A joint design method for airborne MIMO radar transceiver based on feasible point tracking

Abstract

The present invention belongs to the field of radar technology, and specifically relates to a joint design method for airborne MIMO radar transceivers based on feasible point tracking. The method comprises the following steps: Step 1: Establish an airborne MIMO radar waveform-related signal model; Step 2: Establish a joint design problem model of an airborne MIMO radar transmitting waveform and a receiving filter group based on maximizing the worst-case output SCNR; Step 3: For the joint design problem model established in step 2, adopt an airborne MIMO radar transceiver joint design method based on FPP‑SCA to obtain the optimal solution of the joint design problem model in step 2. By designing a group of receiving filters in the area where the target may appear to solve the problem of the decrease in output SCNR caused by the uncertainty of target parameters, a joint design method based on FPP‑SCA is designed to solve the optimal waveform. Simulation shows that the method of the present invention has been significantly improved in the worst output SCNR and operation time, and has better detection performance when there are errors in the target parameters.

Description

Technical Field

[0001] The invention belongs to the field of radar technology, and in particular relates to an airborne MIMO radar transceiver joint design method based on feasible point tracking. Background Art

[0002] Airborne radar can effectively improve the detection performance of low-altitude and long-range targets, but it will encounter very strong ground clutter when working downward, causing the target to be submerged in the clutter background. Space time adaptive processing (STAP) combines the spatial and temporal domains to process the received echo, which can effectively suppress strong ground clutter and improve the detection performance of targets.

[0003] Multiple-input multiple-output (MIMO) radar can flexibly transmit different waveforms through different antennas. MIMO radar can design different transmission waveforms by using the characteristics of waveform diversity. Cognitive radar extends the radar's adaptive reception to the transmitter, forming a fully adaptive architecture of the receiver, transmitter and external environment. It can use feedback information to design the optimal waveform that matches the external environment at the transmitter, thereby improving the performance of the radar system.

[0004] The adaptive processing of the airborne MIMO radar receiver is extended to the transmitter, and the airborne MIMO radar transmit waveform and receive filter are jointly designed. This enables the airborne MIMO radar to design the optimal transmit waveform and receive filter based on actual environmental information, thereby achieving the best match between the system and the environment and improving the ability of the airborne MIMO radar to cope with complex environments.

[0005] Most of the current research on the joint design of airborne MIMO radar transmit waveforms and receive filters is based on the accurate knowledge of prior information. In actual situations, it is difficult to obtain accurate prior information. When the prior information is inaccurate, the designed waveforms and processors not only fail to improve the target detection performance, but also lead to a serious deterioration of system performance. In view of the uncertainty of the target Doppler frequency and angle, a MIMO-STAP radar joint design method with PAPR and transmit power constraints is adopted, but this method has high computational complexity and only considers three independent interferences in the simulation scenario. There are also four robust joint design methods that are proposed based on the known target Doppler frequency and spatial angle statistical distribution, and the average output signal-to-clutter-plus-noise ratio (SCNR) is derived as an optimization criterion. In addition, for the case where the target prior information is unknown, the worst-case SCNR is used as the optimization criterion, and the joint design method of receiving and transmitting under energy constraints, similarity constraints, and peak-to-average ratio constraints is studied. Finally, there is the problem of detecting extended targets in a clutter background. Someone proposed a joint design method of the transmitting waveform and receiving filter based on semi-positive definite programming and randomization, but this method requires two semi-positive definite programming problems and has high computational complexity.

[0006] Therefore, the shortcomings of the current technology are: when the prior information is inaccurate or insufficient, the performance of the existing joint design method of airborne MIMO radar transmit waveform and receive filter is seriously degraded; the traditional method based on semi-definite programming and randomization has high computational complexity, and it is necessary to find a solution algorithm with low computational complexity. Summary of the invention

[0007] The present invention aims at the joint design problem of transmitting waveform and receiving filter of the onboard MIMO radar when the target angle and Doppler parameters are inaccurate, designs a set of filters that match the area where the target may exist, considers the constant modulus and similarity wave constraints of the actual waveform, and establishes a joint design problem based on maximization and minimization with the maximization of the worst-case output SCNR as the optimization goal, and proposes an iterative optimization method to optimize the transmitting waveform and receiving filter group, wherein an algorithm based on FPP-SCA is designed to solve the optimal waveform of constant modulus and similarity constraints. The effectiveness of the proposed method is verified by simulation experiments.

