1-bit Encoded Metasurface Array Signal Direction-of-Arrival Estimation Method Based on Distributed Arrangement

Abstract

The present invention discloses a method for estimating the direction of arrival of a signal of a 1-bit coded metasurface array based on distributed arrangement, which mainly solves the problems of poor flexibility and high cost of the existing direction-of-arrival estimation methods. The implementation scheme is as follows: construct a distributed 1-bit coded metasurface array U, and obtain the received signal Y(t) through U; construct a measurement vector of the received signal Y(t), construct an array manifold dictionary of U, and solve the target vector X based on the compressive sensing method through the measurement vector and the array manifold dictionary; obtain the estimated value of the direction of arrival of the signal by performing a spectral peak search on the target vector X. The present invention has low cost, good array combination freedom, large array aperture, and high accuracy in estimating the direction-of-arrival angle of the signal, and can be used for target positioning in complex environments.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a method for estimating the direction of arrival of an array signal with a distributed arrangement, which can be used for target positioning. Background Art

[0002] Array signal processing is a research focus in signal processing problems. With the increasing improvement of people's living needs, array signal processing technology has undoubtedly become a key application technology to solve people's lives. Array signal processing technology refers to using a sensor array composed of sensors according to a specific geometric structure. The sensor array receives spatial target signals and then extracts the characteristic parameters of the spatial signals according to a specified method, such as parameters such as the arrival angle, frequency, and polarization of the target signal.

[0003] A metasurface is a planar composite structure formed by arranging sub-wavelength metamaterial units on the interface according to a certain rule, also known as two-dimensional metamaterial. The metasurface can cause a phase or amplitude mutation of electromagnetic waves on its surface by relying on its structure, thereby realizing the regulation of electromagnetic waves. Digital coding metasurface is a combination of physics and information science, integrating some concepts and methods in information theory and digital signal processing. It is a characterization of information using a metasurface and can be directly introduced into the design of the metasurface and applied as a new type of array in various fields such as radar and communication systems.

[0004] The direction of arrival (DOA) of a signal refers to the arrival direction of a spatial signal, that is, the direction angle of each signal arriving at the array reference element. The estimation of the signal DOA has always been a research focus in the field of array signal processing and has potential application value in fields such as communication, exploration, biomedicine, and radar. A distributed array uses multiple arrays to jointly receive signals and fuse the data. Compared with a single uniform linear array, a distributed array can not only effectively suppress interference, noise, etc., but also has a larger array aperture and higher angular resolution, thus having better estimation accuracy. For example, the patent application with the application publication number CN113406620A provides a method for measuring the angle of a distributed array based on array decomposition. This method is based on the idea of sub-array division, decomposing the array into multiple sub-arrays to increase the aperture of the distributed array under the condition of ensuring low computational complexity, effectively suppressing interference, and accurately measuring the target angle at the same time. However, this way of decomposing the array increases the cost of the array antenna, and the flexibility of the distributed arrangement of the array is limited, making it unable to meet the construction requirements when constructing a direction-of-arrival estimation antenna array under many specific conditions. Summary of the Invention

[0005] The object of the present invention is to overcome the defects existing in the above-mentioned prior art, and propose a method for estimating the direction of arrival of a signal wave of a 1-bit coded metasurface array based on distributed arrangement, which uses a distributed arrangement method to improve the flexibility during array deployment, so as to meet the construction requirements of an antenna array for direction-of-arrival estimation under many specific conditions. By encoding the weights of the metasurface elements, the accuracy of direction-of-arrival estimation is improved, and the cost of the array antenna is reduced by using a combination of a metasurface array and a traditional array.

[0006] To achieve the above object, the technical solution of the present invention includes the following:

[0007] (1) Construct a distributed 1-bit coded metasurface array U:

[0008] (1a) Construct a 1-bit coded metasurface sub-array formed by linearly arranging M 1-bit coded metasurface elements, and construct a traditional sub-array formed by linearly arranging M traditional elements. The distance between any two adjacent elements of each sub-array is d, d ≤ λ / 2, where λ is the wavelength of the narrowband signal incident on the array, and the value range of M is: M ≥ 2;

