DOA estimation method for single-bit sensor array

Abstract

The invention discloses a DOA (direction of arrival) estimation method for a single-bit sensor array, which relates to the technical field of signal processing and comprises the following steps: acquiring an original signal, performing single-bit quantization on the original signal to obtain a quantization result, and calculating a covariance matrix of the quantization result; vectorizing the covariance matrix to generate a column vector; performing DFT operation on the column vector to obtain frequency spectrum information; obtaining a peak value of the frequency spectrum information and a position of the peak value through a findpeaks function, performing processing to obtain an angle of arrival position, searching left and right boundary positions of the angle of arrival position, and determining an angle of arrival interval; and carrying out frequency refinement on the arrival angle interval by using DTFT, carrying out spectrum peak search on the refined arrival angle interval, and carrying out calculation to obtain final angle estimation. The method is low in calculation complexity, the precision of the estimated angle is higher than that of the algorithm of the same type, and meanwhile the method can be expanded to other nonlinear array structures.

Description

[0001] This application is a divisional application. The application number of the original application is 202410171570.0, the application date is February 6, 2024, and the name of the invention is “A single-bit DOA estimation method and system based on discrete-time Fourier transform”. Technical Field

[0002] The present invention relates to the field of signal processing technology, and more particularly to a DOA estimation method for a single-bit sensor array. Background Art

[0003] Array signal processing is to place multiple sensors at different positions in space to form a sensor array, and use this array to receive and process the spatial signal field to extract the signals received by the array and their characteristic information, while suppressing interference and noise or information of no interest.

[0004] Direction-of-arrival (DOA) estimation is a major research topic in array signal processing and a crucial task in many fields, including radar, communications, and sonar. It has long been a research priority. Traditional DOA estimation algorithms, including MUSIC.ESPRIT and related derivatives, are computationally limited and cannot be directly applied to large-scale arrays. Therefore, DOA estimation algorithms based on parameterized Fourier transforms have shown advantages. Furthermore, with the continuous advancement of research on large-scale arrays, the aperture of array systems has gradually increased, and the number of array elements has also gradually increased. Therefore, due to the considerations of energy consumption and system design complexity, single-bit quantization has attracted attention from scholars both domestically and internationally. However, single-bit correlation algorithms suffer from high computational cost, sensitivity to grid size, and the requirement for a large number of snapshots. While DFT correlation algorithms offer lower computational complexity, they suffer from low angular accuracy when the signal contains multiple target sources with very close incident angles.

[0005] Therefore, how to improve the accuracy of direction of arrival angle estimation is an urgent problem that those skilled in the art need to solve. Summary of the Invention

[0006] In view of this, the present invention provides a DOA estimation method for a single-bit sensor array, which refines the frequency of the rough DFT estimation result through DTFT, further achieving fine estimation, thereby greatly reducing the amount of calculation while ensuring the estimation accuracy.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A DOA estimation method for a single-bit sensor array, comprising:

[0009] S1: Acquire an original signal, perform single-bit quantization on the original signal to obtain a quantization result, and calculate a covariance matrix of the quantization result;

[0010] S2: vectorize the covariance matrix to generate a column vector;

[0011] S3: Perform DFT operation on the column vector to obtain spectrum information;

[0012] S4: obtaining the peaks and peak positions of the spectrum information by using the findpeaks function, processing the peaks and peak positions to obtain the arrival angle position, and finding the left and right boundary positions of the arrival angle position to determine the arrival angle interval;

[0013] S5: Using DTFT to perform frequency refinement on the arrival angle interval, and performing spectrum peak search on the refined arrival angle interval to calculate and obtain a final angle estimate.