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

[0009] A method for joint design of airborne MIMO radar transmission and reception based on feasible point tracking includes the following steps:

[0010] Step 1: Establish a signal model related to the airborne MIMO radar waveform;

[0011] Step 2: Based on the airborne MIMO radar waveform correlation signal model established in step 1, a joint design problem model of the airborne MIMO radar transmit waveform and receive filter bank based on maximizing the worst-case output SCNR is established;

[0012] Step 3: For the joint design problem model established in step 2, the airborne MIMO radar transceiver joint design method based on FPP-SCA is adopted to obtain the optimal solution of the joint design problem model in step 2.

[0013] Preferably, the specific steps of establishing the airborne MIMO radar waveform-related signal model in step 1 include:

[0014] Step 1.1: Define the number of transmitting array elements of the co-located front-side airborne MIMO radar as 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, and the radar transmits M pulses in one coherent processing interval with a repetition frequency of f r The pulse group;

[0015] Step 1.2: Assumptions represents the sampled waveform emitted by the nth transmitting array element, then the transmitting waveform matrix of the radar system can be expressed as Where L represents the number of single pulse samples, and each pulse emits the same waveform;

[0016] Step 1.3: The echo signal received by the airborne MIMO radar, which contains the target signal, signal-related clutter and noise, is expressed as:

[0017]

[0018] That is, the airborne MIMO radar waveform correlation signal model is established, in which, α t 、f t and θ t represent the target’s complex amplitude, normalized Doppler frequency and angle of arrival, respectively.

[0019] 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. is the target space-time steering matrix, where represents the Kronecker product, the superscript T represents the transposition operation, the subscript t represents the target, and I L represents the L×L identity matrix, 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, is the space-time steering matrix of the (p, k)th clutter block, is the shift matrix, s=vec(S), vec(s) represents the vectorization operation of the matrix, The covariance matrix is The noise vector is is the noise power. For convenience, V(f c，p，k ,θ c，p，k ) by V c，p，k To express.

[0020] Preferably, the step 2 of establishing a joint design model of the airborne MIMO radar transmit waveform and receive filter bank based on maximizing the worst case output SCNR comprises:

[0021] Step 2.1: Assume that the normalized Doppler frequency Ψ and spatial angle Ω of the target signal are known, where Ψ = [f tmin , f tmax ] and Ω=[θ tmin ,θ tmax ], indicating the range of Ψ and Ω;

[0022] Step 2.2: Discretize Ψ and Ω in step 2.1 into I and J grid points respectively to obtain the discrete angle-normalized Doppler frequency pair Among them, n1 and n2 are variable parameters. and Represents an index collection, Indicates that index n1 ranges from 1 to I, Indicates that index n2 ranges from 1 to J;

[0023] Step 2.3: Using a set of LMNs R ×1 filter bank, Process the received signal y of step 1, where Denote the (n1, n2)th filter, and tune each receive filter to the angle-normalized Doppler frequency pair Then, the output SINR of the (n1, n2)th branch can be expressed as:

[0024]

[0025] in, represents expectation, and the superscript H represents the conjugate transpose operation. represents the (n1, n2)th discrete angle-normalized Doppler frequency pair, Φ cn (s) is the clutter covariance matrix, which is calculated by the following formula:

[0026]

[0027] in, is the noise power, P represents the number of distance units on both sides of the unit to be detected, Nc represents the number of clutter blocks in a single distance unit, represents the power of the (p, k)th clutter block, φ c，p，k represents the spatial angle of the (p, k)th clutter block;

[0028] Step 2.4: Assume prior information about signal-correlated clutter f c，p，k and θ c，p，k is known, then the output SCNR in the worst case is maximized at all possible normalized Doppler frequencies and spatial angles of the target signal as the optimization criterion, and the output SCNR in the worst case is the optimization target of the joint design of the airborne MIMO radar transmit waveform and receive filter bank, that is:

[0029]

[0030] Among them, subscript n1 belongs to the index set n2 belongs to the index set

[0031] Step 2.5: In an actual radar system, a constant modulus constraint is imposed on the waveform to prevent overloading of the amplifier. represents the nth element of s; at the same time, in order to make the optimized waveform have good fuzzy function characteristics, a similarity constraint is imposed on the waveform, that is, ||s-s0|| ∞ ≤δ, where s0 represents the reference waveform, ||s-s0|| ∞ represents the infinite norm of the matrix, δ is used to control the similarity between the optimized waveform and the reference waveform s0, ||s0|| 2 =1, ||s0|| represents the Euclidean norm of the matrix;

[0032] Therefore, the joint design model of airborne MIMO radar transmit waveform and receive filter bank based on maximizing the worst-case output SCNR is expressed as:

[0033]

[0034] Wherein, δ represents the similarity constraint parameter, and the joint design model (5) is a non-convex maximization minimization optimization problem.

