Single-bit direction finding method and system for special non-uniform linear array
By employing a single-bit direction finding method with a special non-uniform linear array, the challenge of direction finding under impact noise was solved, reducing hardware costs and power consumption, improving the stability and accuracy of direction finding, and expanding the equivalent aperture.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN ENG UNIV
- Filing Date
- 2026-01-30
- Publication Date
- 2026-05-08
AI Technical Summary
Existing methods for finding directions using special non-uniform linear arrays under impact noise conditions present challenges, especially at high signal-to-noise ratios where errors are significant, and also involve high hardware costs and power consumption.
A single-bit direction finding method using a special non-uniform linear array is employed. By setting up a special non-uniform linear array, signal data is acquired and quantized, a fractional low-order matrix is reconstructed, and a virtual uniform linear array is formed. Single-bit subspace decomposition and spectral peak search are then performed to estimate the direction angle of arrival.
It significantly reduces data volume and hardware overhead, suppresses the impact of shock noise, improves direction finding stability and accuracy, expands the equivalent aperture, and improves estimation accuracy.
Smart Images
Figure CN121995304A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of array signal processing technology, and more specifically, to a single-bit direction finding method and system for a special non-uniform linear array. Background Technology
[0002] Direction finding, also known as direction of arrival (DOA) estimation, has always been a hot research topic in array signal processing, and is widely used in communication, radar, and sonar systems. In array signal processing, uniform linear arrays (ULAs) are widely used to estimate the DOA due to their simple structure. The array resolution is determined by the number of elements; increasing the element spacing or the number of elements improves the resolution. However, increasing the number of elements increases the equipment load, impacting signal processing complexity, channel error adjustment, and system reliability. Excessive element spacing produces grating lobe effects, leading to ambiguity in estimation accuracy. Under the constraint of M elements, by optimizing the non-uniform positions, the array spacing set is made to cover all integers from 1 to the maximum aperture D, while maximizing the maximum aperture, ultimately achieving "high resolution, low cost, and anti-grating lobe" DOA estimation performance.
[0003] Sampling and quantizing received signals typically employs a multi-bit analog-to-digital converter (ADC). The increase in the number of quantization bits in an ADC leads to an exponential increase in hardware cost and power consumption, resulting in a massive amount of data generated per antenna, thus burdening data storage and transmission. Low-bit quantization, due to its significant advantages of low cost, low power consumption, and low data volume, shows great potential for application in direction-finding systems. An extreme case of low-bit quantization is single-bit (OB) quantization, which retains only symbolic information from random measurements.
[0004] Existing technical literature reveals that Ofer Bar-Shalom and Anthony J. Weiss, in their paper "DOA Estimation Using One-Bit Quantized Measurements" published in IEEE Transactions on Aerospace and Electronic Systems (Volume: 38, Issue: 3, July 2002), employ a method of estimating DOA by reconstructing the covariance of the sheared signal and then applying r-CBF and r-MVDR. This method only discusses DOA estimation under Gaussian white noise conditions and is highly dependent on the estimated value of the covariance matrix. Huang Xiaodong and Liao Bin, in their paper "One-bit MUSIC" published in IEEE Signal Processing Letters (Volume: 26, Issue: 7, July 2019), use a MUSIC algorithm based on the covariance of the sheared signal, eliminating the need for unquantized covariance reconstruction. However, this method exhibits a relatively larger approximation error at high signal-to-noise ratios. The array used in the above method is a uniform linear array, and the noise background is Gaussian white noise. However, special non-uniform linear arrays can utilize their own redundancy to simulate the performance of a uniform linear array with more array elements by setting fewer array elements, so as to estimate more information sources. At the same time, in order to solve the negative problems such as hardware cost and power consumption caused by multi-bit quantization, a single-bit estimation method for special non-uniform linear arrays is proposed under impulse noise background. Summary of the Invention
[0005] The technical problem to be solved by this invention is:
[0006] The existing challenges of orientation finding using special non-uniform linear arrays under impact noise.
[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:
[0008] This invention provides a single-bit direction finding method for a special non-uniform linear array, comprising the following steps:
[0009] Step 1: Set up a special non-uniform linear array, acquire snapshot sampling data of the array received signal, and quantize the signal data;
[0010] Step 2: Obtain the fractional low-order matrix of the signal and reconstruct the fractional low-order matrix of the quantized signal;
[0011] Step 3: Virtually convert the quantized and reconstructed special non-uniform linear array into a uniform linear array;
[0012] Step 4: Decompose the single-bit subspace;
[0013] Step 5: Use spectral peak search to estimate the incoming wave direction angle.
