Distributed FDA-MIMO radar topology and parameter joint optimization method

Abstract

The invention discloses a distributed FDA-MIMO radar topology and parameter joint optimization method, and mainly solves the problem of poor weak target detection performance in the prior art. According to the implementation scheme, a distributed FDA-MIMO radar system is constructed, a signal # imgabs0 # reflected by a target and a signal # imgabs1 # reflected by clutter scattering points are calculated, a signal ypq received by a qth radar after a signal transmitted by a pth radar is reflected by the target is calculated, a distributed FDA-MIMO radar topology is constructed, a frequency increment is transmitted, and a matched filter joint optimization problem is received. And the optimization problem is converted into independent sub-problems of each radar station position, transmitting frequency increment and a receiving matched filter, alternate optimization is performed on each sub-problem by adopting an MBI algorithm, and optimal results of the distributed FDA-MIMO radar topology, the transmitting frequency increment and the receiving matched filter are obtained. The target detection performance of the radar in the complex environment is improved, and the method can be used for target detection in the complex environment.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and further relates to a radar topology and parameter joint optimization method, which can be used for target detection in complex environments. Background Art

[0002] Existing radars include single-base radars, dual-base radars, phased array radars, and new-system radars. Distributed FDA-MIMO radars combine the technology of FDA radars with that of MIMO radars. Through distributed antenna arrays, targets can be observed from different perspectives to obtain spatial diversity gain, overcome the flickering effect of the target radar cross-sectional area, and improve the radar's detection performance of targets. Among them, the FDA radar technology is used to introduce frequency steps between the transmitting array elements to obtain a three-dimensional transmission pattern of distance-angle-time. By receiving comprehensive matching processing, additional target distance information can be obtained, expanding the dimension of the system's acquisition of target information. In addition, the MIMO radar technology is used to transmit multiple radar signal waveforms and use multiple antennas to simultaneously receive echo signals, thereby obtaining the advantage of waveform diversity. Therefore, the distributed FDA-MIMO radar has the dual advantages of waveform diversity and spatial diversity.

[0003] Augusto Aubry, an associate professor at the University of Naples Federico II, proposed a new method for designing optimal radar deployment based on an optimization framework based on block optimization minimization in the article "A Robust Framework to Design Optimal Radar Deployment for Range-Based Target Localization Technique". This method effectively handles non-uniform measurement noise variance and general radar deployment constraints by minimizing the average CRB trajectory on the grid points of the sampled monitoring area or the maximum CRB trajectory on the grid points. However, this method regards each radar site as a single-channel transceiver array and does not consider the impact of the array element parameter settings within the node.

[0004] Professor Wang Wenqin's team from the University of Electronic Science and Technology of China proposed an optimal FDA-MIMO frequency step design in the article "Designing optimal frequency offsets for frequency diverse array MIMO radar", which improves the accuracy of positioning estimation through prior knowledge of potential target locations. However, this method only studies the impact of the transmission frequency step within the radar site on the system, and does not consider the advantages brought by the cooperation between multiple radar sites. The limited coverage, reduced observation dimensions and unstable tracking performance will not only reduce the accuracy and reliability of target detection, increase the risk of false alarms and missed alarms, but also weaken the radar system's adaptability to complex environments, limit its multi-task processing capabilities, and reduce the flexibility of the system, resulting in a decline in the overall performance of the radar system.

[0005] The patent document with application number CN202410164785.X discloses a target joint parameter estimation method based on FDA-MIMO radar. Based on the frequency offset introduced by FDA, the total echo signal of the FDA-MIMO radar is obtained according to the transmission carrier frequency of the mth transmitting unit; the estimated angle of the target, the estimated speed of the target and the incremental range of the target are obtained according to the total echo signal of the FDA-MIMO radar, and the estimation of the target joint parameters is completed. Since this method only considers the impact of the frequency offset of the transmitting end in the FDA radar, and does not consider the optimization of the radar topology and the receiving end receiving matched filter, it cannot effectively improve the detection performance under high-speed weak targets, and its solution complexity is relatively high. Summary of the invention

[0006] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a distributed FDA-MIMO radar topology and parameter joint optimization method to improve the detection performance of the radar system for weak targets in complex environments and reduce the solution complexity.

