Joint design method for robust target detection in airborne MIMO radar based on maximization minimization

Abstract

The invention discloses a joint design method for robust detection of airborne MIMO radar targets based on maximization minimization, comprising Step 1. establishing an airborne MIMO radar waveform correlation signal model; Step 2. establishing an airborne MIMO radar robust joint design problem model based on maximization minimization on the basis of the airborne MIMO radar waveform correlation signal model; Step 3. designing a robust joint optimization method for airborne MIMO radar transmitting waveform and receiving filter group according to the robust joint design problem model of airborne MIMO radar based on maximization minimization; the method designs a group of filters in an area where a target may appear, takes the worst signal to interference noise ratio at the output end of the receiving filter group as an optimization criterion, and considers the energy constraint and peak-to-average ratio constraint of the waveform at the same time, and proposes a computationally efficient iterative algorithm based on MM technology, which has the characteristics of being able to resist the uncertainty of target prior information and having low computational complexity.

Description

Technical Field

[0001] The invention relates to the field of radar wave technology, and in particular to a joint design method for robust detection of airborne MIMO radar targets based on maximization and minimization. Background Art

[0002] When airborne radars are working downward, they will encounter very strong ground clutter, which is coupled in the angle Doppler domain, seriously affecting the detection performance of moving targets. Space time adaptive processing (STAP) combines spatial and temporal domains to process received waves, which can separate targets from the clutter background and is an effective technology for suppressing ground clutter and active interference. However, traditional airborne radars often transmit fixed waveforms, and adaptive processing is performed at the receiving end to suppress clutter, but they cannot adapt to complex and changing environments. Multiple-Input Multiple-Output (MIMO) radars can transmit multiple signal waveforms at the same time. The waveform diversity characteristics of MIMO radars give them more advantages in target detection and positioning.

[0003] In 2006, the concept of cognitive radar was proposed, and a closed-loop processing architecture from transmission to reception was constructed. The optimal waveform was adaptively designed by making full use of prior information such as the target and the environment to achieve the matching between the system and the working environment, thus improving the target detection performance of the radar system. Based on this, the idea of ​​cognitive radar was introduced into airborne MIMO radar to carry out the joint design of the transmission waveform and the receiving filter, which is of great significance for improving the performance of airborne radar in detecting moving targets in clutter backgrounds.

[0004] However, most of the existing research on joint design of airborne MIMO radar is based on known target prior information (including spatial angle information and Doppler frequency information). When the prior information is accurately known, the designed transmit waveform and receive filter can improve the target detection performance; however, when the prior information is inaccurate, it will reduce the signal-to-noise ratio loss of the system, seriously reducing the target detection performance of the airborne MIMO radar.

[0005] In order to cope with the degradation of system performance caused by the uncertainty of target prior information, scholars have developed a robust joint design method for airborne MIMO radar transmit waveform and receive filter; in the paper "Robust Joint Design of Transmit Waveform and Receive Filter in Space-Time Adaptive Processing of Signal-Dependent Interference MIMO Radar", the robust joint design problem of MIMO-STAP radar under the condition of inaccurate target Doppler frequency and direction information is considered. To solve this problem, this method uses the worst-case output signal-to-noise ratio on the uncertain set of target direction vectors as the optimization criterion; however, the computational complexity of this robust joint design method is too large, and the simulation scenario does not match the actual airborne MIMO radar; in the paper "Robust Cognitive Transmit Waveform and Receive Filter Design in Airborne MIMO Radar Signal-Dependent Clutter Environment", we use the statistically uniform distribution information of target Doppler frequency and spatial frequency, take the average SINR as the optimization target, and propose four robust joint design methods. However, in actual applications, accurate statistical information about target parameters may not be available.

