Low complexity super-resolution DOA estimation method based on frequency-phase cooperative array

Abstract

The application discloses a low-complexity super-resolution DOA estimation method based on frequency-phase cooperative array and belongs to the technical field of radar direction of arrival (DOA) estimation. The application is based on a subspace algorithm based on eigenvalue decomposition, and radar receiving data is processed in two parts in parallel. The ESPRIT algorithm is used to coarsely estimate the DOA of phased array receiving data, fine-grained search space is obtained, and the MUSIC algorithm is used to obtain high-precision DOA estimation values by using frequency control array part data. The method not only retains the extremely high estimation precision of the MUSIC algorithm, but also avoids the extremely high calculation complexity problem caused by the increase of search precision, and can be flexibly adjusted according to the DOA estimation precision requirement in actual projects. The method has the characteristics of low complexity, super-resolution, high universality and flexible design. According to the subspace algorithm based on eigenvalue decomposition, the problem of high calculation complexity in the high-precision estimation of the MUSIC algorithm is solved.

Description

Technical Field

[0001] This invention relates to the field of radar direction of arrival (DOA) estimation technology, specifically to a low-complexity super-resolution DOA estimation method based on a frequency-phase cooperative array. Background Technology

[0002] With the rapid development of radar electronics technology, traditional radar systems are unable to accurately estimate the diverse range of target signals, leading to a sharp decline in radar detection performance. Driven by modern military needs, array radar technology has developed rapidly, from aerospace surveillance and missile defense to target identification and aircraft navigation. Array radar systems are widely used in the defense and military field. To overcome the limitation of early mechanically scanned radars in accurately detecting high-speed moving targets, electronically scanned radars, represented by phased array (PA) radars, have emerged. Phased array radars achieve beam scanning and shaping by controlling the phase between different array elements. However, its beam pointing is independent of range, while in practice, it is often desirable to obtain range-dimensional information to detect and estimate the number and status of targets in the range dimension. However, the beam pointing of a phased array is only azimuth-dependent; at the same azimuth, the signal energy received by the target is a fixed value, independent of range. Its beam is as follows... Figure 1 As shown.

[0003] Thus, the Frequency Diverse Array (FDA) radar was developed. First proposed in 2006 by Antonik et al. at the U.S. Air Force Research Laboratory, FDA radar is a novel radar system. Its main difference from phased array radar lies in the introduction of a small frequency offset between each element. Therefore, the phase superposition relationship of the transmitted signals from each element differs at different distances, adding range dependence to the transmitted signal. Its beam is as follows... Figure 2 As shown in the figure. In summary, a phased array can be considered as a special frequency-controlled array with zero frequency offset. Therefore, applying a frequency-controlled array to a radar system can achieve detection and estimation in the angle-range dimension, which has significant military and civilian value. Although there is already a large amount of research on frequency-controlled array radar and DOA estimation, most of it is based on the purpose of detection and estimation for a single frequency-controlled array radar. It is difficult to decouple the frequency-controlled array beam in the angle-range dimension, and it is also difficult to achieve accurate DOA estimation.

[0004] Super-resolution algorithms for DOA estimation require eigenvalue decomposition of the received signal, subspace partitioning based on the number of targets and eigenvalues, followed by spectral search to find peaks and obtain satisfactory estimates. However, high-precision estimation often faces extremely high computational complexity, especially with the increase in the number of array elements and joint processing snapshots, where the computational complexity grows exponentially. Therefore, it is necessary to invent a low-complexity super-resolution DOA estimation algorithm to meet the overall performance requirements of frequency-controlled array DOA estimation in practice. Since the received data from frequency-phase coordinated array radar can be processed separately, and both echoes contain target information, a low-complexity DOA estimate can be obtained by processing the data step by step. Summary of the Invention

[0005] This invention proposes a low-complexity super-resolution DOA estimation method using a subspace algorithm based on eigenvalue decomposition. It also provides a super-resolution DOA estimation method that meets the performance requirements of DOA estimation in practical engineering.