[0007] The key technology to achieve the purpose of the present invention is to construct a distributed FDA-MIMO radar system model and optimize it with the goal of maximizing the target output SINR. Since the problem is non-convex and NP-hard, it is converted into three independent sub-problems: distributed FDA-MIMO radar topology, transmit frequency increment, and receive matched filter for optimization and solution. For the optimization problem of distributed FDA-MIMO radar topology, the SQP algorithm is used to convert the nonlinear optimization problem into a simpler quadratic programming problem for solution; for the optimization problem of frequency step amount, the MM algorithm is used to find a substitute function, and the closed-form solution of the substitute function is used for approximate solution; for the optimization problem of the receive matched filter, the implicit convex nature of the problem is used to directly find a closed-form solution for solution; the MBI algorithm is used to perform alternating optimization on each independent sub-problem. Its implementation steps include the following:

[0008] (1) A distributed FDA-MIMO radar system consisting of three radar stations is constructed. The first and second radar stations are co-located FDA-MIMO radars with self-transmission and self-reception, and the third radar station is a phased array radar with passive reception. Each radar has M transmitting array elements and N receiving array elements, and the array element spacing is half a wavelength. A frequency step Δf is introduced between the array elements of the transmitting signal, which is much smaller than the carrier frequency.

[0009] (2) Calculate the signals reflected by the target respectively The signal reflected from the clutter scattering point

[0010] (3) For a point target in space, the signal reflected by the target The signal reflected from the clutter scattering point Construct the signal transmitted by the pth radar, reflected by the target and received by the qth radar after down-conversion and matched filtering: Where p = 1, 2, q = 1, 2, 3, and n represents a stable, zero-mean, spatially white Gaussian noise signal;

[0011] (4) Construct the joint optimization problem of distributed FDA-MIMO radar topology, transmit frequency increment, and receive matched filter to maximize the target output SINR;

[0012] (5) The joint optimization problem is transformed into independent sub-problems of radar site location, transmission frequency increment, and receiving matched filter for optimization and solution:

[0013] (5a) Given the receiving matched filter and the radar site location, the joint optimization problem is transformed into the optimization of only the frequency step size, which is expressed as:

[0014]

[0015] Among them, B w The total radar bandwidth for selecting the transmit frequency increment, SINR0 represents the total output of the distributed FDA-MIMO radar system, and SINR 11 It indicates the target output received by the first radar station after the first radar station transmits the signal, SINR 13 It indicates the target output received by the third radar station after the first radar station transmits the signal, SINR 22 It represents the target output received by the second radar station after the second radar station transmits the signal, SINR 23 represents the target output received by the third radar station after the second radar station transmits the signal;

[0016] (5b) Given the frequency step size and radar site location, the optimization problem is transformed into the optimization of the receiving matched filter only, which is expressed as:

[0017]

[0018] Where: w 11 is a receiving matched filter for receiving a signal transmitted by the first radar station and received by the second radar station,

[0019] w 13 is a receiving matched filter for receiving a signal transmitted by the first radar station and received by the third radar station,

[0020] w 22 is a receiving matched filter for receiving the signal transmitted by the second radar station and received by the second radar station,

[0021] w 23 A receiving matched filter for receiving a signal transmitted by the second radar station and received by the third radar station;

[0022] (5c) Given the frequency step size and receiving matched filter, the optimization problem is transformed into the optimization of only the radar site location, which is expressed as:

[0023]

[0024] Where: (θ i ,R i ) represents the position of the i-th radar in space, i = 1, 2, 3,

[0025] Ω i represents the constraint range of the i-th radar in space;

[0026] (6) The MBI algorithm is used to perform alternating updates on the above independent sub-problems to obtain the optimization results of the location of each site, the transmit frequency increment, and the receive matched filter of the distributed FDA-MIMO radar.

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] Firstly, since the present invention constructs a distributed FDA-MIMO radar system including three radar stations, it takes advantage of waveform diversity compared with traditional distributed radars, and takes advantage of spatial diversity compared with FDA-MIMO radars with a single radar station, thereby further improving the detection performance of the radar system for weak targets.