[0006] Therefore, considering the unknown spatial angle and Doppler frequency of the target, it is urgent to design a method for robustly combining the airborne MIMO radar transmit waveform and receive filter bank to solve the above problems. Summary of the invention

[0007] In view of the above-mentioned problems, the present invention aims to provide a joint design method for robust target detection of airborne MIMO radar based on maximization minimization. The method designs a group of filters in the area where the target may appear, and takes the worst signal-to-interference-noise ratio at the output of the filter group as the optimization criterion. At the same time, the energy constraint and peak-to-average ratio constraint of the waveform are considered, and a computationally efficient iterative algorithm based on MM technology is proposed. The method has the characteristics of being able to resist the uncertainty of target prior information and having low computational complexity.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] A joint design method for robust target detection of airborne MIMO radar based on maximization minimization, including

[0010] Step 1. Establish a waveform-related signal model for airborne MIMO radar;

[0011] Step 2. Based on the waveform correlation signal model of airborne MIMO radar, a robust joint design problem model of airborne MIMO radar based on maximization minimization is established;

[0012] Step 3. According to the robust joint design problem model of airborne MIMO radar based on maximization minimization, a robust joint optimization method for airborne MIMO radar transmit waveform and receive filter bank is designed.

[0013] Preferably, the process of establishing the airborne MIMO radar waveform correlation signal model described in step 1 includes:

[0014] Step 101. Consider the side-view airborne MIMO radar, and set the number of transmitting array elements to N. T , the number of receiving array elements is N R , both the transmitting array and the receiving array are uniform linear arrays, the array element spacing is λ / 2, λ is the radar operating wavelength, each transmitting array element transmits K pulses in one coherent processing interval, and the pulse repetition frequency is f r ;

[0015] Step 102. Order Indicates the nth t The lth transmission code of the antenna, where n t =1,2,…,N T ,l=1,2,…,L, L is the code length of a pulse;

[0016] Step 103. Order Represents the transmit waveform matrix, where N T represents the lth code of the antenna;

[0017] Step 104. The received echo signal containing the target, signal-related clutter and noise can be expressed as:

[0018]

[0019] Among them, in formula (1), Respectively represent α t 、f t and θ t are the target’s complex amplitude, normalized Doppler frequency and angle of arrival, α c,p,k 、f c,p,k and θ c,p,k are the complex amplitude, normalized Doppler frequency and angle of arrival of the kth clutter block, respectively. u(f t ), a(θ t ) and b(θ t ) represent the time domain steering vector, the transmitting spatial domain steering vector and the receiving spatial domain steering vector respectively, represents the Kronecker product, is the shift matrix, s=vec(S), The covariance matrix is The noise vector is is the noise power.

[0020] Preferably, the process of establishing the robust joint design problem model of airborne MIMO radar based on maximization minimization described in step 2 includes:

[0021] Step 201. Assume that the normalized Doppler frequency and spatial angle of the target are known and they are within a certain range, that is, Ψ = [f tmin ,f tmax ] and Ω=[θ tmin ,θ tmax ];

[0022] Step 202. Then discretize Ψ and Ω into I and J grid points respectively, and obtain the discrete angle-normalized Doppler frequency pair

[0023] Step 203. In addition, use a group of LMN R ×1 filter Process the received signal y and tune each receive filter to a specific angle-normalized Doppler frequency pair

[0024] Step 204. Therefore, the (n 1 ,n 2 ) The output SINR of the branch is:

[0025]

[0026] Among them, in formula (2), In formula (3), and

[0027] Step 205. Assume that the prior knowledge of known clutter is known. Therefore, the worst-case output SINR is maximized over all possible normalized Doppler frequencies and angles to resolve the uncertainty of the target parameters. In this case, the worst-case output SINR is the optimization target of the robust joint design, i.e.

