CN106093887A - Radar robust adaptive beamforming method based on rarefaction representation - Google Patents

Abstract

The invention discloses a kind of radar robust adaptive beamforming method based on rarefaction representation, its main thought is: set transmitting signal wavelength lambda and radar array element distance d of radar respectively, and then the radar echo signal of L snap of acquisition, and it is calculated the covariance matrix of radar echo signalAngle spatial domain, target setting place scope is [θ_d,θ_u], and by this angle spatial domain scope [θ_d,θ_u] it is divided into K angle value, respectively the conventional beamformer W of K angle value in the range of calculating angle spatial domain, target place_cWith the direct matrix in verse Beam-former W of K angle value in the range of angle spatial domain, target place_s, and then it is calculated the noise power in radar echo signal successivelyWith the interference signals subspace P in radar echo signal_I, and according to W_cAnd W_s, it is calculated the basic matrix B of radar echo signal and the expectation Beam-former w of radar echo signal successively_d, and then calculate the rarefaction representation vector in radar echo signalAnd the final Beam-former of radar echo signal is calculated according to B。

Description

Radar robust adaptive beamforming method based on rarefaction representation

Technical field

The invention belongs to Anti-jamming Technology for Radar field, particularly to a kind of sane self adaptation of radar based on rarefaction representation Beamforming Method, it is adaptable to obtain the Beam-former of the signal to noise ratio of suppression interference, improvement reception signal.

Background technology

Effectively AF panel is the basis that radar carries out target acquisition and tracking, and Adaptive beamformer is a kind of conventional Anti-jamming Technology for Radar, its objective is suppression interference signal while strengthen echo signal, improve receive signal signal to noise ratio； In Beamforming Method in early days, such as conventional beamformer (conventional beamformer) method and direct matrix in verse (direct square Battle array is inverted) method, it is assumed that estimate the noise-plus-interference covariance matrix obtained does not comprises target, and target incident direction is accurate It is known that then use conventional beamformer (conventional beamformer) method and direct matrix in verse (direct matrix in verse) method to obtain Adaptive beam former be respectively provided with good performance above-mentioned assuming immediately, but when above-mentioned hypothesis is false, its AF panel performance all can drastically deteriorate.

In order to improve the performance of said method, Feldman et al. is at document " A projection approach for robust adaptive beamforming,IEEE Trans.Signal Process.,April 1994,vol.42., Pp.867 876 " in propose subspace projection (ESB) method, this subspace projection (ESB) method is by by target apparent side Steering vector upwards projects to estimate that the signal obtained adds interference space, though adaptive beam former in early days can be improved AF panel performance, and subspace projection method also has good performance in the case of high s/n ratio, but in low noise In the case of Bi, its hydraulic performance decline is serious；Bell et al. is at document " A Bayesian approach to robust adaptive Beamforming, IEEE Trans.Signal Process., Feb 2000, vol.51., pp.313 324 " in propose one Planting robust adaptive beamforming method based on Bayes's thought, this Adaptive beamformer method is multiple easily by calculating The weighted sum of the Adaptive beamformer power obtained is to improve clutter recognition performance, but this Adaptive beamformer method is at height Penalty under state of signal-to-noise.

Summary of the invention

The deficiency existed for above prior art, it is an object of the invention to propose a kind of radar based on rarefaction representation Robust adaptive beamforming method, this kind radar based on rarefaction representation robust adaptive beamforming method passes through sparse table Show that method provides a kind of robust adaptive beamforming device and obtains method, it is possible to improve the AF panel performance of radar.

For reaching above-mentioned technical purpose, the present invention adopts the following technical scheme that and is achieved.

A kind of radar robust adaptive beamforming method based on rarefaction representation, comprises the following steps:

Step 1, sets transmitting signal wavelength lambda and radar array element distance d of radar respectively, and then obtains the thunder of L snap Reaching echo-signal, wherein the radar echo signal of the l time snap is x_l, l ∈ 1,2 ..., L}, N are radar element number of array, and L is The snap number of times that radar echo signal comprises；

Step 2, utilizes the radar echo signal of L snap, is calculated the covariance matrix of radar echo signal

