CN115248413A - Off-grid signal direction-of-arrival estimation method suitable for non-uniform linear array - Google Patents
Off-grid signal direction-of-arrival estimation method suitable for non-uniform linear array Download PDFInfo
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- G01—MEASURING; TESTING
- 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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- G01S3/14—Systems for determining direction or deviation from predetermined direction
- G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
Abstract
The invention discloses a method for estimating the direction of arrival of off-grid signals suitable for a non-uniform linear array, which comprises the following steps: s1, acquiring an initial estimation value of a signal direction of arrival on a candidate grid by using a beam forming method according to single snapshot array element data; s2, calculating a complex value signal; s3, separating corresponding signal data from the received data of the array; s4, multiplying the conjugate of the previous element and the next element in the signal data to obtain a construction vector, and extracting the phase of each element of the construction vector; s5, performing ambiguity resolution on the phase of the extracted construction vector, and acquiring a closed expression of the signal direction of arrival according to the ambiguity resolution phase; s6, calculating the arrival direction of the updating signal; and S7, judging whether the signal wave arrival direction is converged or not, or whether the cycle number reaches a preset threshold or not, and if not, returning to the step S2. The method disclosed by the invention can be suitable for both uniform linear arrays and non-uniform linear arrays, can realize high-precision estimation of the signal direction of arrival, and is low in calculation complexity.
Description
Technical Field
The invention relates to the technical field of array signal processing, in particular to an off-grid signal direction of arrival estimation method suitable for a non-uniform linear array.
Background
The Direction of arrival (DOA) refers to the Direction of arrival of the spatial signals, i.e. the Direction angle at which each signal arrives at the array reference array element. The direction of arrival is an important concept in the theory of spatial spectrum estimation, the spatial spectrum is an important concept in array signal processing, and the spatial spectrum represents the energy distribution of signals in all directions in space. The estimation of the direction of arrival is a key technology for practical application of projects such as target positioning, detection and identification, and is widely applied to the fields of military and national economy such as radar, communication, radio astronomy, geophysical, speech recognition, sonar and medical images.
The conventional direction-of-arrival estimation algorithm searches for the incoming wave direction of a signal by uniformly discretizing an angle space domain. The algorithm is also called a grid signal direction of arrival estimation algorithm, and the premise condition is that the incoming signal direction is just positioned on the discretization grid. However, in practical application, the incoming wave direction of the signal is likely not to fall on a grid divided in advance, and at this time, the problem of grid mismatch is caused, so that the estimation of the direction of arrival is inaccurate, and the estimation precision of the algorithm is sharply reduced. In order to solve the problem of grid mismatch, a direction of arrival estimation algorithm of the off-grid signal is proposed at present.
With the continuous research on the direction of arrival estimation algorithm of the off-grid signal, various off-grid signal direction of arrival estimation algorithms are also proposed at present, mainly comprising a off-grid sparse bayesian algorithm, an algorithm based on phase deviation search and a fractional fourier coefficient interpolation algorithm. The method comprises the following steps that a lattice-separated sparse Bayesian algorithm applies first-order Taylor expansion to a real incoming wave direction, and estimates the lattice-separated offset as a hyper-parameter; obtaining initial rough estimation of a signal incoming wave direction through discrete Fourier transform based on an algorithm of phase deviation search, and then correcting the initial rough estimation by using a phase rotation method; and the fractional Fourier coefficient interpolation algorithm obtains high-precision direction-of-arrival estimation by circularly correcting the frequency points which are initially and roughly estimated in the left and right half grid ranges.
However, the existing off-grid signal direction-of-arrival estimation algorithm generally has high computational complexity, slow convergence rate and long operation time, and the direction-of-arrival estimation algorithm with low computational complexity mostly adopts a fourier coefficient interpolation method, is only suitable for uniform linear arrays and cannot be suitable for non-uniform linear arrays which are widely applied in practice.