[0014] Preferably, the S1 specifically includes:

[0015] Denote a single snapshot of the original signal as x, then:

[0016] x=As+n;

[0017] In the formula, A=[α(θ1),...,α(θ K )]∈C M×K represents the steering matrix, α(θ K ) is the steering vector, s=[s1,...,s K ] T Represents a K×1 complex-valued signal, where different signals are independent of each other and have a variance of Circularly symmetric complex Gaussian distribution, n∈C M×1 The variance is Additive Gaussian white noise;

[0018] Next, quantize x to a single bit to get y:

[0019]

[0020] Where Re(·) and Im(·) represent the real and imaginary parts of a vector or matrix, respectively, and sign(·) is the sign function. The estimated value of the covariance matrix of y is expressed as Then we have:

[0021]

[0022] Where T is the number of snapshots and (·)H represents the conjugate transpose operation of a vector or matrix.

[0023] Preferably, the S2 specifically includes The covariance matrix is ​​vectorized and Each column of is stacked in turn to produce a column vector.

[0024] Preferably, S3 specifically includes setting the number of DFT samples to N=1024, calculating the DFT matrix and performing normalization operation, then padding the column vector with zeros to make its length the same as N, and finally performing DFT operation on the column vector to obtain spectrum information.

[0025] Preferably, the S4 specifically includes: finding the peak value and the position of the peak value in the spectrum information by using the findpeaks function, subtracting the peak value from the position Then, the peak values ​​are sorted in descending order from large to small, and then the sorted peak values ​​are mapped to indexes through traversal, and the indexes are sorted in descending order. The first fixed peak positions are the arrival angle positions; the boundary positions of the arrival angle positions are found and stored in an array.

[0026] Preferably, the step of finding the boundary position specifically includes:

[0027] Find the right boundary position: For the right side, start from the peak position and traverse to the right, find the first position where the difference between the current peak and the traversed position is greater than 1, and store this position and its value in the right array; if the difference is less than or equal to 1, find the position with the smallest value between the peak position and the adjacent peak position on the right, and store this position and its value in the right array;

[0028] Find the left boundary position: For the left side, if the current peak is the first peak, directly set the left boundary to the first point of the signal, and store the current peak and the left boundary in the left array; if it is not the first peak, start from the previous peak position to the current peak position, find the first position where the difference between the current peak and the traversed position is greater than 1, and store this position and its value in the left array; if the difference is less than or equal to 1, find the position with the smallest value between the adjacent peak position on the left, and store this position and its value in the left array.

[0029] A single-bit DOA estimation system based on discrete-time Fourier transform, comprising:

[0030] A covariance matrix acquisition module acquires an original signal, performs single-bit quantization on the original signal to obtain a quantization result, and calculates a covariance matrix of the quantization result;

[0031] A column vector generation module, vectorizing the covariance matrix to generate a column vector;

[0032] A spectrum information acquisition module performs a DFT operation on the column vector to obtain spectrum information;

[0033] An interval confirmation module obtains the peak and peak positions of the spectrum information through the findpeaks function, processes the peak and peak positions to obtain the arrival angle position, and finds the left and right boundary positions of the arrival angle position to determine the arrival angle interval;

[0034] The angle acquisition module uses DTFT to perform frequency refinement on the arrival angle interval, performs spectrum peak search on the refined arrival angle interval, and calculates and obtains the final angle estimation.

[0035] It can be seen from the above technical solution that compared with the existing technology, the present invention considers the low-complexity one-bit DOA estimation problem of MULA with a single snapshot, and proposes a single-bit DOA estimation system based on discrete-time Fourier transform. The result of the rough DFT estimation is frequency-refined by DTFT, which further realizes fine estimation. At the same time, the received signal is single-bit quantized. The resulting method is called one-bit DTFT. This method is simple and easy to implement. High-precision DOA estimation of MULA can be obtained through one snapshot, and the computational complexity is significantly lower than the existing one-bit DOA estimation method. In addition, the proposed method is easily extended to multiple snapshot scenarios, and increasing the number of snapshots can further improve the estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0037] Figure 1 The accompanying drawing is a schematic diagram of the overall process provided by the present invention.

