Online Design Method for Radar Anti-Sorting Waveforms Based on Communication Simulation

Abstract

This invention discloses an online design method for radar anti-sorting waveforms based on communication simulation, mainly addressing the problems of high computational load and long optimization time in existing anti-sorting waveform design technologies. The implementation scheme is as follows: Input a transmission matrix and assume that a phase perturbation is applied to it; determine the anti-sorting direction based on prior information, and construct a perturbation angular domain signal from this assumption and the anti-sorting direction; simulate the perturbation angular domain signal as a communication signal, making the perturbation angular domain signal equal to the communication signal to be simulated; solve for the phase perturbation vector based on whether the magnitude of the communication signal to be simulated is fixed; construct a phase perturbation matrix based on the solved phase perturbation vector; add the phase of the phase perturbation matrix to the phase of the input transmission matrix to obtain the radar anti-sorting waveform. This invention reduces computational load, shortens optimization time, and improves the anti-sorting performance of the waveform, meeting the requirements for online design of anti-sorting waveforms and applicable to centralized MIMO radar waveform optimization.

Description

Technical Field

[0001] This invention belongs to the field of radar waveform acquisition technology and relates to an online design method for anti-sorting waveforms, which can be used for centralized MIMO radar waveform optimization. Background Technology

[0002] Based on the distance between antennas, multiple-input multiple-output (MIMO) radars can be divided into two types: distributed MIMO radars and centralized MIMO radars. The radar waveform is the carrier of target and environmental information, therefore it plays a crucial role in both types of radars. In MIMO radar systems, the transmitted waveforms are typically orthogonal to improve the correlation between signals transmitted from different radar antennas. Furthermore, since the power amplifiers at the radar antenna transmitters usually operate in saturation mode, the transmitted waveforms typically exhibit constant-mode characteristics. Compared to distributed MIMO radars, centralized MIMO radars, after coherent synthesis at far-field targets, will result in transmitted waveforms with different spatial characteristics, and the magnitude is usually no longer constant.

[0003] MIMO radar systems typically transmit phase-coded signals. Most existing MIMO radar waveform design methods use the phase of the transmitted signal as a variable, designing corresponding optimization criteria based on specific requirements. Existing optimization criteria include, but are not limited to, designing the desired transmit pattern, reducing signal cross-correlation and autocorrelation, and designing wide pulse compression main lobe waveforms. For example, in 2012, Wang YC et al. published a paper titled "On the Design of Constant Modulus Probing Signals for MIMO Radar" in IEEE Transactions on Signal Processing, which disclosed a centralized MIMO radar waveform optimization method. This method's optimization criteria consider both the transmit pattern and the integrated sidelobe level of the angular domain signal.

[0004] One existing approach to radar anti-sorting waveform design is to disguise radar communication as a communication signal, making it difficult for enemy electronic reconnaissance and electronic support equipment to sort and identify the waveform. For example, in a 2019 paper titled "Joint Radar-Communications Co-Use Waveform Design Using Optimized Phase Perturbation" published in IEEE Transactions on Aerospace and Electronic Systems, Shenghua Zhou et al. disclosed an integrated radar-communication method that applies phase jitter to the communication signal and compresses the autocorrelation sidelobes to give the communication signal radar functionality.

[0005] The two algorithms mentioned above have a large computational load and a long optimization time due to the non-convexity of constant modulus, making it difficult to meet the needs of online design of anti-sorting waveforms in the rapidly changing modern battlefield. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the existing technology by proposing an online design method for radar anti-sorting waveforms based on communication simulation, so as to reduce the amount of computation in the optimization design process and shorten the optimization time.

[0007] The technical idea of ​​this invention is to apply a small phase perturbation to the existing transmitted waveform to simulate the radar signal as a communication signal and construct an optimization criterion; by transforming the optimization criterion into a quadratic programming problem or making the problem obtain an explicit solution, the online design of the anti-sorting waveform of the centralized MIMO radar is realized.

[0008] Based on the above ideas, the technical solution of the present invention includes the following implementation steps:

[0009] 1. An online design method for radar anti-sorting waveforms based on communication simulation, characterized by comprising the following steps:

[0010] (1) Input the transmission matrix S of the centralized MIMO radar, determine the anti-sorting direction α based on prior information, assume that a small phase perturbation Φ is applied to the transmission matrix S, and construct the perturbation angular domain signal x of the i-th row of the perturbation matrix based on this assumption and the anti-sorting direction. i ;

[0011] (2) The perturbation angular domain signal x i The analog signal is a communication signal, and the desired angular domain signal d is constructed from the magnitude and phase information of the communication signal. i ;

[0012] (3) Let the perturbation angular domain signal x i With the desired angular domain signal d i Equal to solve for the phase perturbation vector under the condition that the magnitude of the desired angular domain signal is fixed. Phase perturbation vector under the condition that the magnitude of the desired angular domain signal is not fixed

