CN106772226A - DOA estimation method based on compressed sensing time-modulation array - Google Patents

Abstract

The present invention proposes a kind of arrival bearing (DOA) method of estimation of time-modulation array based on compressed sensing, the fast umber of beats existed for the DOA estimation method for solving existing time-modulation array is few, the low technical problem of estimated accuracy closely in the case of index or signal coherence, realizes that step is：Pulse initial time and pulse duration are optimized；Set up sideband signals and receive model；Array manifold in model is received to sideband signals and is extended rarefaction；The sideband signals received in model sparse to time-modulation array sideband signals carry out singular value decomposition and dimension-reduction treatment；Obtain the sparse recovery problem model of time-modulation array based on compressed sensing；Solve arrival bearing's angle of echo signal.The present invention makes full use of the high-resolution characteristic of sparse reconstructing method according to compressive sensing theory, improves target direction of arrival DOA estimated accuracies.

Description

DOA estimation method based on compressed sensing time-modulation array

Technical field

The invention belongs to signal processing technology field, it is related to a kind of DOA estimation method of time-modulation array, and in particular to A kind of DOA estimation method of the time-modulation array based on compressed sensing, it is few to can be used to processing fast umber of beats, index or believes closely Number relevant time-modulation array antenna high resolution DOA estimation.

Background technology

With the fast development of electronics and the communication technology, various electronic systems propose increasingly harsher to antenna or antenna array Requirement, such as high-gain, Sidelobe, broadband, low-cross polarization component, the sometimes combination of even several rigors. These strict demands to array antenna characteristic parameters often again to the structure precision of antenna array, the feed precision of feeding network, The propositions such as excitation dynamic range extremely harshness, some even unpractical requirements.In order to solve the above problems, twentieth century The sixties propose the concept of Time Modulated Antenna battle array.In Time Modulated Antenna battle array, each element and high speed RF switch (RF) switch connection, it can manually be controlled by specific time series.Joined by the use time in time-modulation array Number, can significantly reduce the high dynamic range ratio of low/ultralow side lobe level (SLL) amplitude excitations, so as to alleviate design feed The difficulty of network.

Used as the important branch of field of signal processing, Array Signal Processing receives the wide of domestic and foreign scholars in recent decades General concern is simultaneously developed rapidly, and its application is throughout every field such as radar, communication, sonar, exploration, antennas for radio astronomy.And The estimation problem of spacing wave arrival direction DOA is a very important research contents in Array Signal Processing field.DOA estimates The basic problem of meter is just to determine while being in the locus of multiple signals interested in a certain region in space, i.e., each is believed Number reach array reference array element deflection, abbreviation direction of arrival.

However, people estimate that using MUSIC algorithms and ESPRIT calculates to the DOA of time-modulation array so far Method, i.e. 4D-MUSIC algorithms and 4D-ESPRIT algorithms.They are using the reception letter at distinct sidebands in time-modulation uniform array Number composition receives data space, then these signals is down-converted to after same intermediate frequency (IF) level, using MUSIC algorithms or ESPRIT algorithms realize that DOA estimates.But these algorithms are limited to Nyquist's theorem, and few in the fast umber of beats for the treatment of, close rope Draw, performance and unsatisfactory when the problems such as signal coherence.Although thering is expert and scholar to propose substantial amounts of decorrelation LMS and performance Optimized algorithm, but need to carry out Eigenvalues Decomposition to the covariance matrix of antenna array receiver data in solution procedure, once Bay number is more, it will the excessively heavy problem of calculating task occur.

And in 2006, Candes et al. proposed a kind of new theory for being gathered on sparse signal and being recovered and compresses sense Know theory.It makes full use of signal openness or compressibility, and appropriate compression is carried out to data while signal sampling, this Significantly reduce data transfer, storage, the burden for the treatment of.Compared with traditional Nyquist sampling theorem, as long as its signal is It is compressible or certain transform domain be it is sparse just can just can essence with the measurement data far fewer than needed for classical sampling theory Really recover primary signal or estimate the parameter of signal.Under this theoretical frame, sampling rate is not dependent on the bandwidth of signal, And depend on information structure and content in the signal.In compressive sensing theory carries out DOA estimations, people utilize array signal Spatial domain it is openness, the coefficient that DOA estimation problems are considered as under over-complete dictionary of atoms is represented into recovery problem, by angular region Discretization sets up sparse reconstruction model, then solves corresponding optimization problem using Second-order cone programming, then obtains high-resolution and estimates Meter.But the DOA of existing time-modulation array estimates and compressive sensing theory is not used to study it.

