CN109581277B - A kind of four-dimensional antenna array DOA estimation method based on compressive sensing theory - Google Patents
A kind of four-dimensional antenna array DOA estimation method based on compressive sensing theory Download PDFInfo
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/78—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using electromagnetic waves other than radio waves
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Abstract
The four-dimensional antenna array DOA estimation method based on compressive sensing theory that the invention discloses a kind of.The sparse signal model that this method is estimated by establishing four-dimensional antenna array DOA, ordered pair sparse signal restores have great influence when caning be found that, one inappropriate timing is likely to be such that the noise after time-modulation becomes coloured noise, severe exacerbation sparse signal recovery capability.Therefore, ordered pair sparse signal restores the influence with noise when introducing matrix correlation and noise covariance matrix quantitatively analyze different, establishes the Optimized model for timing using differential evolution algorithm on this basis.And be applied in traditional battle array based on l1The sparse signal recovery algorithms of norm singular value decomposition expand in four-dimensional antenna array, carry out four-dimensional antenna array DOA estimation in conjunction with the timing of optimization.Numerical Simulation Results show that the method in the present invention compares other four-dimensional battle array DOA estimation method tools in terms of resolution character and accuracy characteristic and has great advantage, especially under the conditions of low signal-to-noise ratio, fewer snapshots.
Description
Technical field
The invention belongs to antenna technology and field of signal processing, involve how to estimate using four-dimensional antenna array to carry out DOA
Meter is specifically constituted using the time-modulation effect bring frequency domain sideband signals of four-dimensional antenna array and center frequency signal
Signal space is limited inherent characteristics using practical incoming signal and establishes sparse signal recovery signal model, compression is utilized to feel
Know the timing of theoretical optimization control switch on-off, realizes four-dimensional antenna array high-performance DOA estimation.
Background technique
DOA estimation, which is called, does Mutual coupling, refers to obtaining target using array antenna received electromagnetic wave signal
Or the angle information of information source facing arrays antenna, including angle and quantity etc..With the rapid development of electronic technology, DOA
Estimation is widely used among target tracking, investigation, electronic countermeasure, mobile communication system etc..In the past few decades
In, the research of high-precision, the DOA estimation method of low-complexity is favored by researcher.It is proposed a variety of DOA estimation methods,
Such as than width method, doppler Method, interferometry and Estimation of Spatial Spectrum method, in these methods, due to Estimation of Spatial Spectrum method
Estimated accuracy with higher, researcher have carried out a large amount of research to it, mainly include MUSIC algorithm, ESPRIT algorithm, most
Maximum-likelihood method etc..However this kind of algorithm estimation performance under the conditions of low signal-to-noise ratio, low number of snapshots, close signal are incident can dislike
Change, and do not pass through some additional processing, it is impossible to be used in estimation coherent signal incidence situation.In order to solve these problems, it grinds
Study carefully personnel and new a kind of estimation method proposed based on compressive sensing theory or sparse signal recovery, this method be utilized into
It penetrates signal number and is limited this inherent characteristics, incoming signal structure after entire spatial discretization for entire space
At excessively complete base under be it is sparse, compressive sensing theory is taught that if this excessively complete base is met certain condition, low
Under conditions of signal-to-noise ratio, low number of snapshots, we still can recover sparse signal, and then obtain incoming wave incident direction.Then
The various DOA algorithm for estimating based on compressive sensing theory develop rapidly, main to wrap from the sparse recovery algorithms of selection
It includes: l1Norm singular value decomposition method, weighting l2,0Norm singular value decomposition method, Bayes's compressed sensing strategy etc..It is worth noting
Be that above-mentioned described method contributes to traditional battle array DOA estimation.For example, being the " nested of CN107450047A in patent publication No.
Compressed sensing DOA estimation method based on unknown mutual coupling information under battle array " discloses one kind and requires no knowledge about mutual coupling information, has certainly
High by degree, resolution performance is excellent, is capable of handling the DOA estimation method of incoming signals more more than physics array number, but for big
Scale array, system complexity is higher, and the data that need to be handled are larger.