[0029] Secondly, the present invention jointly optimizes the distributed FDA-MIMO radar system topology, the transmission frequency step amount, and the receiving matched filter, and proposes a solution algorithm based on MBI-MM-SQP, thereby reducing the solution complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the implementation of the present invention;

[0031] Figure 2 is a radar space distribution diagram of the distributed FDA-MIMO radar system in the present invention;

[0032] Figure 3 This is a result diagram of the target output SINR changing with the number of iterations during the joint optimization of the present invention;

[0033] Figure 4 It is a comparison chart of the results before and after the optimization of the positions of each radar station of the present invention. DETAILED DESCRIPTION

[0034] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without creative work should all fall within the scope of protection of the present invention.

[0035] It should be noted that the step numbers in the specification and claims of the present invention are only for a clear description of the implementation scheme of the present invention to facilitate understanding, and the order of the step numbers is not limited.

[0036] Reference Figure 1 The implementation steps of this example include the following:

[0037] Step 1: Build a distributed FDA-MIMO radar system.

[0038] According to the FDA radar technology, after the frequency step amount is introduced between the transmitting array elements, additional target distance information can be obtained, and the MIMO radar technology transmits multiple radar signal waveforms and uses multiple antennas to receive echo signals, which can obtain waveform diversity advantages, and the distributed antenna array observes the target from different perspectives, which can obtain spatial diversity gain and improve the radar's detection performance of the target. Therefore, the present invention considers the use of a distributed FDA-MIMO radar system including 3 radar stations.

[0039] Reference Figure 2 , the spatial location and function of each radar station are as follows:

[0040] 1.1) Distribution of 3 radar stations:

[0041] The spatial position of the first radar station is (2847.01, 10625.2), which is used to transmit signals and receive its own transmitted signals.

[0042] The spatial position of the second radar station is (2687.01, 2687.01), which is used to transmit signals and receive its own transmitted signals.

[0043] The spatial position of the third radar station is (10392.3, 6000), and is used to receive the transmission signals of the first radar station and the second radar station.

[0044] 1.2) Each distributed FDA-MIMO radar is configured with M transmitting array elements and N receiving array elements, and the spacing between the transmitting and receiving array elements is a uniform co-located linear array of half a wavelength;

[0045] 1.3) Introduce a frequency step Δf between each array element of the transmitting signal, which is much smaller than the carrier frequency, and calculate the transmitting frequency f of the mth array element. m :

[0046] f m =f0+(m-1)Δf

[0047] Wherein, f0 is the carrier frequency of the first array element, and m=1,2,...,M.

[0048] Step 2: Calculate the signal reflected by the target Signal reflected from clutter scattering point and the signal y received by the radar pq .

[0049] 2.1) Calculate the signal after the target is reflected

[0050] 2.1.1) Calculate the receiving guidance vector d of the qth radar to the target q (θ q ):

[0051]

[0052] Where d is the array element spacing, λ0 is the wavelength, and θ q represents the angle of the target relative to the qth radar, q = 1, 2, 3, (·) T Represents a transpose operation;

[0053] 2.1.2) Calculate the angle-dependent emission guidance vector a of the pth radar to the target p (θ p ):

[0054]

[0055] Among them, θ p Indicates the angle of the target relative to the pth radar, p = 1, 2;

[0056] 2.1.3) Calculate the distance-dependent transmission guidance vector of the target received by the qth radar after the pth radar transmits the target

[0057]

[0058] in, t * is the sampling time, represents the time delay of the real target;

[0059] 2.1.4) Based on the results of steps 2.1.1) to 2.1.3), calculate the signal reflected by the target

[0060]

[0061] in, represents the Kronecker product operation, ⊙ represents the Hadamard product operation, Indicates the complex echo coefficient of the target;

[0062] 2.2) Calculate the signal reflected from the clutter scattering point

[0063] 2.2.1) Calculate the receiving guidance vector of the qth radar for the clutter scattering point

[0064]

[0065] in, represents the angle of the clutter scattering point relative to the qth radar, i q Represents the i-th radar relative to the q-th radar qdistance angle unit, i q =1,2,...,I q , where I q represents all range angle units relative to the qth radar;

[0066] 2.2.2) Calculate the angle-dependent launch steering vector of the pth radar to the clutter scattering point

[0067]

[0068] in, represents the angle of the clutter scattering point relative to the pth radar, i p Represents the i-th radar relative to the p-th radar p distance angle unit, i p =1,2,...,I p , where I p represents all range angle units relative to the pth radar;

[0069] 2.2.3) Calculate the distance-dependent transmission steering vector of the pth radar after the qth radar receives the clutter scattering point after the pth radar transmits the clutter scattering point.