The content of the invention

Deficiency it is an object of the invention to be directed to above-mentioned prior art, there is provided one kind is based on compressed sensing time-modulation The DOA estimation method of array, the DOA estimation method for solving existing time-modulation array is processing a small amount of snap, close rope Draw or signal coherence problem when the low technical problem of estimated accuracy.

Technical thought of the invention is：Pulse initial time and pulse duration are carried out using differential evolution algorithm excellent Change, set up sideband signals model, while using compressive sensing theory, the time-modulation battle array of compressed sensing is based on by rational structure Arrange sparse recovery problem model, make full use of the high-resolution characteristic of sparse reconstructing method, realize in a small amount of snap, closely index or Arrival bearing's angle estimation of the echo signal of degree of precision during signal coherence.

According to above-mentioned technical thought, realize that the technical scheme that the object of the invention is taken comprises the following steps：

(1) with the minor level SLL of centre frequency directional diagram_d, the first sidebands levels SBL_dWith lobe width BW_dIt is optimization Target, using differential evolution algorithm to the pulse initial time τ of control time modulation array unit conducting state₀₀And pulse persistance Time τ₀Optimize, obtain optimization afterpulse initial time τ_0fWith optimization afterpulse duration τ_f；

(2) will optimization afterpulse initial time τ_0fWith optimization afterpulse duration τ_fSubstitute into the output of time-modulation array In signal expression, and Fourier expansion is carried out to it, recycle the result launched to set up sideband signals and receive model X= B^TAs+N₁, wherein, B^TIt is the transposition of time complex matrix B, A is array manifold matrix, and s is space incident signal matrix, N₁To make an uproar Sound matrix；

(3) model X=B is received to sideband signals^TAs+N₁In array manifold matrix A be extended rarefaction, formed Complete redundant dictionaryAnd utilize redundant dictionarySideband signals are received into model X=B^TAs+N₁It is converted into time-modulation array The sparse reception model of sideband signalsWherein,It is sparse signal vector；

(4) to the sparse reception model of time-modulation array sideband signalsIn X carry out singular value decomposition And dimension-reduction treatment, obtain low dimensional sideband signals X_SV, incoming signalWith noise signal N_SV；

(5) using low dimensional sideband signals X_SV, incoming signalWith noise signal N_SV, by time-modulation array sideband letter Number sparse reception modelIt is rewritten intoAnd it is changed, obtain based on compression The sparse recovery problem model of time-modulation array of perception；

(6) the sparse problem model that recovers of the time-modulation array based on compressed sensing is converted into Second-order cone programming problem, And the Second-order cone programming problem is solved using convex optimization bag, be restored vectorRecovery vector is searched out again In non-zero position, that is, obtain arrival bearing's angle of echo signal.

The present invention compared with prior art, with advantages below：

The present invention takes full advantage of sparse reconstruct side due to when target DOA angles are obtained, employing compressive sensing theory The high-resolution characteristic of method, compared with prior art, in a small amount of snap, effectively improves in the case of index or signal coherence closely Target direction of arrival DOA estimated accuracies.

Brief description of the drawings

Fig. 1 is of the invention to realize flow chart；

Fig. 2 is pulse working timing figure in embodiments of the invention；

Fig. 3 be in embodiments of the invention algorithm performance with fast umber of beats situation of change figure；

Fig. 4 be the present invention with prior art for three uncorrelated echo signal direction of arrival angles estimation mean square errors with The variation relation figure of signal to noise ratio；

Fig. 5 be the present invention with prior art for three related objective signal waves up to orientation angle estimate mean square error with Signal to noise ratio variation relation figure；

Fig. 6 be the mean square errors that the present invention estimates with prior art in two uncorrelated echo signal direction of arrival angles and The graph of a relation at angle interval.