[0028]

[0029] Step 206. In actual radar systems, to prevent amplifier overload, energy constraints are imposed on the waveform. H s = 1 and peak-to-average ratio constraint, that is

[0030]

[0031] Among them, in formula (5), It represents the parameter for controlling the PAPR level, and its value range is

[0032] Step 207. Considering the energy and PAPR constraints of the waveform, the PAPR constraints are transformed. The robust joint design problem of the airborne MIMO radar transmit waveform and receive filter bank based on maximization minimization can be expressed as:

[0033]

[0034] In formula (6),

[0035] Preferably, the design process of the robust joint optimization method for airborne MIMO radar transmit waveform and receive filter bank described in step 3 includes:

[0036] S301. For the robust joint design problem model of airborne MIMO radar based on maximization minimization, first fix the transmit waveform s and adjust the receive filter The optimization of is expressed as the optimization problem shown in formula (7):

[0037]

[0038] S302. The optimization problem shown in formula (7) is a minimum variance distortion-free response problem, and its closed-form solution is:

[0039]

[0040] S303. By fixing the receiving filter bank To optimize the transmission waveform s, we can substitute formula (8) into formula (2). After transformation, we can get the optimization problem of the transmission waveform, as shown in formula (9):

[0041]

[0042] S304. The problem shown in formula (9) is a maximization-minimization problem. First, solve the internal optimization problem:

[0043]

[0044] S305. Problem (10) is in the area where the target may exist A minimization problem of Denotes a solution to minimize (10). Using the solution of the internal optimization (10), the external optimization problem about the waveform under energy and PAPR constraints is expressed as:

[0045]

[0046] S306. Let g(s) represent the objective function of problem (11), and use MM technology to find a tight lower bound of g(s).

[0047] Preferably, the specific process of using the MM technique to find a tight lower bound of g(s) in step 306 includes:

[0048] (1) Criterion 1: Let f(x,A) be a quadratic function related to x, and A be a positive definite Hermitian matrix. Then for any point The lower bound of f(x,A) is:

[0049]

[0050] According to criterion 1, at the nth iteration s (n) The lower bound of

[0051]

[0052] Among them, in formula (13),

[0053] And const1 represents the constant part;

[0054] In order to obtain a closed-form solution to problem (11), the objective function of problem (11) is further bounded by a quadratic lower bound;

[0055] (2) Criterion 2: Let L and M be n×n Hermitian matrices, and For any point x 0 , the quadratic function x H The upper bound of Lx is:

[0056]

[0057] Based on criterion 2, s H Q(u (n) )s can be expressed as

[0058]

[0059] In formula (17), λ represents Q(u (n) ), const2 represents the constant part;

[0060] Substituting equation (15) into equation (11) and ignoring the irrelevant constant part, we can obtain the second lower bound of the objective function of problem (11); therefore, problem (11) can be transformed into the following optimization problem:

[0061]

[0062] Among them, in formula (18),

[0063] (3) Criterion 3: Without loss of generality, let |v (n) (1)|≥|v (n) (2)|≥…≥|v (n) (N T L)| and v (n) The number of non-zero elements in is Then the optimal solution to problem (18) is

[0064]

[0065] Among them, in formula (20)

[0066]

[0067] In formula (21), min{·,·}, |·| and e jarg(·) is the element-wise operation,

[0068]

[0069] and

[0070]

[0071] Preferably, the algorithm flow of the robust joint optimization method for airborne MIMO radar transmit waveform and receive filter bank established in steps Step 1-Step 3 includes:

[0072] enter:

[0073] Output: Optimal transmit waveform and receive filter bank pair

[0074] S1. Set n = 0, s (0) =s 0 ;

[0075] S2.n=n+1, use formula (3) to calculate Φ cn (s (n-1) ), according to formula (6) we get the optimal receiving filter bank

[0076] S3. Calculate u using formula (14) (n) , use formula (15) to calculate Q(u (n) ), calculate v according to formula (19) (n) , according to formula (20) to obtain the optimal waveform s (n) ;

[0077] S4. Calculate the worst output

[0078] S5.n=n+1, repeat steps S2-S4. The iteration stops when , where ∈ is the parameter that controls the termination of the iteration.

