A 1-bit low-complexity array structure-based DOA estimation method based on atomic norm minimization

Abstract

The application provides a 1-bit low-complexity array structure-based DOA estimation method based on atomic norm minimization, a two-stage partially connected hybrid analog-digital structure is constructed at a receiving end, and a 1-bit ADC is used in an ADC part; a TL-SC HAD array is used to receive a signal and modeling is performed; an initial value of a phase shifter network is designed and an output signal is obtained; dimension reduction is performed according to the output signal, an atomic norm minimization problem is established, and an angle estimation value is obtained according to recovered noiseless components; the obtained angle estimation value is used to update the weight of the phase shifter network, and angle estimation is repeatedly performed until a maximum iteration number or a satisfactory estimation precision is reached, and a final angle estimation value is obtained. The method can reduce the hardware cost and power consumption of the array, and can also achieve high estimation precision.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically a DOA estimation method based on a 1-bit low-complexity array structure with atomic norm minimization, which can be used for DOA estimation scenarios of large-scale / ultra-large-scale arrays. Background Technology

[0002] Direction-of-Arrival (DOA) estimation is an important branch of array signal processing. It uses array antennas to receive spatial signals and processes the received signals through statistical signal processing techniques and various optimization methods to recover the direction of arrival information of the incident signal. It has wide applications in radar, sonar, voice and wireless communication.

[0003] There are generally two approaches to improving the accuracy of DOA estimation. One is to develop high-resolution DOA estimation algorithms, and the other is to optimize the array by increasing the array size to improve estimation accuracy. In recent years, large-scale / very large-scale antenna arrays with a large number of elements have attracted increasing attention due to their ability to provide extremely high DOA estimation accuracy. However, the sheer number of antennas requires a matching number of radio frequency (RF) links, including expensive components such as analog-to-digital converters (ADCs), which significantly increases hardware costs and energy consumption.

[0004] To address the issues of high hardware cost and power consumption, Hybrid Analog and Digital (HAD) array structures using finite RF chains are widely adopted. In a partially connected (SC) HAD structure, each antenna is connected to a phase shifter, and multiple phase shifters are connected to an RF chain, reducing the number of required RF chains. To further reduce the complexity and power consumption of the array structure, the use of low-precision ADCs in the ADC section has received widespread attention. One-bit quantization is an extreme case where the received signal is compared to a pre-set threshold; if the signal is greater than the threshold, it outputs 1, and if it is less than or equal to the threshold, it outputs -1. This threshold is typically set to 0, but can also be set to a time-varying threshold. After quantization, a 1-bit ADC retains only the symbolic information of the received data, reducing the amount of information transmitted and stored, and improving feasibility in large-scale / very large-scale array scenarios.

[0005] However, the SC HAD structure introduces phase ambiguity, requiring multiple time slots to eliminate it. As the number of subarray antennas increases, the DOA measurement delay grows linearly. Furthermore, 1-bit quantization only retains the symbol information of the received signal, posing a challenge to DOA estimation under the SC HAD structure.

[0006] The above-mentioned problems should be considered and solved in the process of DOA estimation of 1-bit low-complexity array structures based on atomic norm minimization. Summary of the Invention

[0007] The purpose of this invention is to provide a DOA estimation method based on a 1-bit low-complexity array structure with atomic norm minimization, which solves the problems in the prior art where existing HAD architectures cause phase ambiguity and the use of a 1-bit ADC reduces estimation accuracy.

[0008] The technical solution of this invention is:

[0009] A method for estimating the Data Occurrence (DOA) of a 1-bit quantized low-complexity array structure based on atomic norm minimization includes the following steps:

[0010] S1. At the receiving end, a 1-bit hybrid analog-digital array is constructed, wherein the array structure adopts a two-level partially connected hybrid analog-digital structure, and the ADC part uses a 1-bit ADC.