[0070]

[0071] in, represents the time delay of the clutter scattering point, k represents the scattering points contained in each range angle unit, k = 1, 2, ..., L, L represents all the scattering points contained in each range angle unit;

[0072] 2.2.4) Based on the results of steps 2.2.1) to 2.2.3), calculate the signal reflected from the clutter scattering point

[0073]

[0074] in, Represents the complex echo coefficient of the clutter scattering point.

[0075] 2.3) According to step 2.1) and step 2.2), calculate the signal y received by the qth radar after the pth radar transmits the signal reflected by the target pq :

[0076]

[0077] Where n represents a stationary, zero-mean, spatially white Gaussian noise signal.

[0078] Step 3: Construct the joint optimization problem of distributed FDA-MIMO radar topology, transmit frequency increment, and receive matched filter.

[0079] In order to further improve the target detection performance of the radar system, it is necessary to optimize the distributed FDA-MIMO radar topology, the transmit frequency increment, and the receive matched filter, because optimizing one aspect alone may not achieve the best effect. For example, although optimizing the antenna topology alone can improve the target detection accuracy, if the transmit frequency is not selected properly, it may lead to the inability to identify the target characteristics; similarly, although optimizing the matched filter can improve the signal-to-noise ratio, if the antenna layout is unreasonable, it may cause interference to the received signal. Therefore, the present invention adopts a solution for jointly optimizing the distributed FDA-MIMO radar topology, the transmit frequency increment, and the receive matched filter, and its implementation steps include the following:

[0080] 3.1) According to the position of the i-th radar in space (θ i ,R i ) and the constraint range Ω of the i-th radar in space i , establish the constraints of the spatial location of the radar site:

[0081] (θ i ,R i )∈Ω i , where i = 1, 2, 3;

[0082] 3.2) According to the total radar bandwidth B w And the number of transmitting array elements M, establish the constraint of the transmitting frequency increment Δf, which is expressed as:

[0083]

[0084] 3.3) According to the parameter that the square of the second norm of each subsystem receiving matched filter is equal to 1, the constraints of the receiving matched filter are established:

[0085]

[0086] Where: w 11 is a receiving matched filter for receiving a signal transmitted by the first radar station and received by the second radar station,

[0087] w 13 is a receiving matched filter for receiving a signal transmitted by the first radar station and received by the third radar station,

[0088] w 22 is a receiving matched filter for receiving the signal transmitted by the second radar station and received by the second radar station,

[0089] w 23A receiving matched filter for receiving a signal transmitted by the second radar station and received by the third radar station;

[0090] 3.4) According to steps 3.1) to 3.3), the overall nonlinear optimization problem is expressed as:

[0091]

[0092] Wherein, SINR0 represents the total output of the distributed FDA-MIMO radar system.

[0093] Step 4, transform the joint optimization problem into independent sub-problems of each radar site location, transmit frequency increment, and receive matched filter;

[0094] In order to solve the non-convex, NP-hard problem in step 3.4), it is necessary to transform the joint optimization problem of distributed FDA-MIMO radar topology, transmit frequency increment, and receive matched filter into independent sub-problems of each radar site location, transmit frequency increment, and receive matched filter. The implementation steps include the following:

[0095] 4.1) Calculate the target output SINR received by the first radar station after the first radar station transmits the signal 11 :

[0096]

[0097] Among them, Σ 11 (Δf) is the clutter covariance matrix when the first radar station receives the signal after the first radar station transmits it, represents the noise power, represents the conjugate transpose operation;

[0098] 4.2) Calculate the target output SINR received by the third radar station after the first radar station transmits the signal 13 :

[0099]

[0100] Among them, Σ 13 (Δf) is the clutter covariance matrix when the signal transmitted by the first radar station is received by the third radar station;

[0101] 4.3) Calculate the target output SINR received by the second radar station after the second radar station transmits the signal 22 :

[0102]