[0013] (4) Iterate through all rows of the transmission matrix using the above process, and construct the phase perturbation matrix Φ based on the magnitude property of the desired angular domain signal:

[0014] If the magnitude is fixed, then the phase perturbation vector with a fixed magnitude... This constitutes the phase perturbation matrix Φ;

[0015] If the magnitude is not fixed, then the phase perturbation vector with a non-fixed magnitude... This constitutes the phase perturbation matrix Φ;

[0016] (5) Construct the anti-sorting waveform S of the centralized MIMO radar from the phase perturbation matrix Φ and the phase Θ of the transmission matrix S. t :

[0017] (5a) Add the phase perturbation matrix Φ to the phase Θ of the transmission matrix to obtain the final phase matrix Φ. t ;

[0018] (5b) The final phase matrix Φ t The input is fed into the transmitter of the centralized MIMO radar and transmitted into the air, resulting in the centralized MIMO radar anti-sorting waveform S. t .

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] 1. This invention improves the anti-sorting performance of the waveform by simulating the angular domain signal of the centralized MIMO radar in the anti-sorting direction as a communication signal, causing the sorting and identification equipment in that direction to mistake the radar signal for a communication signal.

[0021] 2. By applying a small phase perturbation matrix to the transmission phase matrix, the present invention maintains the performance of the original waveform essentially unchanged.

[0022] 3. This invention reduces the computational burden of optimization problems by transforming the solution of the phase perturbation matrix into the solution of the phase perturbation vector, and by converting the optimization criteria in the process of solving the phase perturbation vector into a simpler form, thus enabling online waveform design. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0024] Figure 2 This is the waveform diagram of the centralized MIMO radar transmission matrix input in this invention;

[0025] Figure 3 The waveform diagram of the anti-sorting signal with fixed magnitude and random phase in the desired angular domain is simulated using the present invention.

[0026] Figure 4 This is an anti-sorting waveform diagram with non-fixed magnitude and random phase of the desired angular domain signal according to the present invention;

[0027] Figure 5 This is a waveform diagram of an anti-sorting signal with fixed magnitude and phase in the desired angular domain, simulated using the present invention.

[0028] Figure 6 This is a waveform diagram of an anti-sorting angular domain signal with a non-fixed magnitude and a fixed phase, simulated using the present invention.

[0029] Figure 7 This is an anti-sorting waveform diagram with a desired angular domain signal magnitude of zero, simulated using the present invention. Detailed Implementation

[0030] The embodiments and effects of the present invention will be described in detail below with reference to the accompanying drawings:

[0031] Reference Figure 1 The specific implementation steps of this embodiment are as follows:

[0032] Step 1: Input the emission matrix S.

[0033] The emission matrix is ​​usually a pre-designed emission matrix with a desired emission pattern and good correlation, such as... Figure 2 As shown, where Figure 2 (a) is the emission pattern of the emission matrix. Figure 2 (b) is a graph showing the autocorrelation results of the angular domain signal of the emission matrix. Figure 2 (c) is a diagram showing the cross-correlation results of the angular domain signals of the transmission matrix.

[0034] The antenna arrangement of the transmission matrix S is a uniform linear array, and its expression is:

[0035]

[0036] Where e represents the base of the natural logarithm, and j represents the imaginary unit. Let S be the phase of the emission matrix S. Represents the real number field, N t N represents the number of centralized MIMO radar antennas. s This indicates the number of chips transmitted by each antenna. This represents the vector consisting of the elements of the i-th row of the emission matrix, where i = 1, 2, ..., N. s ,(·) T Indicates transpose. Represents the field of complex numbers;

[0037] Since the power amplifier at the radar transmitter typically operates in saturation mode, the transmitted signal exhibits constant-mode characteristics. Therefore, the transmission matrix can be written as:

[0038]

[0039] in It represents the constant modulus space, meaning that the elements in the emission matrix, in addition to belonging to the complex field, also possess constant modulus properties.

[0040] Step 2: Set the expression for applying phase perturbation to the i-th row of the transmission matrix.

[0041] Since the transmission matrix is ​​usually a pre-designed transmission matrix, it generally does not have anti-sorting capabilities. Therefore, it is necessary to apply a phase perturbation to the input transmission matrix to enable it to have anti-sorting capabilities while maintaining its original performance. To keep the performance of the input transmission matrix essentially unchanged, the phase perturbation should be as small as possible.

[0042] The emission matrix after applying phase perturbation in this example design is represented as follows:

[0043]

[0044] in The i-th row of the perturbated matrix This represents the i-th row of the input emission matrix. i The phase satisfies Let represent the phase perturbation vector, and diag(·) represent a diagonal matrix with (·) as its diagonal elements.

[0045] Step 3: Construct the perturbation angular domain signal.

