CN107656257A - A kind of Optimization Design of missile-borne MIMO radar waveform covariance matrix - Google Patents
A kind of Optimization Design of missile-borne MIMO radar waveform covariance matrix Download PDFInfo
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Abstract
The invention discloses a kind of Optimization Design of missile-borne MIMO radar waveform covariance matrix, its main thought is：Missile-borne MIMO radar is determined, target and clutter be present in the missile-borne MIMO radar detection range；The echo-signal received when missile-borne MIMO radar is detected into target, it is designated as the echo-signal that missile-borne MIMO radar receives in clutter environment, the echo-signal that missile-borne MIMO radar receives in the clutter environment includes echo signal, noise signal and noise signal, determines missile-borne MIMO radar transmitted waveform vector s；Linear filter weight vector is set, and according to s, the combined optimization problem of missile-borne MIMO radar transmitted waveform vector linear filter weight vector in clutter environment is calculated；According to the combined optimization problem of missile-borne MIMO radar transmitted waveform vector linear filter weight vector in clutter environment, the Optimum Design Results of missile-borne MIMO radar waveform covariance matrix are obtained.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to an optimization design method of a missile-borne MIMO radar waveform covariance matrix, which is suitable for suppressing clutter by adopting a multi-carrier signal system, namely ensuring that a missile finishes accurate striking and effectively improves the clutter resistance of a terminal guidance stage by jointly optimizing a transmitting waveform and receiving filtering.
Background
The missile-borne radar echo target detection is a key link of missile terminal guidance, the current battlefield electromagnetic environment is complex, sufficient target information is difficult to obtain by a fixed missile-borne radar emission waveform under the influence of strong clutter, and the guidance performance of a seeker is seriously influenced; an important direction of future development of the missile-borne radar is to realize continuous analysis and processing of target echo, noise and clutter information on the basis of a cognitive theory, reduce interference of environmental clutter and improve target detection performance of the missile-borne radar by designing a transmitting waveform; accordingly, a missile-borne Multiple-input Multiple-output (MIMO) radar having a more flexible operation mode is gradually drawing attention.
Compared with the traditional single carrier radar, on the premise of giving the bandwidth and power constraint of a radar system, the MIMO radar can improve the performance of the MIMO radar by optimally designing each transmitting antenna and the transmitting waveform of each pulse, has higher resolution capability, can improve the target detection performance, improve the angle estimation precision, reduce the minimum detectable speed and the like; the waveform design of the MIMO radar is mainly divided into two research directions of designing a specific time domain waveform and designing a covariance matrix of a transmitting waveform; the MIMO radar is divided into an orthogonal system and a non-orthogonal system from a waveform angle, and the orthogonal system MIMO radar can execute any equivalent transmitting array processing at a receiving end by transmitting orthogonal signals; the MIMO radar with the non-orthogonal system forms a specific transmitting directional diagram by designing a covariance matrix of a transmitting waveform, different MIMO radar working environments and performance indexes of radar system design provide higher and more specific requirements for the transmitting waveform of the MIMO radar, and therefore for a missile-borne radar platform, constraint conditions such as high-speed movement of the platform, hardware limitation, real-time processing and the like need to be considered.
In recent years, scholars at home and abroad develop a great deal of research on radar target detection performance optimization based on a waveform design theory, and Moran and Sira and the like design and optimize waveforms based on a fuzzy function theory, reduce clutter influence and improve signal-to-clutter ratio by aligning grooves of side lobes of the fuzzy function to strong clutter, but need to call a great number of parameters, have high operation complexity and cannot meet the real-time requirement of a cognitive radar; pilai et al use an iterative algorithm to maximize the transmit waveform and optimize the signal-to-noise ratio output by the matched filter, but this method does not consider the effect of environmental clutter; sadjad et al designs a transmit waveform covariance matrix with a fixed form with a maximized output signal-to-interference-and-noise ratio as a target, but the method is only suitable for the situation that discontinuous strong clutter points exist, and target Doppler is not considered; wangceng et al put forward a radar waveform design method with 9 subcarriers in the published paper "orthogonal multicarrier radar waveform design suitable for missile-borne platform", the method adopts inter-pulse waveform agility and subcarrier frequency domain weighting technology, but the method only designs for transmitting waveforms, does not consider joint optimization of a receiving end, and is only suitable for cooperative work occasions of a plurality of missile-borne radars; in a patent of Yan Qing et al (northwest university) applied for 'a high-speed missile-borne radar waveform design method' (application number: 201710154330.X, publication number: 106940442), a high-speed missile-borne radar waveform design method is provided, which mainly solves the problem that a target over-distance unit walking phenomenon is caused by signal-to-noise ratio reduction, main lobe Doppler clutter spectrum width broadening and high-speed motion between missile eyes through the technologies of millimeter waves, large bandwidth, step frequency and high repetition frequency, but the method is still limited to single carrier frequency waveforms.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide an optimization design method of a missile-borne MIMO radar waveform covariance matrix, which is a method for jointly optimizing a transmitted waveform covariance matrix and a receiving filter, namely a waveform covariance matrix optimization method for improving the signal-to-interference-and-noise ratio output by a receiving end, and can optimize the transmitted waveform of the next frame of the radar by using prior information so as to improve the clutter suppression performance of the missile-borne radar.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
An optimal design method of a missile-borne MIMO radar waveform covariance matrix comprises the following steps:
step 1, determining a missile-borne MIMO radar, wherein the missile-borne MIMO radar is in clutter, and a target exists in a detection range of the missile-borne MIMO radar;
step 2, recording an echo signal received when the missile-borne MIMO radar detects a target as an echo signal received by the missile-borne MIMO radar in a clutter environment, wherein the echo signal received by the missile-borne MIMO radar in the clutter environment comprises a target signal, a clutter signal and a noise signal, and determining a launching waveform vector of the missile-borne MIMO radar;
step 3, setting a weight vector of a linear filter, calculating to obtain an echo signal received by the missile-borne MIMO radar in the clutter environment, and outputting a signal-to-interference-and-noise ratio after linear filtering, thereby obtaining a joint optimization problem of a launch waveform vector and the weight vector of the linear filter of the missile-borne MIMO radar in the clutter environment;
and 4, obtaining an optimization design result of the missile-borne MIMO radar waveform covariance matrix according to the joint optimization problem of the missile-borne MIMO radar transmitting waveform vector and the linear filter weight vector in the clutter environment.
