocorrelation function. express The nonperiodic autocorrelation function A point, represented as: （9）； in, express The One point, express The One point, Indicates the conjugate of a complex number; Based on the principle of peak amplitude transformation, the objective function of the optimization problem is expressed as... - Norm problem: （10）； in, express -norm; the narrowband detection signal optimization model can be approximated as: （11）； Step S32: Establish a broadband cover signal optimization model; Broadband cover phase-coded baseband signal Discrete representation is: （12）； in, Represents discrete broadband masking phase-coded baseband signal The One point, , of The point Fourier transform spectrum is represented as: （13）； in, , , express A complex vector of dimension 1 Indicates the number of points in the Fourier transform. This represents the conjugate transpose operation of a matrix. Represents the inverse Fourier transform matrix. The fourth element of the inverse Fourier transform matrix represents the... column vectors, This represents the signal that padded with zeros for discrete broadband masking phase-coded baseband signals. express A zero-dimensional vector; Considering constant modulus constraints, the broadband cover signal optimization problem can be modeled as follows: （14）； in, This indicates the frequency range that needs to be limited to ensure frequency domain coherence performance. Represents an auxiliary variable vector. Represents the auxiliary variable vector The One point, This represents the desired spectral shape of the broadband cover signal. It represents the 2-norm.

4. The method for resisting suppression interference by long-baseline transceiver-multiple radar signal space-frequency code coordination according to claim 3, characterized in that, Step S4 is as follows: Step S41: Solve the narrowband detection signal optimization problem using the near-end multiplier algorithm based on optimization minimization; Equation (11) is decomposed into easily solvable sub-optimization problems using the near-end multiplier algorithm based on optimization minimization, and parallel iterative calculations are performed. The norm problem is transformed into a quadratic function optimization problem for solution using the optimization minimization approximation principle. The autocorrelation function is expressed using the Fast Fourier Transform and Inverse Fast Fourier Transform as follows: （15）； in, The autocorrelation function of a sequence. This represents the discrete narrowband probe phase-coded baseband signal. The signal to fill in zeros, express A zero-dimensional vector If the Hadamard product is represented, then equation (11) can be expressed as: （16）； The proximal augmented Lagrangian function is expressed as: （17）； in, Denotes the proximal augmented Lagrangian function. Indicates the proximal parameter, Indicates the penalty parameter. Represents the extended dual variable. Indicates the first The iteration yielded The result; Introducing auxiliary variables, the specific solution process based on the proximal multiplier algorithm for optimization minimization is as follows: Step S411, let and initialize ; in, Indicates the first The sequence of iterations , Indicates the first The autocorrelation function of the next iteration , Indicates the first The sequence spectrum of the next iteration , Indicates the first The extended dual variable of the next iteration ;when When the time comes, assign initial values ​​to the above parameters; Step S412, let ; Step S413, Fix Solve ; （18）； Where arg represents satisfying Take the minimum value The value as The value of, that is: （19）； Step S414, Fix Solve ; Will Convert to about The optimization problem of the upper bound of a quadratic function: （20）； in, , , , ; Step S415, Fix Solve ; about The sub-optimization problem is simplified to: （21）； in, （22）； （23）； in, This represents a vector whose elements are all 1s. This indicates the operation of taking the real part of the vector element by element. This indicates the phase angle calculation operation. express The The result of the next iteration; Step S416, Fix Solve ; （24）； （25）； Step S417: Determine whether to stop settlement; The stopping condition is: （26）； in, This indicates the residual at which calculations cease. Indicates the first The residual from this calculation is expressed as: （27）； （28）； in, Represents the infinite norm; This represents the maximum number of iterations for the proximal multiplier algorithm based on optimization minimization; If the current calculated value meets the condition, then stop the calculation to obtain the narrowband detection signal. Otherwise, return to step S412; Step S42: Solve the broadband cover signal optimization problem using the spectrum shaping algorithm; Equation (14) is the problem model of the spectrum shaping algorithm under constant modulus constraint. When only the intrapulse spectrum shape is optimized, the spectrum shaping algorithm can be used to solve it. The following minimization problem is introduced: （29）； in, Represents the scalar factor interpretation sequence Any possible energy mismatch and / or constant phase shift between the spectrum; Represents the envelope constraint on a time-domain sequence. and Represents the upper and lower boundary functions for sampling on the spectrum; Representing auxiliary variables The One element, The first envelope constraint represents the first... One element, Denotes the first boundary function of the upper boundary. One element, Describes the first boundary function of the lower boundary. One element; Introducing auxiliary variables, the specific solution process of the spectrum shaping algorithm is as follows: Step S421, let ,initialization , satisfy Initialize temporary variables and ; in, Indicates the first The iteration yielded The value, Indicates the first The discrete broadband shielding baseband signal obtained in the second iteration The value, Indicates the first Auxiliary variables obtained in the next iteration The value; Step S422, let ; Step S423, Fix Solve ; make This is considered as one cycle: like Then let If so, then let In other cases, ; Temporary variables The One element; Step S424, Fix Solve ; （30）； Step S425, Fix Solve ; make This is considered as one cycle: Introduction As an intermediate calculation variable, if ,but ,otherwise ; Indicates intermediate calculation variables The One element; Step S426, Update ; Step S427: Determine whether to stop the calculation; The stopping condition is: （31）； in, This represents the maximum number of iterations set by the spectrum shaping algorithm; if the current calculated value meets the condition, the calculation stops to obtain the broadband cover signal. Otherwise, return to step S422.

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