[0046] The perturbation matrix synthesizes different signals in different directions in space. The signal synthesized by the perturbation matrix in the anti-sorting direction is called the perturbation angular domain signal. By simulating the perturbation angular domain signal as a communication signal, the waveform anti-sorting function can be improved. Therefore, the perturbation angular domain signal must first be constructed, as detailed below:

[0047] Since the perturbation angular domain signal is a function of the anti-sorting direction, the anti-sorting direction located in the sidelobe region of the transmission pattern can be determined based on prior information. Where α k This represents the k-th anti-sorting direction, where k = 1, 2, ..., N. e N e Indicates the number of anti-sorting directions.

[0048] Construct the launch guidance matrix A based on the anti-sorting direction. t :

[0049]

[0050] in f represents the emission steering vector for the k-th anti-sorting direction. k =dsin(α) k ) / λ represents the direction α k The normalized angular frequency, where d represents the antenna spacing and λ represents the wavelength, and when the spacing between adjacent antennas is half the wavelength, f k =0.5sin(α) k )∈[-0.5,0.5];

[0051] By the launch guidance matrix At The perturbation angular domain signal x is calculated. i :

[0052]

[0053] in This represents the undisturbed angular domain signal;

[0054] When the disturbance vector When each element in the matrix approaches zero, the following relationship holds:

[0055]

[0056] in Indicates a dimension of N t A vector of all 1s;

[0057] Substituting the above approximation into the perturbation angular domain signal x i From the expression, the final expression for the perturbation angular domain signal is obtained as follows:

[0058]

[0059] in V represents i The elements in each row of the table.

[0060] Step 4: Construct the desired angular domain signal.

[0061] The perturbation angular domain signal is simulated as a communication signal, and this communication signal is referred to as the desired angular domain signal. The construction steps are as follows:

[0062] 4.1) Let the magnitude of the desired angular domain signal be... Where p in This represents the magnitude of the desired angular domain signal in the nth direction, where n = 1, 2, ..., N. e ;

[0063] The magnitude of the desired angular domain signal includes both fixed and non-fixed values. The non-fixed magnitude can achieve better optimization results through more variables. Therefore, the lower bound vector I of the magnitude of the desired angular domain signal is... i And the upper bound vector of the modulus u i They are defined as follows:

[0064]

[0065]

[0066] Among them l in and u in Let l represent the lower and upper bounds of the expected angular domain signal magnitude in the nth direction, respectively, and have the following relationship: in ≤pin ≤u in ;

[0067] 4.2) Let a i and b i Phase information used to represent the desired angular domain signal. in Let be the symbol set corresponding to the real part of the desired angular domain signal. Let be the symbol set corresponding to the imaginary part of the desired angular domain signal, when and When the desired angular domain signal has a phase of 0 or π, it simulates a binary phase-coded signal; when When the phase of the desired angular domain signal is ±π / 4 or ±3π / 4, the desired angular domain signal simulates a four-phase coded signal.

[0068] 4.3) Combine the magnitude and phase information of the desired angular domain signal into the desired angular domain signal d. i :

[0069] d i =p i ⊙(a i +jb i )

[0070] Where ⊙ represents the Hadamard product.

[0071] 4.4) Based on the desired angular domain signal p i a i and b i Different values ​​of achieve different functions of the disturbance waveform:

[0072] when a i and b i When the value is random, the desired angular domain signal simulates the communication signal, and the perturbation waveform can achieve anti-sorting function;

[0073] when a i and b i As a fixed value, the desired angular domain signal simulates a fixed communication sequence, and the perturbation waveform can realize the integrated radar and communication function on the basis of achieving anti-sorting function;

[0074] When p i When = 0, the expected angular domain signal magnitude is zero, and the disturbance waveform can achieve anti-sorting function through stealth.

[0075] Step 5: Based on the constructed perturbation angular domain signal and the desired angular domain signal, solve for the phase perturbation vector of the desired angular domain signal under the condition of fixed magnitude.

[0076] This step of solving for the phase perturbation vector is a traversal loop process, implemented as follows:

[0077] 5.1) Initialize the current loop count l = 1, and the optimal phase jitter vector. Minimum objective function value Calculate the maximum number of iterations L:

[0078]

[0079] Where N1 represents the symbol set corresponding to the real part of the desired angular domain signal. The number of elements in the set, N2, represents the symbol set corresponding to the imaginary part of the expected angular domain signal. The number of elements in the middle;

[0080] 5.2) Traversing the real part a of the desired angular domain signal i and the imaginary part b of the expected angular domain signal i The value a is obtained from the l-th iteration. il and b il ;

[0081] 5.3) Solve for the phase jitter vector during the l-th traversal.

[0082] 5.3.1) Optimization criteria under the condition of fixed magnitude of desired angular domain signal:

[0083] The optimization criteria for this example are based on the following three considerations:

[0084] To minimize the phase perturbation, this example uses minimizing the L2 norm of the phase perturbation vector as the optimization criterion.

[0085] The equality constraint in this example is to make the perturbation angular domain signal constructed in step three equal to the desired angular domain signal constructed in step four.

[0086] To maintain the anti-sorting waveform in this example as a constant-mode waveform, the phase perturbation vector should be a real vector.