[0103] Among them, Σ 22 (Δf) is the clutter covariance matrix when the signal is received by the second radar station after the second radar station transmits it;

[0104] 4.4) Calculate the target output SINR received by the third radar station after the second radar station transmits the signal 23 :

[0105]

[0106] Among them, Σ 23 (Δf) is the clutter covariance matrix when the signal transmitted by the second radar station is received by the third radar station;

[0107] 4.5) Given the receiving matched filter and radar site location, the joint optimization problem is transformed into the optimization of the frequency step size only, which is expressed as:

[0108]

[0109] 4.6) Given the frequency step size and radar site location, the optimization problem is transformed into the optimization of the receiving matched filter only, and its expression is:

[0110]

[0111] 4.7) Given the frequency step size and receiving matched filter, the optimization problem is transformed into the optimization of the radar site location only, and its expression is:

[0112]

[0113] Step 5: Use the MBI algorithm to perform rotation updates on the above independent sub-problems;

[0114] In order to efficiently solve the three independent sub-problems constructed in step 4, after solving each sub-problem separately, the results are compared, and the sub-problem with the largest target output SINR is selected through the MBI algorithm for variable update. The implementation steps include the following:

[0115] 5.1) Solve the emission frequency increment optimization sub-problem:

[0116] 5.1.1) Finding the alternative function SINR' for the transmission frequency increment optimization subproblem through the MM algorithm o (Δf):

[0117]

[0118] Among them, X o , represents the coefficient of the quadratic term of the quadratic function, represents the constant term of a quadratic function;

[0119] 5.1.2) Using the substitution function as a quadratic function, the substitution function SINR' o(Δf) Take the first-order derivative and set it equal to zero to obtain:

[0120]

[0121] 5.1.3) By shifting the terms in the above equation, we can obtain the approximate solution to the optimization subproblem: in max(·) represents the maximum value operation, and min(·) represents the minimum value operation.

[0122] 5.2) Solve the receive matched filter optimization subproblem:

[0123] 5.2.1) The receive matched filter optimization subproblem is transformed into the optimization problem when the qth radar receives the signal after the pth radar transmits the signal. Its expression is:

[0124]

[0125] in represents the noise power, d q (θ q ) represents the receiving guidance vector of the qth radar to the target, a p (θ p ) represents the angle-dependent emission steering vector of the pth radar to the target, represents the distance-dependent transmission guidance vector of the target received by the qth radar after the pth radar transmits the target, w pq represents the receiving matched filter when the signal transmitted by the pth radar is reflected by the target and received by the qth radar, Σ pq (Δf) represents the clutter covariance matrix when the signal transmitted by the pth radar is received by the qth radar;

[0126] 5.2.2) The expression of step 5.2.1) is equivalently transformed into the minimum variance distortion-free response beamformer problem, and its expression is:

[0127]

[0128] 5.2.3) Solve the expression in step 5.2.2) to obtain the solution w of the minimum variance distortion-free response beamformer problem pq ':

[0129]

[0130] 5.2.4) According to the constraint that the square of the second norm of the matched filter received by each subsystem is equal to 1, the solution w of step 5.2.3) is pq 'Normalize and get the optimal receiving matched filter w when the signal transmitted by the pth radar is received by the qth radar pq :

[0131]

[0132] 5.3) Solve the sub-problem of optimizing the location of each radar site:

[0133] 5.3.1) Use the SQP algorithm to transform the sub-problems of optimizing the location of each site into a quadratic programming problem, which is expressed as:

[0134]

[0135] Among them, C1, C2, C3, and C4 are constant terms;

[0136] 5.3.2) The site location of the i-th radar (θ i ,R i ) is limited to a circular area with a known radius and center, and the site location constraint of the i-th radar is obtained, which is expressed as:

[0137]

[0138] in, represents the center of the circular area where the i-th radar is located, represents the radius of the circular area where the i-th radar is located;

[0139] 5.3.3) Combined with step 5.3.1), the sub-problems of optimizing the location of each site are transformed into quadratic programming problems, and the site range of step 5.3.2) is limited to a circular area with a known radius and center. The fmincon function in MATLAB can be used directly to solve the sub-problems of optimizing the location of each radar site.