Compared with the prior art, the invention has the following improvements:
firstly, the method applies the missile-borne MIMO radar to a missile-borne radar system, aims at the problem of moving target detection in a clutter environment, and compared with a method only processing at a receiving end and only optimizing a transmitting waveform, the method can optimize a waveform covariance matrix according to prior information by jointly optimizing the transmitting waveform covariance matrix and a receiving filter, thereby controlling a transmitting directional diagram of the next frame of missile-borne MIMO radar, effectively inhibiting the clutter while keeping high gain in a target direction, improving the output signal-to-interference-noise ratio and improving the detection performance of the missile-borne MIMO radar.
Secondly, the method adds the constraint conditions in practical application during waveform optimization design: namely, the transmission power constraint and the constant modulus constraint, so that the optimization problem is closer to the practical engineering application.
Drawings
The invention is further explained below with reference to the drawings and the detailed description.
FIG. 1 is a flow chart of an optimization design method of a missile-borne MIMO radar waveform covariance matrix according to the present invention;
FIG. 2 is a spatial geometry diagram of a missile-borne forward array radar platform with a target and clutter;
FIG. 3 is a graph comparing the variation curve of the output SINR with the cycle number of the method of the present invention and the method of B.Tang et al;
FIG. 4 is a comparison graph of the filter output frequency response of the optimized waveform of the method of the present invention with a single carrier phased array waveform, a fully orthogonal waveform, and the method of B.Tang et al;
fig. 5 is a comparison graph of local amplification of the filter output frequency response of the optimized waveform of the method of the present invention and the single carrier phased array waveform, the complete orthogonal waveform, the method of b.tang et al.
Detailed description of the invention
Referring to fig. 1, it is a flowchart of an optimal design method of a missile-borne MIMO radar waveform covariance matrix according to the present invention; the optimization design method of the missile-borne MIMO radar waveform covariance matrix comprises the following steps:
step 1, determining a missile-borne MIMO radar, wherein the missile-borne MIMO radar is in an environment clutter, a target and the clutter exist in a detection range of the missile-borne MIMO radar, and the target is a low-altitude moving target; referring to fig. 2, a space geometric coordinate system between a missile-borne MIMO radar and a target is provided as an embodiment of the present invention.
Neglecting the influence of the curvature of the earth surface, establishing a xoyz three-dimensional coordinate system by taking a vertical projection point of the missile-borne MIMO radar on the ground as an origin o, wherein the missile-borne MIMO radar is a forward-looking array and is erected at the front end of the missile and does not move relative to the missile; setting the missile to have no yaw in the flying process, wherein the normal direction of the missile-borne MIMO radar array surface is parallel to the flying direction of the missile, the height of the missile-borne MIMO radar is H, the missile flies in the positive direction of the y axis, and the flying speed of the missile is V p (ii) a The missile-borne MIMO radar comprises M transmitting array elements and N receiving array elements, wherein the M transmitting array elements and the N receiving array elements are respectively one-dimensional equidistant linear arrays, and the array element intervals of the M transmitting array elements are d T' The array element interval of N receiving array elements is d R (ii) a Uniformly dividing the ground in the action range of the missile-borne MIMO radar into N by taking the origin o of the xoyz three-dimensional coordinate system as the center of a circle r A ring of equal spacing distance, N r Indicates the total number of equally spaced rings, N r Is a positive integer greater than 0.
The maximum action distance of the missile-borne MIMO radar is R max The minimum action distance of the missile-borne MIMO radar is R min The width DeltaR of each equal-spacing distance ring is determined by the working bandwidth B of the missile-borne MIMO radar, namely DeltaR = c/2B, wherein c is the light speed, B represents the working bandwidth of the missile-borne MIMO radar, and the width DeltaR of each equal-spacing distance ring and the maximum action distance of the missile-borne MIMO radar are R max The minimum action distance of the missile-borne MIMO radar is R min And the total number N of equally spaced rings r The relationship between them is: indicating a rounding down operation.
Marking an equal interval distance ring where the target is located as a distance unit to be detected, and uniformly dividing the distance unit to be detected into N c Each clutter block is set to be uniformly distributed, each clutter block is equivalent to a scattering center, and the distance unit to be detected contains N c A plurality of scattering centers; a connecting line of the ith scattering center and a missile-borne MIMO radar receiving antenna phase center in the distance unit to be detected is recorded as a radar sight line, and an included angle between the projection of the radar sight line on the xoy plane and the positive direction of the x axis is an azimuth angle theta of the ith scattering center c,i The included angle between the radar sight line and the xoy plane is the pitch angle of the ith scattering centerThe included angle between the radar sight line and the missile-borne MIMO radar receiving antenna is the space cone angle psi of the ith scattering center c,i The three angular relationships are:wherein, the receiving antenna is a linear array formed by N receiving array elements, i =1 c ，N c The total number of clutter blocks contained in the distance unit to be detected is represented and is equal to the total number of scattering centers contained in the distance unit to be detected in value.
The phase center of the missile-borne MIMO radar receiving antenna is located at (0, H) in the xoyz three-dimensional coordinate system, and N receiving array elements are symmetrically distributed on two sides of the phase center of the missile-borne MIMO radar receiving antenna at equal intervals in a direction parallel to the x axis by taking (0, H) as the center.
Setting the target as a far-field point target, wherein the radial distance of the target is R, and the target is along the negative direction of the y axis and has the velocity of V T ' the velocity of the target moves, the spatial cone angle of the target relative to the missile-borne MIMO radar is psi T' 。
And 2, recording an echo signal received when the missile-borne MIMO radar detects a low-altitude moving target as an echo signal y received by the missile-borne MIMO radar in a clutter environment, wherein the echo signal y received by the missile-borne MIMO radar in the clutter environment comprises a target signal x, a clutter signal c and a noise signal n, namely y = x + c + n.
2.1 missile-borne MIMO radar transmitter transmits K pulse signals within a coherent processing time, with a pulse repetition frequency of f r If the number of discrete sampling points in a pulse is L, the baseband signal transmitted by the mth transmitting array element at the kth pulse and the lth sampling point is s m,k (l)：
Wherein, E t Represents the total transmission power of M transmission array elements of the missile-borne MIMO radar in one pulse,represents the amplitude of the baseband signal transmitted by the mth transmitting array element at the kth pulse and the lth sampling point,the phase of the M-th transmitting array element and the phase of the L-th sampling point for transmitting a baseband signal are represented, L =1, a.