[0038] Figure 2 The accompanying figure is a spectrum diagram of the interval after DTFT refinement when the random angle θ is 31.30 provided by the present invention.

[0039] Figure 3 The accompanying figure is a comparison diagram of the mean absolute error of the DOA estimation results of random angles of different algorithms provided by the present invention as the signal-to-noise ratio changes.

[0040] Figure 4 The accompanying figure is a comparison diagram of the mean absolute error of the DOA estimation results of fixed angles provided by different algorithms as the signal-to-noise ratio changes.

[0041] Figure 5 The accompanying figure is a comparison diagram of the mean absolute error of the DOA estimation results of the One-bit DFT algorithm provided by the present invention as a function of the number of snapshots.

[0042] Figure 6 The accompanying figure is a comparison diagram of the mean absolute error of the DOA estimation result of the present invention as a function of the number of snapshots.

[0043] Figure 7 The accompanying drawing is a comparison chart of the average running time of different algorithms provided by the present invention. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0045] The embodiment of the present invention discloses a DOA estimation method for a single-bit sensor array, such as Figure 1 As shown, including:

[0046] S1: Obtain the original signal, perform single-bit quantization on the original signal to obtain a quantization result, and calculate the covariance matrix of the quantization result;

[0047] S2: Vectorize the covariance matrix to generate a column vector;

[0048] S3: Perform DFT operation on the column vector to obtain spectrum information;

[0049] S4: Obtain the peaks and peak positions of the spectrum information using the findpeaks function. After processing the peaks and peak positions, obtain the arrival angle position. Then find the left and right boundary positions of the arrival angle position to determine the arrival angle range.

[0050] S5: If Figure 2 As shown, the frequency of the arrival angle interval is refined using DTFT, and the spectrum peak search is performed on the refined arrival angle interval to calculate and obtain the final angle estimation.

[0051] In a specific embodiment, S1 specifically includes:

[0052] Denote a single snapshot of the original signal as x, then:

[0053] x=As+n;

[0054] In the formula, A=[α(θ1),...,α(θ K )]∈C M×Krepresents the steering matrix, α(θ K ) is the steering vector, s=[s1,...,s K ] T Represents a K×1 complex-valued signal, where different signals are independent of each other and have a variance of Circularly symmetric complex Gaussian distribution, n∈C M×1 Denotes the variance as δ n 2 Additive Gaussian white noise;

[0055] Next, quantize x to a single bit to get y:

[0056]

[0057] Where Re(·) and Im(·) represent the real and imaginary parts of a vector or matrix, respectively, and sign(·) is the sign function. The estimated value of the covariance matrix of y is expressed as Then we have:

[0058]

[0059] Where T is the number of snapshots, (·) H Represents the conjugate transpose operation of a vector or matrix.

[0060] In a specific embodiment, S2 specifically includes The covariance matrix is ​​vectorized and Each column of is stacked in turn to generate a column vector Z.

[0061] In a specific embodiment, S3 specifically includes setting the number of DFT samples to N=1024, calculating the DFT matrix and performing normalization operation, then padding the column vector Z with zeros to make its length the same as N, and finally performing DFT operation on the column vector Z to obtain spectrum information.

[0062] In a specific embodiment, S4 specifically includes: finding the peak value pks and the peak position locs in the spectrum information by using the find peaks function, subtracting the position locs from To correct the offset relative to the signal length, the peak values ​​pks are sorted in descending order from large to small, and then the sorted peak values ​​pks are mapped to the index loc by traversal. The index loc is sorted in descending order, and the first K peak positions are the arrival angle positions; the boundary positions of the arrival angle positions are found and stored in an array.