Four-dimensional antenna array is and introducing " time " freedom degree in the conventional array with three-dimensional space freedom degree
A kind of array antenna new model formed.Therefore antenna array design can be carried out in the design space of four-dimensional freedom degree, have
More design flexibilities, as the appearance of high performance switch and algorithm becomes research hotspot at the beginning of 21 century.Utilize the four-dimension
Antenna array realizes that DOA estimation is exactly one of them.Estimate compared to traditional battle array DOA, four-dimensional battle array DOA estimation naturally possess the time this
One additional freedom degree, very maximum probability is promoted the performance that DOA estimates by this；On the other hand, traditional battle array DOA estimation is to each
The signal that unit receives is handled, thus a radio-frequency channel is corresponded to behind each unit, for large scale array
For the complexity of system will increase, the data volume of required processing is also very huge, however, four-dimensional antenna array is to utilize center
It constitutes signal space with signal at frequency and sideband and carries out DOA estimation, and the sideband number chosen is not usually high, therefore does not need
There is a radio-frequency channel behind each unit, required port number is equal to the sideband sum utilized, so that the complexity of system is big
It is big to reduce.Some DOA estimation methods based on four-dimensional antenna array also propose in succession.For example, document " G.Li, S.Yang, and
Z.Nie,“Direction of arrival estimation in time modulated linear arrays with
unidirectional phase center motion,”IEEE Trans.Antennas Propag.,vol.58,no.4,
Pp.1105-1111, Apr.2010 " a kind of four-dimensional linear array DOA estimation method based on MUSIC algorithm is disclosed, due to using
MUSIC algorithm estimates that performance is poor under the conditions of low signal-to-noise ratio, low number of snapshots, and the angular range estimated is little.Document
《C.He,A.Cao,J.Chen,X.Liang,W.Zhu,J.Geng and R.Jin,“Direction finding by time-
modulated linear array”,IEEE Trans.Antennas Propag.,vol.66,no.7,pp.3642–3652,
Mar.2018 " disclose it is a kind of using the physical relationship of harmonic wave and incident angle carried out wave up to estimation, from emulate and experiment two
Aspect demonstrates its correctness, however this method can only estimate an incoming signal, under the conditions of identical number of snapshots,
Estimation performance does not have Estimation of Spatial Spectrum class algorithm good.For another example, in document " W.T.Li, Y.J.Lei, and X.W.Shi, " DOA
estimation of time-modulated linear array based on sparse signal recovery”,
IEEE Antennas and Wireless Propag., Letters, vol.16, no.2017 " in disclose it is a kind of based on plus
The four-dimensional antenna array DOA estimation that the sparse signal of power restores, although under the conditions of low signal-to-noise ratio, low number of snapshots estimated accuracy compared with
Height, but the acquisition of weight vector needs first to carry out the DOA estimation of traditional battle array, this undoubtedly considerably increases the complexity of system.It can
See that research four-dimensional antenna array realizes that the method for high-precision estimation and low system complexity is still very necessary, the present invention is exactly herein
It comes into being under background.
Summary of the invention
In view of above-mentioned technical background, the four-dimensional antenna array DOA estimation based on compressive sensing theory that the invention proposes a kind of
Method, it is therefore intended that realize that the DOA of degree of precision estimates under the conditions of low signal-to-noise ratio, low number of snapshots using four-dimensional battle array.