Disclosure of Invention
In order to solve part or all of the technical problems in the prior art, the invention provides an off-grid signal direction of arrival estimation method suitable for a non-uniform linear array.
The technical scheme of the invention is as follows:
a method for estimating the direction of arrival of off-grid signals suitable for a non-uniform linear array is provided, and the method comprises the following steps:
step S1, according to single snapshot array element data, utilizing a beam forming method to obtain an initial estimation value of a signal direction of arrival on a candidate grid;
s2, calculating a complex value signal according to the signal wave arrival direction;
s3, separating corresponding signal data from the received data of the array according to the signal wave arrival direction and the complex value signal;
s4, multiplying the conjugate of the previous element and the next element in the signal data to obtain a construction vector, and extracting the phase of each element of the construction vector;
s5, resolving ambiguity of the phase of the extracted construction vector, and acquiring a closed expression of the signal direction of arrival according to the resolved ambiguity phase;
s6, calculating and updating the signal direction of arrival according to the closed expression of the signal direction of arrival;
and S7, judging whether the signal direction of arrival is converged or not or whether the cycle number reaches a preset threshold value or not, if so, taking the currently calculated signal direction of arrival as a final estimated value, and if not, returning to the step S2.
In some possible implementations, it is set that: n antennas form a non-uniform array, and the position c of the array element n Is an integral multiple of unit array element spacing, N =1,2K far-field narrow-band signals are incident on the array at half wavelength, and the arrival direction is theta = [ theta = [ theta ] 1 ,...,θ K ]，θ 1 ,...,θ K Respectively represent the directions of arrival of the 1 st to K-th signals, and the reception data y of the array is represented As y = As + m, s = [ s ] 1 ,...,s K ] T Represents a vector of K complex-valued deterministic signals, m represents N × 1-dimensional white Gaussian noise, A represents an array manifold matrix, A = [ a (θ) 1 ),a(θ 2 ),...,a(θ K )]，a(θ k ) The array steering vector is represented as a vector of the array,
searching for regions in consideration of angles
M evenly sampled grid points of (a) to obtain
The grid interval is
M represents the number of grids;
and simultaneously setting: the arrival direction of the incident signal does not fall on the pre-divided discrete grid points;
acquiring an initial estimation value of a signal arrival direction on a candidate grid by using a beam forming method, wherein the method comprises the following steps:
defining a normalized MxN-dimensional beamforming matrix F having (p, q) -th element of
Obtaining a space spectrum x = | Fy |, which is formed by a wave beam, according to a defined matrix F;
obtaining the positions corresponding to the K peak values according to the space spectrum x
Based on the corresponding positions of K peak valuesUsing the formula
Determining an initial estimate of the direction of arrival of a corresponding signal
In some possible implementations, calculating a complex-valued signal according to a direction of arrival of the signal includes:
constructing an estimated complex value signal according to the direction of arrival of the signal;
and solving the problem of estimating the complex value signal by using a least square method to obtain a closed-form solution of the complex value signal.
In some possible implementations, the problem of estimating the complex-valued signal is:
the closed-form solution of the complex-valued signal is:
s＝(A H A) -1 A H y
wherein s represents a complex-valued signal, A H Represents the conjugate transpose of a.
In some possible implementations, the corresponding signal data is separated from the received data of the array using the following formula;
wherein, y k Representing the kth signal data, s i Represents the ith complex-valued signal, a (theta) i ) Representing the array steering vector corresponding to the ith signal.
In some possible implementations, the elements of the signal data are determined using the following equations;
wherein, y k,n N-th element, | s, representing the k-th signal k I denotes the amplitude of the kth signal, phi k Representing the phase, ε, of the kth signal n Representing zero mean Gaussian white noise corresponding to the nth element;
defining the construction vector corresponding to the kth signal as r k ∈C N-1 C represents a complex set, constructing a vector r k Is determined using the following formula;
wherein r is k,n Representing a construction vector r k The (n) th element of (a),
denotes y k,n Conjugation of (1).