[0011] S2. Receive the incident signal using the constructed array and model it;

[0012] S3. Design the initial values ​​of the analog phase shifter network and obtain the output signal;

[0013] S4, to Quick Shot Output Signal Perform dimensionality reduction;

[0014] S5. Establish the atomic norm minimization problem and solve it to recover the unquantized noiseless components;

[0015] S6. Based on the recovered noise-free components Obtain the angle estimate. ;

[0016] S7, using the result obtained in step S6 Replace the original phase in step S3, and repeat steps S4 to S6 until the maximum number of iterations or satisfactory estimation accuracy is reached, to obtain the final angle estimate.

[0017] Furthermore, in step S1, a 1-bit hybrid analog-digital array is constructed at the receiving end, specifically as follows:

[0018] S11, Hybrid Analog-Digital Array Includes Each array element is divided into Subarrays;

[0019] S12, The first subarray in the subarray contains Each array element is connected to an RF chain. In each of the subarrays, there are Each array element adopts an SC HAD structure, in which ;

[0020] S13. The output of each RF chain is considered as the output of a virtual array element. The total number of RF chains is... The ADC section deploys a 1-bit ADC.

[0021] Further, in step S2, the incident signal is received and modeled using the constructed array, specifically,

[0022] S21, Assuming the far-field narrowband signal is in azimuth angle Given the incident conditions, the array received signal at time t can be expressed as:

[0023] in It is the antenna receiving the signal. The signal source is of unknown direction. It is an imaginary number. For carrier frequency, It is additive white Gaussian noise. It is an array manifold vector, denoted as Where e is the natural constant, N is the number of array elements, and (·) T Indicates transpose;

[0024] S22. After phase calibration via an analog phase shifter network, the received signal is represented as follows:

[0025]

[0026] in,(·) H This indicates the conjugate transpose. It is a simulated beamforming matrix, represented as

[0027] ,in , ,express 3D identity matrix express

[0028] No. The simulated beamforming vectors of each subarray are represented as follows: ,in, For the first The first subarray The phase of each phase shifter Harmony The first subarray and the second subarray are respectively The number of elements in each subarray;

[0029] S23, RF signal After passing through a parallel RF chain, it is down-converted into a baseband signal. The signal is generated by a 1-bit ADC.

[0030]

[0031] in, This indicates two symbolic functions. The complex-valued element quantization function is expressed as follows: ,in, Represents the complex number Perform the real part operation. Represents the complex number Perform the imaginary part operation, the sign function is: The array output signal is then expressed as

[0032]

[0033] in, For output signal, , This represents the number of snapshots.

[0034] Further, in step S3, the initial values ​​of the analog phase shifter network are designed and the output signal is obtained, specifically as follows:

[0035] S31. Using the quantized data of the first subarray, an initial estimate can be obtained according to the existing method one-bit MUSIC. In an ideal situation, there is ;

[0036] S32, in At that time, this angle value is used to design the phase of the phase shifter network, that is...

[0037]

[0038] S33, No. The output signal of each subarray is

[0039]

[0040] in For the first Additive white Gaussian noise for each subarray The virtual corresponding to each RF chain output

[0041] The array element position set is ,in, For the first The index of each virtual array element. The output signals of each subarray, written in vector form, are

[0042]

[0043] in, It corresponds to a set The guide vector, for

[0044] The gain matrix of the subarray is ,in, To select a matrix,

[0045] The In the line, only The value at the corresponding position is 1, and the values ​​at the other positions are 0;

[0046] S34. Quantize the signal by 1 bit to obtain the output signal. ,

[0047] The output signal of the snap is .

[0048] Furthermore, in step S4, for The output signal of the snap is Dimensionality reduction, specifically, is... Perform singular value decomposition to obtain ,make Used to preserve the signal subspace, to obtain .

[0049] Furthermore, in step S5, the atomic norm minimization problem is established, and the solution to recover the unquantized noiseless component is specifically as follows:

[0050] S51. For the unquantized noise-free component that we want to recover, establish the atomic set as follows: , The atomic norm is expressed as ;

[0051] S52. Establishing the atomic norm minimization problem:

[0052]

[0053] in, The regularization parameter is used to solve for the noise-free component. .

