Configuration carrier frequency joint optimization method for improving main lobe interference resistance of distributed radar

Abstract

The invention discloses a heterogeneous distributed radar configuration carrier frequency joint optimization method based on main lobe interference resistance. According to the technical scheme, the method comprises the following steps of 1, distributed radar anti-interference scene modeling and optimization problem construction; 2, an optimal configuration design algorithm based on a PSO algorithm; and step 3, a sub-pulse frequency point design algorithm based on the minimization PGLL. According to the method, the optimal distributed radar deployment strategy and the sub-pulse frequency point design can be obtained under the conditions that the gains of the main radar and the auxiliary radar are inconsistent and the number of nodes is small, so that the distributed radar can obtain the optimal output signal-to-noise ratio in a certain sub-pulse when interference occurs at any angle in a main lobe.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar configuration optimization, and relates to a configuration carrier frequency joint optimization method for improving the anti-main lobe interference performance of a distributed radar. Background Art

[0002] The intensity of electronic confrontation in modern battlefields is increasing day by day, and the interference threat faced by radars is becoming more and more serious. From the perspective of spatial distribution, radar interference can be divided into sidelobe interference and mainlobe interference. For sidelobe interference, traditional array radars can effectively suppress interference through adaptive beamforming technology or sidelobe cancellers. However, when the jammer and the target are located in the radar main lobe at the same time to form main lobe interference, the interference signal has higher energy after being modulated by the main lobe gain, and the radar is limited by the angular resolution and cannot retain the target signal while suppressing the interference, which will seriously limit the radar's target detection capability.

[0003] Distributed array radar deploys multiple node radars on a long baseline to obtain extremely high angular resolution. When countering main lobe interference, an extremely narrow null can be formed to suppress the interference signal while retaining the energy of the target signal. In the actual application of distributed array radar, considering the cost and convenience issues, the current distributed radar anti-interference mainly adopts a main-auxiliary joint distributed radar system, deploying a main radar that can send and receive and a small number of auxiliary radars that can only receive signals on a long baseline. Existing research on the anti-interference problem of distributed array radars is mostly focused on the design of anti-interference algorithms.

[0004] Since distributed array radars are sparsely deployed on a long baseline, grating lobes are inevitable. Existing research mainly considers reducing the impact of grating lobes by optimizing node positions, usually considering dozens or even hundreds of nodes. However, the one-master and multiple-auxiliary distributed array radar has too few nodes and a long baseline, so relying solely on changes in node positions is not enough to fully reduce the grating lobe level. Summary of the invention

[0005] In view of this, the present invention proposes a method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-mainlobe interference performance. Not only the node positions are optimized, but also multiple sub-pulses of different frequencies are designed, so that the distributed radar can obtain the optimal output signal-to-noise ratio in a certain sub-pulse when interference occurs at any angle in the mainlobe. Compared with the solution of only optimizing the radar node positions, the present invention shows significant advantages in improving the anti-mainlobe interference performance.

[0006] A configuration carrier frequency joint optimization method for improving the anti-main lobe interference performance of distributed radar specifically includes the following steps:

[0007] Step 1: Distributed radar anti-interference scenario modeling and optimization problem construction;

[0008] Step 2: Optimal configuration design algorithm based on PSO algorithm;

[0009] Step 3: Sub-pulse frequency design algorithm based on minimizing PGLL;

[0010] Step 1 includes the following sub-steps:

[0011] (1) Distributed radar anti-interference scenario modeling;

[0012] (2) Construction of the configuration carrier-frequency joint optimization problem;

[0013] Step 2 includes the following sub-steps:

[0014] (1) Particle swarm initialization based on spacing constraints and primary and secondary heterogeneity;

[0015] (2) Fitness calculation based on multi-carrier projection;

[0016] (3) Particle swarm projection based on spacing constraints;

[0017] (4) Particle motion and velocity update;

[0018] (5) Improved particle swarm algorithm based on multiple initializations.

[0019] Furthermore, the optimization function of projecting the frequency point variation range to a single frequency point in step 1 is

[0020] for:

[0021]

[0022] Where Φ is the angle range to be optimized. According to the principle of distributed radar anti-main lobe interference, this range is within the main lobe of the main radar and outside the main lobe of the full array. Since the positions of each subarray of the main radar are determined by the center position of the main radar, the number of nodes that actually need to be optimized is M′+1. In practice, due to the constraints of radar volume and electromagnetic compatibility requirements, it is necessary to ensure that the minimum spacing between nodes is greater than d c , the array baseline length is l.