Step 3, angle spatial domain, target setting place scope is [θ_d,θ_u], and by this angle spatial domain scope [θ_d,θ_u] divide For K angle value, wherein kth angle value is θ_k, then according to transmitting signal wavelength lambda and radar array element distance d of radar, point It is not calculated the conventional beamformer W of K angle value in the range of angle spatial domain, target place_cWith angle spatial domain, target place In the range of the direct matrix in verse Beam-former W of K angle value_s, wherein kth angle value θ_kCorresponding conventional beamformer Device is w_ck, kth angle value θ_kCorresponding direct matrix in verse Beam-former is w_sk；

K ∈ 1,2 ..., K}, K are the angle value number that angle spatial domain, target place scope comprises, θ_dFor the target set The lower limit of angle spatial domain, place scope, θ_uThe upper limit of angle spatial domain, the target place scope for setting；

Step 4, is [θ according to angle spatial domain, target place scope_d,θ_u] and the covariance matrix of radar echo signalMeter Calculating and obtain disturbing in radar echo signal the incident direction of signal, wherein m-th interference signal incident direction isAnd calculate Noise power in radar echo signal

Step 5, according to disturbing the incident direction of signal in radar echo signal, be calculated in radar echo signal is dry Disturb signal subspace P_I；

Step 6, according to the conventional beamformer W of K angle value in the range of angle spatial domain, target place_cWith target place The direct matrix in verse Beam-former W of K angle value in the range of angle spatial domain_s, it is calculated radar echo signal successively The expectation Beam-former w of basic matrix B and radar echo signal_d；

Step 7, according to the interference signals subspace P in radar echo signal_I, noise power in radar echo signal The rarefaction representation vector u to be asked with in radar echo signal, is calculated the sparse model of radar echo signal, its expression formula For:

Meet rarefaction representation vector u to be asked in the radar echo signal of described sparse model condition, believe for radar return Rarefaction representation vector in number

Wherein,For the noise power in radar echo signal, ||·||₂It is two norms, | | | |₁Being a norm, α is the coefficient more than zero artificially determined；ξ is constraint radar echo signal In interference signals subspace P_IAnd the parameter of orthogonality between rarefaction representation vector u to be asked in radar echo signal, δ is about Restraint parameter openness for rarefaction representation vector u to be asked in radar echo signal, and α, ξ and δ are all higher than zero, P_IFor radar return Interference signals subspace in signal, B is the basic matrix of radar echo signal；

Step 8, according to the rarefaction representation vector in radar echo signalWith the basic matrix B of radar echo signal, calculate Final Beam-former to radar echo signal

Beneficial effects of the present invention:

The present invention, by utilizing sparse representation method, utilizes the signal covariance matrix estimating to obtain to be calculated target institute The conventional beamformer W of K angle value in the range of angle spatial domain_cWith direct matrix in verse Beam-former W_s, by conventional ripple Beamformer W_c, direct matrix in verse Beam-former W_sWith the rarefaction representation vector in radar echo signalIt is calculated thunder Reach the final desired Beam-former of echo-signal, effective improve conventional beamformer (conventional beamformer) method, Direct matrix in verse (direct matrix in verse) method, subspace projection (ESB) method and based on Bayes's thought the most adaptive Answer the problem that the signal to noise ratio of Beamforming Method interference rejection capability difference and reception signal is low.

Accompanying drawing explanation

With detailed description of the invention, the present invention is described in further detail below in conjunction with the accompanying drawings.

Fig. 1 be a kind of based on rarefaction representation the radar robust adaptive beamforming method of the present invention realize flow process Figure；Wherein, CBF Beam-former is conventional beamformer, and SMI Beam-former is direct matrix in verse Beam-former；

Fig. 2 is the Signal to Interference plus Noise Ratio situation of change schematic diagram with snr of received signal of the present invention and traditional method；

Fig. 3 is the Signal to Interference plus Noise Ratio situation of change schematic diagram with fast umber of beats of the present invention and traditional method.

Detailed description of the invention

With reference to Fig. 1, for the realization of a kind of based on rarefaction representation the radar robust adaptive beamforming method of the present invention Flow chart；Described radar robust adaptive beamforming method based on rarefaction representation, comprises the following steps:

Step 1, sets transmitting signal wavelength lambda and radar array element distance d of radar respectively, and then obtains the thunder of L snap Reaching echo-signal x, wherein the radar echo signal of the l time snap is x_l, l ∈ 1,2 ..., L}, N are radar element number of array, and L is The snap number of times that radar echo signal x comprises.