[0054] Furthermore, in step 52, the noise-free component is obtained by solving the atomic norm minimization problem, specifically,

[0055] S521, The atomic norm minimization problem can be equivalently represented as the following optimization problem:

[0056]

[0057] in, For free variables, It is a vector The first element, It is by The first column constitutes

[0058] Toeplitz matrix and Let z represent the real part and the imaginary part, respectively.

[0059] S522. The optimization problem is solved using the ADMM method, and the optimization problem is rewritten as follows:

[0060]

[0061] in, and They represent The real and imaginary parts, and As an auxiliary variable;

[0062] S523, The augmented Lagrangian function of this optimization problem is:

[0063]

[0064] in, As a Lagrange multiplier, let

[0065] ,in, , , As a penalty factor;

[0066] S524, The augmented Lagrangian function yields the first... in ADMM. The update steps are as follows

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] in, , , , ,and

[0075] And consider and The corresponding update formula is subjected to eigenvalue decomposition, and all negative eigenvalues ​​are set to zero. ADMM is iterated until convergence, and the noise-free components are obtained. .

[0076] Further, in step S6, based on the recovered noise-free components... Obtain the angle estimate. Specifically, the angle estimation method uses the root-MUSIC algorithm to calculate... covariance matrix , to obtain Perform eigenvalue decomposition and sort the eigenvalues ​​in order of magnitude to obtain the signal subspace and noise subspace, and construct the polynomial. ,in, , Find the roots of the polynomial and take the root that is closest to the unit circle. ,pass The angle estimate is obtained.

[0077] The beneficial effects of this invention are:

[0078] I. This DOA estimation method based on a 1-bit low-complexity array structure with atomic norm minimization fully utilizes the characteristics of nested arrays through a TL-SC HAD array architecture, which can effectively avoid phase ambiguity and beam scanning problems. Furthermore, the use of a 1-bit ADC in the ADC section can further reduce cost and complexity, while ensuring DOA estimation accuracy to a certain extent.

[0079] Second, this DOA estimation method based on the minimization of the atomic norm of a 1-bit low-complexity array structure is not affected by the grid mismatch effect and can avoid the error between the normalized covariance matrix and the unquantized covariance matrix obtained by the covariance matrix reconstruction method in the 1-bit ADC scenario, thus effectively improving the estimation accuracy. Attached Figure Description

[0080] Figure 1 This is a flowchart illustrating the DOA estimation method for a 1-bit low-complexity array structure based on atomic norm minimization, according to an embodiment of the present invention.

[0081] Figure 2 This is a schematic diagram of the 1-bit TL-SC HAD array architecture in the embodiment;

[0082] Figure 3 This is a schematic diagram comparing the performance of the DOA estimation method based on atomic norm minimization of a 1-bit low-complexity array structure described in the embodiment with other existing methods; Detailed Implementation

[0083] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0084] Example

[0085] A method for estimating DOA (Depth of Arrival) of a 1-bit low-complexity array structure based on atomic norm minimization, specifically including the following steps:

[0086] S1. At the receiving end, a 1-bit hybrid analog-digital array is constructed, wherein the array structure adopts a two-level partially connected hybrid analog-digital structure, and the ADC part uses a 1-bit ADC.

[0087] S11, Hybrid Analog-Digital Array Includes Each array element is divided into Subarrays;

[0088] S12, The first subarray in the subarray contains Each array element is connected to an RF unit.

[0089] In each of the subarrays, there are Each array element adopts an SC HAD structure, in which .

[0090] S13. The output of each RF chain is considered as the output of a virtual array element. The total number of RF chains is... The ADC section deploys a 1-bit ADC.

[0091] S2. Receive the incident signal using the constructed array and model it;

[0092] S21, Assuming the far-field narrowband signal is in azimuth angle Given the incident conditions, the array received signal at time t can be expressed as:

[0093]

[0094] in It is the antenna receiving the signal. The signal source is of unknown direction. It is an imaginary number. carrier

[0095] Rate, It is additive white Gaussian noise. It is an array manifold vector, representing Where e is the natural constant and N is the number of array elements. Indicates transpose;

[0096] S22. After phase calibration via an analog phase shifter network, the received signal is represented as follows:

[0097]

[0098] in, This indicates the conjugate transpose. It is a simulated beamforming matrix, represented as ,in, , express 3D identity matrix Let represent the simulated beamforming vector of the k-th subarray, as ,in, For the first The phase of the m-th phase shifter in the subarray Harmony The first subarray and the second subarray are respectively The number of elements in each subarray;

[0099] S23, RF signal The signal is down-converted to baseband signal via a parallel RF chain. The signal is generated by a 1-bit ADC.