[0087] Taking into account the above three points, the following optimization criteria are constructed:

[0088]

[0089] 5.3.2) Simplification and Optimization Criteria:

[0090] Substituting the perturbation angular domain signal constructed in step three and the desired angular domain signal constructed in step four into the equality constraints in the optimization criterion yields the following equation:

[0091]

[0092] Considering that the phase perturbation vector in this invention should be a real vector, the equation is divided into real and imaginary parts to obtain the following set of equations:

[0093]

[0094]

[0095] Where Re(·) represents taking the real part of a vector or matrix, and Im(·) represents taking the imaginary part of a vector or matrix;

[0096] Combine the matrix components of the above system of equations to form a new matrix G. i The vector parts form a new vector g. il The fraction is represented in the following form:

[0097]

[0098]

[0099] The new matrix G i and the new vector g il Substituting the equality constraints and variable constraints from the optimization criteria, we obtain the simplified constraints:

[0100]

[0101] Based on the simplified constraints, the optimization criterion is simplified to:

[0102]

[0103] 5.3.3) Solve the simplified optimization criterion to obtain the phase perturbation vector.

[0104] The equality constraint in the simplified optimization criterion is a system of linear equations, and the objective function is the L2 norm of the phase perturbation vector. Therefore, the solution to this optimization criterion can be directly expressed by the generalized inverse of the matrix as follows:

[0105]

[0106] Where ||·||2 represents the 2-norm of the vector, Represents the Moore-Penrose inverse of a matrix;

[0107] 5.4) By phase perturbation vector Calculate the objective function value during the l-th traversal. And determine the objective function value With minimum objective function value Size:

[0108] like Then let

[0109] Otherwise, proceed to step 5.5);

[0110] 5.5) Update the loop count l, let l = l + 1, and check if the loop count exceeds the maximum value:

[0111] If l > L, terminate the loop and obtain the optimal phase perturbation vector.

[0112] Otherwise, return to step 5.2).

[0113] Step 6: Based on the constructed perturbation angular domain signal and the desired angular domain signal, solve for the phase perturbation vector under the condition that the magnitude of the desired angular domain signal is not fixed.

[0114] The solution process in this step is the same as in step 5, that is, solving for the phase perturbation vector under non-fixed conditions is also a traversal loop process, specifically implemented as follows:

[0115] 6.1) Initialize the current loop count l = 1, and the optimal phase jitter vector. Minimum objective function value Calculate the maximum number of iterations L:

[0116]

[0117] Where N1 represents the symbol set corresponding to the real part of the desired communication signal. The number of elements in the set, N2, represents the symbol set corresponding to the imaginary part of the desired communication signal. The number of elements in the middle, N e Indicates the number of anti-sorting directions;

[0118] 6.2) Traversing the real part a of the desired angular domain signal i and the imaginary part b of the expected angular domain signal i The value a is obtained from the l-th iteration. il and b il ;

[0119] 6.3) Solve for the phase jitter vector during the l-th traversal.

[0120] 6.3.1) Constructing optimization criteria under the condition that the magnitude of the desired angular domain signal is not fixed:

[0121] This example constructs an optimization criterion based on the three considerations in step 5.3.1), which is to set the magnitude p of the desired angular domain signal. i As variables, and with their range of values ​​limited, the following optimization criteria are obtained:

[0122]

[0123] 6.3.2) Constructing new variables

[0124] Combine the two variables in the optimization criterion in step 6.3.1) to form a new variable. And let its range of values ​​be:

[0125]

[0126] in Indicates a dimension of N t A vector of all 1s;

[0127] 6.3.3) Change the new variable y il Substituting the objective function into the optimization criterion in 6.3.1), we obtain the transformed objective function:

[0128]

[0129] in Indicates a dimension of N e A vector consisting entirely of zeros;

[0130] 6.3.4) Simplify the constraints of the optimization criteria in step 6.3.1):

[0131] Substituting the perturbation angular domain signal constructed in step three and the desired angular domain signal constructed in step four into the equality constraints of the optimization criterion in step 6.3.1), and moving the right side of the equality sign to the left side, we obtain the equation:

[0132]

[0133] Use the new variable y il Replacing the original variables in the equation yields:

[0134] v i +[jV i ,diag(-a il -jb il )]y il =0

[0135] Considering that the magnitude and phase perturbation vector of the desired angular domain signal in this example should be real vectors, the above equations are divided into real and imaginary parts, resulting in the following set of equations:

[0136] Re(v i )+Re([jV i ,diag(-a il -jb il )]y il ) = 0

[0137] Im(v i )+Im([jV i ,diag(-a il -jb il)]y il ) = 0

[0138] Combine the matrix components of the equations in step 6.3.4) to form a new matrix G. il The vector parts form a new vector g. i G il and g i The specific form is as follows:

[0139]

[0140]

[0141] The new matrix G il and the new vector g i Substituting the equality constraints and variable constraints from the optimization criterion in step 6.3.1), we obtain the simplified constraint conditions:

[0142] G il y il =g i

[0143] 6.3.5) Simplify the optimization criteria in step 6.3.1):

[0144] Based on the transformed objective function in step 6.3.3) and the simplified constraints in step 6.3.4), the optimization criterion in step 6.3.1) is simplified to:

[0145]

[0146] stG il y il =g i

[0147]

[0148] 6.3.6) Solve the simplified optimization criterion to obtain the phase perturbation vector. That is, the simplified optimization criterion in step 6.3.5) is solved quickly by quadratic programming to obtain the new variable y. il The first N of the new variable t The elements form the phase perturbation vector.