[0140] 5.4) Solve each sub-problem again and perform the next update;

[0141] 5.5) Repeat step 5.4) until SINR0 (n) -SINR0 (n-1) <ε converges, and the optimal site location, transmit frequency increment, and receive matched filter of the distributed FDA-MIMO radar system are obtained, where SINR0 (n) Represents the output of the nth iteration target, SINR0 (n-1) represents the output of the n-1th iteration target, and ε represents the threshold for reaching convergence.

[0142] The effect of the present invention can be further illustrated by the following simulation experiment:

[0143] 1. Simulation parameters

[0144] The simulation parameters include the simulation parameters of the distributed FDA-MIMO radar system, as shown in Table 1.

[0145] Table 1 Simulation parameters of distributed FDA-MIMO radar system

[0146]

[0147] 2. Simulation Content

[0148] Simulation 1: Under the above simulation parameters, the distributed FDA-MIMO radar system target output SINR is simulated with the present invention to obtain the frequency offset optimization curve, the frequency offset weight vector joint optimization curve, and the frequency offset weight vector site location joint optimization curve. The three curves are compared with the weight vector optimization curve as a benchmark. The results are as follows: Figure 3 .from Figure 3 It can be seen that the target output SINR of the frequency offset optimization curve after convergence of the present invention is improved by 5.741dB compared with the weight vector optimization curve, the target output SINR of the frequency offset weight vector joint optimization curve is improved by 7.193dB compared with the weight vector optimization curve, and the target output SINR of the frequency offset weight vector site location joint optimization curve is improved by 9.724dB compared with the weight vector optimization curve.

[0149] Simulation 2: Under the above simulation parameters, the spatial positions of each station of the distributed FDA-MIMO radar system before and after optimization are simulated by the present invention. The results are as follows: Figure 4 The asterisks represent the initial positions of the radar stations, the triangles represent the optimized positions of the radar stations, and the circular areas represent the spatial position constraints of the radar stations. Figure 4 It can be seen that the spatial position of each radar station is effectively optimized within the constraints.

[0150] The above description is only a specific example of the present invention and does not constitute any limitation to the present invention. It is obvious that for professionals in this field, after understanding the content and principles of the present invention, it is possible to make various modifications and changes in form and details without departing from the principles and structures of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

[0151] It should be noted that the step numbers in the specification and claims of the present invention are only for a clear description of the implementation scheme of the present invention to facilitate understanding, and the order of the step numbers is not limited.

Claims

1. A topology and parameter joint optimization method based on distributed FDA-MIMO radar, characterized in that: The steps include: (1) A distributed FDA-MIMO radar system consisting of three radar stations is constructed. The first and second radar stations are co-located FDA-MIMO radars with self-transmission and self-reception, and the third radar station is a phased array radar with passive reception. Each radar has M transmitting array elements and N receiving array elements, and the array element spacing is half a wavelength. A frequency step Δf is introduced between the array elements of the transmitting signal, which is much smaller than the carrier frequency. (2) Calculate the signals reflected by the target respectively The signal reflected from the clutter scattering point (3) For a point target in space, the signal reflected by the target The signal reflected from the clutter scattering point Construct the signal received by the qth radar after the signal transmitted by the pth radar is reflected by the target: Where p = 1, 2, q = 1, 2, 3, and n represents a stable, zero-mean, spatially white Gaussian noise signal; (4) Construct the joint optimization problem of distributed FDA-MIMO radar topology, transmit frequency increment, and receive matched filter to maximize the target output SINR; (5) The joint optimization problem is transformed into independent sub-problems of radar site location, transmission frequency increment, and receiving matched filter for optimization and solution: (5a) Given the receiving matched filter and the radar site location, the joint optimization problem is transformed into the optimization of only the frequency step size, which is expressed as: Among them, B w The total radar bandwidth for selecting the transmit frequency increment, SINR0 represents the total output of the distributed FDA-MIMO radar system, and SINR 11 It indicates the target output received by the first radar station after the first radar station transmits the signal, SINR 13 It indicates the target output received by the third radar station after the first radar station transmits the signal, SINR 22 It represents the target output received by the second radar station after the second radar station transmits the signal, SINR 23 represents the target output received by the third radar station after the second radar station transmits the signal; (5b) Given the frequency step size and radar site location, the optimization problem is transformed into the optimization of the receiving matched filter only, which is expressed as: Where: w 11 is a receiving matched filter for receiving a signal transmitted by the first radar station and received by the second radar station, w 13 is a receiving matched filter for receiving a signal transmitted by the first radar station and received by the third radar station, w 22 is a receiving matched filter for receiving the signal transmitted by the second radar station and received by the second radar station, w 23 A receiving matched filter for receiving a signal transmitted by the second radar station and received by the third radar station; (5c) Given the frequency step size and receiving matched filter, the optimization problem is transformed into the optimization of only the radar site location, which is expressed as: Where: (θ i ,R i ) represents the position of the i-th radar in space, i = 1, 2, 3, Ω i represents the constraint range of the i-th radar in space; (6) The MBI algorithm is used to perform alternating updates on the above independent sub-problems to obtain the optimization results of the location of each site, the transmit frequency increment, and the receive matched filter of the distributed FDA-MIMO radar.