In some possible implementations, the phases of the extracted construction vectors are deblurred using the following formula;
wherein, g n (r k ) Represents the construction vector r k The solution of the nth element of (a) blurs the phase,
represents the construction vector r k Phase of the nth element of (c), ψ n Denotes an integer obtained by rounding off,
round (x) means rounding x;
the deblurred phase of the constructed vector is represented as:
wherein, g (r) k ) Represents the construction vector r k Defuzzification of phase, g 1 (r k ),g 2 (r k ),…,g (N-1) (r k ) Represents the deblurred phase vector g (r) k ) The number of the N-1 elements of (A),
ε represents the colored Gaussian noise vector, [ epsilon ] = [ ε ] 2 -ε 1 ,ε 3 -ε 2 ,...,ε N -ε N-1 ] T 。
In some possible implementations, the obtaining the closed expression of the direction of arrival of the signal according to the deblurred phase includes:
constructing an objective function:
minimizing the target function to obtain a closed expression of the signal direction of arrival;
where Q represents the covariance matrix of the colored gaussian noise vector epsilon.
In some possible implementations, the direction of arrival of the signal is calculated using the following formula;
the technical scheme of the invention has the following main advantages:
the method for estimating the direction of arrival of the off-grid signal suitable for the non-uniform linear array firstly acquires the initial estimation value of the direction of arrival of the signal positioned on the candidate grid through a beam forming method, then processes the received data of the array according to the direction of arrival of the signal to acquire the corresponding signal data and the construction vector, deblurs the phase of the construction vector, determines the closed expression of the direction of arrival of the signal according to the deblurred phase, can reduce the computational complexity of the estimation process of the direction of arrival of the signal, improves the convergence speed, and can be simultaneously suitable for the estimation and the solution of the direction of arrival of the signal of the uniform linear array and the non-uniform linear array.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a method for estimating an off-grid signal direction of arrival suitable for a non-uniform linear array according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a uniform linear array provided by the present invention;
fig. 3 is a schematic diagram of a variation curve of mean square error of estimated values of directions of arrival according to the signal-to-noise ratio, which are obtained by using different algorithms according to example 1 of the present invention;
FIG. 4 is a schematic diagram of an uneven linear array provided by the present invention;
fig. 5 is a schematic diagram of a variation curve of a mean square error of an estimated value of a direction of arrival according to a signal-to-noise ratio, obtained by using different algorithms under a single signal condition according to example 2 of the present invention;
fig. 6 is a schematic diagram of a variation curve of a mean square error of an estimated value of a direction of arrival obtained by using different algorithms with a signal-to-noise ratio under multiple signals according to example 3 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the specific embodiments of the present invention and the accompanying drawings. It is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme provided by the embodiment of the invention is explained in detail in the following with the accompanying drawings.
Referring to fig. 1, an embodiment of the present invention provides a method for estimating an off-grid signal direction of arrival suitable for a non-uniform linear array, including the following steps:
step S1, obtaining an initial estimation value of a signal direction of arrival on a candidate grid by using a beam forming method according to single snapshot array metadata;
s2, calculating a complex value signal according to the signal wave arrival direction;
s3, separating corresponding signal data from the received data of the array according to the signal wave arrival direction and the complex value signal;
s4, multiplying the conjugate of the previous element and the next element in the signal data to obtain a construction vector, and extracting the phase of each element of the construction vector;
s5, performing ambiguity resolution on the phase of the extracted construction vector, and acquiring a closed expression of the signal direction of arrival according to the ambiguity resolution phase;
s6, calculating and updating the signal direction of arrival according to the closed expression of the signal direction of arrival;
and S7, judging whether the signal direction of arrival is converged or not or whether the cycle number reaches a preset threshold value or not, if so, taking the currently calculated signal direction of arrival as a final estimated value, and if not, returning to the step S2.