[0149] 6.4) By phase perturbation vector Calculate the objective function value during the l-th traversal. And determine the objective function value With minimum objective function value Size:

[0150] like Then let

[0151] Otherwise, proceed to step 6.5);

[0152] 6.5) Update the loop count l, let l = l + 1, and check if the loop count exceeds the maximum value:

[0153] If l > L, terminate the loop and obtain the optimal phase perturbation vector.

[0154] Otherwise, return to step 6.2).

[0155] Step 7, construct the phase perturbation matrix Φ:

[0156] 7.1 Determine whether the magnitude of the desired angular domain signal is fixed:

[0157] If the modulus is fixed, proceed to step 7.2;

[0158] Otherwise, proceed to step 7.3.

[0159] 7.2 Phase perturbation vector with fixed magnitude The phase perturbation matrix Φ is represented as follows:

[0160]

[0161] 7.3 Phase perturbation vector with non-fixed magnitude The phase perturbation matrix Φ is represented as follows:

[0162]

[0163] Step 8: Obtain the centralized MIMO radar anti-sorting waveform S t .

[0164] Add the phase perturbation matrix Φ and the phase of the input transmission matrix Θ to obtain the final transmission matrix Φ. t The matrix is ​​input into the transmitter of the centralized MIMO radar and transmitted into the air to obtain the centralized MIMO radar anti-sorting waveform S. t :

[0165]

[0166] The following simulation experiments further illustrate the effectiveness of the present invention.

[0167] I. Simulation Conditions

[0168] The number of transmit matrix antennas input in this invention is N. t =10, and the number of chips transmitted by each antenna is N. s=128, the transmitting antennas are arranged in a uniform linear array with half-wave spacing.

[0169] The input emission matrix is ​​a pre-designed waveform with the desired emission pattern and good correlation, such as... Figure 2 As shown, where Figure 2 (a) is the emission pattern of the input emission matrix. Figure 2 (b) is the autocorrelation plot of the input emission matrix in the angular domain at the normalized angular frequency f1 = [-0.3, 0.3]. Figure 2 (c) is the cross-correlation diagram of the angular domain signal of the input emission matrix at the normalized angular frequency f2 = [-0.475, -0.425, ..., 0.475] and the angular domain signal at f1.

[0170] II. Simulation Content

[0171] Simulation 1: Under the above conditions, assume the anti-sorting direction f = -0.45, the desired angular domain signal magnitude is fixed, and its value is the average energy E of the angular domain signal of the input emission matrix in the anti-sorting direction. The anti-sorting waveform in this invention was simulated, and the simulated phase perturbation matrix was processed with six-bit phase precision. The results are as follows: Figure 3 As shown. Among them. Figure 3 (a) is a constellation diagram of the angular domain signals of the original waveform and the disturbance waveform in the anti-sorting direction. Figure 3 (b) is the autocorrelation plot of the input emission matrix in the angular domain at the normalized angular frequency f1. Figure 3 (c) is the cross-correlation diagram of the angular domain signal of the input emission matrix at the normalized angular frequency f2 and the angular domain signal at f1.

[0172] from Figure 3 (a) It can be seen that the amplitude of the disturbance angular domain signal in the anti-sorting direction is fixed, and the phase of the angular domain signal is basically concentrated near ±π / 4 and ±3π / 4, indicating that the radar disturbance angular domain signal is simulated as a four-phase coded signal, which improves the anti-sorting capability of the waveform.

[0173] from Figure 3 (b) and Figure 2 (b) By comparison, it can be found that the autocorrelation effect of the angular domain signal is small after the phase perturbation of the input emission matrix is ​​applied in this invention.

[0174] from Figure 3 (c) and Figure 2 (c) By comparison, it can be found that the present invention has a small impact on the cross-correlation of the angular domain signal after applying phase perturbation to the input emission matrix.

[0175] Figure 3 (b) and Figure 3(c) indicates that the phase perturbation applied by the present invention does not substantially change the performance of the input transmit matrix.