2.2 making M take 1 to M respectively, and repeatedly executing 2.1 to further obtain the baseband signals s transmitted by the 1 st transmitting array element at the kth pulse and the l sampling point respectively 1,k (l) Base band signal s transmitted by the Mth transmitting array element at the kth pulse and the l sampling point m,k (L) is marked as the transmitting waveform vector s of the M transmitting array elements at the kth pulse and the L sampling point k (l)，s k (l)＝[s 1,k (l),s 2,k (l),...,s m,k (l),...,s M,k (l)] T ， Representing an M x 1 dimensional complex vector space.
Under the narrow-band condition, the k pulse of M transmitting array elements of the missile-borne MIMO radar and the signal transmitted to the target by the l sampling point are as follows: a is a T (ψ T' )s k (l),l＝1,A small diameter, L, wherein T' Representing the space cone angle of the target with respect to the missile-borne MIMO radar, a (ψ) T' ) A transmitted spatial steering vector, s, representing the target k (l) And the transmitted waveform vector of the M transmitting array elements at the kth pulse and the l sampling point is shown, and the superscript T shows transposition operation.
2.3 making L take 1 to L respectively, initializing M to 1, repeatedly executing 2.2 and 2.3, and further obtaining the emission waveform vector s of M emission array elements at the kth pulse and the 1 st sampling point respectively k (1) Transmitting waveform vector s of the k pulse and the L sampling point of the M transmitting array elements k (L) is recorded as a transmission waveform vector s of the M transmission array elements at the k pulse k ，s k ＝[s k (1),s k (2),...,s k (l),...,s k (L)] T The superscript T denotes the transpose operation.
2.4, K is respectively 1 to K, l is initialized to 1, M is initialized to 1, and 2.2, 2.3 and 2.4 are repeatedly executed, so that the transmission waveform vectors s of the M transmission array elements at the 1 st pulse are respectively obtained 1 Transmitting waveform vector s of the K-th pulse of the M transmitting array elements K And is recorded as a missile-borne MIMO radar transmission waveform vector s, s = [ s ] 1 ,s 2 ,…,,...s K ]， Representing an ML × 1 dimensional complex vector space.
2.5 in clutter environment, the target signal x in the echo signal y received by the missile-borne MIMO radar is:
x＝α T' V t (f T'_d ,ψ T' )s (2)
the target signal x in an echo signal y received by the missile-borne MIMO radar in the clutter environment is a target echo signal in coherent processing time; alpha is alpha T' Representing the complex amplitude, V, of a target echo signal received by a missile-borne MIMO radar in a clutter environment t (f T'_d ,ψ T' ) Virtual leads representing a targetIn the direction of the vector,p(f T'_d ,ψ T' ) Time-domain steering vector, a (ψ), representing the target T' ) Transmitted spatial steering vector, I, representing a target L Representing an L × L dimensional identity matrix, b (ψ) T' ) A received spatial steering vector representing the target,f T'_d indicating the Doppler frequency, f, of the target T'_d ＝2V T' /λf r +2V p cosψ T' /λf r λ represents the operating wavelength of the missile-borne MIMO radar, V T' Representing the magnitude of the speed of movement, V, of the target in the negative y-axis direction p The speed of the missile-borne MIMO radar platform along the positive direction of the y axis is represented,d T ' array element spacing representing M transmit array elements, d R Array element interval representing N receiving array elements, s represents a missile-borne MIMO radar transmitting waveform vector, and s = [ s ] 1 ,s 2 ,…,,...s K ]，s k ＝[s k (1),s k (2),...,s k (l),...,s k (L)] T ，s k (l)＝[s 1,k (l),s 2,k (l),...,s m,k (l),...,s M,k (l)] T ，s m,k (l) The base band signal s of the m-th transmitting array element transmitted at the k-th pulse and l-th sampling point k Representing the transmit waveform vector, s, of the M transmit elements at the k-th pulse k (l) The transmitting waveform vector of M transmitting array elements at the kth pulse and the L sampling point is shown, K =1,2The total number of transmitting array elements included in the MIMO-loaded radar, and K represents the total number of pulse signals transmitted by the missile-borne MIMO radar transmitter in coherent processing time.
Clutter signals received by the missile-borne MIMO radar are formed by superposing echo signals of all clutter blocks in a distance unit to be detected, the condition of no distance ambiguity is considered, and clutter signals c in echo signals y received by the missile-borne MIMO radar in a clutter environment are as follows:
the clutter signal c in the echo signal y received by the missile-borne MIMO radar in the clutter environment is an echo signal of clutter in coherent processing time; alpha is alpha c,i Representing the complex amplitude, V, of the echo signal of the ith scattering center in the distance unit to be detected c,i (f c,i_d ,ψ c,i ) Representing a virtual steering vector of the ith scattering center in the distance cell to be detected, f c,i_d Indicating the Doppler frequency, f, of the ith scattering center in the range cell to be detected c,i_d ＝2V p cosψ c,i /λf r And λ represents the missile-borne MIMO radar operating wavelength, # c,i Representing the spatial cone angle of the ith scattering center in the distance unit to be detected; noise signals n in echo signals y received by missile-borne MIMO radar in clutter environment respectively obey zero-mean Gaussian distribution in space domain and time domain, namely R n ＝E[nn H ]＝σ n 2 I KNL Wherein R is n A covariance matrix, I, representing the noise signal n in the echo signal y received by the missile-borne MIMO radar in a cluttered environment KNL Expressing a KNL XKNL dimensional identity matrix, E expressing expectation, superscript H expressing a conjugate transpose operation, σ n 2 Representing the noise power; therefore, the echo signal y received by the missile-borne MIMO radar in the clutter environment is:
wherein alpha is T' Representing the complex amplitude, V, of a target echo signal received by a missile-borne MIMO radar in a clutter environment t (f T'_d ,ψ T' ) A virtual steering vector representing a target, s represents a missile-borne MIMO radar transmission waveform vector, alpha c,i Representing the complex amplitude, V, of the echo signal of the ith scattering center in the range unit to be detected c,i (f c,i_d ,ψ c,i ) The method includes the steps that a virtual guide vector of the ith scattering center in a distance unit to be detected is represented, N represents a noise signal in an echo signal y received by the missile-borne MIMO radar in a clutter environment, and i =1 c ，N c The total number of clutter blocks contained in the distance unit to be detected is represented and is equal to the total number of scattering centers contained in the distance unit to be detected.