Firstly, we first establish the signal model for carrying out DOA estimation using four-dimensional antenna array.As shown in Figure 1, considering one
N unit interval is the four-dimensional linear array of d uniformly motivated, it is assumed that has K narrowband, with frequently with power signal respectively from θkDirection is incident
To this four-dimensional battle array, after N points 1 of power splitter, receiving signal can be write as:
Wherein Un(t) the period sequential function of control switch on-off, s are indicatedk(t) k-th incident of signal, n are indicatedn(t)
It is σ that expression mean value, which is 0 variance,2White Gaussian noise, f0Indicate operating frequency of antenna.Due to the periodicity of period sequential function, Un
(t) it can use Fourier space to be unfolded
Reception signal at q rank sideband can be obtained by bringing (1) formula into:
In general, in order to reduce system complexity, positive and negative Q rank sideband signals are used to construct signal space.(3) each side in formula
After band signal passes sequentially through low noise, frequency mixer, low-pass filter and D/A conversion unit by Fig. 1, at q rank sideband signal with
How soon umber of beats form can be write as:
Assuming that number of snapshots are L, (4) can be written as follow matrix form:
Y (l)=BΤ(As (l)+n (l)), (l=1,2 ..., L) (5)
Wherein
Y (l)=[y-Q(l),y-Q+1(l),…,yQ(l)]Τ (6)
S (l)=[s1(l),s2(l),…,sK(l)]Τ (7)
N (l)=[n1(l),n2(l),…,nN(l)]Τ (8)
A=[a (θ1),a(θ2),…,a(θK)] (10)
It is worth noting that matrix B is determined by the timing of control switch on-off, matrix A is array prevalence matrix, is
It is determined by array topology.In order to utilize compressive sensing theory, on the basis of the signal model of foundation, we also need to establish
One sparse signal Restoration model.Assuming that entire space be separated into forPractical incident signal is only possible to
Several limited directions therein, according to discrete space, we can construct an excessively complete basic matrixIncoming signal can regard a sparse signal vector as under this complete basic matrixIf k-th of incoming signal is from θiDirection is incident, and i-th of element of this sparse signal is not
0, other situations are 0.In general discrete space number NθMuch larger than incoming signal number K, array element number N and taken
Sideband sum Q.In conjunction with (5) formula, the sparse signal model for receiving signal can be write as:
Y=BΤ(AS+N)=BΤAS+BΤN (12)
Wherein:
N=[n (1), n (2) ..., n (L)] ∈ CN×L (14)
Y=[y (1), y (2) ..., y (L)] ∈ C(2Q+1)×L (15)
According to compressive sensing theory, BTIt is considered as observation matrix, enables M=BTA, M are considered as perception matrix, enable N1=
BTA,N1It can be regarded as the new noise matrix after time-modulation.Due to array structure be it is determining, matrix A is constant, without
The same corresponding matrix B of timingTIt is not identical, therefore we can design perception matrix by designing different timing, so that
Sparse signal recovery capability is as strong as possible.On the other hand, the dimension for being far smaller than sparse matrix S due to receiving the dimension of signal Y,
(12) equation group of formula is a underdetermined system of equations, theoretically there is countless multiple groups solutions.Nevertheless, compressive sensing theory tells me
, as long as meeting following three conditions, sparse matrix S still can be recovered correctly.
1) suitable calculation matrix B is designedT, so that the critical information of K sparse signal S will not because of dimension reduction and
By serious broken meeting；
2) suitable calculation matrix B is designedT, so that by noise N new after time-modulation1Still close to white Gaussian noise；
3) excellent sparse signal recovery algorithms are designed and completely restores sparse matrix S.
For first condition, we are firstly introduced into following formula to measure observing matrix and excessively complete basic matrix correlation journey
Degree:
p1Indicate calculation matrix BTLine number, p2The columns of the excessively complete basic matrix A of table.(16) describe observing matrix and
The worst degree of relevancy of complete basic matrix is crossed, correlative study shows that worst degree of relevancy is smaller and is more conducive to sparse signal
Recovery.
For second condition, we introduce noise covariance matrix.New noise N1Noise covariance matrix can write
At:
Since former noise N is white Gaussian noise, so its noise covariance matrix is equal to RN=NNH/ L=σ2I.It substitutes into
(17) have:
It can be found that inappropriate design calculation matrix BT, new noise N1It may become coloured noise.Therefore, we are in order to allow
As close possible to white Gaussian noise, the covariance matrix of new noise is just needed as close possible to a diagonal matrix new noise, in
Be introduce following parameter measure its close to diagonal matrix degree.