[0023] Furthermore, in step 2, a particle swarm optimization (PSO) algorithm is used to solve the optimization problem, and a strategy of gradually optimizing the PGLL is adopted to select the sub-pulse frequency; the main radar position is optimized as a separate parameter.

[0024] Furthermore, the angle range to be optimized in step 2 is the angle range outside the main lobe of the entire array and within the main lobe range of the main radar; during the optimization process, only the center position of the main radar is considered, and the main radar is expanded into multiple sub-arrays for calculation only when calculating the fitness.

[0025] Furthermore, the method for projecting the particles before and after the movement in step 2 is:

[0026] Project d to x before moving

[0027] d=[d 1 ,d 2 ,…,d M′+1 ]

[0028] =[0,x 2 +d c ,…,x i +(i-1)d c ,…,l]

[0029] =x+D c

[0030] in:

[0031] x=[0,x 2 ,…,x i ,…,l] 0≤x 2 …≤x i …≤x M′ ≤l-(M′+1)d c

[0032] D c =[0,d c ,…,(i-1)d c ,…,0]

[0033] After the particles move, the sorted x and D c After summing, the projection is made to d to ensure that the particles always meet the spacing constraint.

[0034] Furthermore, the speed update formula of the particle swarm algorithm in step 2 is as follows:

[0035]

[0036] Where x Iopt is the optimal solution of the current particle history, x Gopt is the current global optimal solution; x i k is the current particle, is the velocity of the current particle; ω v is the inertia coefficient, which can change within a certain range with the iteration process; c 1 is the individual learning factor, which is used to adjust the influence of the particle's historical optimal solution on the particle's motion direction; c 2 is the global learning factor, which is used to adjust the influence of the current global optimal solution on the direction of particle movement; r 1 and r2 Provide random numbers for individual and global learning, which increases the randomness of the search process to a certain extent; is the updated particle velocity.

[0037] Furthermore, in step 2, in order to reduce the poor fitness of the initialized particles and cause the algorithm to fall into the local optimal solution, only the optimal particles are retained and the particle swarm is reinitialized after every 100 iterations to obtain better optimization results.

[0038] Furthermore, the strategy for progressively optimizing the sub-pulse frequencies in step 3 is: if there is a frequency point within the frequency range that can reduce the PGLL, then the frequency point is added to the current frequency point set.

[0039] Furthermore, the response of the cost function at each angle in step 3 is the minimum value of the response at each frequency point and is expressed as:

[0040] L(θ j )=minL n (θ j )

[0041]

[0042] Where f n is the nth frequency point, L n is the cost function value at the nth frequency point, L is the overall cost function value after integrating the minimum cost function of each frequency point, d Gopt is the optimal configuration obtained by the particle swarm algorithm.

[0043] Beneficial effects:

[0044] 1. Based on the design of the node positions of the distributed array radar, the present invention adopts a plurality of sub-pulses with different frequencies to introduce the frequency parameter as a new "increment" into the distributed array radar to improve the anti-interference performance.

[0045] 2. Aiming at the constraints such as inconsistent primary and auxiliary gains and radar spacing, the present invention proposes a new optimization function and optimization framework, and realizes the optimization of radar position considering the change of sub-pulse frequency through a constrained PSO algorithm.

[0046] 3. Based on the existing optimized array configuration, the present invention proposes a progressive optimization strategy for sub-pulse frequencies, which effectively reduces the optimization dimension. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a schematic diagram of a distributed array radar;

[0048] Figure 2 It is a schematic diagram of multi-carrier interference suppression processing;

[0049] Figure 3 It is a schematic diagram of scaling the carrier frequency term;

[0050] Figure 4 Generate schematic diagrams for particles with constraints;

[0051] Figure 5 Schematic diagram of the upper and lower bounds of the angle expansion caused by frequency change;

[0052] Figure 6 For the optimized configuration;

[0053] Figure 7 is the cost function value at different frequency points;

[0054] Figure 8 It is the result of joint optimization of multiple frequency points;

[0055] Fig. 9 For PGLL comparison;

[0056] Fig.10 For the comparison of anti-main lobe interference performance. DETAILED DESCRIPTION

[0057] In order to facilitate the understanding of the present invention, the specific embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thoroughly understood.