[0079] The beneficial effects of the present invention are as follows: the present invention discloses a joint design method for robust detection of airborne MIMO radar targets based on maximization and minimization. Compared with the prior art, the improvements of the present invention are as follows:

[0080] Aiming at the problems in the prior art that when the prior information is inaccurate or insufficient, the performance of the joint design method of the existing airborne MIMO radar transmitting waveform and receiving filter is seriously degraded; the traditional robust joint design method has high computational complexity and fails to fully explore the real-time and efficient optimization algorithm, the present invention uses the area where the target may appear as prior information, and designs a joint design method for robust detection of airborne MIMO radar targets based on maximization and minimization. The method designs a group of filters and takes the worst SINR at the output end of the receiving filter group as the optimization criterion, while considering the energy constraint and peak-to-average ratio constraint of the waveform, and establishes a joint design problem based on maximization and minimization, which can obtain better target detection performance under the condition of uncertain target parameters; at the same time, the method introduces the MM (Majorization-Minimization, MM) algorithm, and proposes an efficient iterative algorithm based on MM technology. Compared with the traditional robust joint design method, the method has lower computational complexity, is convenient for the real-time realization of the airborne radar system, has the advantages of being able to resist the uncertainty of the target prior information, and has low computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 The present invention is a design flow chart of the joint design method for robust airborne MIMO radar target detection based on maximizing minima.

[0082] Figure 2 In the embodiment 1 of the present invention, SDP-PAPRC and Algorithm 1 are constrained by PAPR The relationship between the output SINR curve and the number of iterations in the worst case.

[0083] Figure 3 This is a variation curve of the worst output SINR target parameter error in embodiment 1 of the present invention. DETAILED DESCRIPTION

[0084] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0085] See attached Figure 1-3 The joint design method for robust detection of airborne MIMO radar targets based on maximization minimization is shown, including

[0086] Step 1. Establish an airborne MIMO radar waveform-related signal model, which specifically includes:

[0087] Step 101. Consider the side-view airborne MIMO radar, and set the number of transmitting array elements to N. T , the number of receiving array elements is N R , both the transmitting array and the receiving array are uniform linear arrays, the array element spacing is λ / 2, λ is the radar operating wavelength, each transmitting array element transmits K pulses in one coherent processing interval, and the pulse repetition frequency is f r ;

[0088] Step 102. Order Indicates the nth t The lth transmission code of the antenna, where n t =1,2,…,N T ,l=1,2,…,L, L is the code length of a pulse;

[0089] Step 103. Order Represents the transmit waveform matrix, where N T represents the lth code of the antenna;

[0090] Step 104. The received echo signal containing the target, signal-related clutter and noise can be expressed as:

[0091]

[0092] Among them, in formula (1), Respectively represent α t 、f t and θ t are the target’s complex amplitude, normalized Doppler frequency and angle of arrival, α c,p,k 、f c,p,k and θ c,p,k are the complex amplitude, normalized Doppler frequency and angle of arrival of the kth clutter block, respectively. u(f t ), a(θ t ) and b(θ t ) represent the time domain steering vector, the transmitting spatial domain steering vector and the receiving spatial domain steering vector respectively, represents the Kronecker product, is the shift matrix, s=vec(S), The covariance matrix is The noise vector is is the noise power; for convenience of expression, V(f c,p,k ,θ c,p,k ) by Vc,p,k To express;

[0093] Step 2. Based on the waveform correlation signal model of airborne MIMO radar, a robust joint design problem model of airborne MIMO radar based on maximization minimization is established. The specific process includes:

[0094] Step 201. To improve the target detection performance under strong clutter background, the output SINR maximization is used as the optimization criterion. To solve the system performance degradation caused by the uncertainty of target parameters, it is assumed that some prior knowledge of the target is known. Specifically, the normalized Doppler frequency and spatial angle of the target are known and they are within a certain range, that is, Ψ = [f tmin ,f tmax ] and Ω=[θ tmin ,θ tmax ];

[0095] Step 202. Then discretize Ψ and Ω into I and J grid points respectively, and obtain the discrete angle-normalized Doppler frequency pair

[0096] Step 203. In addition, use a group of LMN R ×1 filter Process the received signal y and tune each receive filter to a specific angle-normalized Doppler frequency pair

[0097] Step 204. Therefore, the (n 1 ,n 2 ) The output SINR of the branch can be written as:

[0098]

[0099] Among them, in formula (2), In formula (3), and

[0100] Step 205. Here we assume that the prior knowledge of clutter is known (including f c,p,k and θ c,p,k ), which can be obtained from the geographic information system and previous scans. Therefore, the worst-case output SINR is maximized over all possible normalized Doppler frequencies and angles to resolve the uncertainty of the target parameters. In this case, the worst-case output SINR is the optimization target of the robust joint design, i.e.