γ[BT(BT)H]=| | CT(CT)H||f (19)
Wherein the diagonal element of C matrix is equal to 0, and off-diagonal element is equal to the off-diagonal element of matrix B.||·||fIt indicates
Not this black norm of Luo Beini.
In order to keep the parameter of (16) formula and (19) formula as small as possible, we optimize calculation matrix B using differential evolution algorithmT
(i.e. Improving Working Timing).Assuming that translating timing using pulse, the fitness function of differential evolution algorithm can be write as:
fj(ξ)=w1·μ(BΤ,A)+w2·γ[BΤ(BΤ)H] (20)
Wherein ξ=[τ1,τ2,…,τN,t1,t2,…,tN] it is optimized variable, including switch conduction duration and switch are led
Logical moment, w1And w2It is corresponding weighting coefficient, j indicates evolutionary generation.Once the calculation matrix of optimization passes through differential evolution algorithm
It acquires, above-mentioned condition 1 and condition 2 can meet.
After (1) (2) condition satisfaction, for third condition, has many documents and research was carried out to traditional battle array, compare
That simple and applicable is l1Norm singular value decomposition method, he is extended to four-dimensional battle array by we here.(12) sparse signal S is extensive in formula
It can convert again are as follows:
Wherein:
It can be found that (21) formula optimized variable dimension is higher under the conditions of big number of snapshots, solution is quite time-consuming, in order to improve
Solution efficiency can carry out singular value decomposition to receipt signal matrix Y
Y=U Σ VH (23)
Enable Ysv=U Σ DK,SSV=S Σ DKAnd NSV=N Σ DK, wherein DK=[IK,0]T, 0 is a K × (L-K) rank zero moment
Battle array.Our available following formulas:
YSV=BΤASSV+BΤNSV (24)
Therefore, (21) formula can convert are as follows:
Obvious above-mentioned optimization problem is a convex problem, can use convex optimization Efficient Solution, when sparse matrix S is recovered
After coming, his every column element is not 0 corresponding position signal incident direction i.e. to be asked.
Novelty of the invention essentially consists in quantitative analysis observing matrix (timing) and restores to sparse signal and noise
It influences, the model based on differential evolution algorithm optimization observing matrix is established on this basis, then the l for traditional battle array1
Norm singular value decomposition method extends to four-dimensional battle array, realizes the four-dimensional antenna array DOA estimation based on compressive sensing theory, passes through number
Value simulation result shows that the method in the present invention compares other four-dimension battle array DOA estimation in terms of resolution character and accuracy characteristic
Method tool has great advantage, especially under the conditions of low signal-to-noise ratio, fewer snapshots.
Detailed description of the invention
Fig. 1 is system block diagram when four-dimensional battle array carries out DOA estimation.
The timing of unit 8 four-dimension linear array optimization when Fig. 2 is Q=2.
The timing of unit 8 four-dimension linear array optimization when Fig. 3 is Q=3.
Fig. 4 is that unidirectional phase center is mobile timing (only one cell operation of any time in a cycle).
Fig. 5 is the spatial spectrum of the method for the present invention optimization with the variation of signal-to-noise ratio.
Fig. 6 is the spatial spectrum of MUSIC algorithm calculating with the variation of signal-to-noise ratio.
Fig. 7 compares figure with signal-to-noise ratio variation for the method for the present invention and the resoluting probability of MUSIC algorithm estimation.
Fig. 8 compares figure with number of snapshots variation for the method for the present invention and the resoluting probability of MUSIC algorithm estimation.
Fig. 9 is variation of the root-mean-square error estimated of the method for the present invention and MUSIC algorithm with signal-to-noise ratio.
Table 1 is in embodiment 1, and the relevant parameter that different timing calculate compares.