[0058] A configuration carrier frequency joint optimization method for improving the anti-main lobe interference performance of distributed radar specifically includes the following steps:

[0059] Step 1: Distributed radar anti-interference scenario modeling and optimization problem construction

[0060] (1) Distributed Radar Anti-interference Scenario Modeling

[0061] In order to solve the problem that the antenna gain of the low-cost receiving auxiliary radar is inconsistent with that of the main radar, the present invention splits the main radar into multiple sub-arrays with the same gain as the auxiliary radar and evenly distributed, which is convenient for subsequent modeling. The distributed array radar in the present invention is only used for main lobe interference suppression, so even if the spacing between the sub-arrays after splitting is greater than half a wavelength, it does not affect the modeling of signals within the main lobe angle range. The schematic diagram of the distributed array radar is shown in Figure 1 shown.

[0062] Since ground-based distributed array radars can usually only improve angular resolution in azimuth to counter main lobe interference, they are usually one-dimensional arrays. Consider the full array echo of a single interference scenario:

[0063] s(t)=a(θ 0 )s 0(t)+a(θ j )s j (t)+N(t) (1)

[0064] Where a(θ 0 ), a(θ j ) are the K-dimensional steering vectors of the target and interference, respectively, and K is the number of channels in the full array (the number of main radar subarrays + the number of auxiliary radars). The number of main radar subarrays is M, the number of auxiliary radars is M′, and the gain of each channel is consistent. 0 (t), s j (t) are the complex envelopes of the target and interference respectively, and N(t) is the noise matrix.

[0065] Assuming that the interference + noise covariance matrix R is available, the optimal weight vector for anti-interference is:

[0066]

[0067] The output signal-to-noise ratio obtained by this weight vector is:

[0068]

[0069] Where:

[0070]

[0071] According to the Sherman-Morrison formula: It can be concluded that

[0072]

[0073] Where ε j is the single channel interference-noise power ratio

[0074] Substitute this into the equation for the output signal-to-noise ratio:

[0075]

[0076] Where ε s is the target signal-to-noise power ratio.

[0077] When the interference-to-noise ratio is large enough, the above formula can be simplified to:

[0078]

[0079] It can be seen from the above formula that the parameter that determines the output signal-to-noise ratio is the inner product of the target signal and the interference guidance vector, which represents the spatial correlation between the target and the interference.

[0080] However, the distributed array radar has fewer nodes distributed on a longer baseline, which inevitably produces the grating lobe problem. When the interference is located at the grating lobe position of the target angle, the guidance vector correlation between the target direction and the interference direction is extremely high. According to formula (7), a grating zero point will be formed at the target, resulting in a loss of output signal-to-noise ratio.

[0081] It can be seen that when the target angle is fixed and the interference appears at any angle in the main lobe, the output signal-to-noise ratio after anti-interference is positively correlated with the pattern gain at the interference point when the beam is pointed at the target. Therefore, in order to obtain a higher output signal-to-noise ratio, it is necessary to reduce the peak grating lobe level (PGLL) of the full array pattern as much as possible.

[0082] (2) Construction of configuration-carrier-frequency joint optimization problem

[0083] |a(θ j ) H (θ 0 )| 2 Expand to write:

[0084]

[0085] In the formula, the value of the inner product of the steering vector is not only related to the target, the interference angle, and the array configuration, but also to the carrier frequency. Using a reasonable carrier frequency can avoid interference appearing at the grating lobe position of the target. This can be achieved by optimizing the array configuration (with d i related) and the signal carrier frequency (related to f), so that the interference is at an angle θ j , the target is at an angle θ 0 When the output signal-to-noise ratio reaches the theoretical optimum, the following optimization problem is considered:

[0086]

[0087] However, in practice, it is usually impossible to directly obtain the angular relationship between the interference and the target. Therefore, the main radar can emit a series of sub-pulses with different carrier frequencies so that the ideal output signal-to-noise ratio can always be obtained in a certain sub-pulse.

[0088] Therefore, considering the optimization goal of interference at any angle within the main lobe, multiple carrier frequencies are used so that any interference angle can obtain a smaller cost function value at a certain carrier frequency. Figure 2 shown.

[0089] According to formula (8), if the radar uses multiple carrier frequencies for anti-interference processing, it is equivalent to changing the carrier frequency term f to scale the angle term sinθ j -sinθ 0 , so the effect of carrier frequency change on beam pattern can be equivalent to scaling in angle dimension, such as Figure 3shown.