Step 2, utilizes the radar echo signal x of the l time snap_l, it is calculated the covariance matrix of radar echo signalIts expression formula is:

$\hat{R}=\frac{1}{L}\underset{l=1}{\overset{L}{\Σ}}{x}_l^H{x}_l$

Wherein, []^HRepresenting matrix conjugate transpose, x_lIt is the radar echo signal of the l time snap, l ∈ 1,2 ..., L}, L The snap number of times comprised for radar echo signal x.

Step 3, angle spatial domain, target setting place scope is [θ_d,θ_u], and by this angle spatial domain scope [θ_d,θ_u] divide For K angle value, wherein kth angle value is θ_k, then according to transmitting signal wavelength lambda and radar array element distance d of radar, point It is not calculated the conventional beamformer W of K angle value in the range of angle spatial domain, target place_cWith angle spatial domain, target place In the range of the direct matrix in verse Beam-former W of K angle value_s, wherein kth angle value θ_kCorresponding conventional beamformer Device is w_ck, kth angle value θ_kCorresponding direct matrix in verse Beam-former is w_sk；

K ∈ 1,2 ..., K}, K are the angle value number that angle spatial domain, target place scope comprises, θ_dFor the target set The lower limit of angle spatial domain, place scope, θ_uThe upper limit of angle spatial domain, the target place scope for setting, its expression formula is respectively as follows:

θ_d=θ₀-B/2

θ_u=θ₀+B/2

Wherein, θ₀Pointing to for desired radar beam center, B is the width between half-power points of desired radar beam, and B= 50.1/Nd, N are radar element number of array, and d is radar array element distance.

(3a) target setting place angle spatial domain scope is [θ_d,θ_u], and by this angle spatial domain scope [θ_d,θ_u] it is divided into K Individual angle value, wherein kth angle value is θ_k, expression formula is:

${\mathrm{\θ}}_k={\mathrm{\θ}}_d+\frac{2k-1}{2K}({\mathrm{\θ}}_u-{\mathrm{\θ}}_d)$

Wherein, k ∈ 1,2 ..., K}, K are the angle value number that angle spatial domain, target place scope comprises, θ_dFor set The lower limit of angle spatial domain, target place scope, θ_uThe upper limit of angle spatial domain, the target place scope for setting.

(3b) according to transmitting signal wavelength lambda, radar array element distance d and the kth angle value θ of radar_k, calculate successively The conventional beamformer W of K angle value in the range of angle spatial domain, target place_cWith kth angle value θ_kCorresponding conventional ripple Beamformer w_ck, its expression formula is:

W_c=[w_c1,…,w_ck,…,w_cK]

$w_{\mathrm{ck}}={\left[\begin{array}{c}1,...,e^{j2\mathrm{\π}(n-1)d\sin \left({\mathrm{\θ}}_k\right)/\mathrm{\λ}},...,e^{j2\mathrm{\π}(N-1)d\sin \left({\mathrm{\θ}}_k\right)/\mathrm{\λ}}\end{array}\right]}^T$

Wherein, []^TRepresenting matrix transposition, n ∈ 1,2 ..., N}, N are radar element number of array.

(3c) according to transmitting signal wavelength lambda, radar array element distance d and the kth angle value θ of radar_k, calculate successively The direct matrix in verse Beam-former of K angle value in the range of angle spatial domain, scope target place, angle spatial domain, target place W_sWith kth angle value θ_kCorresponding direct matrix in verse Beam-former w_sk, its expression formula is:

W_s=[w_s1,…,w_sk,…,w_sK]

$w_{sk}=\mathrm{\α}{\hat{R}}^{-1}a\left({\mathrm{\θ}}_k\right)$

Wherein, n ∈ 1,2 ..., N}, N are radar element number of array, a (θ_k) it is kth angle value θ_kSteering vector,α is the normalization coefficient set, For the covariance matrix of radar echo signal, n ∈ 1,2 ..., N}, N are radar element number of array, []^TRepresenting matrix transposition.