The off-grid signal direction-of-arrival estimation method suitable for the non-uniform linear array provided by the embodiment of the invention firstly obtains an initial estimation value of a signal direction-of-arrival on a candidate grid through a beam forming method, then processes received data of the array according to the signal direction-of-arrival to obtain corresponding signal data and a construction vector, defuzzifies the phase of the construction vector, determines a signal direction-of-arrival closed expression according to the defuzzified phase, can reduce the computational complexity of the signal direction-of-arrival estimation process, improves the convergence speed, and can be simultaneously suitable for estimation and solution of the signal direction-of-arrival of the uniform linear array and the non-uniform linear array.
The following specifically describes the steps and principles of the off-grid signal direction of arrival estimation method suitable for the non-uniform linear array according to an embodiment of the present invention:
and S1, acquiring an initial estimation value of a signal direction of arrival on the candidate grid by using a beam forming method according to the single snapshot array metadata.
Specifically, the following are set: n antennas form a non-uniform array, and the position c of the array element n N =1, 2.. And N, the unit array element spacing d is set to be half of the wavelength, K far-field narrow-band signals are incident to the array, and the arrival direction is theta = [ theta ] = 1 ,...,θ K ]，θ 1 ,...,θ K Representing the direction of arrival of the 1 st to kth signals, the received data y of the array is represented As y = As + m, s = [ s ]) 1 ,...,s K ] T A vector representing K complex-valued deterministic signals, m representing white Gaussian noise of dimension Nx 1, and a noise power of
A represents an array manifold matrix, A = [ a (θ) 1 ),a(θ 2 ),...,a(θ K )]，a(θ k ) The array steering vector is represented as a vector of the array,
searching area in consideration of angle
M evenly sampled grid points of (a) to obtain
The grid interval is
M represents the number of meshes, and simultaneously: the direction of arrival of the incident signal does not fall on the pre-divided discrete grid points.
Based on the setting, the method for acquiring the initial estimation value of the signal direction of arrival on the candidate grid by using the beam forming method comprises the following steps:
defining a normalized MxN-dimensional beamforming matrix F having (p, q) -th element of
Obtaining a space spectrum x = | Fy |, after beam forming, according to a defined matrix F;
obtaining the positions corresponding to the K peak values according to the space spectrum x
Based on the corresponding positions of the K peak values, using a formula
Determining an initial estimate of the direction of arrival of a corresponding signal
And S2, calculating a complex value signal according to the signal wave arrival direction.
In an embodiment of the present invention, the complex-valued signal may be calculated by using a least square method according to the direction of arrival of the signal.
Specifically, the method for calculating the complex value signal by using the least square method according to the signal arrival direction comprises the following steps:
constructing an estimated complex value signal according to the direction of arrival of the signal;
and solving the problem of estimating the complex value signal by using a least square method to obtain a closed-form solution of the complex value signal.
In an embodiment of the present invention, the problem of estimating the complex-valued signal may be constructed as follows:
the minimization problem in the constructed problem of estimating the complex value signal can be solved by using a least square method, and then a closed-form solution of the complex value signal is obtained.
Specifically, the least square method solves the problem of the constructed estimated complex value signal, and can obtain a closed-form solution of the complex value signal as follows:
s＝(A H A) -1 A H y
wherein s represents a complex-valued signal, A H Represents the conjugate transpose of a.
And S3, separating corresponding signal data from the received data of the array according to the signal wave arrival direction and the complex value signal.
In order to estimate the angle of arrival of a signal, i.e. the direction of arrival of the signal, the corresponding signal needs to be separated from the received data of the array.
Specifically, taking the k-th signal to be separated from the received data of the array as an example, in an embodiment of the present invention, the corresponding signal data may be separated from the received data of the array by using the following formula:
wherein, y k Representing the kth signal data, s i Represents the ith complex-valued signal, a (θ) i ) Representing the array steering vector corresponding to the ith signal.