[0090] The figure shows the response of a distributed radar at other angles when the beam is pointed at 0° under two different carrier frequencies. It can be observed that switching different carrier frequencies is equivalent to translation in the angle dimension. j -sinθ 0 The change of θ j -θ 0 The change of is not a linear relationship, so the translation amount also changes with θ j Assuming that the beam points to 0°, the angular expansion range corresponding to the carrier frequency range can be calculated by equation (8). Assuming the center frequency is f 0 , the frequency variation range is Δf.

[0091]

[0092] According to formula (10), when the carrier frequency is switched, the frequency f 0 +Δf is located at sinθ j The response at is equivalent to the frequency f 0 At the time Therefore, in the case of multiple carrier frequencies, the quality of the anti-interference effect at a certain angle depends on the value of the smallest inner product of the steering vector within the surrounding angle range zoomed out by the multiple carrier frequencies. 0 -Δf,f 0 +Δf], so the optimization function is set as:

[0093]

[0094] Where Φ is the angle range to be optimized. According to the principle of distributed radar anti-main lobe interference, this range is within the main lobe of the main radar and outside the main lobe of the full array. Since the positions of each subarray of the main radar are determined by the center position of the main radar, the number of nodes that actually need to be optimized is M′+1. In practice, due to the constraints of radar volume and electromagnetic compatibility requirements, it is necessary to ensure that the minimum spacing between nodes is greater than d c , the array baseline length is l.

[0095] In addition, according to equation (8), assuming that the azimuth angle of the target relative to the baseline increases, the beam points to the target. When the angle between the target and the interference remains unchanged, sinθ j -sinθ 0 The value of θ 0 It increases and gradually decreases, which is reflected in the response of the cost function, which is still an expansion. After the optimization is completed, the PGLL when the target is at 0° is still the PGLL when the target is at other azimuths, so it is only necessary to optimize the case where the target is at 0°.

[0096] The present invention considers a distributed array radar system with one main and multiple auxiliary radars, where the main radar transmits signals and all node radars in the entire array receive signals. The system parameters are as follows:

[0097]

[0098] The algorithm parameters are as follows

[0099]

[0100] Step 2: Optimal configuration design algorithm based on PSO algorithm

[0101] Obviously, the optimization problem of formula (11) is non-convex. Considering the algorithm convergence speed and other aspects, the present invention uses particle swarm optimization (PSO) to solve the optimization problem of formula (11). Then, the sub-pulse frequency is selected by using the strategy of gradually optimizing PGLL.

[0102] (1) Particle swarm initialization based on spacing constraints and primary and secondary heterogeneity

[0103] In order to consider the problem of node heterogeneity, the main radar position needs to be optimized as a separate parameter. Therefore, when initializing particles, the present invention considers generating particles with the main radar as the origin, such as Figure 4 As shown, the black dots are the main radar and the white dots are the auxiliary radar.

[0104] With baseline length l, minimum node spacing d c As a constraint, the main radar is located at the origin 0, and the left node is randomly generated first. The left node can be generated at l-2d c When the left node is generated, the right node can be determined according to the baseline length constraint l. To strictly ensure that the node spacing is greater than d c , the remaining nodes need to be generated in l-(M′+1)d c After the generation of the particle swarm is completed, all particles are translated so that the left endpoints of all configurations are at 0 and the right endpoints are at l.

[0105] (2) Fitness calculation based on multi-carrier projection

[0106] Due to the symmetry of the antenna pattern, only half of the angle range needs to be calculated for fitness. And the present invention is mainly aimed at main lobe interference, and only the angle range within the main lobe range of the main radar needs to be considered. Therefore, the angle range to be optimized is the angle range outside the main lobe of the full array and within the main lobe range of the main radar.

[0107] According to the multi-carrier projection method in the previous section, the angle range corresponding to the carrier frequency range is calculated. Under certain parameters, the angle expansion range is as follows: Figure 5 shown.

[0108] During the optimization process, only the center position of the main radar is considered, and the main radar is expanded into multiple sub-arrays for calculation only when calculating the fitness.

[0109] (3) Particle swarm projection based on spacing constraints

[0110] The initially created particles are strictly constrained, so they can meet the spacing constraints in the optimization problem. However, in order to ensure that the constraints are still met during the movement of the particles, the original particles need to be preprocessed. We projected the particles before and after the movement in the following way, projecting d to x before the movement, as shown in Equation 13.