[0009] (1b) Arbitrarily distribute and arrange Q1 1-bit coded metasurface sub-arrays and Q2 traditional sub-arrays on a spatial plane to form a distributed 1-bit coded metasurface array where U q represents the q-th sub-array of the distributed array U, and it is defined that represents the angular offset of the sub-array U q from the horizontal plane, Q1 ≥ 1, Q2 ≥ 1, 2 ≤ q ≤ Q1 + Q2;

[0010] (2) Obtain the received signal Y(t) of the distributed 1-bit coded metasurface array:

[0011] (2a) Assume that there are K narrowband signals emitted by far-field signal sources in space, and use the elements in the sub-array U q to sample the target signal in space to obtain the sub-array received signal Y q (t):

[0012] Y q (t) = [Y q1 (t), Y q2 (t), …, Y qm (t), …, Y qM (t)] T ,

[0013] where Y qm (t) represents the sub-array U qThe received signal of the m-th array element, where t represents discrete time, 1 ≤ t ≤ L, and L represents the number of sampling points of the signal in the time domain, [·] T denotes the transpose operation. The range of m is: 1 ≤ m ≤ M, and the range of K is: 1 ≤ K ≤ (Q1 + Q2)M;

[0014] (2b) Receive the signal Y using all sub-arrays q (t) jointly form the received signal of the distributed 1-bit coded metasurface array U:

[0015]

[0016] (3) Construct the direction vector of the received signal Y(t) of the distributed 1-bit coded metasurface array

[0017] (3a) Utilize the sub-array received signal Y q (t) to calculate the sub-array covariance matrix

[0018]

[0019] where, [·] H denotes the conjugate transpose operation;

[0020] (3b) According to the covariance matrix construct the direction vector of the received signal Y(t) of the distributed 1-bit coded metasurface array:

[0021]

[0022] where, is the direction vector of the q-th sub-array, and vec{·} represents the operation of straightening the matrix by columns;

[0023] (4) Construct the array manifold dictionary of the distributed 1-bit coded metasurface array U

[0024] (4a) Adopt the spatial domain partitioning method, and according to the spatial domain sparse characteristics of the signal source, evenly partition the observed spatial domain [-90°, 90°] into V fixed-angle values where V >> K, represents the v-th fixed angle value;

[0025] (4b) Through the sub-array U q and the fixed angle value construct the steering vector corresponding to the sub-array U q of where B q represents the array weight coding matrix of the metasurface sub-array, Gq is the wave path difference matrix introduced by the distances from each element of the metasurface subarray to the receiving feed is the wave path difference offset vector of this subarray. If this subarray is a traditional array, the steering vector I represents the diagonal identity matrix;

[0026] (4c) Calculate the steering vector of subarray U q of the Kronecker product of

[0027]

[0028] where, represents the Kronecker product operation;

[0029] (4d) Use the steering vector Kronecker product of subarray U q at all angles in the observation airspace to construct the dictionary matrix of subarray U q of

[0030]

[0031] where,

[0032] (4e) Use all the subarray dictionary matrices to jointly form the array manifold dictionary of the distributed 1-bit coded metasurface array

[0033] (5) Obtain the direction-of-arrival estimation value of the signal based on the compressive sensing method

[0034] (5a) Adopt the formula for solving the convex optimization problem, and construct the constraint condition through the measurement vector and the array manifold dictionary : Calculate to obtain the target vector X = [X1,..., X v ,..., X V T , where, ||·||2 represents calculating the 2-norm of the vector, and ε represents the noise estimation value;

[0035] (5b) Take the value of as the x-axis coordinate, and take the target vector X = [X1,..., X v ,..., X V T ​​The value is the y-axis coordinate. An amplitude spectrum diagram is plotted. From this amplitude spectrum diagram, the top K spectral peaks with larger amplitudes are found in descending order. The x-axis coordinates corresponding to the peak points of these spectral peaks are the estimated values of the directions of arrival of the K far-field signals sought. where represents the direction of arrival of the k-th signal, where 1 ≤ k ≤ K.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] 1) The present invention uses a distributed array for direction-of-arrival estimation. The distribution positions and placement angles of the sub-arrays have high flexibility. At the same time, a compressive sensing algorithm is introduced to improve the accuracy of direction-of-arrival estimation and the estimation performance under low signal-to-noise ratio conditions.