Further, the kth signal data y is set based on the above-mentioned step S1 and the above-mentioned signal data separation formula k Can be expressed as:
wherein, | s k I denotes the amplitude of the kth signal, phi k Indicating the phase of the k-th signal.
And S4, multiplying the conjugate of the previous element and the next element in the signal data to obtain a constructed vector, and extracting the phase of each element of the constructed vector.
Since in practical applications, when the signal-to-noise ratio is usually large, taking the kth signal as an example, in the case of large signal-to-noise ratio, the kth signal data element can be approximately expressed as:
wherein, y k,n Representing the nth element, epsilon, of the kth signal n Represents zero mean Gaussian white noise, epsilon, corresponding to the nth element n Has a variance of
Further, defining the construction vector corresponding to the kth signal as r k ∈C N-1 And C represents a complex set. Since the elements in the construction vector are obtained by multiplying the conjugate of the previous element by the next element in the signal data, for this reason, in one embodiment of the present invention, based on the above setting, the construction vector has N-1 elements, and the construction vector r is k Can be determined using the following formula:
wherein r is k,n Represents the construction vector r k The (n) th element of (a),
denotes y k,n Conjugation of (1).
Further, a construction vector r is set k Has a phase of
Indicating phase
1 to N-1, then the ith element
Can be recorded as
Wherein e is i The method is characterized in that (N-1) multiplied by 1-dimensional column vectors are represented, the ith position of each column vector is 1, the rest positions are 0, and the angle (·) represents the extraction phase.
And S5, deblurring the phase of the extracted construction vector, and acquiring a closed expression of the signal arrival direction according to the deblurred phase.
Considering that modulo 2 pi is required for phase representation, when the array element spacing of the non-uniform line array is greater than half wavelength, the corresponding phase will be blurred because the period number is unknown. To this end, in an embodiment of the present invention, the phase of the extracted construction vector is deblurred to overcome the above problem.
Specifically, taking the kth signal as an example, the phase of the extracted construction vector can be deblurred using the following formula:
wherein, g n (r k ) Represents the construction vector r k The solution of the nth element of (a) blurs the phase,
representing a construction vector r k Phase of the nth element of (2), psi n Denotes an integer obtained by rounding off,
round (x) means rounding x.
Further, based on the aforementioned settings and formulas, a vector r is constructed k The deblurred phase of (d) can be expressed as:
wherein, g (r) k ) Represents the construction vector r k Deblurring phase of g 1 (r k ),g 2 (r k ),…,g (N-1) (r k ) Represents the deblurred phase vector g (r) k ) The number of the N-1 elements of (A),
ε represents the colored Gaussian noise vector, [ epsilon ] = [ ε ] 2 -ε 1 ,ε 3 -ε 2 ,...,ε N -ε N-1 ] T 。
From the above expression of the deblurring phase of the construction vector, it is necessary to estimate the direction of arrival of the signal under colored gaussian noise. Therefore, in an embodiment of the present invention, according to the deblurring phase, a weighted least square method may be used to calculate and obtain a closed expression of the signal direction of arrival.
Specifically, taking the kth signal as an example, the method for obtaining the closed expression of the direction of arrival of the signal according to the deblurring phase includes the following steps:
constructing an objective function:
minimizing the target function to obtain a closed expression of the signal arrival direction;
wherein Q represents the covariance matrix of the colored Gaussian noise vector ε,
by minimizing the constructed objective function
Can obtain pi sin theta k And obtaining a closed expression of the signal direction of arrival by the maximum likelihood estimation.
In an embodiment of the present invention, a closed expression of the signal direction of arrival may be obtained by minimizing the objective function, and the closed expression of the signal direction of arrival may be specifically expressed as:
and S6, calculating and updating the signal direction of arrival according to the closed expression of the signal direction of arrival.
In an embodiment of the present invention, the signal direction of arrival may be calculated according to the obtained closed expression of the signal direction of arrival.