2. The method according to claim 1, characterized in that The spatial locations of the three radar stations described in step (1) are as follows: The spatial position of the first radar station is (2847.01, 10625.2), which is used to transmit signals and receive its own transmitted signals. The spatial position of the second radar station is (2687.01, 2687.01), which is used to transmit signals and receive its own transmitted signals. The spatial position of the third radar station is (10392.3, 6000), and is used to receive the transmission signals of the first radar station and the second radar station.

3. The method according to claim 1, characterized in that In step (2), the signal after the target reflection is calculated The formula is as follows: in, is the receiving guidance vector of the qth radar to the target, is the angle-dependent emission steering vector of the pth radar to the target, is the distance-dependent transmission steering vector of the pth radar transmitted and reflected by the target and received by the qth radar; d represents the array element spacing, λ0 represents the wavelength, θ q represents the angle of the target relative to the qth radar, θ p represents the angle of the target relative to the pth radar, represents the Kronecker product operation, ⊙ represents the Hadamard product operation, represents the complex echo coefficient of the target, t * is the sampling time, represents the delay of the real target, (·) T Represents a transpose operation.

4. The method according to claim 1, characterized in that: The signal after the clutter scattering point is calculated in step (2) The formula is as follows: in, is the receiving guidance vector of the qth radar to the clutter scattering point, is the angle-dependent launch steering vector of the pth radar to the clutter scattering point, is the distance-dependent transmission steering vector of the pth radar after the pth radar transmits and is reflected by the clutter scattering point and received by the qth radar; represents the complex echo coefficient of the clutter scattering point, represents the delay of the clutter scattering point, k represents the scattering points contained in each distance angle unit, k=1,2,...,L, L represents all the scattering points contained in each distance angle unit, represents the angle of the clutter scattering point relative to the qth radar, represents the angle of the clutter scattering point relative to the pth radar, i p Represents the i-th radar relative to the p-th radar p distance angle unit, i p =1,2,...,I p , where I p represents all the range angle units relative to the pth radar, i q Represents the i-th radar relative to the q-th radar q distance angle unit, i q =1,2,...,I q , where I q Represents all range angle units relative to the qth radar.

5. The method according to claim 1, characterized in that Step (4) constructs the joint optimization problem of distributed FDA-MIMO radar topology, transmit frequency increment, and receive matched filter, which is implemented as follows: (4a) According to the position of the i-th radar in space (θ i ,R i ) and the constraint range Ω of the i-th radar in space i , establish the constraints of the spatial position of the radar site, and its expression is: (i i ,R i )∈Ω i ; (4b) Based on the total radar bandwidth B w And the number of transmitting array elements M, establish the constraint of the transmitting frequency increment Δf, which is expressed as: (4c) Based on the square of the second norm of each subsystem receiving matched filter being equal to 1, the constraints of the receiving matched filter are established, and the expression is: (4d) The overall nonlinear optimization problem established by the above three constraints is expressed as:

6. The method according to claim 1, characterized in that The output signals of each radar in step (5a) are respectively expressed as follows: The target output SINR received by the first radar station after the first radar station transmits the signal 11 : Among them, Σ 11 (Δf) is the clutter covariance matrix when the first radar station receives the signal after the first radar station transmits it, represents the noise power, represents the conjugate transpose operation; The target output SINR after the first radar station transmits the signal and the third radar station receives it 13 : Among them, Σ 13 (Δf) is the clutter covariance matrix when the signal transmitted by the first radar station is received by the third radar station; The target output SINR received by the second radar station after the second radar station transmits the signal 22 : Among them, Σ 22 (Δf) is the clutter covariance matrix when the signal is received by the second radar station after the second radar station transmits it; The target output SINR after the second radar station transmits the signal and the third radar station receives it 23 : Among them, Σ 23 (Δf) is the clutter covariance matrix when the signal transmitted by the second radar station is received by the third radar station.