[0101]

[0102] Step 206. In actual radar systems, to prevent amplifier overload, energy constraints are imposed on the waveform. H s = 1 and peak-to-average ratio (PAPR), that is

[0103]

[0104] Among them, in formula (5), It represents the parameter for controlling the PAPR level, and its value range is

[0105] Step 207. Considering the energy and PAPR constraints of the waveform, the PAPR constraints are transformed. The robust joint design problem of the airborne MIMO radar transmit waveform and receive filter bank based on maximization minimization can be expressed as:

[0106]

[0107] In formula (6), From the non-convex constraints of the fractional programming objective function of non-convex maximization and minimization, we can see that problem (6) is an NP-hard problem;

[0108] Step 3. Design a robust joint optimization method for airborne MIMO radar transmit waveform and receive filter bank based on the maximization-minimization airborne MIMO radar robust joint design problem model. The specific steps include:

[0109] S301. Design an iterative algorithm to handle the maximin-minimum joint design problem model (6). Specifically, first fix the transmit waveform s and calculate the receive filter The optimization of is expressed as the optimization problem shown in formula (7):

[0110]

[0111] S302. The optimization problem shown in formula (7) is a minimum variance distortion-free response problem, and its closed-form solution is:

[0112]

[0113] S303. By fixing the receiving filter bank To optimize the transmission waveform s, we can substitute formula (8) into formula (2). After transformation, we can get the optimization problem of the transmission waveform, as shown in formula (9):

[0114]

[0115] S304. The problem shown in formula (9) is a maximization-minimization problem. First, solve the internal optimization problem:

[0116]

[0117] S305. Problem (10) is in the area where the target may exist A minimization problem of Denotes a solution to minimize (10). Using the solution of the internal optimization (10), the external optimization problem about the waveform under energy and PAPR constraints is expressed as:

[0118]

[0119] S306. Let g(s) represent the objective function of problem (11), and use MM technology to find a tight lower bound of g(s), specifically including:

[0120] (1) Criterion 1: Let f(x,A) be a quadratic function related to x, and A be a positive definite Hermitian matrix. Then for any point The lower bound of f(x,A) is:

[0121]

[0122] According to criterion 1, at the nth iteration s (n) The lower bound of

[0123]

[0124] Among them, in formula (13), And const1 represents the constant part;

[0125] In order to obtain a closed-form solution to problem (11), the objective function of problem (11) is further bounded by a quadratic lower bound;

[0126] (2) Criterion 2: Let L and M be n×n Hermitian matrices, and For any point x 0 , the quadratic function x H The upper bound of Lx is:

[0127]

[0128] Based on criterion 2, s H Q(u (n) )s can be expressed as

[0129]

[0130] In formula (17), λ represents Q(u (n) ), const2 represents the constant part;

[0131] Substituting equation (15) into equation (11) and ignoring the irrelevant constant part, we can obtain the second lower bound of the objective function of problem (11); therefore, problem (11) can be transformed into the following optimization problem:

[0132]

[0133] Among them, in formula (18),

[0134] (3) Criterion 3: Without loss of generality, let |v (n) (1)|≥|v (n) (2)|≥…≥|v (n) (N T L)| and v (n) The number of non-zero elements in is Then the optimal solution to problem (18) is

[0135]

[0136] Among them, in formula (20)

[0137]

[0138] In formula (21), min{·,·}, |·| and e jarg(·) is the element-wise operation,

[0139]