Specifically, taking the kth signal as an example, based on the above-mentioned closed expression of the signal direction of arrival, the following formula is used to calculate the signal direction of arrival:
and S7, judging whether the signal direction of arrival is converged or not or whether the cycle number reaches a preset threshold value or not, if so, taking the currently calculated signal direction of arrival as a final estimated value, and if not, returning to the step S2.
In an embodiment of the present invention, the preset thresholds of the convergence condition and the cycle number may be specifically set according to the estimation accuracy of the signal direction of arrival actually required.
The following describes beneficial effects of the off-grid signal direction-of-arrival estimation method suitable for the non-uniform linear array according to an embodiment of the present invention with reference to specific examples.
Example 1
Referring to fig. 2, in this example 1, 10 antennas are used to form a uniform linear array, the array element position is in units of half of the source wavelength, the signal incidence angle is 30.5 °, and the fast beat number is 1.
In this example 1, the prior art is used to estimate the direction of arrival of a signal by using a bayesian sparse algorithm, an algorithm based on phase deviation search, a fractional fourier sparse interpolation algorithm, and the method for estimating the direction of arrival of a off-grid signal according to an embodiment of the present invention, and the mean square error of the estimated value of the direction of arrival of the signal is used as a metric, so as to obtain a schematic diagram of the variation curve of the mean square error of the estimated value of the direction of arrival obtained by different algorithms as shown in fig. 3 along with the signal-to-noise ratio, where the simulation result is the statistical result of 200 monte carlo experiments.
It can be seen that the mean square error corresponding to the off-grid sparse bayes algorithm cannot reach the cramer-perot boundary, when the signal-to-noise ratio is greater than 5dB, the mean square error corresponding to the algorithm based on the phase deviation search can reach the cramer-perot boundary, and when the signal-to-noise ratio is greater than 10dB, both the fractional fourier coefficient interpolation algorithm and the mean square error corresponding to the off-grid signal direction-of-arrival estimation method provided by an embodiment of the present invention can reach the cramer-perot boundary, but the algorithm based on the phase deviation search and the fractional fourier coefficient interpolation algorithm can only be applied to uniform linear arrays.
Example 2
Referring to fig. 4, in this example 2, 10 antennas are used to form an uneven line array, the position of an array element is in units of half of the source wavelength, the incident angle of a signal is 30.5 °, and the fast beat number is 1.
In this example 2, the prior art, the sparse bayesian algorithm of the de-lattice and the method for estimating the direction of arrival of the de-lattice signal provided in an embodiment of the present invention are respectively used to estimate the direction of arrival of the signal, and the mean square error of the estimated value of the direction of arrival of the signal is used as a measurement standard, so as to obtain a schematic diagram of a variation curve of the mean square error of the estimated value of the direction of arrival of the signal obtained by different algorithms as shown in fig. 5 along with the signal-to-noise ratio, where the simulation result is a statistical result of 200 monte carlo experiments.
It can be seen that the mean square error corresponding to the off-lattice sparse bayes algorithm cannot reach the cramer-perot boundary, and when the signal-to-noise ratio is greater than 5dB, the mean square error corresponding to the off-lattice signal direction-of-arrival estimation method provided by the embodiment of the invention can reach the cramer-perot boundary.
Example 3
Referring to fig. 4, in this example 3, 10 antennas are also used to form an uneven line array, the positions of the array elements are in units of half of the source wavelength, the number of signals is 3, the incidence angles of 3 incoherent signals are 20.5 °, 40.5 ° and 60.5 °, and the fast beat number is 1.
In this example 3, the prior art bayesian sparse algorithm and the off-grid signal direction-of-arrival estimation method provided in an embodiment of the present invention are respectively adopted to estimate the direction of arrival of a signal, and the mean square error of the estimated value of the direction of arrival of the signal is used as a measurement standard, so as to obtain a schematic diagram of a variation curve of the mean square error of the estimated value of the direction of arrival with the signal-to-noise ratio, which is obtained by using different algorithms as shown in fig. 6, where a simulation result is a statistical result of 200 monte carlo experiments.