[0006] The technical solution adopted in this invention is as follows:

[0007] A low-complexity super-resolution DOA estimation method based on frequency-phase cooperative arrays, comprising:

[0008] Step 1: Acquire the echo signal of the frequency-phase cooperative array radar through the dual-mode array radar, calculate and estimate the covariance matrix based on the echo signal and perform eigenvalue decomposition;

[0009] The dual-mode array radar includes: an L+M element uniform linear transmitting array and an N element uniform linear receiving array. The transmitting array includes a phased array composed of L uniform array elements and a frequency-controlled array composed of M uniform array elements, and the array element spacing of the PA array, FDA array and receiving array is the same.

[0010] Step 2: For each eigenvector after decomposing the estimated covariance matrix, based on the number of target signal sources K, consider the eigenvectors corresponding to the first K largest eigenvalues ​​as the signal subspace E. S The remaining M×N×LK eigenvectors are considered as the noise subspace E. N and the signal subspace E S The space is divided into two identical subarrays, denoted as E1 and E2;

[0011] Step 3: Solve eigenvalues ​​λ k ,according to Obtain the estimated value of the target azimuth. Where k = 1, 2, ..., K; that is, to solve for the eigenvalues ​​of two identical submatrix spaces and to make a coarse estimate of the angle of arrival;

[0012] Step 4: Estimated value based on the target azimuth angle Set the search spectrum range for the k-th target as follows: A spectral peak search is performed within this search spectral range to obtain a precise estimate of the target azimuth angle of the k-th target, where τ represents the preset spectral peak search width. This is based on the coarse estimate... As the search center, adjust the search granularity and width based on performance. For the decomposed subspace (E) N Perform spectral peak search according to the set parameters to obtain a high-precision DOA estimate.

[0013] The technical solution provided by this invention brings at least the following beneficial effects:

[0014] (1) Current research on frequency-controlled array radars mainly focuses on the frequency control array itself. However, phased arrays can play a synergistic and auxiliary role compared to frequency-controlled arrays, and there has been insufficient research on frequency-phase coordinated arrays. This invention fills this gap to some extent and has reference and application value.

[0015] (2) Compared with existing estimation methods, the method proposed in this invention avoids the retrieval of redundant search space and has the characteristics of low complexity and super resolution.

[0016] (3) Compared with existing estimation methods, the present invention can flexibly adjust the search width according to the angle estimation performance requirements of actual projects, and has the characteristics of high universality and flexible design. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of a uniform linear frequency phase-coordinated array structure;

[0019] Figure 2 This is a diagram of the phased array's transmitted beam.

[0020] Figure 3 This is a diagram of the frequency-controlled array's transmit beam.

[0021] Figure 4 This is a performance comparison chart between the step-by-step algorithm and the ESPRIT algorithm. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0023] This invention proposes a low-complexity super-resolution DOA estimation method using a subspace algorithm based on eigenvalue decomposition. It also provides a super-resolution DOA estimation method that meets the performance requirements of DOA estimation in practical engineering.

[0024] The technical solution of the low-complexity super-resolution DOA estimation method based on frequency-phase cooperative array provided in this invention is as follows:

[0025] Step 1: Obtain the echo signal of the frequency phase-coordinated array radar, obtain the estimated covariance matrix and perform eigenvalue decomposition.

[0026] The transmitting array employs a dual-mode array radar, such as... Figure 1 As shown, an L+M element uniform linear transmitting array and an N element uniform linear receiving array are used. The transmitting array includes a phased array (PA array) composed of L uniform array elements and a frequency-controlled array (FDA array) composed of M uniform array elements. The element spacing of the PA array, FDA array and receiving array is the same, denoted by d. Figure 2 , Figure 3 These are the transmission radiation patterns of phased array and frequency-controlled array radars, respectively. The echo signal of the frequency-phase co-operated array radar can be derived from the transmission radiation pattern.

[0027] Step 2: According to the order of eigenvalue size, the eigenvectors corresponding to the first K largest eigenvalues ​​(with values ​​consistent with the number of signal sources) are regarded as the signal subspace, and the remaining MNL-K eigenvectors are regarded as the noise subspace. The signal subspace is then divided into two identical subarray spaces, where L+M represents the number of array elements of the transmission array.