Step 3, setting a weight vector w of the linear filter under the conditions of transmitting power constraint and waveform constant modulus constraint by taking the output signal-to-interference-and-noise ratio as a target function of the waveform optimization problem,the method comprises the steps of representing a KNL multiplied by 1 dimensional complex vector space, forming a deep notch in the clutter direction and simultaneously ensuring high gain in the target direction; the output signal-to-interference-and-noise ratio SINR of an echo signal y received by the missile-borne MIMO radar in the clutter environment after linear filtering is as follows:
wherein x represents a target signal in an echo signal y received by the missile-borne MIMO radar in a clutter environment, and R cn (s) covariance matrix, R, representing clutter plus noise cn (s)＝E[(c+n)(c+n) H ]＝R c +R n ，R c Covariance matrix, R, representing clutter signal c in echo signal y received by a missile-borne MIMO radar in a clutter environment n Representing a covariance matrix of a noise signal n in an echo signal y received by the missile-borne MIMO radar in a clutter environment; further, the joint optimization problem of the missile-borne MIMO radar transmitting waveform vector s and the linear filter weight vector w in the clutter environment is obtained as follows:
wherein s is m,k (l) The baseband signal transmitted by the mth transmitting array element at the kth pulse and the lth sampling point is shown,s.t. represents a constraint, α T' Representing the complex amplitude of a target echo signal received by the missile-borne MIMO radar in a clutter environment, s representing the transmitting waveform vector of the missile-borne MIMO radar, V t (f T'_d ,ψ T ) Virtual steering vector, R, representing an object cn (s) represents the covariance matrix of clutter plus noise, | | | represents the modulo operation, E t And the total transmission power of M transmission array elements of the missile-borne MIMO radar in one pulse is represented.
And 4, obtaining an optimization design result of the missile-borne MIMO radar waveform covariance matrix according to the joint optimization problem of the missile-borne MIMO radar transmitting waveform vector and the linear filter weight vector in the clutter environment.
4a) Setting a waveform covariance matrix of an missile-borne MIMO radar to R s In order to solve the optimization problem, the optimization problem is further simplified by utilizing the waveform covariance matrix R of the missile-borne MIMO radar, and the waveform covariance matrix R of the missile-borne MIMO radar is used s Expressed as:
R s ＝ss H (7)
waveform covariance matrix R of missile-borne MIMO radar s The method is characterized in that the correlation of waveforms among M transmitting array elements of the missile-borne MIMO radar is described; and then converting the joint optimization problem of the missile-borne MIMO radar transmitting waveform vector s and the linear filter weight vector w in the clutter environment into a constrained optimization problem with two groups of variables to be optimized:
wherein the content of the first and second substances,represents the matrix inequality, i.e. ifThen R is s Is a semi-positive definite matrix; diag denotes the operation on the diagonal elements of the matrix, tr denotes the trace of the matrix, rank denotes the rank of the matrix, and dot product.
The two groups of variables to be optimized in the constrained optimization problem with the two groups of variables to be optimized are waveform covariance matrixes R of the missile-borne MIMO radar s And a linear filter weight vector w; the optimization problem is solved by using a circular optimization method, and the specific substep of the step 4 is as follows:
initialization: let q be the q-th cycle, the initial value of q be 1, and in the q-th cycle, the waveform vector after the q-th cycle is set as s (q) The waveform covariance matrix corresponding to the waveform vector after the qth cycle is Wherein the content of the first and second substances, represents the phase of the transmitted baseband signal at the ith sampling point of the M transmitting array elements, tr represents the trace of the matrix, CN represents the Gaussian distribution, represents obedience, e represents belonging,representing an ML x 1-dimensional complex vector space,and (3) representing a waveform covariance matrix corresponding to the waveform matrix after the q +1 th cycle.
4b) At this time, the constrained optimization problem with two sets of variables to be optimized is converted into an unconstrained convex optimization problem with only one set of variables to be optimized:
wherein w (q) Representing the linear filter weight vector after the q-th cycle,represents the waveform covariance matrix, R, of the missile-borne MIMO radar after the qth cycle cn (s (q) ) Representing a covariance matrix of clutter plus noise after the q-th cycle; obviously, the equation (9) is a form of a generalized Rayleigh quotient, and the optimal value of the linear filter for maximizing the objective function after the q-th cycle is calculated
Wherein the content of the first and second substances,after the covariance matrix representing clutter plus noise after the q-th cycle is inverted, the square is taken,is composed ofThe feature vector corresponding to the largest feature value of (b),indicating the after-treatment of the q-th cycleA waveform covariance matrix of the MIMO-based radar; therefore, the echo signal y received by the missile-borne MIMO radar in the clutter environment after the q-th cycle is subjected to linear filtering, and the output signal-to-interference-and-noise ratio is SINR (q) ：
Wherein R is cn (s (q) ) Representing a covariance matrix of clutter plus noise after the q-th cycle; this completes the q cycle.
4c) Let the weight vector of the linear filter after the q +1 th cycle be w (q+1) And is made ofw (q+1) Representing the linear filter weight vector after the q +1 th cycle,represents the optimal value of the linear filter to maximize the objective function after the q-th cycle, and the weight vector w of the linear filter after the q + 1-th cycle (q+1) Matrixing to obtain a weight vector matrix W of the linear filter after the q +1 th cycle (q+1) ， Representing an L xKN dimensional complex matrix space; at this time, the formula xAx is used H ＝tr(Axx H ) Converting the constrained optimization problem with two groups of variables to be optimized into a constrained non-convex optimization problem with only one group of variables to be optimized:
wherein the content of the first and second substances,
wherein, I M Representing an M x M dimensional identity matrix, b (psi) T' ) A received null steering vector, a (ψ), representing a target T' ) A transmitted spatial steering vector, p (f), representing the target T'_d ,ψ T' ) Time-domain steering vector, p (f), representing the target c,i_d ,ψ c,i ) Representing the time-domain steering vector of the ith scattering center in the distance unit to be detected, f c,i_d Indicating the Doppler frequency, # of the ith scattering center in the range cell to be detected c,i Representing the spatial cone angle of the ith scattering center in the range cell to be detected, b (psi) c,i ) A (ψ) represents a receive space vector of the ith scattering center in the range bin to be detected c,i ) Representing the transmit spatial steering vector, R, of the ith scattering center in the range bin to be detected n A covariance matrix representing the noise signal n in the echo signal y received by the missile-borne MIMO radar in a clutter environment,represents the waveform covariance matrix of the missile-borne MIMO radar after the q +1 th cycle, and 1 represents the waveform covariance matrix of the missile-borne MIMO radar after the q +1 th cycleAll 1 matrices of the same dimension, representing dot product.