[0035] Preferably, the specific operations of step 3 include:

[0036] Step 3.1: Define the number of iterations as i, and initialize it to i=1;

[0037] Step 3.2: Calculate the clutter covariance matrix Φ cn (s (i-1) ) and receive filter banks represents the (n1, n2)th receiving filter at the i-th iteration;

[0038] Step 3.3: Solve problem (5) using the FPP-SCA-based joint design method to obtain the optimal waveform s (i) ;

[0039] Step 3.4: If Stop the loop; otherwise, return to step 2, where n represents the iteration termination condition;

[0040] Step 3.5: Output s * =s (i) and That is, the optimal solution is obtained.

[0041] Preferably, in step 3.2, the clutter covariance matrix Φ is calculated cn (s (i-1) ) are as follows:

[0042]

[0043] Preferably, the receive filter bank is calculated in step 3.2 The process includes:

[0044] Step 3.2.1: Fixed transmit waveform S, and the receive filter bank The optimization expression is:

[0045]

[0046] Step 3.2.2: The optimization problem (12) has IJ independent The corresponding objective function, therefore, the optimization of problem (12) can be transformed into Optimization, about The closed-form solution of can be expressed as:

[0047]

[0048] Among them, s (i-1) Represents the waveform at the (i-1)th iteration.

[0049] Preferably, the specific operations of step 3.3 include:

[0050] Step 3.3.1: Fix the receive filter bank The optimized expression of the transmission waveform s is:

[0051]

[0052] Step 3.3.2: Substitute equation (7) into the objective function of equation (8) and transform problem (8) into problem (9) after sorting:

[0053]

[0054] Step 3.3.3: Problem (9) is a non-convex maximization minimization problem. An auxiliary variable t is introduced to transform problem (9) into:

[0055]

[0056] in: Q has no actual meaning. For the convenience of calculation later, the left side of the formula is used instead of the right side.

[0057] The objective function of formula (10) is convex, but the three constraints are non-convex. Then the three constraints are expanded to obtain formulas (13), (16) and (17);

[0058] Step 3.3.4: Replace the non-convex constraints in equation (10) with convex approximations (13), (16) and (17), and you can get the convex approximation of equation (10):

[0059]

[0060] Among them, s f represents any feasible solution, the superscript * represents conjugate, and Re represents taking the real part of a complex number;

[0061] because and There is only one intersection, and equation (18) has only a single feasible solution;

[0062] Step 3.3.5: Add a non-negative auxiliary variable u to the third constraint of equation (18), and add ||u||1 to the objective function, where ||u||1 represents the 1-norm of the matrix. At the i-th iteration, equation (18) is transformed into:

[0063]

[0064] Among them, ρ and κ represent positive penalty parameters;

[0065] Step 3.3.6: Assumption (s (i) , t (i)) represents the solution of equation (19) at the i-th iteration. By continuously iteratively solving the optimization problem, the solution s of the original problem (8) or (10) can be obtained. (i) .

[0066] Preferably, the first constraint 1 of formula (10) in step 3.3.3,

[0067] Step 3.3.3.1.1: Due to is a semi-positive definite matrix, then for any feasible solution of problem (10) The following inequality holds:

[0068]

[0069] Step 3.3.3.1.2: Expand the left side of equation (11) to obtain:

[0070]

[0071] Step 3.3.3.1.3: Substitute inequality (12) into the first constraint of problem (10) to obtain:

[0072]

[0073] Preferably, the second constraint 2 of formula (10) in step 3.3.3 is

[0074] Step 3.3.3.2.1: The second constraint of equation (10) can be expressed as and The intersection of is convex, and It is a non-convex constraint;

[0075] Step 3.3.3.2.2: Use the first-order condition of convex function to approximate the lower bound:

[0076]

[0077] Step 3.3.3.2.3: It can be approximated as:

[0078]

[0079] Step 3.3.3.2.4: Arrange equation (15) to obtain:

[0080]

[0081] Preferably, the third constraint 3 of equation (10) in step 3.3.3 is to expand the third constraint in problem (10) and express it as a convex quadratic constraint:

[0082] |s(n)-s0(n)| 2 ≤δ 2 , n=1,…,N T L (17).