[0176] Simulation 2: Under the above conditions, assume the anti-sorting direction f = -0.45, the magnitude of the desired angular domain signal is non-fixed, with a lower bound of 0.5E and an upper bound of positive infinity. The anti-sorting waveform in this invention was simulated, and the simulated phase perturbation matrix was processed with six-bit phase precision. The results are as follows: Figure 4 As shown. Among them. Figure 4 (a) is a constellation diagram of the angular domain signals of the original waveform and the disturbance waveform in the anti-sorting direction. Figure 4 (b) is the autocorrelation plot of the input emission matrix in the angular domain at the normalized angular frequency f1. Figure 4 (c) is the cross-correlation diagram of the angular domain signal of the input emission matrix at the normalized angular frequency f2 and the angular domain signal at f1.

[0177] from Figure 4 (a) It can be seen that the amplitude of the disturbance angular domain signal in the anti-sorting direction is not fixed, and its lower limit is shown by the dotted line in the figure. The phase of the angular domain signal is basically concentrated near ±π / 4 and ±3π / 4, indicating that the radar disturbance angular domain signal is simulated as a four-phase coded signal, which improves the anti-sorting capability of the waveform.

[0178] from Figure 4 (b) and Figure 2 (b) By comparison, it can be found that the autocorrelation effect of the angular domain signal is small after the phase perturbation of the input emission matrix is ​​applied in this invention.

[0179] from Figure 4 (c) and Figure 2 (c) By comparison, it can be found that the present invention has a small impact on the cross-correlation of the angular domain signal after applying phase perturbation to the input emission matrix.

[0180] Figure 4 (b) and Figure 4 (c) indicates that the phase perturbation added in this invention does not significantly change the performance of the input transmit matrix.

[0181] Simulation 3: Under the above conditions, assuming the anti-sorting direction f = 0.15, the magnitude of the desired angular domain signal is fixed at E, and the communication sequence to be simulated is a random four-phase coded signal, with the phase of the desired angular domain signal being the same as that of the communication sequence to be simulated, the anti-sorting waveform in this invention is simulated, and the simulated phase perturbation matrix is ​​processed with six-bit phase precision. The results are as follows: Figure 5 As shown. Among them. Figure 5 (a) is the phase diagram of the perturbation angular domain signal and the desired angular domain signal. Figure 5 (b) is an amplitude diagram of the perturbation angular domain signal and the desired angular domain signal. Figure 5(c) is the autocorrelation plot of the input emission matrix in the angular domain at the normalized angular frequency f1. Figure 5 (d) is the cross-correlation diagram of the angular domain signal of the input emission matrix at the normalized angular frequency f2 and the angular domain signal at f1.

[0182] from Figure 5 (a) It can be seen that the phases of the perturbed angular domain signal and the desired angular domain signal are basically coincident. Figure 5 (b) It can be seen that the magnitude of the perturbation angular domain signal is basically near the expected magnitude. Figure 5 (a) and Figure 5 (b) indicates that the radar disturbance angular domain signal simulation is the desired communication signal, which can further realize the radar communication integration function on the basis of realizing the anti-sorting function.

[0183] from Figure 5 (c) and Figure 2 (b) By comparison, it can be found that the autocorrelation effect of the angular domain signal is small after the phase perturbation of the input emission matrix is ​​applied in this invention.

[0184] from Figure 5 (d) and Figure 2 (c) By comparison, it can be found that the present invention has a small impact on the cross-correlation of the angular domain signal after applying phase perturbation to the input emission matrix.

[0185] Figure 5 (c) and Figure 5 (d) indicates that the phase perturbation applied by the present invention does not significantly change the performance of the input emission matrix.

[0186] Simulation 4: Under the above conditions, assuming the anti-sorting direction f = 0.15, the magnitude of the desired angular domain signal is not fixed, with a lower bound of 0.5E and an upper bound of positive infinity. Assuming the communication sequence to be simulated is a random four-phase coded signal, and the phase of the desired angular domain signal is the same as that of the communication sequence to be simulated, the anti-sorting waveform in this invention is simulated. The simulated phase perturbation matrix is ​​then processed with six-bit phase precision. The results are as follows: Figure 6 As shown. Among them. Figure 6 (a) is the phase diagram of the perturbation angular domain signal and the desired angular domain signal. Figure 6 (b) is an amplitude diagram of the perturbation angular domain signal and the desired angular domain signal. Figure 6 (c) is the autocorrelation plot of the input emission matrix in the angular domain at the normalized angular frequency f1. Figure 6 (d) is the cross-correlation diagram of the angular domain signal of the input emission matrix at the normalized angular frequency f2 and the angular domain signal at f1.

[0187] from Figure 6 (a) It can be seen that the phases of the perturbed angular domain signal and the desired angular domain signal are basically coincident. Figure 6(b) It can be seen that the magnitude of the perturbation angular domain signal is not fixed and has a lower bound. Figure 6 (a) and Figure 6 (b) indicates that the radar disturbance angular domain signal simulates the desired communication signal, which can further realize the integrated radar communication function on the basis of realizing the anti-sorting function.

[0188] from Figure 6 (c) and Figure 2 (b) By comparison, it can be found that the autocorrelation effect of the angular domain signal is small after the phase perturbation of the input emission matrix is ​​applied in this invention.