Specific embodiment

Below in conjunction with the drawings and specific embodiments, the object, technical solutions and advantages of the present invention are described in detail.It is aobvious So, based on the embodiment in the present invention, those of ordinary skill in the art are obtained on the premise of creative work is not made Every other embodiment, belong to the scope of protection of the invention.

A kind of reference picture 1, DOA estimation method of the time-modulation array based on compressed sensing, realizes that step is as follows：

Step 1, using differential evolution algorithm to the pulse initial time τ of control time modulation array unit conducting state₀₀ And pulse duration τ₀Optimize, comprise the following steps that：

Step 1a, determines maximum cycle and population scale SN, and to population at individual Y_ijInitialized, wherein, i Represent that i-th individual, i=1,2 ..., SN, j represent j-th optimization component, j=1,2 ..., D, D are variable number to be optimized；

Step 1b, calculates population at individual Y_i,GFitness fit_i：

Wherein, f (Y_i,G)=ω₁·max|SLL_max-SLL_d|+ω₂·|Bw₀-Bw_d|+ω₃·U(SBL_max-SBL_d) it is G for i-th individuality of population target function value, BW₀, SLL_maxAnd SBL_maxPopulation at individual Y is represented respectively_i,GCentre frequency Maximum sidebands levels at the zero point main lobe width at place, maximum sidelobe levels and the first sideband frequency, ω₁, ω₂, ω₃Point Wei not weight coefficient；

Step 1c, to individual Y_i,GMutation operation is carried out, the individual V after being made a variation_i,G+1：

V_i,G+1=Y_r1,G+F·(Y_r2,G-Y_r3,G)

Wherein, r₁,r₂,r₃∈ { 1,2 ..., SN }, r₁,r₂,r₃Randomly select, and meet i ≠ r₁≠r₂≠r₃, F is variation The factor；

Step 1d, to by the individual V after variation_i,G+1Crossover operation is carried out, obtains testing individual U_i,G+1：

U_i,G+1=(u_1i,G+1,u_2i,G+1,…u_Di,G+1)

Wherein,Rand (j) is the random number in [0,1], CR is to intersect the factor, rnbr (i) ∈ { 1,2 ..., D }, and rnbr (i) is randomly selected；

Step 1e, calculates experiment individuality U_i,G+1Fitness function value fit_i', and and Y_i,GFitness function value fit_i Contrasted, selection fitness function value population at individual high is used as population at individual Y of future generation_i,G+1：

Step 1f, repeats step (1b)~step (1e), until meeting optimization aim requirement or completing largest loop During number of times, jump out and circulate and export new population optimal location G_b' optimization is completed, wherein, G'_b=[τ_0fτ_f], i.e. τ_0fIt is optimization Afterpulse initial time and τ_fIt is the optimization afterpulse duration；

Step 2, sets up sideband signals and receives model, comprises the following steps that：

Step 2a, setting time modulation array parameter：Array element number is M, and fast umber of beats is N, and space far-field signal number is K, carrier frequency is f₀, unit interval is d, and the high speed RF switch cycle is T_p, the most exponent number of high-order sideband is Q；

Step 2b, by optimization afterpulse initial time τ_0fWith optimization afterpulse duration τ_fSubstitute into time-modulation array defeated Go out and signal expression x (t)：

Wherein, U_mT () is m-th antenna element high speed RF switch periodic switch function, its expression formula is adjusted with the time The modulation system of array processed and the pulse initial time τ of control time modulation array unit conducting state_0mWith duration τ_mHave Close, τ_0m∈τ_0f, τ_m∈τ_f, s_kT signal that () is launched by k-th space far-field signal source, θ_kIt is k-th space far-field signal Space angle where source, β=2 π/λ, λ is wavelength, n_mT () represents m-th noise of antenna element, and assume that noise is zero The white Gaussian noise of average, its variance is σ², the noise statisticses between each antenna element are uncorrelated, and noise is also counted not with signal It is related；

Step 2c, fourier progression expanding method is carried out to x (t), obtains q rank sideband signals expression formulas x_q(t)：

Wherein,It is m-th array element in the time compound excitation of q rank sidebands, f_p=1/ T_p；

Step 2d, to x_qT () carries out down-converted, obtain the q rank sideband signals expression formulas x' after down coversion_q(t)：