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] In order to improve the target detection performance of airborne MIMO radar when there are errors in target parameters, a joint design method of airborne MIMO radar transceiver based on FPP-SCA iteration is proposed. A set of receiving filters are designed in the area where the target may appear to solve the decrease in output SCNR caused by target parameter uncertainty. Considering the constant modulus and similarity constraints of the waveform, an FPP-SCA algorithm is designed to solve the optimal waveform. Simulation results show that compared with the traditional method based on semi-positive programming and randomization, the method of the present invention has been significantly improved in the worst output SCNR and operation time. In addition, the method can still maintain excellent detection performance when there are errors in target parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0086] In the attached picture:

[0087] Figure 1 is a flow chart of the method of the present invention;

[0088] Figure 2 The worst output SCNR of the present invention varies with the number of iterations;

[0089] Figure 3 It is the variation of the worst output SCNR of the present invention with the uncertainty of the target parameters. DETAILED DESCRIPTION

[0090] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0091] Example:

[0092] See attached Figure 1-3 As shown, a joint design method for airborne MIMO radar transmission and reception based on feasible point tracking includes the following steps:

[0093] Step 1: Establish an airborne MIMO radar waveform-related signal model, including the following steps:

[0094] Step 1.1: Define the number of transmitting array elements of the co-located front-side airborne MIMO radar as 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, and the radar transmits M pulses in one coherent processing interval with a repetition frequency of f r The pulse group;

[0095] Step 1.2: Assumptions represents the sampled waveform emitted by the nth transmitting array element, then the transmitting waveform matrix of the radar system can be expressed as Wherein, L represents the number of single pulse samples, and each pulse emits the same waveform;

[0096] Step 1.3: The echo signal received by the airborne MIMO radar, which contains the target signal, signal-related clutter and noise, is expressed as:

[0097]

[0098] That is, the airborne MIMO radar waveform correlation signal model is established, in which, α t 、 t and θ t Respectively represent 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. is the target space-time steering matrix, where represents the Kronecker product, the superscript T represents the transposition operation, the subscript t represents the target, and I L represents the L×L identity matrix, 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, is the space-time steering matrix of the (p, k)th clutter block, is the shift matrix, s=vec(S), vec(s) represents the vectorization operation of the matrix, The covariance matrix is The noise vector is is the noise power. For convenience, V(f c，p，k ,θ c，p，k ) by V c，p，k To express.

[0099] Step 2: Based on the airborne MIMO radar waveform-related signal model established in step 1, a joint design problem model of the airborne MIMO radar transmit waveform and receive filter bank based on maximizing the worst-case output SCNR is established, including:

[0100] Step 2.1: Assume that the normalized Doppler frequency Ψ and spatial angle Ω of the target signal are known, where Ψ = [f tmin , f tmax ] and Ω=[θ tmin ,θ tmax ], indicating the range of Ψ and Ω;

[0101] Step 2.2: Discretize Ψ and Ω in step 2.1 into I and J grid points respectively to obtain the discrete angle-normalized Doppler frequency pair Among them, n1 and n2 are variable parameters. and Represents an index collection, Indicates that index n1 ranges from 1 to I, Indicates that index n2 ranges from 1 to J;

[0102] Step 2.3: Using a set of LMNs R ×1 filter bank, Process the received signal y of step 1, where Denote the (n1, n2)th filter, and tune each receive filter to the angle-normalized Doppler frequency pair Then, the output SINR of the (n1, n2)th branch can be expressed as:

[0103]

[0104] in, represents expectation, and the superscript H represents the conjugate transpose operation. represents the (n1, n2)th discrete angle-normalized Doppler frequency pair, Φ cn (s) is the clutter covariance matrix, which is calculated by the following formula:

[0105]

[0106] in, is the noise power, P represents the number of distance units on both sides of the unit to be detected, N c Indicates the number of clutter blocks in a single range unit, represents the power of the (p, k)th clutter block, φ c，p，k represents the spatial angle of the (p, k)th clutter block;

[0107] Step 2.4: Assume prior information about signal-correlated clutter f c，p，k and θ c，p，k is known, then the output SCNR in the worst case is maximized at all possible normalized Doppler frequencies and spatial angles of the target signal as the optimization criterion, and the output SCNR in the worst case is the optimization target of the joint design of the airborne MIMO radar transmit waveform and receive filter bank, that is:

[0108]

[0109] Among them, subscript n1 belongs to the index set n2 belongs to the index set