[0100]

[0101] in, This indicates two symbolic functions. The complex-valued element quantization function is expressed as follows: ,in, This indicates that the real part of the complex number x is taken. This represents the operation of taking the imaginary part of a complex number x, with the sign function being: The array output signal is then expressed as

[0102]

[0103] in, For output signal, , This represents the number of snapshots.

[0104] S3. Design the initial values ​​of the analog phase shifter network and obtain the output signal;

[0105] S31. Using the quantized data of the first subarray, a one-bit MUSIC can be obtained according to the existing method.

[0106] Initial estimate In an ideal situation, there is ;

[0107] S32, in At that time, this angle value is used to design the phase of the phase shifter network, that is...

[0108]

[0109] S33, the output signal of the i-th subarray is

[0110]

[0111] in, For the first Additive white Gaussian noise for each subarray The virtual corresponding to each RF chain output

[0112] The array element position set is ,in, For the first The index of each virtual array element. The output signals of each subarray, written in vector form, are

[0113]

[0114] in, It corresponds to a set The guide vector, for

[0115] The gain matrix of the subarray is specifically... ,in, To select a matrix, , The In the line, only The value at the corresponding position is 1, and the values ​​at the other positions are 0;

[0116] S34. Quantize the signal by 1 bit to obtain the output signal. , The output signal of the snap is .

[0117] S4, to The output signal of the snapshot is reduced in dimension;

[0118] In step S4, for Quick Shot Output Signal Dimensionality reduction, specifically, for Perform singular value decomposition to obtain ,make Used to preserve the signal subspace, to obtain .

[0119] S5. Establish the atomic norm minimization problem and solve it to recover the unquantized noiseless components;

[0120] S51, for the unquantized noise-free component that we wish to recover is Establish an atomic set as , The atomic norm is expressed as ;

[0121] S52. Establishing the atomic norm minimization problem:

[0122]

[0123] in, The regularization parameter is used to solve for the noise-free component. .

[0124] In step 52, the noise-free component is obtained by solving the atomic norm minimization problem. Specifically

[0125] S521, The atomic norm minimization problem can be equivalently represented as the following optimization problem:

[0126]

[0127] in, For free variables, It is a vector The first element, It is by The first column constitutes

[0128] Toeplitz matrix and They represent The real and imaginary parts;

[0129] S522. The optimization problem is solved using the ADMM method, and the optimization problem is rewritten as follows:

[0130]

[0131] in, and They represent The real and imaginary parts, and As an auxiliary variable;

[0132] S523, The augmented Lagrangian function of this optimization problem is:

[0133]

[0134] in, As a Lagrange multiplier, let ,in, , , As a penalty factor;

[0135] S524, The augmented Lagrangian function yields the first... in ADMM. The update steps are as follows

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] in, , , , And consider and The corresponding update formula is subjected to eigenvalue decomposition, and all negative eigenvalues ​​are set to zero. ADMM is iterated until convergence, and the noise-free components are obtained. .

[0144] S6. Based on the recovered noise-free components Obtain the angle estimate. ;

[0145] In step S6, based on the recovered noise-free components To obtain the estimated angle value Specifically, the angle estimation method uses the root-MUSIC algorithm to calculate... covariance matrix , to obtain Perform eigenvalue decomposition, sort the eigenvalues ​​in order of magnitude to obtain the signal subspace and noise subspace, and construct the polynomial. ,in, , Find the roots of the polynomial and take the root that is closest to the unit circle. ,pass The angle estimate is obtained.

[0146] S7, using the result obtained in step S6 Replace the original phase in step S3, and repeat steps S4 to S6 until the maximum number of iterations or satisfactory estimation accuracy is reached, to obtain the final angle estimate.