The expression formula of its matrix form is：

X (n)=B^T[As (n)+N (n)], n=1,2 ..., N,

Wherein, X (n)=[x'_-Q(n)x'_-Q+1(n)…x'_q(n)…x'_Q(n)]^TIt is the snap being made up of each sideband signals Column vector, s (n)=[s₁(n)s₂(n)…s_k(n)…s_K(n)]^TIt is space incident signal column vector, s_kN () represents s_kThe base of (t) Band sampled signal, N (n)=[n₁(n)n₂(n)…n_N(n)]^TFor noise column vector is tieed up in M × 1；

When fast umber of beats is N, the expression formula of sideband signals matrix form can be expressed as sideband signals and receive model：

X=B^TAs+N₁

Wherein X=[X (1) X (2) ... X (N)], s=[s (1) s (2) ... s (N)], N=[N (1) N (2) ... N (N)], N₁= B^TN；

Sideband signals are received model X=B by step 3^TAs+N₁In array manifold matrix A be extended rarefaction, specifically Step is as follows：

Step 3a, N is divided into by whole space_θPart, i.e.,And assume that each angle for dividing is corresponded to Angle where K signal source of one potential signal source and physical presence all falls on the grid for dividing just, then array stream Type A is extendable to one and crosses perfect set

Sideband signals under framework of sparse representation, are received model X=B by step 3b^TAs+N₁It is transformed into time-modulation array Sparse signal receives model：

Wherein In only exist K position of signal Element value is non-zero, other N_θThe element value of-K position is 0, then sparse signal vectorIt is K sparse matrixes；

Step 4, to the sparse reception model of time-modulation array sideband signalsIn X carry out singular value point Solution and dimension-reduction treatment, comprise the following steps that：

Step 4a, singular value decomposition X=U Λ V are carried out to X^H, obtain singular value matrix Λ, left singular value vector matrix U, Right singular value vector matrix V；

Step 4b, dimension-reduction treatment is carried out using right singular value vector matrix to X, obtains the matrix X after dimensionality reduction_SV= XVD_K, wherein D_K=[I_K0], I_KK × K unit matrixs are represented, 0 represents the null matrix of K × (N-K) dimensions, can similarly obtainAnd N_SV=N₁VD_K；

Step 5, the sparse recovery problem model of time-modulation array based on compressed sensing, its obtaining step is：

Step 5a, model is received to time-modulation array sparse signalLeft and right is same to multiply VD_K, obtain new Time-modulation array sparse signal receives model:

Due toIn element and redundant dictionaryEach row correspond, i.e., corresponded with the incoming wave of signal, by it Middle nonzero element position can uniquely determine the corresponding incident angle of source signal.As long as therefore using sparse restructing algorithm Exact recovery SignalThe DOA that can obtain signal estimates.BecauseWithIt is openness with identical, then redundant dictionaryDOA can be made Angle parameter estimate be converted into solutionProblem, now, new time-modulation array sparse signal receives model and can see As the optimization problem of L1 norm constraints：

Wherein, ε is a parameter relevant with noise level, | | | |₁、||·||₂L1 norms and L2 models are represented respectively Number；

The optimization problem of step 5b, L1 norm constraint can be further rewritten as based on compression using method of Lagrange multipliers The sparse recovery problem model of time-modulation array of perception：

Wherein η is hyper parameter, for the balance between control signal degree of rarefication and residual error；

Step 6, arrival bearing's angle of echo signal, its obtaining step is：

The sparse solution for recovering problem model of time-modulation array based on compressed sensing is converted into Second-order cone programming to ask It is entitled：

Wherein η is hyper parameter, and the recovery vector in the sparse recovery problem for constructing is solved using convex optimization software bagRecover vectorThe position of middle nonzero element is the arrival bearing's angle for representing echo signal.