[0110] Step 2.5: In an actual radar system, a constant modulus constraint is imposed on the waveform to prevent overloading of the amplifier. represents the nth element of s; at the same time, in order to make the optimized waveform have good fuzzy function characteristics, a similarity constraint is imposed on the waveform, that is, ||s-s0|| ∞ ≤δ, where s0 represents the reference waveform, ||s-s0|| ∞ represents the infinite norm of the matrix, δ is used to control the similarity between the optimized waveform and the reference waveform s0, ||s0|| 2 =1, ||s0|| represents the Euclidean norm of the matrix;

[0111] Therefore, the joint design model of airborne MIMO radar transmit waveform and receive filter bank based on maximizing the worst-case output SCNR is expressed as:

[0112]

[0113] Wherein, δ represents the similarity constraint parameter, and the joint design model (5) is a non-convex maximization minimization optimization problem.

[0114] Step 3: For the joint design problem model established in step 2, the airborne MIMO radar transceiver joint design method based on FPP-SCA is used to obtain the optimal solution of the joint design problem model in step 2. The specific operations include:

[0115] Step 3.1: Define the number of iterations as i, and initialize it to i=1;

[0116] Step 3.2: Calculate the clutter covariance matrix Φ cn (s (i-1) ) and receive filter banks represents the (n1, n2)th receive filter at the i-th iteration.

[0117] Calculate the clutter covariance matrix Φ cn (s (i-1) ) are as follows:

[0118]

[0119] Compute receive filter bank The specific steps are:

[0120] Step 3.2.1: Fixed transmit waveform S, and the receive filter bank The optimization expression is:

[0121]

[0122] Step 3.2.2: The optimization problem (12) has IJ independent The corresponding objective function, therefore, the optimization of problem (12) can be transformed into Optimization, about The closed-form solution of can be expressed as:

[0123]

[0124] Among them, s (i-1) Represents the waveform at the (i-1)th iteration.

[0125] Step 3.3: Use the FPP-SCA algorithm to solve problem (19) and obtain the optimal waveform s (i) Specific operations include:

[0126] Step 3.3.1: Fix the receive filter bank The optimized expression of the transmission waveform s is:

[0127]

[0128] Step 3.3.2: Substitute equation (7) into the objective function of equation (8) and transform problem (8) into problem (9) after sorting:

[0129]

[0130] Step 3.3.3: Problem (9) is a non-convex maximization minimization problem. An auxiliary variable t is introduced to transform problem (9) into:

[0131]

[0132] in: Q has no actual meaning. For the convenience of calculation later, the left side of the formula is used instead of the right side.

[0133] The objective function of formula (10) is convex, but the three constraints are non-convex. Then the three constraints are expanded to obtain formulas (13), (16) and (17);

[0134] Step 3.3.3.1.1: Due to is a semi-positive definite matrix, then for any feasible solution of problem (10) The following inequality holds:

[0135]

[0136] Step 3.3.3.1.2: Expand the left side of equation (11) to obtain:

[0137]

[0138] Step 3.3.3.1.3: Substitute inequality (12) into the first constraint of problem (10) to obtain:

[0139]

[0140] The second constraint 2 of formula (10):

[0141] Step 3.3.3.2.1: The second constraint of equation (10) can be expressed as and The intersection of is convex, and It is a non-convex constraint;

[0142] Step 3.3.3.2.2: Use the first-order condition of convex function to approximate the lower bound:

[0143]

[0144] Step 3.3.3.2.3: It can be approximated as:

[0145]

[0146] Step 3.3.3.2.4: Arrange equation (15) to obtain:

[0147]

[0148] The third constraint 3 of formula (10):

[0149] Step 3.3.3.3: Expand the third constraint in problem (10) and express it as a convex quadratic constraint:

[0150] |s(n)-s0(n)| 2 ≤δ2 , n=1,…,N T L (17).

[0151] Step 3.3.4: Replace the non-convex constraints in equation (10) with convex approximations (13), (16) and (17), and you can get the convex approximation of equation (10):

[0152]

[0153] Among them, s f represents any feasible solution, the superscript * represents conjugate, and Re represents taking the real part of a complex number;

[0154] because and There is only one intersection, and equation (18) has only a single feasible solution;

[0155] Step 3.3.5: Add a non-negative auxiliary variable u to the third constraint of equation (18), and add ||u||1 to the objective function, where ||u||1 represents the 1-norm of the matrix. At the i-th iteration, equation (18) is transformed into:

[0156]

[0157] Among them, ρ and κ represent positive penalty parameters;

[0158] Step 3.3.6: Assumption (s (i) , t (i) ) represents the solution of equation (19) at the i-th iteration. By continuously iteratively solving the optimization problem, the solution s of the original problem (8) or (10) can be obtained. (i) .