Step 4, is [θ according to angle spatial domain, target place scope_d,θ_u] and the covariance matrix of radar echo signalMeter Calculating and obtain disturbing in radar echo signal the incident direction of signal, wherein m-th interference signal incident direction isAnd calculate Noise power in radar echo signal

(4a) according to the spatial domain angular range [θ at target place_d,θ_u] and the covariance matrix of radar echo signalAnd adopt With document " Robust adaptive beamforming based on interference covariance matrix Sparse reconstruction, Signal Process., Mar.2014, vol.96., pp.375 381 " the middle side proposed Method, is calculated in radar echo signal the incident direction disturbing signal, and wherein m-th interference signal incident direction ism ∈ 1,2 ..., M}, M are the interference signal number that radar echo signal comprises, and subscript i represents incident direction.

(4b) covariance matrix to radar echo signalCarry out Eigenvalues Decomposition, obtain the association side of radar echo signal Difference matrixMinimal eigenvalue η_min, and then the noise power being calculated in radar echo signal

Step 5, according to disturbing the incident direction of signal in radar echo signal, be calculated in radar echo signal is dry Disturb signal subspace P_I。

Specifically, according to radar echo signal disturbs the incident direction of signal, it is calculated in radar echo signal Interference signals subspace P_I, its expression formula is:

P_I=[p₁,…,p_m,…p_M]

$p_m={\left[\begin{array}{c}1,...,e^{j2\mathrm{\π}(n-1)d\sin \left({\mathrm{\θ}}_{\mathrm{im}}\right)/\mathrm{\λ}},...,e^{j2\mathrm{\π}(N-1)d\sin \left({\mathrm{\θ}}_{\mathrm{im}}\right)/\mathrm{\λ}}\end{array}\right]}^T$

Wherein, p_mFor the m-th interference signals subspace in radar echo signal, m ∈ 1,2 ..., M}, M are that radar returns The interference signal number that ripple signal packet contains, λ is the transmitting signal wavelength of radar, and d is radar array element distance, n ∈ 1,2 ..., N}, N is radar element number of array, n ∈ 1,2 ..., N}, N are radar element number of array.

Step 6, according to the conventional beamformer W of K angle value in the range of angle spatial domain, target place_cWith target place The direct matrix in verse Beam-former W of K angle value in the range of angle spatial domain_s, it is calculated radar echo signal successively The expectation Beam-former w of basic matrix B and radar echo signal_d。

(6a) according to the conventional beamformer W of K angle value in the range of angle spatial domain, target place_cWith angle, target place The direct matrix in verse Beam-former W of K angle value in the range of degree spatial domain_s, it is calculated the basic matrix of radar echo signal B, its expression formula is:

B=[W_c,W_s]

(6b) utilize the basic matrix B of radar echo signal, be calculated the expectation Beam-former w of radar echo signal_d, And then obtain rarefaction representation vector u to be asked in radar echo signal.

Specifically, the expectation Beam-former w of described radar echo signal_d, its expression formula is:

w_d=Bu

Wherein, u is rarefaction representation vector to be asked.

Step 7, according to the interference signals subspace P in radar echo signal_I, noise power in radar echo signal The rarefaction representation vector u to be asked with in radar echo signal, is calculated the sparse model of radar echo signal, its expression formula For:

Meet rarefaction representation vector u to be asked in the radar echo signal of described sparse model condition, believe for radar return Rarefaction representation vector in number

Wherein,B=[W_c,W_s], W_cFor the conventional ripple of K angle value in the range of angle spatial domain, target place Beamformer, W_sAsk for the direct matrix of K angle value in the range of angle spatial domain, scope target place, angle spatial domain, target place Inverse beamforming device,For the noise power in radar echo signal, | | | |₂It is two norms, | | | |₁For One norm, α is the coefficient more than zero artificially determined, typically takes 30；ξ is that the interference signal subspace in constraint radar echo signal is empty Between P_IAnd the parameter of orthogonality between rarefaction representation vector u to be asked in radar echo signal, δ is in constraint radar echo signal Parameter openness for rarefaction representation vector u to be asked, and α, ξ and δ be all higher than zero, P_IFor the interference signal in radar echo signal Subspace, B is the basic matrix of radar echo signal.

Step 8, according to the rarefaction representation vector in radar echo signalWith the basic matrix B of radar echo signal, calculate Final Beam-former to radar echo signalIts expression formula is:

${\hat{w}}_d=B\hat{u}$

By following emulation experiment, effect of the present invention is verified explanation further.