At this time, the objective function in the problem (12) is a convex function, but the constraint condition isIs a non-convex set; to further solve this problem, constraints are imposedAbandoning and introducing auxiliary variable P, and laying auxiliary variable matrix P, which has only one group to be optimizedTransforming the constrained non-convex optimization problem of the variables into a semi-positive definite planning problem:
wherein the content of the first and second substances,p represents a matrix of spread-aided variables,p represents the auxiliary variable, p ∈ R,represents the matrix inequality, i.e. ifThen R is s Is a semi-positive definite matrix; diag represents the operation of taking diagonal elements of the matrix, tr represents the trace of the matrix, rank represents the rank of the matrix, and s.t. represents the constraint condition; waveform covariance matrix of missile-borne MIMO radar after q +1 th cycleThe optimal solution of (A) can be obtained from the solution of the problem (15) semi-definite programming problem, the optimal solution of the problem (15) semi-definite programming problem being (P) ★ ,p ★ )， Represents the optimal value of the linear filter, P, to maximize the objective function after the q +1 cycle ★ Representing an optimal matrix of spread aiding variables, p ★ Representing an optimal auxiliary variable; at the moment, the echo signal y received by the missile-borne MIMO radar in the clutter environment after the q +1 th cycle is obtained and is subjected to linear filtering, and then the signal to interference plus noise ratio SINR is output (q+1) Comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,represents the optimal value of the linear filter that maximizes the objective function after the q +1 th cycle.
4d) If | SINR (q+1) -SINR (q) |/SINR (q) And if the value is more than or equal to epsilon, adding 1 to the value of q and returning to 4 b).
If | SINR (q+1) -SINR (q) |/SINR (q) &If t, the circulation is stopped and the corresponding time when the circulation is stoppedAnd w (q +1) Optimal waveform covariance matrices R, denoted as missile-borne MIMO radars, respectively s,opt Sum linear filter optimal weight vector w opt ， Representing a KNL x 1-dimensional complex vector space, the linear filter optimal weight vector w opt Each data in the linear filter is the optimal weight and is recorded as the optimal weight w of the linear filter opt The optimal weight w of the linear filter opt The method is used as an optimization design result of the covariance matrix of the missile-borne MIMO radar waveform.
The effects of the present invention can be further illustrated by the following experiments in conjunction with the simulation diagrams.
Simulation conditions:
the simulation experiment environment is as follows: MATLAB R2015b, intel (R) Core (TM) 2Duo CPU 3.6GHz, windows7 flagship edition.
(II) simulation content and result analysis:
the working wavelength of the missile-borne MIMO forward-looking array radar is 0.03m, the missile-borne MIMO forward-looking array radar is provided with 4 transmitting array elements and 4 receiving array elements, the 4 transmitting array elements and the 4 receiving array elements are all one-dimensional equidistant linear arrays, the distance between the transmitting array elements is twice the wavelength, and the distance between the receiving array elements is half the wavelength; the height of the missile-borne MIMO forward-looking array radar platform is 6km, and the flying speed of the missile is 800m/s; the number of the emission pulses in one coherent processing time is 8, the pulse repetition frequency is 10kHz, the bandwidth is 5MHz, and the number of sampling points in one pulse is 16. The simulated echo includes clutter, moving objects, and noise. The clutter component has a clutter ratio of 20dB, the moving target is a single point target, the radial distance of the target is 10km, the signal-to-noise ratio is 10dB, and the radial speed of the target is 30m/s. The method simulates the output signal-to-interference-and-noise ratio and the frequency domain response of the missile-borne MIMO forward-looking array radar after filtering, and respectively adopts the optimized waveform obtained by the method, the single-carrier phased array waveform, the completely orthogonal waveform and the waveform obtained by the optimization of the method provided by B.Tang et al.
Fig. 3 is a comparison curve of the variation of the output signal to interference plus noise ratio of the filter according to the method of the present invention and the method proposed by b.tang et al with the cycle number, the abscissa indicates the cycle optimization number, the ordinate indicates the output signal to interference plus noise ratio after being processed by the filter in each cycle, the curve with asterisk is the simulation result of the method of the present invention, and the curve with circle indicates the simulation result of the optimization method proposed by b.tang et al; as can be seen from FIG. 3, when the SNR is 10dB and the SNR is 20dB, the output SINR optimized by the method of the present invention reaches 20dB after the first cycle, and tends to be stable after the 5 th cycle, reaching the maximum output SINR of 26.6 dB; in the optimization method provided by B.Tang et al, the output signal to interference plus noise ratio obtained after the first cycle is 17dB, the output signal to interference plus noise ratio reaches the maximum and tends to be stable after the 6 th cycle, and the maximum output signal to interference plus noise ratio is 25.4dB; compared with the method of B.Tang et al, the cyclic optimization method provided by the invention can improve the output signal-to-interference-and-noise ratio and has faster algorithm convergence.
FIG. 4 is a comparison curve of the output SINR of the optimized waveform of the method of the present invention with the single carrier phased array waveform, the completely orthogonal waveform, and the optimized waveform of the method of B.Tang et al, which varies with the Doppler frequency, the abscissa represents the normalized Doppler frequency, the ordinate represents the output SINR, the curve with triangle represents the frequency response simulation result of the single carrier phased array waveform after being processed by the filter, the curve with diamond represents the frequency response simulation result of the completely orthogonal waveform after being processed by the filter, the curve with asterisk represents the frequency response simulation result of the optimized waveform of the method of the present invention after being processed by the filter, and the curve with circle represents the frequency response simulation result of the optimized waveform of B.Tang et al after being processed by the filter; as can be seen from FIG. 4, under the constraint of the same transmitting power, the maximum output signal-to-interference-and-noise ratio of the waveform optimized by the method provided by the invention after being processed by the filter is 26.6dB, the maximum output signal-to-interference-and-noise ratio of the waveform optimized by the method provided by B.Tang et al is 25.4dB, the maximum output signal-to-interference-and-noise ratio of the single carrier phased array waveform is 23.8dB, and the maximum output signal-to-interference-and-noise ratio of the completely orthogonal waveform is 15.7dB. Compared with other waveforms, the optimized waveform of the method has higher output signal-to-interference-and-noise ratio and narrower notch in a low Doppler region.