[0159] Step 3.4: If Stop the loop; otherwise, return to step 2, where n represents the iteration termination condition;

[0160] Step 3.5: Output s * =s (i) and That is, the optimal solution is obtained.

[0161] Simulation experiment:

[0162] The simulation scenario is as follows: The airborne MIMO radar with co-located transmitter and receiver has N transmitting array elements. T =4, the number of receiving array elements is N R =4, the array element spacing is d T =d R =λ / 2, the number of pulses in the coherent processing interval is M=4, and the pulse repetition frequency is f r=2000, the number of single pulse samples is L=8. The aircraft altitude is 8000m, and the flight speed is V p =140m / s. Receive clutter of 5 range units (P=2), the number of clutter blocks in a single range unit is N c =181, the clutter power is Among them, R0 and R p Represent the distances from the unit to be detected and the pth distance unit to the carrier respectively. The noise power is 0dB. The true position of the target in the space-time two-dimensional plane is (0.2, -0.2), the target uncertainty set is Ψ = [0.1, 0.3] and Ω = [-0.3, -0.1], the uniform sampling step is 0.02, then the number of samples is I = J = 11. The signal-to-noise ratio is 20dB. The orthogonal linear frequency modulation waveform is used as the reference waveform, that is:

[0163]

[0164] Among them, n t =1,…,N T and l = 1, ..., L, and s0 = vev(S0). The parameters of the FPP-SCA iterative algorithm are set as follows: η = 10 -4 , κ=10 -5 The comparison algorithm is based on semi-positive programming and randomization method, referred to as SDP-R method, and the parameters are set as follows: the iteration termination condition is 10 -4 , the number of random trials is 1000. The simulation experiment platform is a notebook (i7-8550U CPU and 16GB RAM) Matlab 2016b.

[0165] Simulation 1: Output SINR changes with the number of iterations

[0166] like Figure 2 , the worst output SCNR curves of different methods with the number of iterations are given, and the similarity parameters are γ = 0.4, γ = 1 and γ = 2, where, The penalty parameter ρ of FPP-SCA is set to 1.

[0167] from Figure 2 It can be seen that the worst output SCNR obtained by FPP-SCA and SDP-R gradually increases with the increase of the number of iterations. When the similarity parameter increases, the worst output SCNR obtained by FPP-SCA and SDP-R also increases. It is worth noting that when γ = 0.4, 1 and 2, the worst output SCNR obtained by the proposed FPP-SCA is significantly better than that of SDP-R. For example, when γ = 0.4, 1 and 2, FPP-SCA is about 5.27dB higher than SDP-R.

[0168] Simulation 2: Comparison of operation time of different methods

[0169] Table 2 shows the comparison of the single iteration running time of FPP-SCA and SDP-R, where γ = 0.4, 1 and 2. It can be seen from Table 2 that when γ = 0.4, 1 and 2, the running time of FPP-SCA and SDP-R single iteration changes slightly. In particular, when γ = 0.4, the running time of FPP-SCA and SDP-R single iteration is the largest, and when γ = 1, the smallest. For a fixed γ, the running time of FPP-SCA single iteration is significantly less than that of SDP-R.

[0170] In fact, the SDP-R algorithm involves solving two SDP problems, and the computational complexity is and Moreover, the more constraints there are, the longer the computation time of the SDP-R algorithm will be.

[0171] Table 2 Comparison of single iteration algorithm running time Unit: s

[0172] algorithm γ=0.4 γ=1 γ=2 SDP-R 164.94 143.61 146.27 FPP-SCA 1.98 1.88 1.91

[0173] Simulation 3: Worst output SINR changes with target parameter uncertainty

[0174] Figure 3 The variation of the worst output SCNR with target parameter uncertainty is given, where the target normalized Doppler frequency error and the target spatial frequency error both increase from 0 to 0.2. The FPP-SCA robustness represents the worst output SCNR obtained by using the proposed FPP-SCA iterative algorithm, and the FPP-SCA non-robustness represents the worst output SCNR obtained by using the proposed FPP-SCA iterative algorithm but without robustness design (the number of filter banks is set to 1 in the simulation).