[0028] Step 3: Solve for the eigenvalues ​​of the two identical subarray spaces and make a coarse estimate of the angle of arrival.

[0029] Step 4: Obtain the search center based on the coarse estimate, and set the search fineness and width according to performance. Perform a spectral peak search on the decomposed subspace according to the set parameters to obtain a high-precision DOA estimate.

[0030] like Figure 1 The dual-mode array radar shown has the same spatial azimuth angle for the co-located transmit and receive arrays when targeting far-field targets. The transmitted signal of its m-th element is:

[0031]

[0032]

[0033] In the formula Let represent the baseband waveforms transmitted by the m-th element of the phased array and the frequency-controlled array, respectively, and let represent the waveforms of the transmitted signals at different carrier frequencies, respectively, satisfying the orthogonality condition, i.e. in(·) * Indicates complex conjugation. T p The pulse duration is given. f0 represents the phased array signal carrier frequency, f m f represents the carrier frequency of the transmitted signal of the m-th element of the frequency control array. m =f0+(m-1)Δf, where Δf is the frequency increment and Δf << f0.

[0034] Now, assuming the target is located at an arbitrary distance-angle (R, θ) in the far field, the signal received by the nth array element can be expressed as:

[0035]

[0036] Where ξ represents the target complex amplitude. This indicates the two-way delay of the PA's transmitted signal. This represents the two-way delay of the FDA's transmitted signal. Here, 'c' represents the speed of light. At the receiving end, the received signal undergoes down-conversion, matched filtering, and digital mixing. The signal can be represented as two parts: the PA and the FDA received signal.

[0037]

[0038]

[0039] Where Δf << f0, The quadratic phase term is ignored. By arranging PA and FDA, a dual-mode radar receiver signal model can be constructed as follows:

[0040]

[0041] Where b(θ) represents the receive steering vector, a(R, θ) represents the FDA transmit steering vector, and l = 1, 2, ..., L, where L is the number of times time t is used. The noise vector n(l) can be modeled as an independent and identically distributed vector with zero mean and variance. Gaussian random variables.

[0042] Among subspace DOA estimation algorithms based on array covariance, the Multiple Signal Classification (MUSIC) algorithm is the most classic. It performs spectral peak search in the spatial domain to determine the source direction of attack. High-resolution estimation results can be obtained as long as the antenna array structure is known. Taking a phased array as an example, the array covariance matrix R can be expressed as...

[0043]

[0044] In the formula, y represents the received signal vector, y sLet R represent a submatrix whose dimension is the number of signal sources (K) after sorting the elements of y according to their eigenvalues, corresponding to the received signal vector of the signal source. U represents the steering vector of the phased array, and R represents the signal vector of the signal source. S The covariance matrix of the signal. Let R represent the noise power, and I represent the identity matrix. Assuming the signal and noise are independent, R can be partitioned into two spaces, namely... Among them, U S U represents the steering vector corresponding to the signal source, i.e., the signal subspace. N Σ represents the steering vector corresponding to the noise, i.e., the noise subspace. S Σ N These represent diagonal matrices for the signal source and noise, respectively.

[0045] based on achievable

[0046]

[0047] According to equation (8), we get

[0048] a(θ)R S a H (θ)U N =0 (9)

[0049] Signal covariance matrix R S Since it is a full-rank matrix and non-singular, it has an inverse. Therefore, the above equation can be transformed into a. H (θ)U N =0, which indicates that each column vector in the steering vector matrix is ​​orthogonal to the noise subspace, thus yielding the phased array spatial spectrum function.

[0050]

[0051] This causes θ in the formula to change. By finding the spectral peak to estimate the angle of arrival, the estimated value of the azimuth angle of arrival can be expressed as:

[0052]

[0053] Among them, P a =a(θ)(a H (θ)a(θ)) -1 a H (θ) is the projection matrix of a(θ), arg x minf(x) represents the value of the variable that minimizes the objective function f(x), and tr{·} represents the trace operation of the matrix.