(1) simulated conditions:

In emulation experiment of the present invention, software emulation platform is MATLAB R2010a, setting array antenna number N=in experiment 10, transmitting signal wavelength is λ, array element distance d=λ 2, parameter alpha, ξ and δ is respectively set as 10,10^-4With 10^-1.Receive in signal There are two interference signals, its incident direction is respectively-35 ° and 40 °, and power is respectively 30 decibels, truly entering of echo signal Penetrating direction is 0 °, and the apparent incident direction of target is 3 °, and obtaining spatial domain, target place scope according to prior information is [-5 °, 5 °], Noise power is set as 0 decibel.For the effect of relative analysis the inventive method, emulation experiment gives simultaneously directly The result of matrix inversion technique, subspace projection method and bayes method.

(2) emulation content and result:

Emulation 1, this experiment is for verifying that the output Signal to Interference plus Noise Ratio of the inventive method and traditional method is with receiving signal noise The situation of change of ratio.Under these conditions, the power of echo signal has-25 decibels to change to 25 decibels, i.e. incoming signal noise Ratio is changed to 25 decibels by-25 decibels, receives snap number of times L=100, is respectively adopted the inventive method and classical signal process is right The echo-signal of target processes, and independently carries out 300 experiments under each signal to noise ratio, obtains the inventive method and tradition letter The average Signal to Interference plus Noise Ratio of number processing method with the situation of change of snr of received signal as in figure 2 it is shown, Fig. 2 is the present invention and tradition The Signal to Interference plus Noise Ratio of method is with the situation of change schematic diagram of snr of received signal.

As shown in Figure 2, direct matrix in verse method and bayes method have good performance when low signal-to-noise ratio situation, But its performance severe exacerbation in the case of high s/n ratio, and subspace projection method is functional in the case of high s/n ratio, And at low signal-to-noise ratio situation hydraulic performance decline, and the inventive method has good Signal to Interference plus Noise Ratio performance always.

Emulation 2, this experiment is for contrasting the output Signal to Interference plus Noise Ratio change with fast umber of beats of the inventive method and traditional method Situation.Under these conditions, target setting signal power is 0 difference, receives fast umber of beats L and is changed to 300 by 10, is respectively adopted The inventive method and classical signal process the echo-signal to target and process, and independently carry out 300 times under each fast umber of beats Experiment, obtains the average Signal to Interference plus Noise Ratio of the inventive method and the classical signal processing method situation of change such as Fig. 3 institute with fast umber of beats Showing, Fig. 3 is the Signal to Interference plus Noise Ratio situation of change schematic diagram with fast umber of beats of the present invention and traditional method.

From the figure 3, it may be seen that traditional method has a good performance when fast umber of beats is more, but property in the case of fewer snapshots Can decline, and the inventive method still has good performance little taking soon, this illustrates that the inventive method has preferably Robustness.

In summary, the inventive method has good AF panel performance, it is possible to the interference in radar system presses down Make, and emulation experiment demonstrates the correctness of the present invention, validity and reliability.

Obviously, those skilled in the art can carry out various change and the modification essence without deviating from the present invention to the present invention God and scope；So, if these amendments of the present invention and modification belong to the scope of the claims in the present invention and equivalent technologies thereof Within, then the present invention is also intended to comprise these change and modification.

Claims (9)

1. a radar robust adaptive beamforming method based on rarefaction representation, it is characterised in that comprise the following steps:

Step 1, sets transmitting signal wavelength lambda and radar array element distance d of radar respectively, and then the radar obtaining L snap returns Ripple signal, wherein the radar echo signal of the l time snap is x_l, l ∈ 1,2 ..., L}, N are radar element number of array, and L is radar The snap number of times that echo-signal comprises；

Step 2, utilizes the radar echo signal of L snap, is calculated the covariance matrix of radar echo signal

Step 3, angle spatial domain, target setting place scope is [θ_d, θ_u], and by this angle spatial domain scope [θ_d, θ_u] it is divided into K Angle value, wherein kth angle value is θ_k, then according to transmitting signal wavelength lambda and radar array element distance d of radar, count respectively Calculate and obtain the conventional beamformer W of K angle value in the range of angle spatial domain, target place_cWith angle spatial domain, target place scope The direct matrix in verse Beam-former W of interior K angle value_s, wherein kth angle value θ_kCorresponding conventional beamformer is w_ck, kth angle value θ_kCorresponding direct matrix in verse Beam-former is w_sk；