[0175] from Figure 3 It can be seen that when the target parameter uncertainty is relatively small, the worst output SCNR of FPP-SCA non-robustness is better than that of FPP-SCA robustness. When the target parameter uncertainty value is greater than 0.08, the worst output SCNR of FPP-SCA non-robustness decreases significantly, while the robustness of FPP-SCA decreases slowly. The simulation results verify that FPP-SCA is robust to the uncertainty of target parameters.

[0176] 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 airborne MIMO radar transmission and reception based on feasible point tracking, characterized by: The following steps are involved: Step 1: Establish a signal model related to the airborne MIMO radar waveform; The specific steps of establishing the airborne MIMO radar waveform correlation signal model in step 1 include: Step 1.1: Define the number of transmitting array elements of the co-located front-side airborne MIMO radar as 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, and the radar transmits M pulses in one coherent processing interval with a repetition frequency of f r The pulse group; Step 1.2: Assumptions represents the sampled waveform emitted by the nth transmitting array element, then the transmitting waveform matrix of the radar system can be expressed as Where L represents the number of single pulse samples, and each pulse emits the same waveform; Step 1.3: The echo signal received by the airborne MIMO radar, which contains the target signal, signal-related clutter and noise, is expressed as: That is, the airborne MIMO radar waveform correlation signal model is established, in which, α t 、f t and θ t Respectively represent 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. is the target space-time steering matrix, where represents the Kronecker product, the superscript T represents the transposition operation, the subscript t represents the target, and I L represents the L×L identity matrix, 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, is the space-time steering matrix of the (p,k)th clutter block, is the shift matrix, s=vec(S), vec(s) represents the vectorization operation of the matrix, The covariance matrix is The noise vector is is the noise power. For convenience, V(f c,p,k ,θ c,p,k ) by V c,p,k To express; Step 2: On the basis of the airborne MIMO radar waveform correlation signal model established in step 1, a joint design problem model of the airborne MIMO radar transmit waveform and receive filter group based on maximizing the worst-case output SCNR is established; the step 2 establishing the joint design model of the airborne MIMO radar transmit waveform and receive filter group based on maximizing the worst-case output SCNR includes: Step 2.1: Assume that the normalized Doppler frequency Ψ and spatial angle Ω of the target signal are known, where Ψ = [f tmin ,f tmax ] and Ω=[θ tmin ,θ tmax ], indicating the range of Ψ and Ω; Step 2.2: Discretize Ψ and Ω in step 2.1 into I and J grid points respectively to obtain the discrete angle-normalized Doppler frequency pair Among them, n1 and n2 are variable parameters. and Represents an index collection, Indicates that index n1 ranges from 1 to I, Indicates that index n2 ranges from 1 to J; Step 2.3: Using a set of LMNs R ×1 filter bank, Process the received signal у of step 1, where Denotes the (n1, n2)th filter, and tunes each receive filter to the angle-normalized Doppler frequency pair Then, the output SINR of the (n1, n2)th branch can be expressed as: in, represents expectation, and the superscript H represents the conjugate transpose operation. represents the (n1, n2)th discrete angle-normalized Doppler frequency pair, Φ cn (s) is the clutter covariance matrix, which is calculated by the following formula: in, is the noise power, P represents the number of distance units on both sides of the unit to be detected, N c Indicates the number of clutter blocks in a single range unit, represents the power of the (p,k)th clutter block, φ c,p,k represents the spatial angle of the (p,k)th clutter block; Step 2.4: Assume prior information about signal-correlated clutter f c,p,k and θ c,p,k is known, then the output SCNR in the worst case is maximized at all possible normalized Doppler frequencies and spatial angles of the target signal as the optimization criterion, and the output SCNR in the worst case is the optimization target of the joint design of the airborne MIMO radar transmit waveform and receive filter bank, that is: Among them, subscript n1 belongs to the index set n2 belongs to the index set Step 2.5: In an actual radar system, a constant modulus constraint is imposed on the waveform to prevent overloading of the amplifier. s(n) represents the nth element of s; at the same time, in order to make the optimized waveform have good fuzzy function characteristics, a similarity constraint is imposed on the waveform, that is, ||s-s0|| ∞ ≤δ, where s0 represents the reference waveform, ||s-s0|| ∞ represents the infinite norm of the matrix, δ is used to control the similarity between the optimized waveform and the reference waveform s0, ||s0|| 2 =1, ||s0|| represents the Euclidean norm of the matrix; Therefore, the joint design model of airborne MIMO radar transmit waveform and receive filter bank based on maximizing the worst-case output SCNR is expressed as: Where δ represents the similarity constraint parameter. The joint design model of formula (5) is a non-convex maximization minimization optimization problem. Step 3: For the joint design problem model established in step 2, an airborne MIMO radar transceiver joint design method based on FPP-SCA is adopted to obtain an optimal solution to the joint design problem model in step 2; the specific operations of step 3 include: Step 3.1: Define the number of iterations as i, and initialize it to i=1; Step 3.2: Calculate the clutter covariance matrix Φ cn (s (i-1) ) and receive filter banks represents the (n1,n2)th receiving filter at the i-th iteration; Step 3.3: Solve problem (5) using the FPP-SCA-based joint design method to obtain the optimal waveform s (i) ; Step 3.4: If Stop the loop; otherwise, return to step 2, where n represents the iteration termination condition; Step 3.5: Output s * =s (i) and That is, the optimal solution is obtained.