[0054] Based on the above analysis, the steps of the MUSIC estimation algorithm can be summarized as follows:

[0055] (1) Obtain the estimated value of the covariance matrix based on L sampled data of the received signal vector. And decompose its eigenvalues ​​into

[0056] (2) In order of eigenvalue magnitude, the eigenvector corresponding to the largest eigenvalue (equal to the number of signals K) is considered as the signal subspace, while the eigenvectors corresponding to the remaining NML-K smaller eigenvalues ​​are considered as the noise subspace. Then we have...

[0057] (3) Change the value of θ, calculate the spectral function value in formula (10), and obtain the estimated value of the direction of arrival by finding the peak value.

[0058] Consider the FDA portion of the received signal vector in equation (6)

[0059]

[0060] The combined transmit-receive steering vectors of K target signal sources can be represented in the following matrix form.

[0061]

[0062] The above formula can be further expressed as

[0063]

[0064] In the formula D represents the Khatri-Rao product operation. n (b) represents the operation of extracting the elements of the nth row of matrix b and constructing a diagonal matrix, where the FDA transmit steering vector and receive steering vector are respectively represented as...

[0065]

[0066]

[0067] The corresponding rotation-invariant operator is

[0068] Φ=diag{exp{j2πf0dsinθ1 / c},…, exp{j2πf0dsinθ K}} (17)

[0069] Assuming that the guide vectors a and b remain unchanged over L snapshots, equation (12) can be further expressed as follows:

[0070] Y = US + N (18)

[0071] in For FDA joint launch-receive steering vector, The signal is represented by a matrix. Let represent the noise sampling matrix. Then, the covariance matrix of equation (18) can be obtained by eigenvalue decomposition.

[0072]

[0073] In the formula Λ S This represents a diagonal matrix whose diagonal elements are the first K largest eigenvalues, and the corresponding signal subspace is E. S The diagonal matrix of the remaining MN-K smaller eigenvalues ​​is Λ N The corresponding noise subspace is E N Then there exists a unique, non-singular K×K dimensional full-rank matrix T such that the following equation holds.

[0074] E S =UT (20)

[0075] To satisfy the rotation invariance required by the ESPRIT estimation method, the receiving array needs to be divided into two identical subarrays, consisting of the first N-1 elements and the last N-1 elements of the receiving array, respectively, with the corresponding rotation operator being Φ. Therefore, E in equation (20) S U can also be divided into two corresponding parts, where the first (N-1)M rows form matrices U1 and E1 respectively, and the last (N-1)M rows form matrices U2 and E2 respectively. Therefore, we can obtain...

[0076] U2=U1Φ (21)

[0077] Then there is

[0078] E2=E1Ψ (22)

[0079]

[0080] In the formula (·) + This represents the pseudo-inverse operation of a matrix. Ψ = T -1 ΦT represents the equivalent rotation operator of the frequency-controlled array radar, where Ψ is similar to Φ, i.e., it has the same eigenvalue, and its eigenvalue λ k Let be the k-th diagonal element of matrix Φ. Therefore, the estimated target azimuth angle can be obtained as...

[0081]

[0082] Based on the above analysis, the steps of the ESPRIT estimation algorithm can be summarized as follows:

[0083] (1) Obtain the estimated value of the covariance matrix based on L sampled data of the received signal vector. And decompose its eigenvalues ​​into

[0084] (2) In order of the magnitude of the eigenvalues, the eigenvector corresponding to the largest eigenvalue that is equal to the number of signals K is regarded as the signal subspace E. S It is decomposed into two parts, E1 and E2.

[0085] (3) Solve eigenvalues ​​λ k Thus, the estimated value of the target azimuth is obtained.

[0086] In summary, the computational complexity required to search the spatial power spectrum using the MUSIC algorithm is... The total computational cost required to solve for the target's azimuth using the ESPRIT algorithm can be expressed as follows: In comparison, both of the above algorithms have better distance resolution, but as can be seen from the spectral function of the MUSIC algorithm, its estimation accuracy is related to the spectral search accuracy.