Fig. 5 is a comparison curve of the output signal-to-interference-and-noise ratio of the method of the present invention with the single carrier phased array waveform, the complete orthogonal waveform, and the method of b.tang et al, along with the change of the doppler frequency, in a low doppler region after the filtering process. The abscissa represents normalized Doppler frequency, a low Doppler region from-0.1 to 0.1 is intercepted and amplified, the ordinate represents output signal-to-interference-and-noise ratio, a curve with a triangle represents a frequency response simulation result of a single carrier phased array waveform processed by a filter, a curve with a diamond represents a frequency response simulation result of a completely orthogonal waveform processed by the filter, a curve with an asterisk represents a frequency response simulation result of an optimized waveform processed by the filter, and a curve with a circle represents a frequency response simulation result of an optimized waveform processed by the filter, which is proposed by B.Tang et al; as can be seen from fig. 5, the method of the present invention has a narrower notch in the low doppler region than other methods, i.e., the method of the present invention can reduce the minimum detectable speed and has better detection performance for low-speed moving targets.
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the method.
It will be apparent to those skilled in the art that various changes and modifications may be made therein without departing from the spirit and scope thereof; thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (9)
1. An optimal design method for a missile-borne MIMO radar waveform covariance matrix is characterized by comprising the following steps:
step 1, determining a missile-borne MIMO radar, wherein the missile-borne MIMO radar is in clutter, and a target exists in a detection range of the missile-borne MIMO radar;
step 2, recording an echo signal received when the missile-borne MIMO radar detects a target as an echo signal received by the missile-borne MIMO radar in a clutter environment, wherein the echo signal received by the missile-borne MIMO radar in the clutter environment comprises a target signal, a clutter signal and a noise signal, and determining a launch waveform vector of the missile-borne MIMO radar;
step 3, setting a weight vector of a linear filter, calculating to obtain an echo signal received by the missile-borne MIMO radar in the clutter environment, outputting a signal-to-interference-and-noise ratio after linear filtering according to the launch waveform vector of the missile-borne MIMO radar, and further obtaining a joint optimization problem of the launch waveform vector of the missile-borne MIMO radar and the weight vector of the linear filter in the clutter environment;
and 4, obtaining an optimization design result of the missile-borne MIMO radar waveform covariance matrix according to the joint optimization problem of the missile-borne MIMO radar transmitting waveform vector and the linear filter weight vector in the clutter environment.
2. The method as claimed in claim 1, wherein in step 1, a space geometric coordinate system between the missile-borne MIMO radar and the target is established according to the missile-borne MIMO radar and the target, and the establishment process is as follows:
taking vertical projection point of missile-borne MIMO radar on the ground as origino, establishing a xoyz three-dimensional coordinate system, wherein the missile-borne MIMO radar is a forward-looking array and is erected at the front end of the missile and does not move relative to the missile; setting that no yaw exists in the flying process of the missile, the normal direction of the missile-borne MIMO radar array surface is parallel to the flying direction of the missile, the height of the missile-borne MIMO radar is H, the missile flies in the positive direction of the y axis, and the flying speed of the missile is V p (ii) a The missile-borne MIMO radar comprises M transmitting array elements and N receiving array elements, wherein the M transmitting array elements and the N receiving array elements are respectively one-dimensional equidistant linear arrays, and the array element intervals of the M transmitting array elements are d T ', the array element interval of N receiving array elements is d R (ii) a Uniformly dividing the ground in the action range of the missile-borne MIMO radar into N by taking the origin o of the xoyz three-dimensional coordinate system as the center of a circle r A plurality of equally spaced rings, N r Indicates the total number of equally spaced rings, N r Is a positive integer greater than 0, and is, denotes a round-down operation, R max For missile-borne MIMO radar maximum range, R min The minimum action distance of the missile-borne MIMO radar is represented by DeltaR, the width of each equal-interval distance ring is represented by DeltaR = c/2B, B represents the working bandwidth determination of the missile-borne MIMO radar, and c represents the light speed;
marking an equidistant distance ring where the target is positioned as a distance unit to be detected, and uniformly dividing the distance unit to be detected into N c Each clutter block is set to be uniformly distributed, each clutter block is equivalent to a scattering center, and the distance unit to be detected contains N c A plurality of scattering centers; a connecting line of the ith scattering center and a missile-borne MIMO radar receiving antenna phase center in the distance unit to be detected is recorded as a radar sight line, and an included angle between the projection of the radar sight line on the xoy plane and the positive direction of the x axis is an azimuth angle theta of the ith scattering center c,i The included angle between the radar sight line and the xoy plane is the pitch angle of the ith scattering centerThe included angle between the radar sight line and the missile-borne MIMO radar receiving antenna is the space cone angle psi of the ith scattering center c,i The three angular relationships are:wherein, the receiving antenna is a linear array formed by N receiving array elements, i =1 c ，N c The total number of clutter blocks contained in the distance unit to be detected is represented and is equal to the total number of scattering centers contained in the distance unit to be detected.