[0140] and

[0141]

[0142] Preferably, the algorithm flow of the robust joint optimization method for airborne MIMO radar transmit waveform and receive filter bank established in steps Step 1-Step 3 includes:

[0143] enter:

[0144] Output: Optimal transmit waveform and receive filter bank pair

[0145] S1. Set n = 0, s (0) =s 0 ;

[0146] S2.n=n+1, use formula (3) to calculate Φ cn (s(n-1) ), according to formula (6) we get the optimal receiving filter bank

[0147] S3. Calculate u using formula (14) (n) , use formula (15) to calculate Q(u (n) ), calculate v according to formula (19) (n) , according to formula (20) to obtain the optimal waveform s (n) ;

[0148] S4. Calculate the worst output

[0149] S5.n=n+1, repeat steps S2-S4. The iteration stops when , where ∈ is the parameter that controls the termination of the iteration.

[0150] Example 1: Simulation analysis to verify the performance of the proposed robust joint design method

[0151] (1) Simulation environment setting: Considering the front-side view airborne MIMO radar, its transmitting array element, receiving array element, array element spacing, number of pulses during CPI, and pulse repetition frequency (PRF) are set to N T =4, N R =4, d t =d r =λ / 2, M=4 and f r =1 / T r =2000, the code length of each pulse is 16; the carrier frequency and waveform bandwidth are 1GHz and 2.5MHz respectively; the platform height is 8000m, the platform speed is 140m / s, and for clutter echo, it is set to P=1, N c =181, the clutter covariance is The noise covariance matrix is ​​I NrMK , the noise power is 0dB; the actual position of the target on the space-time plane is (0.15, -0.2), the target uncertainty set is Ψ = [0.14, 0.16] and Ω = [-0.21, -0.19], the uniform sampling step is 0.01, and the signal-to-noise ratio is 20dB; the termination condition of the algorithm is ε = 10 -3 ; For comparison, a robust joint design based on semidefinite programming (SDP) with energy and PAPR constraints is named SDP-PAPRC and used as a reference; The number of randomized trials for SDP-PAPRC is 1000; All experiments were performed using Matlab 2016b on a standard laptop (i7-8550U CPU and 16GB RAM);

[0152] (2) Simulation Result 1: Output SINR Variation with the Number of Iterations

[0153] The simulation results are as follows Figure 2 As shown, Figure 2 Plot SDP-PAPRC and Algorithm 1 with PAPR constraint as constraint The relationship curve between the output SINR curve and the number of iterations in the worst case is shown in Fig. 1. It can be seen that with the increase of the number of iterations, the output SINR of all algorithms will increase with the increase of the number of iterations, thus verifying that the proposed algorithm 1 has the characteristic of monotonically increasing. In addition, from Figure 2 It can be seen that the worst output SINR of Algorithm 1 is better than that of SDP-PAPRC. In particular, when reaching convergence, the output SINR of Algorithm 1 is about 1.22 dB higher than that of SDP-PAPRC.

[0154] (3) Simulation result 2: Comparison of the number of iterations and computational complexity of different methods

[0155] Table 1 gives the computational performance of SDP-PAPRC and Algorithm 1, including the number of iterations, total number of calculations, and number of single iterations;

[0156] Table 1: Comparison of number of iterations and amount of computation

[0157] algorithm SDP-PAPRC Algorithm 1 Iterations 3.2 8 Total operation time (s) 29.111 3.696 Single iteration time (s) 9.097 0.462

[0158] It can be seen from Table 1 that compared with SDP-PAPRC, Algorithm 1 has a lower computational complexity; this is because the implementation of SDP-PAPRC involves two SDP problems, while the proposed Algorithm 1 is implemented in the computationally efficient MM framework; specifically, a single iteration of Algorithm 1 requires 0.462 s, while SDP-PAPRC requires 9.097 s; it can be seen that the computational complexity of the proposed Algorithm 1 is significantly reduced.