[0063] In a specific embodiment, finding the boundary position specifically includes:

[0064] Find the right boundary position: For the right side, start from the peak position and traverse to the right, find the first position where the difference between the current peak and the traversed position is greater than 1, and store this position and its value in the right array; if the difference is less than or equal to 1, find the position with the smallest value between the peak position and the adjacent peak position on the right, and store this position and its value in the right array;

[0065] Find the left boundary position: For the left side, if the current peak is the first peak, directly set the left boundary to the first point of the signal, and store the current peak and the left boundary in the left array; if it is not the first peak, start from the previous peak position to the current peak position, find the first position where the difference between the current peak and the traversed position is greater than 1, and store this position and its value in the left array; if the difference is less than or equal to 1, find the position with the smallest value between the adjacent peak position on the left, and store this position and its value in the left array.

[0066] A single-bit DOA estimation system based on discrete-time Fourier transform, comprising:

[0067] A covariance matrix acquisition module acquires the original signal, performs single-bit quantization on the original signal to obtain a quantization result, and calculates the covariance matrix of the quantization result;

[0068] Column vector generation module, which vectorizes the covariance matrix and generates column vectors;

[0069] The spectrum information acquisition module performs DFT operation on the column vector to obtain spectrum information;

[0070] The interval confirmation module obtains the peak and peak positions of the spectrum information through the findpeaks function, processes the peak and peak positions to obtain the arrival angle position, and finds the left and right boundary positions of the arrival angle position to determine the arrival angle interval;

[0071] The angle acquisition module uses DTFT to refine the frequency of the arrival angle interval, performs spectrum peak search on the refined arrival angle interval, and calculates and obtains the final angle estimate.

[0072] The present invention will be further described below in conjunction with MATLAB simulation experiment results:

[0073] The simulation results show that the present invention (single-bit DTFT algorithm) is compared with the single-bit DFT algorithm and the One-bit-MUSIC algorithm. Figure 3-Figure 6 As shown in Figure 2, in all simulations, the number of array elements M = 500, the signal source power p is all 1, and the signal to noise ratio (SNR) is defined as:

[0074]

[0075] The angle estimation performance is evaluated using mean-absolute error (MAE):

[0076]

[0077] For where N is the number of Monte Carlo runs, represents the incident angle θ of the nth Monte Carlo test k The estimated value of , K is the number of information sources.

[0078] Figure 3 Given four random signal sources impinging on an array, the performance of the single-bit DTFT algorithm is compared with that of the single-bit DFT algorithm, where N=100 is simulated. Figure 4 Four signal sources with θ = [-40.61, -10.37, 30.61, 60.24] are given to impact the array, and the One-bit-MUSIC algorithm is added for performance comparison, where N = 100 is simulated.

[0079] Depend on Figure 3 It can be seen that the performance is improved after using DTFT to refine the interval based on the DFT algorithm. Figure 4 It can be seen that the method proposed in the present invention outperforms all other compared methods. When the input signal-to-noise ratio is low, it can be observed that the estimation errors of all methods are large. Due to the limited resolution of the DFT operation, the accuracy of the initial estimation is not improved when the SNR is greater than -4dB. Even in the case of high signal-to-noise ratio, as long as the exact position of the peak point is determined, the DFT method will not cause performance loss in the initial estimation. After phase rotation, the accuracy of the one-bit DFT precise estimation is significantly improved, which is worse than the one-bit MUSIC method, but not as good as the method proposed in the present invention. When the input signal-to-noise ratio is high, the one-bit MUSIC can almost always find the grid point closest to the true DOA, and the estimation accuracy is mainly affected by the off-grid error. However, finer grid division will significantly increase the running time. Figure 5 and Figure 6 This is the effect of different snapshot numbers on the algorithm under the same conditions. By comparing the two figures, it can be seen that with the increase in the number of snapshots, the accuracy of the precise estimation of the two methods is improved, and the accuracy of the present invention is better than that of the One-bit DFT algorithm. Figure 7 The average running time of all methods is shown. The proposed method is much lower than other methods.