[0111]

[0112] in:

[0113] x=[0,x 2 ,…,x i ,…,l] 0≤x 2 …≤x i …≤x M′ ≤l-(M′+1)d c (13)

[0114] D c =[0,d c ,…,(i-1)d c ,…,0] (14)

[0115] After the particles move, the sorted x and D c After summing, projecting to d can ensure that the particles always meet the spacing constraint.

[0116] (4) Particle motion and velocity update

[0117] The speed update formula of the particle swarm algorithm is as follows:

[0118]

[0119] Where x Iopt is the optimal solution of the current particle history, x Gopt is the current global optimal solution; x i k is the current particle, is the velocity of the current particle; ω v is the inertia coefficient, which can change within a certain range with the iteration process; c 1 is the individual learning factor, which is used to adjust the influence of the particle's historical optimal solution on the particle's motion direction; c 2is the global learning factor, which is used to adjust the influence of the current global optimal solution on the direction of particle movement; r 1 and r 2 Provide random numbers for individual and global learning, which increases the randomness of the search process to a certain extent; is the updated particle velocity.

[0120] It should be noted that since the power and aperture of the main radar are inconsistent with those of other radars, the main radar needs to be moved as a separate item.

[0121] (5) Improved particle swarm algorithm based on multiple initializations

[0122] In order to reduce the possibility that the algorithm falls into a local optimal solution due to poor fitness of initialized particles, only the optimal particles are retained and the particle swarm is reinitialized after every 100 iterations to obtain better optimization results.

[0123] According to the PSO optimal configuration solution method based on frequency range projection proposed in the present invention, combined with formula (11) and the system parameters and algorithm parameters in step 1, the optimal configuration is obtained as shown in the following table and Figure 6 shown.

[0124]

[0125] Step 3: Sub-pulse frequency design algorithm based on minimizing PGLL

[0126] The above algorithm is used to optimize the configuration and obtain the deployment position of each node radar. Although the sub-pulse frequency variation range has been coupled into the optimization function, in practice, considering the real-time requirements, the number of sub-pulses should be limited. It is necessary to further obtain the specific frequency of the sub-pulse based on the configuration optimization results.

[0127] According to the multi-sub-pulse anti-interference scheme proposed in the present invention, the response of the cost function at each angle is the minimum value of the response at each frequency point, as shown in formula (16).

[0128]

[0129] Where f n is the nth frequency point, L n is the cost function value at the nth frequency point, L is the overall cost function value after integrating the minimum cost function of each frequency point, d Gopt is the optimal configuration obtained by the particle swarm algorithm.

[0130] Therefore, for any frequency point set U, the PGLL after adding the new frequency point must be less than or equal to the original PGLL. The present invention considers a step-by-step sub-pulse frequency point design scheme, that is, calculating the cost function response under the current frequency point set, obtaining the angle where the PGLL is located, searching for new frequency points within the frequency range to minimize the cost function response of this angle, and adding the new frequency points to the original frequency point set. Repeat this process until the PGLL value approaches the upper bound of the PSO optimization result or reaches the upper limit of the number of sub-pulses. When initializing the frequency point set U, the maximum frequency point or the minimum frequency point is added first to improve the efficiency of the algorithm.

[0131] Substitute the radar position optimization result into the sub-pulse frequency design algorithm to obtain the cost function value of each frequency point within the angle range as follows: Figure 7 The optimized sub-pulse frequencies are shown in the following table.

[0132]

[0133] After algorithm processing, under the current configuration, only 6 frequency points have made PGLL reach the upper limit of the optimization result. Adding additional sub-pulses will not further reduce the fitness. At this time, the cost function value in the main lobe after integrating the configuration optimization result and the sub-pulse frequency optimization result is as follows: Figure 8 To prove the effectiveness and performance advantages of the joint optimization method, the optimization results of the present invention are compared with the results of only optimizing the configuration (using the PSO algorithm). Fig. 9 shown.

[0134] A target signal of about 19dB and a noise suppression jammer of 40dB are constructed. The target is always located at 0°, while the angle of the jammer varies between 0 and 1.5°. Two beamforming algorithms (MVDR and MMSE) are used to calculate the weights for main lobe interference suppression. The output signal-to-noise ratio is Fig.10 shown.

[0135] Fig.10 The results show that the proposed configuration carrier frequency joint optimization method has obvious performance benefits in resisting main lobe interference. Compared with the solution of only optimizing the node position, the output signal-to-noise ratio is improved overall. When using the MVDR algorithm, the worst output signal-to-noise ratio is also improved by more than 2.8dB; when using the MMSE algorithm, the worst output signal-to-noise ratio is improved by 5.4dB.