3. The method according to claim 2, wherein in step 2, the echo signal received by the missile-borne MIMO radar in the clutter environment is denoted as y, and the expression is as follows:
x＝α T' V t (f T'_d ,ψ T' )s
wherein x represents that a target signal in an echo signal y received by the missile-borne MIMO radar in the clutter environment is a target echo signal in coherent processing time, c represents a clutter signal in the echo signal y received by the missile-borne MIMO radar in the clutter environment, and alpha T' Representing complex amplitude, V, of target echo signal received by missile-borne MIMO radar in clutter environment t (f T'_d ,ψ T' ) A virtual guide vector representing the target is shown,p(f T'_d ,ψ T' ) Time-domain steering vector, a (ψ), representing an object T' ) Transmitted spatial steering vector, I, representing a target L Representing an L × L dimensional identity matrix, b (ψ) T' ) A received spatial steering vector representing the target,f T'_d indicating the Doppler frequency, f, of the target T'_d ＝2V T' /λf r +2V p cosψ T' /λf r ，f r Denotes the pulse repetition frequency, lambda denotes the operating wavelength of the missile-borne MIMO radar, V T' Representing the magnitude of the speed of movement, V, of the target in the negative y-axis direction p The speed of the missile-borne MIMO radar platform along the positive direction of the y axis is represented,d T' array element spacing, d, representing M transmit array elements R Array element intervals of N receiving array elements are represented, s represents a launch MIMO radar launching waveform vector, L represents the number of discrete sampling points in a pulse, M represents the total number of launching array elements included by the launch MIMO radar, and K represents the total number of pulse signals launched by a launch MIMO radar transmitter in a coherent processing time; alpha is alpha c,i Representing the complex amplitude, V, of the echo signal of the ith scattering center in the distance unit to be detected c,i (f c,i_d ,ψ c,i ) Representing a virtual steering vector of the ith scattering center in the distance cell to be detected, f c,i_d Indicating the Doppler frequency, f, of the ith scattering center in the range cell to be detected c,i_d ＝2V p cosψ c,i /λf r And λ represents the missile-borne MIMO radar operating wavelength, # c,i Representing the spatial cone angle of the ith scattering center in the distance unit to be detected; i =1 c ，N c The total number of clutter blocks contained in the distance unit to be detected is represented and is equal to the total number of scattering centers contained in the distance unit to be detected in value.
4. The method of claim 3, wherein the s represents a transmit waveform vector of the missile-borne MIMO radar, and the obtaining process is as follows:
2.1 missile-borne MIMO radar transmitter transmits K pulse signals within a coherent processing time, with a pulse repetition frequency of f r If the number of discrete sampling points in a pulse is L, the baseband signal transmitted by the mth transmitting array element at the kth pulse and the lth sampling point is s m,k (l)：
Wherein E is t Represents the total transmission power of M transmission array elements of the missile-borne MIMO radar in one pulse,represents the amplitude of the baseband signal transmitted by the mth transmitting array element at the kth pulse and the lth sampling point,the phase of the baseband signal transmitted by the mth transmitting array element and the ith sampling point is represented, L =1,.. Multidot.L, K =1,. Multidot.K, L represents the number of discrete sampling points in a pulse, M represents the total number of transmitting array elements included by the missile-borne MIMO radar, K represents the total number of pulse signals transmitted by a missile-borne MIMO radar transmitter in a coherent processing time, e represents an exponential function, and j represents an imaginary number unit;
2.2 making M take 1 to M respectively, repeating the execution for 2.1, and further obtaining the baseband signal s transmitted by the 1 st transmitting array element at the kth pulse and the l sampling point respectively 1,k (l) Base band signal s transmitted from kth pulse to ith transmitting array element and from ith sampling point m,k (L) is recorded as the transmitting waveform vector s of the M transmitting array elements at the kth pulse and the L sampling point k (l)，s k (l)＝[s 1,k (l),s 2,k (l),...,s m,k (l),...,s M,k (l)] T ；
2.3 let L take 1 to L respectively, initialize m to 1, repeat 2.2 and 2.3, and then execute 2.2 and 2.3 respectivelyObtaining the transmitting waveform vector s of the M transmitting array elements at the kth pulse and the 1 st sampling point k (1) Transmitting waveform vector s of the k pulse and the L sampling point of the M transmitting array elements k (L) is recorded as a transmission waveform vector s of the M transmission array elements at the k pulse k ，s k ＝[s k (1),s k (2),...,s k (l),...,s k (L)] T The superscript T denotes the transpose operation;
2.4 making K take 1 to K respectively, initializing l to 1, initializing M to 1, repeatedly executing 2.2, 2.3 and 2.4, and further obtaining the emission waveform vectors s of M emission array elements at the 1 st pulse 1 To the transmitting waveform vector s of the M transmitting array elements at the K pulse K And is recorded as a missile-borne MIMO radar transmission waveform vector s, s = [ s ] 1 ,s 2 ,…,,...s K ]。
5. The method according to claim 3, wherein in step 3, the output signal-to-interference-and-noise ratio of the echo signals received by the missile-borne MIMO radar in the clutter environment after linear filtering is recorded as SINR:
wherein x represents a target signal in an echo signal y received by the missile-borne MIMO radar in a clutter environment, and R cn (s) covariance matrix, R, representing clutter plus noise cn (s)＝E[(c+n)(c+n) H ]＝R c +R n ，R c Covariance matrix, R, representing clutter signal c in echo signal y received by a missile-borne MIMO radar in a clutter environment n Representing a covariance matrix of a noise signal n in an echo signal y received by the missile-borne MIMO radar in a clutter environment, E representing an expectation, and w representing a weight vector of a linear filter;
the method comprises the following steps that a joint optimization problem of a missile-borne MIMO radar transmitting waveform vector and a linear filter weight vector in the clutter environment is as follows;
s.t.s H s＝E t
wherein s is m,k (l) The baseband signal transmitted by the mth transmitting array element at the kth pulse and the lth sampling point is shown,s.t. represents a constraint, α T' Representing the complex amplitude of a target echo signal received by the missile-borne MIMO radar in a clutter environment, s represents a launch waveform vector of the missile-borne MIMO radar, V t (f T'_d ,ψ T ) Virtual steering vector, R, representing an object cn (s) covariance matrix representing clutter plus noise, | | | representing modulo operation, E t And the total transmission power of M transmission array elements of the missile-borne MIMO radar in one pulse is represented.