K ∈ 1,2 ..., K}, K are the angle value number that angle spatial domain, target place scope comprises, θ_dFor the angle, target place set The lower limit of degree spatial domain scope, θ_uThe upper limit of angle spatial domain, the target place scope for setting；

Step 4, is [θ according to angle spatial domain, target place scope_d, θ_u] and the covariance matrix of radar echo signalCalculate Disturbing the incident direction of signal in radar echo signal, wherein m-th interference signal incident direction isAnd be calculated Noise power in radar echo signal

Step 5, according to disturbing the incident direction of signal in radar echo signal, the interference being calculated in radar echo signal is believed Work song space P_I；

Step 6, according to the conventional beamformer W of K angle value in the range of angle spatial domain, target place_cWith target place angle The direct matrix in verse Beam-former W of K angle value in the range of spatial domain_s, it is calculated the group moment of radar echo signal successively Battle array B and the expectation Beam-former w of radar echo signal_d；

Step 7, according to the interference signals subspace P in radar echo signal_I, noise power in radar echo signalAnd thunder Reaching rarefaction representation vector u to be asked in echo-signal, be calculated the sparse model of radar echo signal, its expression formula is:

$\underset{u}{\min imize}\left|\right|u^H{\hat{R}}_{y}u-{\mathrm{\σ}}_u^2|{|}_2$

subject to||P_IBu||₂≤ ξ, | | u | |₁≤δ

Meeting rarefaction representation vector u to be asked in the radar echo signal of described sparse model condition is in radar echo signal Rarefaction representation vector

Wherein,B=[W_c, W_s], For the noise power in radar echo signal, | | | |₂For Two norms, | | | |₁Being a norm, α is the coefficient more than zero artificially determined；ξ is the interference in constraint radar echo signal Signal subspace P_IAnd the parameter of orthogonality between rarefaction representation vector u to be asked in radar echo signal, δ returns for constraint radar Parameter openness for rarefaction representation vector u to be asked in ripple signal, and α, ξ and δ be all higher than zero, P_IFor in radar echo signal Interference signals subspace, B is the basic matrix of radar echo signal；

Step 8, according to the rarefaction representation vector in radar echo signalWith the basic matrix B of radar echo signal, it is calculated thunder Reach the final Beam-former of echo-signal

A kind of radar robust adaptive beamforming method based on rarefaction representation, its feature exists In, in step 2, the covariance matrix of described radar echo signalIts expression formula is:

$\hat{R}=\frac{1}{L}\underset{l=1}{\overset{L}{\Σ}}{x}_l^H{x}_l$

Wherein, []^HRepresenting matrix conjugate transpose, x_lIt is the radar echo signal of the l time snap, l ∈ 1,2 ..., L}, L are thunder Reach the snap number of times that echo-signal comprises.

A kind of radar robust adaptive beamforming method based on rarefaction representation, its feature exists In, the sub-step of step 3 is:

(3a) target setting place angle spatial domain scope is [θ_d, θ_u], and by this angle spatial domain scope [θ_d, θ_u] it is divided into K angle Angle value, wherein kth angle value is θ_k, expression formula is:

${\mathrm{\θ}}_k={\mathrm{\θ}}_d+\frac{2k-1}{2K}({\mathrm{\θ}}_u-{\mathrm{\θ}}_d)$

Wherein, k ∈ 1,2 ..., K}, K are the angle value number that angle spatial domain, target place scope comprises, θ_dFor the target set The lower limit of angle spatial domain, place scope, θ_uThe upper limit of angle spatial domain, the target place scope for setting；

(3b) according to transmitting signal wavelength lambda, radar array element distance d and the kth angle value θ of radar_k, it is calculated mesh successively The conventional beamformer W of K angle value in the range of mark angle spatial domain, place_cWith kth angle value θ_kCorresponding conventional wave beam shape Grow up to be a useful person w_ck；

(3c) according to transmitting signal wavelength lambda, radar array element distance d and the kth angle value θ of radar_k, it is calculated mesh successively The direct matrix in verse Beam-former W of K angle value in the range of mark angle spatial domain, scope target place, angle spatial domain, place_sWith Kth angle value θ_kCorresponding direct matrix in verse Beam-former w_sk。