[0038] 2) The distributed 1-bit coded metasurface array constructed by the present invention, compared with the traditional array, has a lower cost and a smaller volume for the coded metasurface array. It can increase the array aperture under low-cost conditions, and by weighting and coding the 1-bit coded metasurface array elements, the accuracy of direction-of-arrival estimation is improved; at the same time, a combination of the 1-bit coded metasurface array and the traditional array is used to overcome the problem of high computational complexity when the number of metasurface array elements is too large. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of the implementation of the present invention;

[0040] Figure 2 is a schematic diagram of the received signal model of the distributed 1-bit coded metasurface array constructed in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0042] Referring to Figure 1 , the implementation steps of this example are as follows:

[0043] Step 1, construct a distributed 1-bit coded metasurface array U.

[0044] Referring to Figure 2 , the specific implementation of this step is as follows:

[0045] 1.1) Construct a 1-bit coded metasurface sub-array linearly arranged by M 1-bit coded metasurface array elements, and construct a traditional sub-array linearly arranged by M traditional array elements. Among them, the distance between two adjacent array elements of each sub-array is d, d ≤ λ / 2, where λ is the wavelength of the narrowband signal incident on the array, and the value range of M is: M ≥ 1;

[0046] 1.2) The distributed 1-bit coded metasurface array is formed by randomly arranging and distributing Q1 1-bit coded metasurface sub-arrays and Q2 traditional sub-arrays on a spatial plane. Among them, U q represents the q-th sub-array of the distributed array U, and is defined as indicating the sub-array U q The angular offset from the horizontal plane, Q1≥1, Q2≥1, 1≤q≤Q1 + Q2;

[0047] Step 2, obtain the received signal Y(t) of the distributed 1-bit coded metasurface array:

[0048] 2.1) Construct the weight coding matrix B q of the metasurface sub-array U q :

[0049]

[0050] Among them, represents the weight coding of the m-th element of the coded metasurface sub-array for the n x -th time, and n X is the number of times the coded metasurface sub-array encodes the incident signal in one snapshot, 1≤n x ≤n X .

[0051] 2.2) Construct the wave path difference diagonal matrix G q of the metasurface sub-array U q ;

[0052]

[0053] Among them, g qm = exp(-j2πw qm ), representing the wave path difference between the m-th element and the receiving feed in the q-th coded metasurface sub-array, and w qm represents the distance between the m-th element and the receiving feed in the q-th sub-array.

[0054] 2.3) Assume that there are K narrowband signals emitted by far-field signal sources in space, and use the elements in the sub-array U q to sample the target signal in space to obtain the sub-array received signal Y q (t):

[0055] Y q (t)=[Y q1 (t),Y q2 (t),…,Y qm (t),…,Y qM (t)] T,

[0056] Among them, Y qm (t) represents the received signal of the m-th array element in the subarray U q , t represents discrete time, 1 ≤ t ≤ L, L represents the number of sampling points of the signal in the time domain, [·] T represents the transpose operation, the value range of m is: 1 ≤ m ≤ M, and the value range of K is: 1 ≤ K ≤ (Q1 + Q2)M;

[0057] 2.4) Decompose the received signal Y q (t) of the subarray into:

[0058] Y q (t) = B q G q A q (θ)s(t) + N q ,

[0059] Among them, A q (θ) represents the array manifold of the coded metasurface subarray U q , N q represents the white noise received by the coded metasurface subarray U q . When using a traditional array to receive signals, B q G q = I, where I is the identity diagonal matrix;

[0060] 2.5) Use all the received signals Y q (t) of the subarrays to jointly form the received signal of the distributed 1-bit coded metasurface array U:

[0061]

[0062] Step 3, construct the measurement vector of the received signal Y(t) of the distributed 1-bit coded metasurface array

[0063] 3.1) Use the received signal Y q (t) of the subarray to calculate the subarray covariance matrix

[0064]

[0065] Among them, [·] H represents the conjugate transpose operation;

[0066] 3.2) According to the covariance matrix construct the direction finding vector of the received signal Y(t) of the distributed 1-bit coded metasurface array

[0067]

[0068] wherein, is the direction finding vector of the q-th sub-array, and vec{·} represents the operation of straightening a matrix by column;

[0069] Step 4, construct the array manifold dictionary of the distributed 1-bit coded metasurface array U