[0087]

[0088] This causes θ in the formula to change, and the angle of arrival is estimated by finding spectral peaks. It is assumed that the upper and lower bounds of the search spectrum are θ∈[θ]. left θ right Without any prior information, θ can be known from the characteristics of the phased array. left =-90°, θ right = 90°. The search spectrum refinement Δθ determines the accuracy of the angle estimation; a smaller search spectrum refinement yields better angular resolution, but also results in a rapidly increasing computational complexity. The number of search units can be expressed as (θ... right -θ left To achieve better estimation accuracy while reducing computational complexity, the number of search units needs to be minimized while maintaining a small Δθ. Therefore, some prior knowledge is required to ensure that θ... right -θ left To reduce complexity, this section proposes a low-complexity super-resolution algorithm based on frequency-phase coordination. Since the array transmits in a coordinated manner using both phased and frequency-controlled arrays, the received data can be divided into two parts: the phased array and the frequency-controlled array. During processing, the ESPRIT algorithm can be used for rapid estimation of the phased array portion, or a lower-precision angle estimate can be obtained. At this point, it's equivalent to having obtained some prior information about the target; therefore, the upper and lower bounds of the search unit in the MUSIC algorithm can be set to... Where τ is the mean square error of the ESPRIT estimation, the number of search units is then... It is evident that even with a small search precision Δθ, low computational complexity can be maintained.

[0089] Example

[0090] This invention, based on a frequency-phase coordinated array system, proposes a step-by-step super-resolution algorithm to address the high complexity issue of high-precision angle estimation for frequency-controlled arrays, taking into account the performance requirements of angle estimation. Furthermore, it proposes a super-resolution DOA estimation method tailored to the properties of radar arrays. The specific implementation steps are as follows:

[0091] Step 1: Obtain the echo signal from the frequency-phase coordinated array radar, obtain the estimated covariance matrix, and perform eigenvalue decomposition. In this step, L received data snapshots are processed together to obtain the received data matrix, and the estimated covariance matrix is ​​calculated. And perform eigenvalue decomposition on it.

[0092] Step 2: According to the order of eigenvalue size, the eigenvectors corresponding to the K largest eigenvalues ​​are regarded as the signal subspace, and the remaining MNL-K eigenvectors are regarded as the noise subspace. The signal subspace is then divided into two identical sub-matrix spaces.

[0093] In this step, the eigenvector corresponding to the largest eigenvalue that is equal to the number of signals K is regarded as the signal subspace E, in order of the magnitude of the eigenvalues. S It is decomposed into two parts, E1 and E2, and the eigenvectors corresponding to the remaining NML-K small eigenvalues ​​constitute the noise subspace. Then we have...

[0094] Step 3: Solve for the eigenvalues ​​of the two identical subarray spaces and make a coarse estimate of the angle of arrival.

[0095] In this step, the solution is... eigenvalues ​​λ k Thus, the estimated value of the target azimuth is obtained.

[0096] Step 4: Obtain the search center based on the coarse estimate, and set the search fineness and width according to performance. Perform a spectral peak search on the decomposed subspace according to the set parameters to obtain a high-precision DOA estimate.

[0097] In this step, the search spectrum range of the k-th target using the MUSIC algorithm is calculated. Calculate the spectral function value by varying the value of θ within this range. A high-precision estimate of the direction of arrival is obtained by finding the peak value, where τ is the spectral search width set according to performance requirements.

[0098] Based on the above method, an example is provided for verification. The specific simulation parameters are as follows:

[0099] The linear transmit phased array has L = 8 elements, the frequency control array has M = 8 elements, the receiver has N = 16 elements, and the element spacing is d = c / (2f0). The number of snapshots is K = 100, the frequency offset Δf = 30kHz, and the reference carrier frequency f0 = 10GHz. Assume the target is located at (56.789°, 12.345km). The signal-to-noise ratio (SNR) is [-20, 40]dB.