Below in conjunction with emulation experiment, technique effect of the invention is described in further detail：

1st, experiment condition and content：

Assuming that Time Modulated Antenna is uniform straight line array, array element is at intervals of half wavelength, target numbers, it is known that space lattice Unified is 0.1 °, the scope from -90 ° to 90 °, array number M=24, f₀=300MHz, T_p=1s, sideband Q=10, using based on battle array The time-modulation mode of row afocal variable size (VAS), minor level SLL_d=-30dB, the first sidebands levels SBL_d=-20dB With lobe width BW_d=70, ω₁=1.2, ω₂=0.1, ω₃=0.3, maximum cycle 500 and population scale 24, profit Optimize gained time series with differential evolution algorithm as shown in Figure 2；

1.1st, assume that space far-field has 1 signal source, incident angle is 30 °, fast umber of beats from 1 to 20 with 2 for interval is carried out Change, signal to noise ratio snr is 20dB, and 50 Monte Carlo experiments are done at each fast umber of beats, is obtained to 1 echo signal direction of arrival The mean square error of angle estimation with fast umber of beats variation relation, as shown in Figure 3；

1.2nd, assume that space far-field there are 3 mutually incoherent signal sources, incident angle is respectively -12 °, -2 °, 30 °, snap Number takes N=50, and signal to noise ratio snr is changed to 20dB from -10dB by interval of 5dB, and 50 Meng Teka are under each signal to noise ratio Sieve test, obtain to three estimation mean square errors of uncorrelated echo signal direction of arrival angle with signal to noise ratio variation relation, As shown in Figure 4；

1.3rd, assume that space far-field there are 3 relevant signal sources, incident angle is respectively -12 °, -2 °, 30 °, and fast umber of beats takes N=50, signal to noise ratio snr is changed to 20dB from -10dB by interval of 5dB, and 50 Monte Carlo realities are done under each signal to noise ratio Test, obtain reaching three Coherent Targets signal waves the estimation mean square error of orientation angle with the variation relation of signal to noise ratio, such as Fig. 5 institutes Show；

1.4th, assume that space far-field has individual signal source, incidence angle θ₁=15 °, θ₂=θ₁+ Δ θ, Δ θ ∈ [- 5 °, 5 °], noise It is 10dB than SNR, obtains the pass at the mean square error and angle interval estimated two uncorrelated echo signal direction of arrival angles System, as shown in Figure 6；

2nd, analysis of simulation result：

Reference picture 2, due to using VAS modulation systems in this experiment, then control time modulation array unit conducting The pulse initial time τ of state₀₀It is 0, now ordinate is to represent as excellent by the result that obtains of differential evolution algorithm optimization Pulse duration τ after change_f。

Reference picture 3, when fast umber of beats is 1, algorithm of the invention estimates mean square error to echo signal direction of arrival angle Less than 0.4 is reached, mean square error has leveled off to 0 when fast umber of beats reaches 10, illustrates that the present invention breaches Nai Kuisi Specific reason, can realize that echo signal direction of arrival angle is accurately estimated in few snap even single snap.

Reference picture 4, two kinds of algorithms when signal incoherent, angle spacing are larger with the change of signal to noise ratio snr, with phase Near mean square error, when SNR reaches 0, mean square error has leveled off to 0, illustrate the two signal incoherent, angle spacing compared with Echo signal direction of arrival angle can be estimated in the case of big correctly estimated, and with close estimation performance.

Reference picture 5, when signal coherence, 4D-MUSIC algorithms reach side with the increase of signal to noise ratio snr to echo signal ripple It is still very big to angle estimation mean square error, illustrate when signal coherence, can not 4D-MUSIC algorithms even if increasing signal to noise ratio Estimated accuracy make moderate progress, and inventive algorithm in SNR=-5dB its to echo signal direction of arrival angle estimate it is equal Square error is to tend to 0, even illustrating in the case of signal coherence, inventive algorithm still can accurately estimate target letter Number direction of arrival angle.

Reference picture 6,4D-MUSIC algorithms are in the sigtnal interval, and | Δ θ | can tell adjacent target at >=2 °, and of the invention The mean square error that two adjacent echo signal direction of arrival angles are estimated has been tended towards stability when angle is at intervals of 0.2 °, explanation The present invention exists.

From Fig. 3~Fig. 6, it can be seen that the present invention can realize the estimation to echo signal direction of arrival angle, and fast Umber of beats is few, closely index, still has estimated accuracy higher in the case of signal coherence.