[0070] 4.1) Adopt the spatial domain division method, and according to the spatial domain sparse characteristics of the signal source, equally divide the observed spatial domain [-90°, 90°] into V fixed angle values wherein, V >> K, represents the v-th fixed angle value;

[0071] 4.2) Construct the wave path difference offset vector of the sub-array

[0072]

[0073] wherein, represents the wave path difference offset vector of the m-th element of the sub-array U q

[0074] 4.3) Through the weight coding matrix B q of the sub-array U q and the wave path difference diagonal matrix G q as well as the wave path difference offset vector construct the steering vector q corresponding to the sub-array U

[0075]

[0076] 4.4) Calculate the Kronecker product q of the steering vector of the sub-array U

[0077]

[0078] wherein, represents the Kronecker product operation;

[0079] 4.5) Use the Kronecker product q of the steering vectors at all angles in the observed spatial domain of the sub-array U to construct the dictionary matrix

[0080]

[0081] wherein,​

[0082] 4.6) Use all the sub-array manifold dictionaries to jointly form the array manifold dictionary of the distributed 1-bit coded metasurface array

[0083]

[0084] where represents the dictionary matrix of the q-th sub-array.

[0085] Step 5, obtain the direction-of-arrival (DOA) estimate of the signal based on the compressive sensing method

[0086] 5.1) Calculate the target vector X = [X1,..., X v ,..., X V T ;

[0087] 5.1.1) Adopt the formula for solving the convex optimization problem, and construct the constraint condition through the measurement vector and the array manifold dictionary :

[0088]

[0089] where ||·||2 represents the 2-norm of the vector, and ε represents the noise estimate value;

[0090] 5.1.2) Calculate the minimum value of the 1-norm of the target vector X, min||X||1, based on the constraint condition, and obtain the optimal value of the target vector X = [X1,..., X v ,..., X V T , and the formula is as follows:

[0091] min||X||1

[0092]

[0093] where min represents finding the minimum value, s.t. represents the constraint relationship, and ||·||1 represents the 1-norm of the vector.

[0094] 5.2) Use the value of as the x-axis coordinate, and use the target vector X = [X1,..., X v ,..., X V T ​​​The value is the y-axis coordinate. An amplitude spectrum diagram is plotted, and the top K spectral peaks with larger amplitudes are found from this amplitude spectrum diagram in descending order. The x-axis coordinates corresponding to the peak points of these spectral peaks are the estimated values of the directions of arrival of the K far-field signals sought. where represents the direction of arrival of the k-th signal, where 1 ≤ k ≤ K.