A kind of radar robust adaptive beamforming method based on rarefaction representation, its feature exists In, described θ_dThe lower limit of angle spatial domain, the target place scope for setting, θ_uFor angle spatial domain, target place scope upper set Limit, its expression formula is respectively as follows: θ_d=θ₀-B/2, θ_u=θ₀+B/2；

The conventional beamformer W of K angle value in the range of angle spatial domain, described target place_c, described kth angle value θ_kRight The conventional beamformer w answered_ck, K angle value in the range of angle spatial domain, scope target place, angle spatial domain, described target place Direct matrix in verse Beam-former W_sWith described kth angle value θ_kCorresponding direct matrix in verse Beam-former w_sk, Its expression formula is respectively as follows:

W_c=[w_c1..., w_ck..., w_cK]

$w_{ck}={\[1,...,e^{j2\mathrm{\π}(n-1)dsin\left({\mathrm{\θ}}_k\right)/\mathrm{\λ}},...,e^{j2\mathrm{\π}(N-1)dsin\left({\mathrm{\θ}}_k\right)/\mathrm{\λ}}\]}^T$

W_s=[w_s1..., w_sk..., w_sK]

$w_{sk}=\mathrm{\α}{\hat{R}}^{-1}a\left({\mathrm{\θ}}_k\right)$

Wherein, θ₀Pointing to for desired radar beam center, B is the width between half-power points of desired radar beam, and B=50.1/ Nd, d are radar array element distance, []^TRepresenting matrix transposition, n ∈ 1,2 ..., N}, N are radar element number of array, a (θ_k) it is kth Individual angle value θ_kSteering vector,α is the normalization set Coefficient, For the covariance matrix of radar echo signal, n ∈ 1,2 ..., N}, N are radar battle array Unit's number, []^TRepresenting matrix transposition.

A kind of radar robust adaptive beamforming method based on rarefaction representation, its feature exists In, in step 4, described radar echo signal disturbs the incident direction of signal, specifically according to the angle, spatial domain at target place Degree scope [θ_d, θ_u] and the covariance matrix of radar echo signalIt is calculated in radar echo signal the incidence disturbing signal Direction, wherein m-th interference signal incident direction isM ∈ 1,2 ..., M}, M are the interference letter that radar echo signal comprises Number number, subscript i represents incident direction；

Noise power in described radar echo signal Covariance matrix for radar echo signal's Minimal eigenvalue.

A kind of radar robust adaptive beamforming method based on rarefaction representation, its feature exists In, in steps of 5, the interference signals subspace P in described radar echo signal_I, its expression formula is:

P_I=[p₁,…,p_m,…p_M]

$p_m={\[1,...,e^{j2\mathrm{\π}(n-1)dsin\left({\mathrm{\θ}}_{im}\right)/\mathrm{\λ}},...,e^{j2\mathrm{\π}(N-1)dsin\left({\mathrm{\θ}}_{im}\right)/\mathrm{\λ}}\]}^T$

Wherein, p_mFor the m-th interference signals subspace in radar echo signal, m ∈ 1,2 ..., M}, M are radar echo signal The interference signal number comprised, λ is the transmitting signal wavelength of radar, and d is radar array element distance, n ∈ 1,2 ..., N}, N are thunder Reach element number of array, n ∈ 1,2 ..., N}, N are radar element number of array.

A kind of radar robust adaptive beamforming method based on rarefaction representation, its feature exists In, the sub-step of step 6 is:

(6a) according to the conventional beamformer Beam-former W of K angle value in the range of angle spatial domain, target place_cWith target institute The direct matrix in verse Beam-former W of K angle value in the range of angle spatial domain_s, it is calculated the base of radar echo signal Matrix B；

(6b) utilize the basic matrix B of radar echo signal, be calculated the expectation Beam-former w of radar echo signal_d, and then Obtain rarefaction representation vector u to be asked in radar echo signal.

A kind of radar robust adaptive beamforming method based on rarefaction representation, its feature exists In, the basic matrix B of described radar echo signal and the expectation Beam-former w of radar echo signal_d, its expression formula is respectively as follows:

B=[W_c,W_s], w_d=Bu

Wherein, rarefaction representation vector to be asked in being radar echo signal for u.

A kind of radar robust adaptive beamforming method based on rarefaction representation, its feature exists In, in step 8, the final Beam-former of described radar echo signalIts expression formula is:B is that radar returns The basic matrix of ripple signal,For the rarefaction representation vector in radar echo signal.