[0147] This DOA estimation method based on a 1-bit low-complexity array structure with atomic norm minimization fully utilizes the characteristics of nested arrays through a TL-SC HAD array architecture, which can effectively avoid phase ambiguity and beam scanning problems. Furthermore, the use of a 1-bit ADC in the ADC section can further reduce cost and complexity, while ensuring DOA estimation accuracy to a certain extent.

[0148] This DOA estimation method based on a 1-bit low-complexity array structure minimized by atomic norm can effectively improve estimation accuracy by avoiding the error between the normalized covariance matrix and the unquantized covariance matrix obtained by the covariance matrix reconstruction method in the 1-bit ADC scenario through a matching effect.

[0149] The effects of the present invention will be further described below with reference to simulation examples.

[0150] Simulation example: A far-field narrowband signal is incident at a direction of 10°. The array contains 120 array elements, divided into 11 subarrays. The first subarray has 10 array elements and 200 snapshots.

[0151] The DOA estimation method of this embodiment based on atomic norm minimization of a 1-bit low-complexity array structure is compared with the estimation performance of other existing methods as follows: Figure 3 As shown. Among them, the covariance reconstruction method is a 1-bit estimation method that uses the arcsine rule to reconstruct the covariance matrix; the infinite-precision quantization estimation method indicates that the ADC part in the array structure uses an infinite-precision ADC, and the estimation method is a subspace-based estimation method based on the synthetic array; in the nested array 1-bit estimation method, the structure of the nested array is the same as the virtual array structure considered by the RF chain output, and the angle estimation uses the 1-bit estimation method of covariance matrix reconstruction. Figure 3It can be seen that the proposed method can achieve estimation performance comparable to that of the infinite precision quantization estimation method under low signal-to-noise ratio conditions. Although it is greatly affected by quantization noise at high signal-to-noise ratio conditions, it can still achieve high estimation accuracy. The estimation accuracy is better than that of the covariance reconstruction method and the nested matrix 1-bit estimation method. The above results demonstrate the effectiveness of the proposed method.

[0152] In summary, the proposed method combines the nested array concept with the HAD array structure and uses a 1-bit ADC in the ADC section, which can effectively reduce hardware costs and complexity. At the same time, the proposed method can also achieve high estimation accuracy.

[0153] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for estimating the DOA of a 1-bit low-complexity array structure based on atomic norm minimization, characterized in that: The process includes the following steps: S1, constructing a 1-bit hybrid analog-digital array at the receiving end, wherein the array structure adopts a two-level partially connected hybrid analog-digital structure, specifically, the hybrid analog-digital array consists of a total of Each array element It consists of several subarrays, the first subarray being composed of... It consists of several array elements, each connected to an RF chain; the rest... All subarrays are constructed using the SC HAD structure. Each subarray consists of several array elements, and all elements of each subarray are connected to a single RF chain. The total number of RF chains is The ADC section deploys a 1-bit ADC; S2. Receive the incident signal using the constructed array and model it; S3. Design the initial values ​​of the analog phase shifter network and obtain the output signal; S4, to Quick Shot Output Signal Perform dimensionality reduction; S5. Establish the atomic norm minimization problem and solve it to recover the unquantized noiseless components; S6. Based on the recovered noise-free components Obtain the angle estimate. ; S7, using the result obtained in step S6 Replace the original phase in step S3, and repeat steps S4 to S6 until the maximum number of iterations or satisfactory estimation accuracy is reached, to obtain the final angle estimate.