Above example is only used to illustrate the present invention in uniform linear array and the time-modulation based on VAS modulation systems Feasibility in array, rather than its limitations；Although having been carried out in detail to implementation steps of the present invention with reference to the foregoing embodiments It is bright, it will be understood by those within the art that：It can still modify or to it to previous embodiment Middle part or all technical characteristic carry out equivalent, and these are changed or are replaced, and do not make the sheet of appropriate technical solution Matter departs from the scope of technical solution of the present invention.

Claims (7)

1. a kind of DOA estimation method based on compressed sensing time-modulation array, it is characterised in that comprise the following steps：

(1) with the minor level SLL of centre frequency directional diagram_d, the first sidebands levels SBL_dWith lobe width BW_dIt is optimization aim, Using differential evolution algorithm to the pulse initial time τ of control time modulation array unit conducting state₀₀And the pulse duration τ₀Optimize, obtain optimization afterpulse initial time τ_0fWith optimization afterpulse duration τ_f；

(2) will optimization afterpulse initial time τ_0fWith optimization afterpulse duration τ_fSubstitute into time-modulation array is exported and letter In number expression formula, and Fourier expansion is carried out to it, recycle the result launched to set up sideband signals and receive model X=B^TAs+ N₁, wherein, B^TIt is the transposition of time complex matrix B, A is array manifold matrix, and s is space incident signal matrix, N₁It is noise square Battle array；

(3) model X=B is received to sideband signals^TAs+N₁In array manifold matrix A be extended rarefaction, formed complete Redundant dictionaryAnd utilize redundant dictionarySideband signals are received into model X=B^TAs+N₁It is converted into time-modulation array sideband The sparse reception model of signalWherein,It is sparse signal vector；

(4) to the sparse reception model of time-modulation array sideband signalsIn X carry out singular value decomposition and drop Dimension treatment, obtains low dimensional sideband signals X_SV, incoming signalWith noise signal N_SV；

(5) using low dimensional sideband signals X_SV, incoming signalWith noise signal N_SV, time-modulation array sideband signals are dilute Dredge and receive modelIt is rewritten intoAnd it is changed, obtain based on compressed sensing The sparse recovery problem model of time-modulation array；

(6) the sparse problem model that recovers of the time-modulation array based on compressed sensing is converted into Second-order cone programming problem, and profit The Second-order cone programming problem is solved with convex optimization bag, be restored vectorRecovery vector is searched out againIn Non-zero position, that is, obtain arrival bearing's angle of echo signal.

2. the DOA estimation method based on compressed sensing time-modulation array according to claim 1, it is characterised in that step Suddenly pulse initial time τ of the use differential evolution algorithm described in (1) to control time modulation array unit conducting state₀₀With Pulse duration τ₀Optimize, comprise the following steps：

(1a) determines the scale SN of maximum cycle and population, and to population at individual Y_ijInitialized, wherein, i is represented I-th individual, i=1,2 ..., SN, and j represents j-th optimization component, and j=1,2 ..., D, D are variable number to be optimized；

(1b) calculates population at individual Y_i,GFitness fit_i：

${\mathrm{fit}}_i=\left\{\begin{array}{cc}\frac{1}{1+f\left(Y_{i,G}\right)},& f\left(Y_{i,G}\right)\&GreaterEqual;0\\ 1+\left|f\left(Y_{i,G}\right)\right|,& f\left(Y_{i,G}\right)<0\end{array}\right.$

Wherein, f (Y_i,G) it is target function values of the G for i-th individuality of population；

(1c) is to individual Y_i,GMutation operation is carried out, the individual V after being made a variation_i,G+1：

V_i,G+1=Y_r1,G+F·(Y_r2,G-Y_r3,G)

Wherein, r₁,r₂,r₃∈ { 1,2 ..., SN }, r₁,r₂,r₃Randomly select, and meet i ≠ r₁≠r₂≠r₃, F is mutagenic factor；

(1d) is to by the individual V after variation_i,G+1Crossover operation is carried out, obtains testing individual U_i,G+1：

U_i,G+1=(u_1i,G+1,u_2i,G+1,…u_Di,G+1)

Wherein,Rand (j) is the random number in [0,1], and CR is The intersection factor, rnbr (i) ∈ { 1,2 ..., D }, rnbr (i) is randomly selected；