[0159] (4) Simulation result 3: Change of worst output SINR with target parameter uncertainty

[0160] Simulation 3 verifies the robustness of Algorithm 1 to the uncertainty of target parameters; specifically, two cases are used to verify the effectiveness of SDP-PAPRC and Algorithm 1: "non-robust" means that the robust design is not adopted in the simulation, and "robust" means that the robust joint design method proposed is adopted and the worst output SINR is used to represent it;

[0161] Figure 3The worst-case SINR variations of SDP-PAPRC and Algorithm 1 with target parameter errors are given; the results show that the robust joint design of both methods is better than the non-robust joint design; and the advantage of the robust design over the non-robust design increases with the increase of the target parameter error; in addition, the performance of Algorithm 1 is better than that of SDP-PAPRC in both cases; therefore, it can be concluded that Algorithm 1 has a better SINR and is more robust to target parameter uncertainty.

[0162] From the above three points, it can be seen that the airborne MIMO radar target robust detection joint design method based on maximization minimization described in the present invention is:

[0163] Based on the prior information of the area where the target may exist, a set of receiving filter groups matching the target parameters are designed in this area, and the worst SINR at the output of the receiving filter group is used as the optimization criterion; considering the energy constraint and peak-to-average ratio constraint of the waveform, a maximum-minimum joint design problem is established, and an efficient iterative algorithm based on MM technology is proposed to solve the maximum-minimum joint design problem, which can not only resist the uncertainty of the target prior information, but also significantly reduce the computational complexity.

[0164] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A joint design method for robust detection of airborne MIMO radar targets based on maximization minimization, characterized by: include Step 1. Establish a waveform-related signal model for airborne MIMO radar; The process of establishing the airborne MIMO radar waveform correlation signal model described in step 1 includes: Step 101. Consider the side-view airborne MIMO radar, and set the number of transmitting array elements to N. T , the number of receiving array elements is N R , both the transmitting array and the receiving array are uniform linear arrays, the array element spacing is λ / 2, λ is the radar operating wavelength, each transmitting array element transmits K pulses in one coherent processing interval, and the pulse repetition frequency is f r ; Step 102. Order Indicates the nth t The lth transmission code of the antenna, where n t =1,2,...,N T ,l=1,2,...,L, L is the code length of a pulse; Step 103. Order Represents the transmit waveform matrix, where N T represents the lth code of the antenna; Step 104. The received echo signal containing the target, signal-related clutter and noise can be expressed as: Among them, in formula (1), Respectively represent α t 、f t and θ t are the target’s complex amplitude, normalized Doppler frequency and angle of arrival, α c,p,k 、f c,p,k and θ c,p,k are the complex amplitude, normalized Doppler frequency and angle of arrival of the kth clutter block, respectively. u(f t ), a(θ t ) and b(θ t ) represent the time domain steering vector, the transmitting spatial domain steering vector and the receiving spatial domain steering vector respectively, represents the Kronecker product, is the shift matrix, s = vec(S), The covariance matrix is The noise vector is is the noise power; Step 2. Based on the waveform correlation signal model of airborne MIMO radar, a robust joint design problem model of airborne MIMO radar based on maximization minimization is established; The process of establishing the robust joint design problem model of airborne MIMO radar based on maximization minimization described in step 2 includes: Step 201. Assume that the normalized Doppler frequency and spatial angle of the target are known and they are within a certain range, that is, Ψ = [f tmin ,f tmax ] and Ω=[θ tmin ,θ tmax ]; Step 202. Then discretize Ψ and Ω into I and J grid points respectively, and obtain the discrete angle-normalized Doppler frequency pair Step 203. In addition, use a group of LMN R ×1 filter Process the received signal y and tune each receive filter to a specific angle-normalized Doppler frequency pair Step 204. Therefore, the output SINR of the (n1, n2)th branch is: Among them, in formula (2), In formula (3), and Step 205. Assume that the prior knowledge of known clutter is known. Therefore, the worst-case output SINR is maximized over all possible normalized Doppler frequencies and angles to resolve the uncertainty of the target parameters. In this case, the worst-case output SINR is the optimization target of the robust joint design, i.e. Step 206. In actual radar systems, to prevent amplifier overload, energy constraints are imposed on the waveform. H s = 1 and peak-to-average ratio constraint, that is, Among them, in formula (5), It represents the parameter for controlling the PAPR level, and its value range is Step 207. Considering the energy and PAPR constraints of the waveform, the PAPR constraints are transformed. The robust joint design problem of the airborne MIMO radar transmit waveform and receive filter bank based on maximization minimization can be expressed as: In formula (6), Step 3. Design a robust joint optimization method for airborne MIMO radar transmit waveform and receive filter bank based on the maximization-minimization airborne MIMO radar robust joint design problem model; The design process of the robust joint optimization method for airborne MIMO radar transmit waveform and receive filter bank described in step 3 includes: S301. For the robust joint design problem model of airborne MIMO radar based on maximization minimization, first fix the transmit waveform s and adjust the receive filter The optimization of is expressed as the optimization problem shown in formula (7): S302. The optimization problem shown in formula (7) is a minimum variance distortion-free response problem, and its closed-form solution is: S303. By fixing the receiving filter bank To optimize the transmission waveform s, we can substitute formula (8) into formula (2). After transformation, we can get the optimization problem of the transmission waveform, as shown in formula (9): S304. The problem shown in formula (9) is a maximization-minimization problem. First, solve the internal optimization problem: S305. Problem (10) is in the area where the target may exist A minimization problem of Denotes a solution to minimize (10). Using the solution of the internal optimization (10), the external optimization problem about the waveform under energy and PAPR constraints is expressed as: S306. Let g(s) represent the objective function of problem (11), and use MM technology to find a tight lower bound of g(s).