6. The method as claimed in claim 5, wherein in step 4, the optimal design result of the missile-borne MIMO radar waveform covariance matrix is obtained by:
4a) Converting a joint optimization problem of a missile-borne MIMO radar transmitting waveform vector s and a linear filter weight vector w in a clutter environment into a constrained optimization problem with two groups of variables to be optimized;
initialization: let q be the q-th cycle, the initial value of q be 1, and in the q-th cycle, the waveform vector after the q-th cycle is set as s (q) The waveform covariance matrix corresponding to the waveform vector after the qth cycle is Wherein the content of the first and second substances,l＝1,2,...,L， denotes the phase of the transmitted baseband signal at the ith sampling point of the M transmit array elements, tr denotes the trace of the matrix, CN denotes the Gaussian distribution,. Sub.w denotes obedient,. Epsilon.denotes belonging,representing a waveform covariance matrix corresponding to the waveform matrix after the q +1 th cycle;
4b) Converting the constrained optimization problem with two groups of variables to be optimized into an unconstrained convex optimization problem with only one group of variables to be optimized, and calculating the optimal value of a linear filter for maximizing an objective function after the q-th cycleAnd then calculating the output signal-to-interference-plus-noise ratio (SINR) of the echo signal y received by the missile-borne MIMO radar in the clutter environment after the q-th cycle is subjected to linear filtering (q) ；
4c) Let the weight vector of the linear filter after the q +1 th cycle be w (q+1) And is andconverting the constrained optimization problem with two groups of variables to be optimized into the constrained non-convex optimization problem with only one group of variables to be optimized, and converting the constrained non-convex optimization problem with only one group of variables to be optimized into the semi-positive optimization problemThe planning problem is solved, and then the echo signal y received by the missile-borne MIMO radar in the clutter environment after the q +1 th cycle is obtained through calculation and output signal to interference plus noise ratio (SINR) after linear filtering (q+1) ；
4d) If SINR (q+1) -SINR (q) |/SINR (q) If the value of q is more than or equal to epsilon, adding 1 to the value of q, and returning to 4 b);
if | SINR (q+1) -SINR (q) |/SINR (q) &If the epsilon is less than the preset threshold, the circulation is stopped, and the corresponding epsilon when the circulation is stoppedAnd w (q+1) Optimal waveform covariance matrices R, denoted as missile-borne MIMO radars, respectively s,opt Sum linear filter optimal weight vector w opt ， Representing a KNL x 1-dimensional complex vector space, the linear filter optimal weight vector w opt Each data in the linear filter is the optimal weight and is recorded as the optimal weight w of the linear filter opt Optimizing the weight w of the linear filter opt The method is used as an optimization design result of the covariance matrix of the missile-borne MIMO radar waveform.
7. The method according to claim 6, wherein there are two sets of constrained optimization problems for the variables to be optimized in 4 a):
s.t.tr(R s )＝E' t
rank(R s )＝1
wherein the content of the first and second substances,represents the matrix inequality, i.e. ifThen R is s Is a semi-positive definite matrix; diag represents the operation of taking diagonal elements of the matrix, tr represents the trace of matrix solving, rank represents the rank of matrix solving, and dot multiplication represents;
the two groups of variables to be optimized in the constrained optimization problem with the two groups of variables to be optimized are the waveform covariance matrix R of the missile-borne MIMO radar s And a linear filter weight vector w.
8. The method according to claim 6, wherein the unconstrained convex optimization problem of only one set of variables to be optimized in 4 b) is:
wherein, w (q) Representing the linear filter weight vector after the q-th cycle,representing the wave covariance matrix, R, of the missile-borne MIMO radar after the qth cycle cn (s (q) ) Representing a covariance matrix of clutter plus noise after the q-th cycle; and then calculating to obtain the optimal value of the linear filter for maximizing the objective function after the q-th cycle
Wherein the content of the first and second substances,the covariance matrix representing clutter plus noise after the q-th cycle is inverted and then squared,is composed ofThe feature vector corresponding to the largest feature value of (b),representing a waveform covariance matrix of the missile-borne MIMO radar after the q-th cycle; therefore, after the q-th cycle, the echo signal y received by the missile-borne MIMO radar in the clutter environment is subjected to linear filtering, and the output signal-to-interference-plus-noise ratio is SINR (q) ：
Wherein R is cn (s (q) ) Representing the covariance matrix of clutter plus noise after the q-th cycle.
9. The method of claim 6, wherein the process of 4 c) is as follows:
let the weight vector of the linear filter after the q +1 th cycle be w (q+1) And is made ofw (q+1) Representing linear filtering after the q +1 th cycleA vector of weights for the device is calculated,represents the optimal value of the linear filter to maximize the objective function after the q-th cycle, and weights the linear filter weight vector w after the q + 1-th cycle (q+1) Matrixing to obtain a weight vector matrix W of the linear filter after the q +1 th cycle (q+1) Then, the constrained optimization problem with two groups of variables to be optimized is converted into a constrained non-convex optimization problem with only one group of variables to be optimized:
wherein, the first and the second end of the pipe are connected with each other,
wherein, I M Representing an M x M dimensional identity matrix, b (psi) T' ) A received null steering vector, a (ψ), representing a target T' ) A transmitted spatial steering vector, p (f), representing the target T'_d ,ψ T' ) Time-domain steering vector, p (f), representing the target c,i_d ,ψ c,i ) Representing the time-domain steering vector of the ith scattering center in the distance unit to be detected, f c,i_d Indicating the Doppler frequency, # of the ith scattering center in the range cell to be detected c,i Representing the spatial cone angle of the ith scattering center in the range cell to be detected, b (psi) c,i ) A (psi) representing the received spatial steering vector of the ith scattering center in the range bin to be detected c,i ) Representing the transmitted spatial guide vector, R, of the ith scattering center in the distance cell to be detected n A covariance matrix representing the noise signal n in the echo signal y received by the missile-borne MIMO radar in a cluttered environment,represents the waveform covariance matrix of the missile-borne MIMO radar after the q +1 th cycle, and 1 represents the waveform covariance matrix of the missile-borne MIMO radar after the q +1 th cycleAll 1 matrices of the same dimension, representing dot product;
then, converting the constrained non-convex optimization problem with only one group of variables to be optimized into a semi-positive definite planning problem:
s.t.tr[Z(W (q+1) )P]＝1
p≥0
wherein the content of the first and second substances,p represents a spread-aided variable matrix, P represents an aided variable, P belongs to R,represents the matrix inequality, i.e. ifThen R is s Is a semi-positive definite matrix; diag represents the operation of taking diagonal elements of the matrix, tr represents the trace of solving the matrix, rank represents the rank of solving the matrix, and s.t. represents a constraint condition;
the optimal solution of the semi-definite programming problem is (P) ★ ,p ★ )， Represents the optimal value of the linear filter, P, to maximize the objective function after the q +1 cycle ★ Representing the optimal matrix of spread aided variables, p ★ Representing an optimal auxiliary variable; at the moment, the echo signal y received by the missile-borne MIMO radar in the clutter environment after the q +1 th cycle is obtained and is subjected to linear filtering to output the SINR (q+1) Comprises the following steps:
wherein the content of the first and second substances,represents the optimal value of the linear filter to maximize the objective function after the q +1 th cycle.
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