[0080] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0081] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A DOA estimation method for a single-bit sensor array, characterized in that: include: S1: Obtain the original signal, perform single-bit quantization on the original signal to obtain a quantization result, and calculate the covariance matrix of the quantization result; S2: vectorize the covariance matrix to generate a column vector; S3: Perform DFT operation on the column vector to obtain spectrum information; S4: obtain the peak values ​​and peak positions of the spectrum information through the findpeaks function, obtain the arrival angle position after processing the peak values ​​and peak positions, and find the left and right boundary positions of the arrival angle position to determine the arrival angle range; S5: Use DTFT to refine the frequency of the arrival angle interval, perform spectrum peak search on the refined arrival angle interval, calculate and obtain the final angle estimation; It also includes simulations in MATLAB, where the signal-to-noise ratio (SNR) is defined as: The mean absolute error (MAE) is used to evaluate the angle estimation performance: Where: A=[a(θ1),...,a(θ k )]∈C M×K represents the steering matrix, a(θ k ) is the steering vector, s=[s1,...,s K ] T represents a K×1 complex-valued signal, represents the variance, M is the number of array elements; K is the number of information sources, and N is the number of Monte Carlo runs. represents the incident angle θ of the nth Monte Carlo test k The estimated value of .

2. A DOA estimation method for a single-bit sensor array according to claim 1, characterized in that: S1 specifically includes: Let x represent a single snapshot of the original signal, then: x=As+n; In the formula, A=[α(θ1),...,α(θ K )]∈C M×K represents the steering matrix, α(θ K ) is the steering vector, s=[s1,...,s K ] T Represents a K×1 complex-valued signal, where different signals are independent of each other and have a variance of Circularly symmetric complex Gaussian distribution, k = 1, 2, ..., K, K is the number of information sources, n ∈ C M×1 The variance is Additive Gaussian white noise; Next, quantize x to get y: Where Re(·) and Im(·) represent the real and imaginary parts of a vector or matrix, respectively, and sign(·) is the sign function. The estimated value of the covariance matrix of y is expressed as Then we have: Where T is the number of snapshots and (·)H represents the conjugate transpose operation of a vector or matrix.

3. A DOA estimation method for a single-bit sensor array according to claim 2, characterized in that: S2 specifically includes The covariance matrix is ​​vectorized and Each column of is stacked in turn to produce a column vector.

4. A DOA estimation method for a single-bit sensor array according to claim 1, characterized in that: S3 specifically includes setting the number of DFT samples to N=1024, calculating the DFT matrix and performing a normalization operation, then padding the column vector with zeros to make its length the same as N, and finally performing a DFT operation on the column vector to obtain spectrum information.

5. A DOA estimation method for a single-bit sensor array according to claim 1, characterized in that: S4 specifically includes: finding the peak value and the position of the peak in the spectrum information by using the find peaks function, and subtracting the position from Then sort the peak values ​​in descending order from large to small, and then map the sorted peak values ​​to the index by traversal, sort the index in descending order, and the first fixed peak positions are the arrival angle positions; find the boundary position of the arrival angle position and store it in the array.

6. A DOA estimation method for a single-bit sensor array according to claim 5, characterized in that: Finding the boundary location specifically includes: Find the right boundary position: For the right side, start from the peak position and traverse to the right, find the first position where the difference between the current peak and the traversed position is greater than 1, and store this position and its value in the right array; if the difference is less than or equal to 1, find the position with the smallest value between the adjacent peak position on the right, and store this position and its value in the right array; Find the left boundary position: For the left side, if the current peak is the first peak, directly set the left boundary to the first point of the signal, and store the current peak and the left boundary in the left array; if it is not the first peak, traverse from the previous peak position to the current peak position, find the first position where the difference between the current peak and the traversed position is greater than 1, and store this position and its value in the left array; if the difference is less than or equal to 1, find the position with the smallest value between the adjacent peak position on the left, and store this position and its value in the left array.

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