2. The airborne MIMO radar transceiver joint design method based on feasible point tracking according to claim 1, characterized in that: The clutter covariance matrix Φ is calculated in step 3.2 cn (s (i-1) ) are as follows:

3. The airborne MIMO radar transceiver joint design method based on feasible point tracking according to claim 2, characterized in that: The receive filter bank is calculated in step 3.2 The process includes: Step 3.2.1: Fixed transmit waveform S, and the receive filter bank The optimization expression is: Step 3.2.2: The optimization problem (6) has IJ independent The corresponding objective function, therefore, the optimization of the optimization problem (6) can be transformed into the optimization of each Optimization, about The closed-form solution of can be expressed as: Among them, s (i-1) Represents the waveform at the (i-1)th iteration.

4. The airborne MIMO radar transceiver joint design method based on feasible point tracking according to claim 3 is characterized in that: The specific operations of step 3.3 include: Step 3.3.1: Fix the receive filter bank The optimized expression of the transmission waveform s is: Step 3.3.2: Substitute equation (7) into the objective function of equation (8) and transform problem (8) into problem (9) after sorting: Step 3.3.3: Problem (9) is a non-convex maximization minimization problem. An auxiliary variable t is introduced to transform problem (9) into: in: Q has no actual meaning. For the convenience of calculation later, the left side of the formula is used instead of the right side. The objective function of formula (10) is convex, but the three constraints are non-convex. Then the three constraints are expanded to obtain formulas (13), (16) and (17); Step 3.3.4: Replace the non-convex constraints in equation (10) with convex approximations (13), (16) and (17) to obtain the convex approximation of equation (10): Among them, s f represents any feasible solution, the superscript * represents conjugate, and Re represents taking the real part of a complex number; because and There is only one intersection, and equation (18) has only a single feasible solution; Step 3.3.5: Add a non-negative auxiliary variable u to the third constraint of equation (18), and add ||u||1 to the objective function, where ||u||1 represents the 1-norm of the matrix. At the i-th iteration, equation (18) is transformed into: t≥ (i-1) (19) Among them, ρ and κ represent positive penalty parameters; Step 3.3.6: Assumption (s (i) ,t (i) ) represents the solution of equation (19) at the i-th iteration. By continuously iteratively solving the optimization problem, the solution s of the original problem (8) or (10) can be obtained. (i) .

5. The airborne MIMO radar transceiver joint design method based on feasible point tracking according to claim 4 is characterized in that: The first constraint 1 of equation (10) in step 3.3.3 is, Step 3.3.3.1.1: Due to is a semi-positive definite matrix, then for any feasible solution of problem (10) The following inequality holds: Step 3.3.3.1.2: Expand the left side of equation (11) to obtain: Step 3.3.3.1.3: Substitute inequality (12) into the first constraint of problem (10) to obtain:

6. The airborne MIMO radar transceiver joint design method based on feasible point tracking according to claim 5, characterized in that: The second constraint 2 of equation (10) in step 3.3.3 is, Step 3.3.3.2.1: The second constraint of equation (10) can be expressed as and The intersection of is convex, and It is a non-convex constraint; Step 3.3.3.2.2: Use the first-order condition of convex function to approximate the lower bound: Step 3.3.3.2.3: It can be approximated as: Step 3.3.3.2.4: Arrange equation (15) to obtain:

7. The airborne MIMO radar transceiver joint design method based on feasible point tracking according to claim 6, characterized in that: The third constraint 3 in equation (10) in step 3.3.3 is to expand the third constraint in problem (10) and express it as a convex quadratic constraint: |s(n)-s0(n)| 2 ≤δ 2 ,n=1,…,N T L (17)。

Images