Specific embodiment
Embodiment 1:8 unit half-wavelength four-dimension linear array optimum timing
Consider the uniform four-dimensional linear array an of unit 8.Centre frequency and switch modulation frequency are respectively set to f0=3GHz
And fp=100KHz, timing translate timing using pulse.In order to which the angle as far as possible comprising entire space combines calculating effect
Rate, entire upper half-space from -90 to 90 are divided evenly into 180 parts, that is, are spaced 1 degree and are sampled, the later period is substantially knowing letter
After number incident direction range, more accurately angular divisions can be carried out.Above-mentioned mentioned differential evolution algorithm is used for Improving Working Timing
So that the fitness function value of (20) is as small as possible.While in order to analyze the influence of taken sideband number, Q=2 and Q=3 are used respectively
In timing optimization.
Fig. 2 and Fig. 3 respectively indicates the timing optimized using differential evolution algorithm, and wherein Fig. 2 corresponds to Q=2, and Fig. 3 corresponds to Q=
3.Observation Fig. 2 and Fig. 3 can be found that the two timing all and have the characteristics that one it is identical: any time is always in one cycle
Only one unit is in running order.The physical significance that this Improving Working Timing contains behind is when each antenna element is different
When working, after time-modulation, the noise that antenna array receives is still white Gaussian noise.Due to this Improving Working Timing and
The mobile timing feature having the same of unidirectional phase center as shown in Figure 4, therefore it is also included in our research, in order to fixed
Amount analyzes the superiority and inferiority of these three timing, we have calculated separately them and have corresponded to the value of (16) formula and (19) formula, as shown in table 1.
It can be seen that the value that they correspond to (16) formula is equal to 1, the value of corresponding (19) formula is not much different, all close to 0.For convenience,
We choose modulation timing of the unidirectional phase center in Fig. 4 mobile timing (Q=3) as four-dimensional battle array switch, according to this timing
Place observation matrix B can be calculatedT, then carry out DOA estimation.
The spatial spectrum of embodiment 2:8 unit half-wavelength four-dimension linear array DOA estimation
The validity of four-dimension battle array DOA estimation is used in order to illustrate the timing of optimization, above-mentioned Improving Working Timing to be used for DOA
Estimation is illustrated here mainly by the spatial spectrum for calculating estimation.Assuming that there are three narrow band signal respectively with identical frequency,
θ of the equal-wattage from far field1=-10 °, θ2=0 ° and θ3=5 ° are incident on this unit 8 four-dimension linear array.Other relative parameters settings
It is as follows: number of snapshots L=100, sideband number Q=3.Fig. 5 indicates the sky calculated according to Improving Working Timing by sparse signal recovery algorithms
Between spectrum with signal-to-noise ratio variation.Even if can see under the conditions of lower signal-to-noise ratio, can also be estimated using the timing of optimization
Signal incident direction out.In order to as a comparison, Fig. 6 shows that down space is arranged in identical parameters using MUSIC algorithm in four-dimensional battle array
Compose the variation with signal-to-noise ratio, it can be seen that when signal-to-noise ratio is lower than 10dB, MUSIC algorithm can not accurately estimate letter
Number direction.
The resoluting probability of embodiment 3:8 unit four-dimension linear array DOA estimation
In order to continue to explain the validity that the timing of optimization is used for four-dimension battle array DOA estimation, here by comparing point of estimation
Probability is distinguished to be illustrated.Assuming that there are two narrow band signals respectively with identical frequency, equal-wattage from the θ in far field1=-10 ° and θ2
=0 ° is incident on this unit 8 four-dimension linear array.Other relative parameters settings are as follows: number of snapshots L=100, sideband number Q=3.Fig. 7 is retouched
When having stated mentioned method of the invention and MUSIC algorithm and carrying out DOA estimation under the conditions of identical parameters, the resoluting probability of estimation is with letter
It makes an uproar the variation of ratio.It can be found that present invention estimated probability under Low SNR is higher than MUSIC algorithm.Then, we keep
The signal-to-noise ratio (SNR=-5dB) of two methods is identical, calculates the resoluting probability of its estimation with the variation of number of snapshots, concrete outcome is such as
Shown in Fig. 8.It can be seen that the present invention under the conditions of low number of snapshots estimated probability also above MUSIC algorithm.