7. The method according to claim 1, characterized in that Step (6) uses the MBI algorithm to perform alternating updates on the independent sub-problems, which is implemented as follows: (6a) Using the MM-SQP algorithm and the closed-form solution method to solve each sub-problem respectively, and compare the results, the sub-problem with the largest target output SINR is selected through the MBI algorithm to update the variables; (6b) Solve each sub-problem again and perform the next update; (6c) Repeat (6b) until SINR0 (n) -SINR0 (n-1) <ε converges, where SINR0 (n) Represents the output of the nth iteration target, SINR0 (n-1) represents the output of the n-1th iteration target, and ε represents the threshold for reaching convergence.

8. The method according to claim 7, characterized in that Step (6a) uses the MM algorithm to solve the transmission frequency step optimization sub-problem, and the implementation steps are as follows: (6a1) For the transmission frequency step optimization subproblem, the MM algorithm is used to find the alternative function SINR' o (Δf): Among them, X o , represents the coefficient of the quadratic term of the quadratic function, represents the constant term of a quadratic function; (6a2) Using the substitution function as a quadratic function, the substitution function SINR' o (Δf) Take the first-order derivative and set it equal to zero to obtain: (6a3) By shifting the terms in the above equation, we can obtain the approximate solution of the optimization subproblem: in max(·) represents the maximum value operation, and min(·) represents the minimum value operation.

9. The method according to claim 7, characterized in that Step (6a) uses the implicit convexity of the receive matched filter optimization subproblem to directly find a closed-form solution for solving it. The implementation steps are as follows: (6a4) The receive matched filter optimization subproblem is transformed into the optimization problem when the qth radar receives the signal after the pth radar transmits the signal. Its expression is: in represents the noise power, d q (θ q ) represents the receiving guidance vector of the qth radar to the target, a p (θ p ) represents the angle-dependent emission steering vector of the pth radar to the target, represents the distance-dependent transmission guidance vector of the target received by the qth radar after the pth radar transmits the target, w pq represents the receiving matched filter when the signal transmitted by the pth radar is reflected by the target and received by the qth radar, Σ pq (Δf) represents the clutter covariance matrix when the signal transmitted by the pth radar is received by the qth radar; (6a5) The expression of step (6a4) is equivalently transformed into the minimum variance distortionless response beamformer problem, which is expressed as: (6a6) Solve the expression in step (6a5) to obtain the solution to the minimum variance distortionless response beamformer problem w pq ': (6a7) According to the constraint that the square of the bi-norm of the matched filter received by each subsystem is equal to 1, the solution w of step (6a6) pq 'Normalize and get the optimal receiving matched filter w when the signal transmitted by the pth radar is received by the qth radar pq :

10. The method according to claim 7, characterized in that Step (6a) uses the SQP algorithm to transform the radar site location optimization sub-problem into a quadratic programming problem for solution. The implementation steps are as follows: (6a8) The sub-problem of optimizing the location of each site is transformed into a quadratic programming problem, which is expressed as follows: Among them, C1, C2, C3, and C4 are constant terms; (6a9) The site location of the i-th radar (θ i ,R i ) is limited to a circular area with a known radius and center, and the site location constraint of the i-th radar is obtained, which is expressed as: in, represents the center of the circular area where the i-th radar is located, represents the radius of the circular area where the i-th radar is located; (6a10) Combined with step (6a8), the subproblem of optimizing the location of each site is transformed into a quadratic programming problem, and the site range of step (6a9) is limited to a circular area with a known radius and center. The fmincon function in MATLAB can be used directly to solve the subproblem of optimizing the location of each radar site.

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