(1e) calculates experiment individuality U_i,G+1Fitness function value fit '_i, and and Y_i,GFitness function value fit_iContrasted, Selection fitness function value population at individual high is used as population at individual Y of future generation_i,G+1：

$Y_{i,G+1}=\left\{\begin{array}{cc}{Y}_{i,G+1}& {\mathrm{fit}}_i^{\&prime;}>{\mathrm{fit}}_i\\ Y_{i,G}& {\mathrm{fit}}_i^{\&prime;}<{\mathrm{fit}}_i\end{array}\right.$

(1f) repeats step (1b)~step (1e), until when meeting optimization aim requirement or completing maximum cycle, Jump out and circulate and export new population optimal location G_b' optimization is completed, wherein, G'_b=[τ_0fτ_f], i.e. τ_0fFor optimization afterpulse rises Begin moment and τ_fIt is the optimization afterpulse duration.

3. the DOA estimation method based on compressed sensing time-modulation array according to claim 1, it is characterised in that step Suddenly the sideband signals of setting up described in (2) receive model X=B^TAs+N₁, comprise the following steps：

(2a) setting time modulation array parameter：Array element number is M, and fast umber of beats is N, and space far-field signal number is K, carrier frequency Rate is f₀, unit interval is d, and the high speed RF switch cycle is T_p, the most exponent number of high-order sideband is Q；

(2b) will optimize afterpulse initial time τ_0fWith optimization afterpulse duration τ_fSubstitute into the sum of time-modulation array output Signal expression x (t)：

$x\left(t\right)=\underset{m=1}{\overset{M}{\&Sigma;}}{U}_m\left(t\right)\&CenterDot;\&lsqb;\underset{k=1}{\overset{K}{\&Sigma;}}{s}_k\left(t\right)\&CenterDot;e^{j(m-1){\mathrm{\&beta;dsin\&theta;}}_k}+n_m\left(t\right)\&rsqb;,$

Wherein, U_mT () is m-th antenna element high speed RF switch periodic switch function, its expression formula and time-modulation array Modulation system and control time modulation array unit conducting state pulse initial time τ_0mWith duration τ_mIt is relevant, τ_0m∈ τ_0f, τ_m∈τ_f, s_kT signal that () is launched by k-th space far-field signal source, θ_kWhere k-th space far-field signal source Space angle, β=2 π/λ, λ is wavelength, n_mT () represents m-th noise of antenna element；

(2c) carries out fourier progression expanding method to x (t), obtains q rank sideband signals expression formulas x_q(t)：

$x_q\left(t\right)=\underset{m=1}{\overset{M}{\&Sigma;}}\underset{k=1}{\overset{K}{\&Sigma;}}{b}_{q,m}\&lsqb;s_k\left(t\right)e^{j2{\mathrm{\&pi;qf}}_{p}t}\&CenterDot;e^{j(m-1){\mathrm{\&beta;dsin\&theta;}}_k}+n_m\left(t\right)\&rsqb;$

Wherein,It is m-th array element in the time compound excitation of q rank sidebands, f_p=1/T_p；

(2d) is to x_qT () carries out down-converted, obtain the q rank sideband signals expression formulas x' after down coversion_q(t)：

$x_q^{\&prime;}\left(t\right)=\underset{m=1}{\overset{M}{\&Sigma;}}\underset{k=1}{\overset{K}{\&Sigma;}}{b}_{q,m}\&lsqb;s_k\left(t\right)\&CenterDot;e^{j(m-1){\mathrm{\&beta;dsin\&theta;}}_k}+n_m\left(t\right)\&rsqb;,$

The expression formula of its matrix form is：

X (n)=B^T[As (n)+N (n)], n=1,2 ..., N,

Wherein, X (n)=[x'_-Q(n)x'_-Q+1(n)…x'_q(n)…x'_Q(n)]^TBe the snap being made up of each sideband signals arrange to Amount, s (n)=[s₁(n)s₂(n)…s_k(n)…s_K(n)]^TIt is space incident signal column vector, s_kN () represents s_kT the base band of () is adopted Sample signal, N (n)=[n₁(n)n₂(n)…n_N(n)]^TFor noise column vector is tieed up in M × 1；

When fast umber of beats is N, the expression formula of sideband signals matrix form can be expressed as sideband signals and receive model：