[0189] from Figure 6 (d) and Figure 2 (c) By comparison, it can be found that the present invention has a small impact on the cross-correlation of the angular domain signal after applying phase perturbation to the input emission matrix.

[0190] Figure 6 (c) and Figure 6 (d) indicates that the phase perturbation applied by the present invention does not significantly change the performance of the input matrix.

[0191] Simulation 5: Under the above conditions, with the anti-sorting direction f = ±0.05 and the desired magnitude of the angular domain signal set to 0, the anti-sorting waveform in this invention is simulated. The simulated phase perturbation matrix is ​​then processed with six-bit phase accuracy. The results are as follows: Figure 7 As shown. Among them. Figure 7 (a) shows the transmission patterns of the disturbance waveform and the original waveform. Figure 7 (b) is the autocorrelation plot of the input emission matrix in the angular domain at the normalized angular frequency f1. Figure 7 (c) is the cross-correlation diagram of the angular domain signal of the input emission matrix at the normalized angular frequency f2 and the angular domain signal at f1.

[0192] like Figure 7 As shown in (a), the transmit pattern decreases from -29.83dB to -72.89dB at f = -0.05 and from -29.83dB to -73.26dB at f = 0.05. The decrease in the transmit pattern indicates that the radiated power of the disturbance angular domain signal is reduced in the anti-sorting direction, and the anti-sorting function of the disturbance waveform can be achieved through stealth.

[0193] from Figure 7 (b) and Figure 2 (b) By comparison, it can be found that the autocorrelation effect of the angular domain signal is small after the phase perturbation of the input emission matrix is ​​applied in this invention.

[0194] from Figure 7 (c) and Figure 2 (c) By comparison, it can be found that the present invention has a small impact on the cross-correlation of the angular domain signal after applying phase perturbation to the input emission matrix.

[0195] Figure 7 (b) and Figure 7 (c) indicates that the phase perturbation applied by the present invention does not substantially change the performance of the input matrix.

[0196] The simulation results above show that the perturbation waveform designed in this invention has good anti-sorting performance and basically does not change the performance of the original input transmission matrix.

Claims

1. A method for online design of radar anti-sorting waveforms based on communication simulation, characterized in that, comprising the steps of: (1) Input centralized MIMO radar transmission matrix Determine the anti-sorting direction based on prior information. For the emission matrix Apply a small phase perturbation, and construct the perturbation matrix based on this perturbation and the anti-sorting direction. Perturbation angular domain signal of the line The implementation is as follows: (1a) input transmit matrix : ； wherein denotes the base of the natural logarithm, denotes the imaginary unit, is a transmit matrix whose phase, denotes the real domain, denotes the number of centralized MIMO radar antennas, denotes the number of transmitted chips per antenna, denotes a vector consisting of the elements of the first row of the transmit matrix, , denotes the transpose, denotes the complex domain; the arrangement of the transmit antennas should be a uniform linear array; (1b) Suppose a phase perturbation is applied to the transmit matrix, the first column of the transmit matrix becomes row after the perturbation : ； wherein denotes the phase of , denotes the phase perturbation vector denotes the diagonal matrix with as diagonal elements; (1c) constructing a perturbation angle domain signal: Determining antisort direction according to prior information wherein represents the target number; constructing a transmission steering matrix : ； wherein , denotes the transmit steering vector for the th target direction, denotes the normalized angular frequency in direction , denotes the antenna spacing, denotes the wavelength; By The first chip of the angle domain signal in the anti-sorting direction consists of a perturbed angle domain signal : ； wherein represents the undisturbed angular domain signal; When the perturbation vector is small, the approximation is where denotes the full vector of dimension The perturbation angle domain signal is finally approximated as: ， wherein represents each element in the row of (2) The perturbation angle domain signal The simulation is a communication signal, and the expected angle domain signal is constructed by the modulus value and phase information of the communication signal , as follows: ； wherein denotes the Hadamard product, denotes the modulus of the desired angular domain signal in the anti-sorting direction, denotes the modulus of the desired angular domain signal in the th direction, , denotes the number of anti-sorting directions, , , is a symbol set corresponding to the real part of the communication signal to be simulated, is a symbol set corresponding to the imaginary part of the communication signal to be simulated; the modulus of the desired angular domain signal exists a lower bound and an upper bound wherein and denote the lower bound and the upper bound of the modulus of the desired angular domain signal in the th direction, respectively, and ; (3) Let the perturbed angle domain signal equal to the desired angle domain signal , solve the phase perturbation vector under the condition of the desired angle domain signal modulus fixed and the phase perturbation vector under the condition of the desired angle domain signal modulus not fixed ; (4) The above process is traversed for all rows of the transmit matrix, and a phase perturbation matrix is constructed according to the modulus properties of the desired angular domain signals : If the modulus is fixed, then the phase perturbation vector is fixed by the modulus constitutes a phase perturbation matrix ; If the modulus is not fixed, then the phase perturbation vector is not fixed by the modulus The phase perturbation matrix is constructed ; (5) From the phase perturbation matrix and emission matrix phase Constructing a centralized MIMO radar anti-sorting waveform : (5a) adding the phase perturbation matrix to the phase of the transmit matrix to obtain the final phase matrix ; (5b) the final phase matrix is input to the transmitting end of the centralized MIMO radar and transmitted into the air, obtaining the anti-sorting waveform of the centralized MIMO radar .