2. The airborne MIMO radar target robust detection joint design method based on maximization minima according to claim 1, characterized in that: The specific process of using the MM technique to find a tight lower bound of g(s) in step 306 includes: (1) Criterion 1: Let f(x,A) be a quadratic function related to x, and A be a positive definite Hermitian matrix. Then for any point The lower bound of f(x,A) is: According to criterion 1, at the nth iteration s (n) The lower bound of Among them, in formula (13), And const1 represents the constant part; In order to obtain a closed-form solution to problem (11), the objective function of problem (11) is further bounded by a quadratic lower bound; (2) Criterion 2: Let L and M be n×n Hermitian matrices, and M ≥ L. For any point x0, the quadratic function x H The upper bound of Lx is: Based on criterion 2, s H Q(u (n) )s can be expressed as In formula (17), λ represents Q(u (n) ), const2 represents the constant part; Substituting equation (15) into equation (11) and ignoring the irrelevant constant part, we can obtain the second lower bound of the objective function of problem (11); therefore, problem (11) can be transformed into the following optimization problem: Among them, in formula (18), (3) Criterion 3: Without loss of generality, let |v (n) (1)|≥|v (n) (2)|≥...≥|v (n) (N T L)| and v (n) The number of non-zero elements in is Then the optimal solution to problem (18) is Among them, in formula (20) In formula (21), min{·,·}, |·| and e jarg() is the element-wise operation, and 3. The airborne MIMO radar target robust detection joint design method based on maximization minima according to claim 2, characterized in that: The algorithm flow of the robust joint optimization method of airborne MIMO radar transmit waveform and receive filter bank established in Step 1-Step 3 includes: enter: Output: Optimal transmit waveform and receive filter bank pair S1. Set n = 0, s (0) =s0; S2.n=n+1, use formula (3) to calculate Φ cn (s (n-1) ), according to formula (6) we get the optimal receiving filter bank S3. Calculate u using formula (14) (n) , use formula (15) to calculate Q(u (n) ), calculate v according to formula (19) (n) , according to formula (20) to obtain the optimal waveform s (n) ; S4. Calculate the worst output SINR S5.n=n+1, repeat steps S2-S4. The iteration stops when , where ∈ is the parameter that controls the termination of the iteration.

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