It can be seen that, under the condition of three signals, the mean square errors corresponding to the off-grid sparse bayesian algorithm cannot reach the cramer-perot boundary, and when the signal-to-noise ratio is greater than 15dB, the mean square errors of the three signals corresponding to the off-grid signal direction-of-arrival estimation method provided by the embodiment of the invention can reach the cramer-perot boundary.
Further, the computation complexity of the prior art, such as the sparse Bayes algorithm with the lattice, the algorithm based on the phase deviation search, the fractional Fourier sparse interpolation algorithm, and the estimation method of the direction of arrival of the lattice signal provided by the embodiment of the present invention, is analyzed, and the computation complexity shown in the following table can be obtained;
| algorithm | Complexity of calculation |
| Sparse Bayesian algorithm | O(HNM 2 ) |
| Algorithm based on phase deviation search | O(Nlog 2 N+N+DKN) |
| Fractional FourierInterpolation algorithm for leaf coefficient | O(Nlog z N) |
| The invention relates to a method for estimating the direction of arrival of off-grid signals | O(K 2 H+N) |
In the above table, H denotes the number of cycles of the algorithm, N denotes the number of antennas of the array, D denotes the number of search grids, M denotes the number of grid points, and K denotes the number of signals.
It can be seen that the computation complexity of the off-grid signal direction of arrival estimation method provided in an embodiment of the present invention is smaller than that of the off-grid sparse bayesian algorithm and that of the algorithm based on phase deviation search, and although the computation complexity of the fractional fourier coefficient interpolation algorithm is smaller than that of the off-grid signal direction of arrival estimation method provided in an embodiment of the present invention, it can only be applied to the case of uniform linear arrays.
Therefore, the method for estimating the direction of arrival of the off-grid signal provided by the embodiment of the invention can be suitable for both the uniform linear array and the non-uniform linear array, can realize high-precision estimation of the direction of arrival of the signal, and has low calculation complexity.
It is noted that, in this document, relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. In addition, "front", "rear", "left", "right", "upper" and "lower" in this document are all referred to the placement state shown in the drawings.
Finally, it should be noted that: the above examples are only for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (9)
1. A method for estimating the direction of arrival of off-grid signals suitable for a non-uniform linear array is characterized by comprising the following steps:
step S1, according to single snapshot array element data, utilizing a beam forming method to obtain an initial estimation value of a signal direction of arrival on a candidate grid;
s2, calculating a complex value signal according to the signal wave arrival direction;
s3, separating corresponding signal data from the received data of the array according to the signal wave arrival direction and the complex value signal;
s4, multiplying the conjugate of the previous element and the next element in the signal data to obtain a construction vector, and extracting the phase of each element of the construction vector;
s5, resolving ambiguity of the phase of the extracted construction vector, and acquiring a closed expression of the signal direction of arrival according to the resolved ambiguity phase;
s6, calculating and updating the signal direction of arrival according to the closed expression of the signal direction of arrival;
and S7, judging whether the signal direction of arrival is converged or not, or whether the cycle number reaches a preset threshold or not, if so, taking the currently calculated signal direction of arrival as a final estimation value, and if not, returning to the step S2.