X=B^TAs+N₁

Wherein X=[X (1) X (2) ... X (N)], s=[s (1) s (2) ... s (N)], N=[N (1) N (2) ... N (N)], N₁=B^TN。

4. the DOA estimation method based on compressed sensing time-modulation array according to claim 1, it is characterised in that step Suddenly model X=B is received to sideband signals described in (3)^TAs+N₁In array manifold matrix A be extended rarefaction, including Following steps：

Whole space is divided into N by (3a)_θPart, i.e.,And the result that utilization space is divided is to array manifold matrix A is extended sparse, obtains perfect set

Sideband signals are received model X=B by (3b) under framework of sparse representation^TAs+N₁It is transformed into the sparse letter of time-modulation array Number receive model be：

$X=B^T\stackrel{\&OverBar;}{A}\stackrel{\&OverBar;}{s}+N_1.$

5. the DOA estimation method based on compressed sensing time-modulation array according to claim 1, it is characterised in that step Suddenly described in (4) to the sparse reception model of time-modulation array sideband signalsIn X carry out singular value point Solution and dimension-reduction treatment, comprise the following steps：

(4a) carries out singular value decomposition X=U Λ V to X^H, obtain singular value matrix Λ, left singular value vector matrix U, right singular value Vector matrix V；

(4b) carries out dimension-reduction treatment using right singular value vector matrix to X, obtains the matrix X after dimensionality reduction_SV=XVD_K, wherein D_K =[I_K0], I_KK × K unit matrixs are represented, 0 represents the null matrix of K × (N-K) dimensions, can similarly obtainAnd N_SV= N₁VD_K。

6. the DOA estimation method based on compressed sensing time-modulation array according to claim 1, it is characterised in that step Suddenly the sparse recovery problem model of the time-modulation array based on compressed sensing described in (5), its obtaining step is：

(5a) receives model to time-modulation array sparse signalLeft and right is same to multiply VD_K, obtain new time-modulation Array sparse signal receives model:

$X_{SV}={\mathrm{XVD}}_K=B^T\stackrel{\&OverBar;}{A}\stackrel{\&OverBar;}{s}{\mathrm{VD}}_K+N_1{\mathrm{VD}}_K=B^T\stackrel{\&OverBar;}{A}{\stackrel{\&OverBar;}{s}}_{SV}+N_{SV},$

And be considered as being the optimization problem of L1 norm constraints by the solution of the reception model：

$\begin{array}{ccc}\underset{{\stackrel{\&OverBar;}{s}}_{SV}}{min}\left|\right|\stackrel{\&OverBar;}{s}|{|}_1& s.t.& \left|\right|X_{SV}-B^T\stackrel{\&OverBar;}{A}{\stackrel{\&OverBar;}{s}}_{SV}|{|}_2^2<\mathrm{\&epsiv;}\end{array}$

Wherein, ε is a parameter relevant with noise level, | | | |₁、||·||₂L1 norms and L2 norms are represented respectively；

(5b) uses method of Lagrange multipliers, and the optimization problem to L1 norm constraints is rewritten, and obtains based on compressed sensing The sparse recovery problem model of time-modulation array：

$\underset{{\stackrel{\&OverBar;}{s}}_{SV}}{min}\frac{1}{2}\left|\right|X_{SV}-B^T\stackrel{\&OverBar;}{A}{\stackrel{\&OverBar;}{s}}_{SV}|{|}_2^2+\mathrm{\&eta;}|\left|\stackrel{\&OverBar;}{s}\right|{|}_1$

Wherein η is hyper parameter, for the balance between control signal degree of rarefication and residual error.

7. the DOA estimation method based on compressed sensing time-modulation array according to claim 1, it is characterised in that step Suddenly arrival bearing's angle of the echo signal described in (6), its obtaining step is：

The sparse solution for recovering problem model of time-modulation array based on compressed sensing is converted into Second-order cone programming problem is：

min p+ηq

s.t.||r||₁≤q

K=1,2 ..., K

N=1,2 ..., N_θ

Wherein η is hyper parameter, and the recovery vector in the sparse recovery problem for constructing is solved using convex optimization software bagRecover VectorThe position of middle nonzero element is the arrival bearing's angle for representing echo signal.