2. The method of claim 1, wherein, Solving the phase perturbation vector under the condition of fixed modulus in step (3) This is implemented as follows: (3a) initialize the current number of loops optimal phase jitter vector minimum objective function value calculate the maximum number of loops : ； wherein represents a symbol set corresponding to the real part of the communication signal to be simulated the number of elements in represents a symbol set corresponding to the imaginary part of the communication signal to be simulated the number of elements in represents the number of anti-sorting directions; (3b) iterate over the real part of the desired angle domain signal and the imaginary part of the desired angle domain signal to obtain the nth iteration value and ; (3c) solving for the phase jitter vector at the second pass : (3c1) constructing an optimization criterion: ； wherein denotes the two-norm of a vector, denotes the perturbed angular domain signal, denotes the desired angular domain signal, denotes the number of centralized MIMO radar antennas, denotes the real number domain; (3c2) simplifying the constraints in the optimization criterion to: ； where: ； wherein denotes the real part of a matrix or vector, denotes the imaginary part of a matrix or vector, denotes a diagonal matrix with as diagonal elements, denotes the undisturbed angle domain signal, denotes the rows of denotes the modulus of the desired angle domain signal; (3c3) constructing a final optimization criterion based on the simplified constraints: ； (3c4) The phase perturbation vector is solved from the final optimization criterion : ； wherein denotes the Moore-Penrose inverse of a matrix; (3d) the phase perturbation vector the objective function value at the first iteration the objective function value at the second iteration and determine the size of the objective function value and the minimum objective function value . If then let , ; else perform (3e); (3e) update the number of cycles , let , determine if the number of cycles exceeds a maximum value: If , terminate the loop and obtain the optimal phase perturbation vector , else return to step (3b).

3. The method of claim 1, wherein, Solving the phase perturbation vector under the condition of non-fixed modulus in step (3) This is implemented as follows: (3f) initializing the current number of loops optimal phase jitter vector minimum objective function value calculating the maximum number of loops : ； wherein represents a symbol set corresponding to the real part of the communication signal to be simulated the number of elements in represents a symbol set corresponding to the imaginary part of the communication signal to be simulated the number of elements in represents the number of anti-sorting directions (3g) iterate over the real part of the desired angle domain signal and the imaginary part of the desired angle domain signal to obtain the nth iteration value and ; (3h) solving the phase jitter vector at the second pass : (3h1) constructing an optimization criterion: ； in The L2 norm of a vector. Indicates the perturbation angular domain signal. Represents the desired angular domain signal. This represents the magnitude of the expected angular domain signal. and These represent the lower and upper bounds of the expected angular domain signal magnitude, respectively. Indicates the number of centralized MIMO radar antennas. The dimension is The whole vector; (3h2) composing new variables from the variables in the optimization criterion and composing new variables from the variables in the optimization criterion , the new variables having a range of values ； wherein ; (3h3) Simplify the equality constraints in the optimization criterion to: , where: ； wherein denotes the real part of a matrix or vector, denotes the imaginary part of a matrix or vector, denotes a diagonal matrix with as diagonal elements, denotes the undisturbed angle domain signal, denotes the rows of (3h4) constructing a final optimization criterion based on the transformed constraints: ； wherein , denotes the all vector, the subscript denotes the dimension; (3h5) is obtained from the final optimization criterion solution , take the first element to get the phase disturbance vector ; (3i) from the phase perturbation vector the objective function value at the first iteration the objective function value at the second iteration and determine the size of the objective function value and the minimum objective function value . If , then let , ; else perform (3j); (3j) updating the number of cycles , let , determining whether the number of cycles exceeds a maximum value: If , terminate the loop and obtain the optimal phase perturbation vector ; else, return to step (3g).

4. The method of claim 1, wherein, The phase perturbation vector in step (4) is fixed modulo The phase perturbation matrix is constructed is represented as follows: ； wherein represents the number of centralized MIMO radar antennas, represents the number of chips transmitted per antenna, represents the real number field.

5. The method of claim 1, wherein, The phase perturbation vector in step (4) is not fixed modulo The phase perturbation matrix is constructed is represented as follows: ； wherein denotes the number of centralized MIMO radar antennas, denotes the number of transmitted chips per antenna, denotes the real domain.

6. The method of claim 1, wherein, The concentrated MIMO radar anti-sorting waveform obtained in step (5) is represented as follows: ； wherein represents the base of the natural logarithm, represents the imaginary unit, represents the final transmit matrix.

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