[0095] The above description is only a specific example of the present invention and does not constitute any limitation to the present invention. Obviously, for professionals in the field, after understanding the content and principle of the present invention, various modifications and changes in form and details may be made without departing from the principle and structure of the present invention. However, these corrections and changes based on the idea of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A method for estimating the direction of arrival of a signal of a 1-bit coding metasurface array based on distributed arrangement, characterized in that Including: (1) Constructing a distributed 1-bit coded metasurface array U: (1a) Constructing a 1-bit coded metasurface sub-array formed by linearly arranging M 1-bit coded metasurface elements, and constructing a traditional sub-array formed by linearly arranging M traditional elements. The distance between any two adjacent elements of each sub-array is d, where d ≤ λ / 2, λ is the wavelength of the narrowband signal incident on the array, and the value range of M is: M ≥ 2; (1b) It is formed by randomly distributing and arranging Q1 1-bit encoded metasurface sub-arrays and Q2 traditional sub-arrays on a spatial plane to form a distributed 1-bit encoded metasurface array. Among them, U q represents the q-th sub-array of the distributed array U, and is defined as representing the sub-array U q the angular offset from the horizontal plane, Q1 ≥ 1, Q2 ≥ 1, 2 ≤ q ≤ Q1 + Q2; (2) Obtaining the received signal Y(t) of the distributed 1-bit coded metasurface array: (2a) Assume that there are narrowband signals emitted by K far-field signal sources in space, and the array elements in sub-array U q are used to sample the target signal in space to obtain the received signal Y q (t) of the sub-array: Y q (t) = [Y q1 (t), Y q2 (t), …, Y qm (t), …, Y qM (t)] T , Among them, Y qm (t) represents the received signal of the m-th array element in the sub-array U q where t represents discrete time, 1 ≤ t ≤ L, L represents the number of sampling points of the signal in the time domain, [·] T represents the transpose operation, the value range of m is: 1 ≤ m ≤ M, and the value range of K is: 1 ≤ K ≤ (Q1 + Q2)M; (2b) Receive the signal Y with all sub-arrays q (t) jointly constitute the received signal of the distributed 1-bit coded metasurface array U: (3)Construct the direction vector of the received signal Y(t) by the distributed 1-bit coded metasurface array (3a) Receive the signal Y using the subarray q (t), and calculate the subarray covariance matrix where, [·] H denotes the conjugate transpose operation; (3b) According to the covariance matrix Construct the direction vector of the received signal Y(t) of the distributed 1-bit coded metasurface array: Among them, is the direction finding vector of the q-th subarray, and vec{·} represents the operation of straightening a matrix by columns; (4) Construct the array manifold dictionary of the distributed 1-bit coded metasurface array U (4a) Adopt the spatial domain division method, and according to the spatial domain sparsity characteristics of the signal source, equally divide the observed spatial domain [-90°, 90°] into V angular values with fixed values. where V >> K, represents the v-th fixed angular value; (4b) via sub-array U q and a fixed angle value construct the steering vector corresponding to sub-array U q where B denotes the array weight encoding matrix of the metasurface sub-array, and G q is the wave path difference matrix introduced by the distance from each element of the metasurface sub-array to the receiving feed, q is the wave path difference offset vector of this sub-array. If this sub-array is a conventional array, the steering vector I represents the diagonal identity matrix;​ (4c) Calculate the steering vector of subarray U q of the Kronecker product of Among them, represents the Kronecker product operation; (4d) Using subarray U q Kronecker product of steering vectors at all angles in the observation airspace Construct subarray U q Dictionary matrix of Among them, (4e) Use all the sub-array dictionary matrices to jointly form the array manifold dictionary of the distributed 1-bit coded metasurface array (5) Obtain the direction-of-arrival estimation value of the signal based on the compressive sensing method (5a) Using the formula for solving the convex optimization problem, through the measurement vector and the array manifold dictionary to construct the constraint condition: Calculate the target vector X = [X1,..., X v ,..., X V T , where, ||·||2 represents the 2-norm of the vector, and ε represents the noise estimate value;​ (5b)With as the x-axis coordinate value, and with the target vector X = [X1,..., X v ,..., X V T as the y-axis coordinate value, plot the amplitude spectrum diagram, and find the top K spectral peaks with larger amplitudes in descending order from this amplitude spectrum diagram. The x-axis coordinate values corresponding to the peak points of these spectral peaks are the estimated values of the directions of arrival of the K far-field signals where represents the direction of arrival of the k-th signal, 1 ≤ k ≤ K.​ 2. The method according to claim 1, characterized in that, The wave path difference offset vector of the neutron sub-array (4b) is as follows: is expressed as follows: Among them, represents the path difference offset vector of the m-th array element of the sub-array U q ​ 3. The method according to claim 1, wherein The array weight coding matrix B of the 1-bit coded metasurface of the (4b) subarray q , is expressed as follows: Among them, represents the weight coding of the n-th time of the m-th array element of the sub-array, x where n X is the number of times the coding metasurface sub-array encodes the incident signal in one snapshot, and 1 ≤ n x ≤ n X .

4. The method according to claim 1, wherein The wave path difference diagonal matrix G introduced by the distance from each element of the neutron array (4b) to the receiving feed q , is expressed as follows: where, g qm = exp(-j2πw qm ), representing the optical path difference between the m-th element of the q-th coded metasurface subarray and the receiving feed, w qm represents the distance from the m-th element in the q-th subarray to the receiving feed.

5. The method according to claim 1, wherein The said (4e) with all jointly constitute the array manifold dictionary of the distributed 1-bit coding metasurface array which is expressed as follows: Among them, represents the array manifold dictionary of the q-th subarray.

6. The method according to claim 1, characterized in that, In (5a), a convex optimization problem is formulated, and the target vector X is calculated through the measurement vector and the array manifold dictionary as follows: min||X||1 where ||·||1 represents the 1-norm of the vector, min represents finding the minimum value, and s.t. represents the constraint relationship.

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