2. The off-grid signal direction-of-arrival estimation method suitable for the nonuniform linear arrays according to claim 1, characterized by setting: n antennas form a non-uniform arrayColumn, array element position c n N =1, 2.. And N, the unit array element spacing d is set to be half of the wavelength, K far-field narrow-band signals are incident to the array, and the arrival direction is theta = [ theta ] = 1 ,...,θ K ]，θ 1 ,...,θ K Representing directions of arrival of the 1 st to K-th signals, respectively, and the reception data y of the array is represented As y = As + m, s = [ s ] = 1 ,...,s K ] T Represents a vector of K complex-valued deterministic signals, m represents N × 1-dimensional white Gaussian noise, A represents an array manifold matrix, A = [ a (θ) 1 ),a(θ 2 ),...,a(θ K )]，a(θ k ) The array steering vector is represented as a vector of the array,
searching area in consideration of angle
M evenly sampled grid points of (a) to obtain
The grid interval is
M represents the number of grids;
and simultaneously setting: the arrival direction of the incident signal does not fall on the pre-divided discrete grid points;
acquiring an initial estimation value of a signal arrival direction on a candidate grid by using a beam forming method, wherein the method comprises the following steps:
defining a normalized MxN-dimensional beamforming matrix F having (p, q) -th element of
Obtaining a space spectrum x = | Fy |, which is formed by a wave beam, according to a defined matrix F;
obtaining the positions corresponding to the K peak values according to the space spectrum x
Based on the corresponding positions of the K peak values, using a formula
Determining an initial estimate of the direction of arrival of a corresponding signal
3. The method for estimating the direction of arrival of off-grid signals suitable for the nonuniform linear arrays according to claim 1 or 2, wherein calculating a complex-valued signal according to the direction of arrival of the signals comprises:
constructing an estimated complex value signal according to the direction of arrival of the signal;
and solving the problem of estimating the complex value signal by using a least square method to obtain a closed-form solution of the complex value signal.
4. The method for estimating off-grid signal direction of arrival applicable to non-uniform linear arrays according to claim 3, wherein the problem of estimating complex-valued signals is:
the closed-form solution of the complex-valued signal is:
s＝(A H A) -1 A H y
wherein s represents a complex-valued signal, A H Represents the conjugate transpose of a.
5. The off-grid signal direction-of-arrival estimation method suitable for the nonuniform linear arrays according to any one of claims 2 to 4, characterized in that the corresponding signal data is separated from the received data of the array by using the following formula;
wherein, y k Representing the kth signal data, s i Represents the ith complex-valued signal, a (θ) i ) Indicating the array steering vector corresponding to the ith signal.
6. The off-grid signal direction-of-arrival estimation method suitable for the nonuniform linear arrays according to claim 5, characterized in that the elements of the signal data are determined by using the following formula;
wherein, y k,n N-th element, | s, representing the k-th signal k I denotes the amplitude of the kth signal, phi k Representing the phase, ε, of the kth signal n Representing zero mean Gaussian white noise corresponding to the nth element;
defining the construction vector corresponding to the kth signal as r k ∈C N-1 C represents a complex set, constructing a vector r k Is determined using the following formula;
wherein r is k,n Representing a construction vector r k The (n) th element of (a),
denotes y k,n And (3) conjugation.
7. The method for estimating off-grid signal direction of arrival applicable to the nonuniform linear arrays according to claim 6, wherein the phases of the extracted construction vectors are deblurred by using the following formula;
wherein, g n (r k ) Representing a construction vector r k The solution of the nth element of (a) blurs the phase,
representing a construction vector r k Phase of the nth element of (2), psi n Denotes an integer obtained by rounding off,
round (x) means rounding x;
the deblurred phase of the constructed vector is represented as:
wherein, g (r) k ) Represents the construction vector r k Deblurring phase of g 1 (r k ),g 2 (r k ),…,g (N-1) (r k ) Representing the deblurred phase vector g (r) k ) The number of the N-1 elements of (A),
ε represents the colored Gaussian noise vector, [ epsilon ] = [ ε ] 2 -ε 1 ,ε 3 -ε 2 ,...,ε N -ε N-1 ] T 。
8. The method as claimed in claim 7, wherein said obtaining a closed expression of signal direction of arrival according to the deblurred phase comprises:
constructing an objective function:
minimizing the target function to obtain a closed expression of the signal arrival direction;
where Q represents the covariance matrix of the colored gaussian noise vector epsilon.
9. The off-grid signal direction-of-arrival estimation method suitable for the nonuniform linear arrays according to claim 8, wherein the signal direction-of-arrival is calculated by using the following formula;
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