[0100] Based on the low-complexity super-resolution algorithm based on frequency-phase coordination proposed in this paper, the received data is first mixed, down-converted, and matched filtered according to step 1. The received signal is divided into two parts, the phased array received signal and the frequency-controlled array received signal, which are processed in parallel to obtain their respective sampling covariance matrices. Then, according to step 2, eigenvalue decomposition is performed. The eigenvectors corresponding to the first K eigenvalues ​​are selected in descending order of eigenvalues ​​and regarded as the signal subspace, while the next LMN-K eigenvalues ​​are regarded as the noise subspace. The signal subspace is divided into two identical subspaces, E1 and E2. Proceed to step 3 to solve... eigenvalues ​​λ k Thus, the estimated value of the target azimuth is obtained. Based on step 4, calculate the search spectrum range of the k-th target using the MUSIC algorithm. By varying the value of θ within this range, and defining the search range, a high-precision MUSCI algorithm search is performed. The DOA estimate is obtained based on the spectral peak search results, and its performance is as follows: Figure 4 As shown.

[0101] Table 1 Comparison of estimation accuracy and computation time

[0102] algorithm Search precision Estimated value / Actual value computation time ESPRIT \ 56.7737° / 56.789° 0.0403 seconds MUSIC 0.001 56.8120° / 56.789° 2.4011 seconds ESPRIT+MUSIC 0.001° 56.7867° / 56.789° 0.0491 seconds

[0103] As shown in the table above, compared with the ESPRIT and MUSIC algorithms, the proposed algorithm, based on frequency-phase coordination, maintains the computational complexity of the ESPRIT algorithm while achieving the high accuracy of the MUSIC algorithm, demonstrating promising application prospects in DOA estimation. Simulations can further verify the correctness of the proposed algorithm.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0105] The above descriptions are merely some embodiments of the present invention. Those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A low-complexity super-resolution DOA estimation method based on frequency-phase cooperative array, characterized in that, Includes the following steps: Step 1: Acquire the echo signal of the frequency-phase cooperative array radar through the dual-mode array radar, calculate and estimate the covariance matrix based on the echo signal and perform eigenvalue decomposition; The dual-mode array radar comprises: an L+M element uniform linear transmitting array and an N element uniform linear receiving array. The transmitting array includes a phased array (PA) composed of L uniform elements and a frequency-controlled array (FDA) composed of M uniform elements. The element spacing between the PA array, FDA array, and receiving array is the same. ,in, Represents the speed of light. Indicates the reference carrier frequency; Among them, the spatial azimuth angles of the co-located transmit and receive arrays are the same, the first The transmitted signals of each array element are: ； ； In the formula , Representing the phased array and frequency-controlled array respectively The baseband waveforms transmitted by each array element, and the transmitted signal waveforms at different carrier frequencies satisfy the orthogonality condition. The duration of the pulse. Indicates the frequency control array Each array element transmits a carrier frequency for the signal. , For frequency increment and ; For any distance-angle , No. Each element receives the signal as follows: ； in, Indicates the target complexity. express Two-way delay of the transmitted signal, express Two-way delay of the transmitted signal; Will Arrange the signals to construct a dual-mode radar receiving signal model: ； in, Indicates the receiving guide vector. express Launch guide vector, , For time Number of times used, noise vector It can be modeled as independent and identically distributed zero-mean, with variance of Gaussian random variables; Step 2: For each eigenvector after decomposing the estimated covariance matrix, based on the number K of target signal sources, consider the eigenvectors corresponding to the first K largest eigenvalues ​​as the signal subspace. The remaining M×N×LK eigenvectors are considered as the noise subspace. and the signal subspace The space divided into two identical subarrays is denoted as and ; Step 3: Solve eigenvalues ,according to Obtain the estimated value of the target azimuth. ,in, ; Step 4: Estimated value based on the target azimuth angle Set the search spectrum range for the k-th target as follows: A spectral peak search is performed within this search spectrum range to obtain a precise estimate of the target azimuth angle of the k-th target. This indicates the preset peak search width.

2. The method as described in claim 1, characterized in that, In step 4, the spectral function value during peak search is: Among them, angle .

3. The method as described in claim 1, characterized in that, The estimated covariance matrix is: ,in, Represents the received signal vector Data sampling snapshot count.

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