2. The DOA estimation method for a 1-bit low-complexity array structure based on atomic norm minimization as described in claim 1, characterized in that: In step S2, the incident signal is received and modeled using the constructed array. Specifically, in step S21, it is assumed that the far-field narrowband signal is received at an azimuth angle. Given the incident conditions, the array received signal at time t can be expressed as: in It is the antenna receiving the signal. For signal sources of unknown direction, It is an imaginary number. For carrier frequency, It is additive white Gaussian noise. It is an array manifold vector, denoted as Where e is the natural constant, N is the number of array elements, and (·) T Indicates transpose; S22. After phase calibration via an analog phase shifter network, the received signal is represented as follows: in,(·) H This indicates the conjugate transpose. It is a simulated beamforming matrix, represented as in , express 3D identity matrix Indicates the first The simulated beamforming vectors of each subarray are represented as follows: ,in For the first The first subarray The phase of each phase shifter Harmony The first subarray and the second subarray are respectively The number of elements in each subarray; S23, RF signal After passing through a parallel RF chain, it is down-converted into a baseband signal. This signal is generated by a 1-bit ADC. in, This indicates two symbolic functions. The complex-valued element quantization function is expressed as follows: ,in, Represents the complex number Perform the real part operation. Represents the complex number Perform the imaginary part operation, the sign function is: The array output signal is then expressed as in, For output signal, , This represents the number of snapshots.

3. The DOA estimation method for a 1-bit low-complexity array structure based on atomic norm minimization as described in claim 2, characterized in that: In step S3, the initial values ​​of the analog phase shifter network are designed and the output signal is obtained, specifically as follows: S31. Using the quantized data of the first subarray, an initial estimate can be obtained according to the existing method one-bit MUSIC. In an ideal situation, there is ; S32, in At that time, the phase of the phase shifter network is designed using angle values, that is... S33, No. The output signal of each subarray is in For the first Additive white Gaussian noise for each subarray The set of virtual element positions corresponding to the outputs of each RF chain is: ,in, For the first The index of each virtual array element. The output signals of each subarray, written in vector form, are in, It corresponds to a set The guiding vector, where D is a submatrix. The gain matrix of the column, specifically in, To select a matrix, , The In the line, only The value at the corresponding position is 1, and the values ​​at the other positions are 0; S34. Quantize the signal by 1 bit to obtain the output signal. , The output signal of the snap is .

4. A DOA estimation method for a 1-bit low-complexity array structure based on atomic norm minimization as described in any one of claims 1-3, characterized in that: In step S4, for Quick Shot Output Signal Dimensionality reduction, specifically, for Perform singular value decomposition to obtain ,make Used to preserve the signal subspace, to obtain .

5. The DOA estimation method for a 1-bit low-complexity array structure based on atomic norm minimization as described in claim 3, characterized in that: In step S5, an atomic norm minimization problem is established, and the unquantized noise-free component is recovered by solving it. Specifically, S51, for the unquantized noise-free component that we wish to recover is Establish an atomic set as , The atomic norm is expressed as ； S52. Establishing the atomic norm minimization problem: in, The regularization parameter is used to solve for the noise-free component. .

6. The DOA estimation method for a 1-bit low-complexity array structure based on atomic norm minimization as described in claim 5, characterized in that: In step 52, the noise-free component is obtained by solving the atomic norm minimization problem. Specifically, the S521 atomic norm minimization problem can be equivalently represented as the following optimization problem: in, For free variables, It is a vector The first element, It is by The Toeplitz matrix formed by the first column. and Let z represent the real and imaginary parts, respectively; S522, the optimization problem is solved using the ADMM method, and the optimization problem is rewritten as... in, and They represent The real and imaginary parts, α and α are auxiliary variables; S523, The augmented Lagrangian function of this optimization problem is: in, As a Lagrange multiplier, let That middle , , As a penalty factor; S524, The augmented Lagrangian function yields the first... in ADMM. The update steps are as follows in, , , , and test consider and The corresponding update formula is subjected to eigenvalue decomposition, and all negative eigenvalues ​​are set to zero. ADMM is iterated until convergence, and the noise-free components are obtained. .

7. The DOA estimation method for a 1-bit low-complexity array structure based on atomic norm minimization as described in claim 1, characterized in that: In step S6, based on the recovered noise-free components Obtain the angle estimate. Specifically, the angle estimation method uses the root-MUSIC algorithm to calculate... covariance matrix , to obtain Perform eigenvalue Decompose the eigenvalues ​​and sort them in order of magnitude to obtain the signal subspace and noise subspace, and construct the polynomial. ,in, Find the roots of the polynomial and take The root closest to the unit circle ,pass The angle estimate is obtained.

Images