[0136] In summary, the above are only implementation cases of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for joint optimization of carrier frequency of heterogeneous distributed radar configuration based on anti-main lobe interference performance, characterized in that: The following steps are involved: Step 1: Distributed radar anti-interference scenario modeling and optimization problem construction; Step 2: Optimal configuration design algorithm based on PSO algorithm; Step 3: Sub-pulse frequency design algorithm based on minimizing PGLL; Step 1 includes the following sub-steps: (1) Distributed radar anti-interference scenario modeling; (2) Construction of the configuration carrier-frequency joint optimization problem; Step 2 includes the following sub-steps: (1) Particle swarm initialization based on spacing constraints and primary and secondary heterogeneity; (2) Fitness calculation based on multi-carrier projection; (3) Particle swarm projection based on spacing constraints; (4) Particle motion and velocity update; (5) Improved particle swarm algorithm based on multiple initializations.

2. The method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-main lobe interference performance according to claim 1, characterized in that: The optimization function for projecting the frequency range to a single frequency in step 1 is: Where Φ is the angle range to be optimized. According to the principle of distributed radar anti-main lobe interference, this range is within the main lobe of the main radar and outside the main lobe of the full array. Since the positions of each sub-array of the main radar are determined by the center position of the main radar, the number of nodes that actually need to be optimized is M′+1. In practice, due to the constraints of radar volume and electromagnetic compatibility requirements, the minimum distance between nodes must be greater than d c , the array baseline length is l.

3. The method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-main lobe interference performance according to claim 1, characterized in that: In step 2, the particle swarm optimization (PSO) algorithm is used to solve the optimization problem, and the sub-pulse frequency is selected by adopting a strategy of gradually optimizing the PGLL. The main radar position is optimized as a single parameter.

4. The method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-main lobe interference performance according to claim 1, characterized in that: The angle range to be optimized in step 2 is the angle range outside the main lobe of the entire array and within the main lobe range of the main radar. During the optimization process, only the center position of the main radar is considered, and the main radar is expanded into multiple sub-arrays for calculation only when calculating the fitness.

5. The method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-main lobe interference performance according to claim 1, characterized in that: The method for projecting particles before and after movement in step 2 is: Project d to x before moving d=[d1,d2,…,d M′+1 ] =[0,x2+d c ,…,x i +(i-1)d c ,…,l] =x+D c in: x=[0,x2,…,x i ,…,l]0≤x2…≤x i …≤x M′ ≤l-(M′+1)d c D c =[0,d c ,…,(i-1)d c ,…,0] After the particles move, the sorted x and D c After summing, the projection is made to d to ensure that the particles always meet the spacing constraint.

6. The method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-main lobe interference performance according to claim 1, characterized in that: The speed update formula of the particle swarm algorithm in step 2 is as follows: Where x Iopt is the optimal solution of the current particle history, x Gopt is the current global optimal solution; x i k is the current particle, is the velocity of the current particle; ω v is the inertia coefficient, which can change within a certain range with the iteration process; c1 is the individual learning factor, which is used to adjust the influence of the historical optimal solution of the particle on the particle's motion direction; c2 is the global learning factor, which is used to adjust the influence of the current global optimal solution on the particle's motion direction; r1 and r2 are individual learning and global learning random numbers, which increase the randomness of the search process to a certain extent; v i k+1 is the updated particle velocity.

7. The method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-main lobe interference performance according to claim 1, characterized in that: In step 2, in order to reduce the poor fitness of the initialized particles and cause the algorithm to fall into the local optimal solution, only the optimal particles are retained and the particle swarm is reinitialized after every 100 iterations to obtain better optimization results.

8. The method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-main lobe interference performance according to claim 1, characterized in that: The strategy for progressively optimizing the sub-pulse frequency in step 3 is: if there is a frequency point in the frequency range that can reduce the PGLL, then add the frequency point to the current frequency point set.

9. The method for joint optimization of carrier frequencies of heterogeneous distributed radar configurations based on anti-main lobe interference performance according to claim 1, characterized in that: The response of the cost function at each angle in step 3 is the minimum value of the response at each frequency point and is expressed as: L(θ j )=minL n (i j ) Where f n is the nth frequency point, L n is the cost function value at the nth frequency point, L is the overall cost function value after integrating the minimum cost function of each frequency point, d Gopt is the optimal configuration obtained by the particle swarm algorithm.

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