The accuracy of embodiment 4:8 unit four-dimension linear array DOA estimation
The validity of four-dimension battle array DOA estimation is used in order to further illustrate the timing of optimization, here by comparing estimation
Accuracy is illustrated.Assuming that there is a narrow band signal respectively from the θ in far field0=0 ° is incident on this unit 8 four-dimension linear array.Its
His relative parameters setting is as follows: number of snapshots L=100, sideband number Q=3.Fig. 9 indicates that condition is arranged in identical parameters in two methods
When lower progress DOA estimation, the root-mean-square error of estimation with signal-to-noise ratio variation.It can be found that the present invention is in Low SNR
The root-mean-square error of lower estimation is lower than in MUSIC algorithm.
Claims (1)
1. a kind of four-dimensional antenna array DOA estimation method based on compressive sensing theory, be primarily characterized in that according to optimization when
Sequence constructs observing matrix, utilizes the l for being applied to tradition battle array DOA estimation of expansion1Norm singular value decomposition method carries out sparse signal
Restore, and then obtain the angle information of incoming signal, mainly comprises the following steps that
1) establish following how soon the sparse signal of the reception signal under the conditions of umber of beats restores mould according to selected pulse translation timing
TypeWhat wherein Y indicated to receive includes signal at centre frequency and positive and negative preceding Q sideband
Matrix, BTIndicate the observing matrix determined by the timing of control switch on-off,It indicates popular by array and space divides and determines
Excessively complete basic matrix, S indicates that sparse signal matrix to be asked under excessively complete base, N indicate white Gaussian noise matrix；
2) parameter for measuring observing matrix and excessively complete basic matrix degree of relevancy is introduced according to compressive sensing theoryWherein p1Indicate observing matrix BTLine number, p2Indicated complete basic matrixColumns；
3) influence of the noise covariance matrix measure time modulation to noise, new noise N are introduced1=BTThe noise covariance matrix of N
It can be write asIn order to make new noise as close possible to white Gaussian
Noise, the covariance matrix of new noise need to introduce parameter γ [B as close possible to a diagonal matrixT(BT)H]=| | CT(CT)H||f
It is measured close to the degree of diagonal matrix, wherein the diagonal element of C matrix is equal to 0, and off-diagonal element is equal to the non-diagonal of matrix B
Element, | | | |fIndicate not this black norm of Luo Beini；
4) in order to make the parameter μ in step 2) and step 3), γ is as small as possible, and wherein μ is indicated to measure described in step 2) and be seen
Survey matrix BTCross complete basic matrixThe parameter of degree of relevancy, γ indicate step 3) described in noise covariance matrix and
The parameter of the degree of closeness of one diagonal matrix, timing used by being optimized using differential evolution algorithm, differential evolution algorithm
Fitness function isWherein ξ=[τ1,τ2,…,τN,t1,t2,…,tN] it is excellent
Change variable, including switch conduction duration and switch turn on moment, w1And w2It is corresponding weighting coefficient, j indicates generation of evolving
Number；
5) using step 4) optimization come timing calculating observation matrix, establish solve sparse signal matrix S Optimized modelWherein λ indicates a regularization parameter, in order to reduce the complexity of optimization problem, to reception
Signal matrix Y carries out singular value decomposition, i.e. Y=U Σ VH, wherein U, V indicate a unitary matrice, enable Ysv=U Σ DK,SSV=S
ΣDKAnd NSV=N Σ DK, wherein DK=[IK,0]T, 0 is a K × (L-K) rank null matrix, obtains the reception signal an of dimensionality reduction
MatrixTo obtain the four-dimensional antenna array dimensionality reduction Optimized model based on compressive sensing theory
6) it calls convex optimization packet to solve above formula, finds out sparse signal matrix S, each column of sparse signal matrix S is not 0 yuan
Position corresponding to element is signal incident direction to be asked.
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| CN106526532A (en) * | 2016-10-31 | 2017-03-22 | 电子科技大学 | Doppler direction finder based on four-dimensional antenna array |
| CN106772226A (en) * | 2016-12-26 | 2017-05-31 | 西安电子科技大学 | DOA estimation method based on compressed sensing time-modulation array |
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