[0014] Furthermore, step one includes the following steps:
[0015] definition A far-field narrowband signal from the direction Incident to On a special non-uniform linear array composed of isotropic antennas; the placement of the array satisfies the following condition: the first... The spacing between each array element and the first array element ,and ,in If the minimum element spacing is set to Then the coordinates of the array elements ,in All are integers, and the set It is a continuous set of natural numbers;
[0016] The array received by the first wave of the signal under impulse noise conditions The sampled data from the quick snapshot is represented as follows:
[0017]
[0018] In the formula, for dimensional guiding matrix, where the first... Guide vectors , , The wavelength of the incident signal, for 3D array snapshot data vector, where For the number of snapshots, , The maximum number of snapshots. for The independent and identically distributed dimensional satisfy Distributed impact noise vector;
[0019] Quantize the signal, the first Individual Element The single-bit quantized signal of the next snapshot is represented as:
[0020]
[0021] in, and They represent the real and imaginary parts, respectively. Indicates two The complex-valued element-level quantization function is composed of... The imaginary unit, For variables The symbolic function is represented as:
[0022]
[0023] Then the first The single-bit quantized received signal vector of the next snapshot is .
[0024] Furthermore, step two includes the following steps:
[0025] Define the fractional low-order matrix of the signal after single-bit quantization between the received data of the array elements as follows: , of which Line number Column elements , , , These are the parameters of the fractional low-order matrix; Represents conjugation;
[0026] Define the reconstruction coefficients of a fractional low-order matrix as:
[0027]
[0028] in, Indicates the first Fractional low-order matrix reconstruction coefficients of each array element;
[0029] Reconstructing the quantized fractional low-order matrix yields the following reconstructed fractional low-order matrix:
[0030] .
[0031] Furthermore, step three includes the following steps:
[0032] The non-uniform linear array is virtualized into a uniform linear array with more elements, and the maximum correlation delay of the array is... The number of elements in the virtual uniform linear array is then... Integers between, sampled and quantized reconstructed Fractional low-order matrices for:
[0033]
[0034] Among them, let , , , , To obtain the mean function: then the virtual uniform linear array dimensional extended fractional low-order matrix for:
[0035]
[0036] Then the extended steering matrix of the original array of the virtual uniform linear array is: , of which The extended directional vectors are .
[0037] Furthermore, step four includes the following steps:
[0038] For fractional low-order matrices Perform eigenvalue decomposition ,in Represents conjugate transpose. A diagonal matrix composed of eigenvalues, arranged in descending order. , This represents a diagonal matrix, and its corresponding eigenvectors are... , It is from the front The large eigenvalues form a diagonal matrix. The eigenvector matrix is a diagonal matrix composed of small eigenvalues. From the eigenvector matrix of the signal subspace and signal subspace eigenvector matrix Its signal subspace is composed of Then its noise subspace is represented as Due to the orthogonality between the signal subspace and the noise subspace, , It is a matrix composed of 0s. Based on the orthogonality between the noise eigenvector and the signal direction vector, the single-bit spatial spectrum estimation equation of the array is obtained as follows:
[0039]
[0040] in Indicates that after single-bit quantization, The peak values of the spectrum obtained by the algorithm.
[0041] This invention provides a single-bit direction finding system for a special non-uniform linear array. The system has a program module corresponding to the steps of any of the methods described in the above technical solutions, and executes the steps in the single-bit direction finding method for the special non-uniform linear array described above when running.
[0042] The present invention provides a computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps of the single-bit direction-finding method for a special non-uniform linear array as described in any of the above technical solutions.
[0043] Compared with the prior art, the beneficial effects of the present invention are:
[0044] Compared with existing special non-uniform linear array direction finding, the single-bit estimation method of special non-uniform linear array of the present invention significantly reduces the amount of data and hardware overhead by performing single-bit quantization on the received signal, and introduces FLOM robust reconstruction to suppress the influence of impulse noise. At the same time, it utilizes the redundant differential of the special non-uniform linear array to realize virtual uniform array expansion to increase the equivalent aperture, thereby improving the stability and estimation accuracy of direction finding. Attached Figure Description
[0045] Figure 1 This is a flowchart of a single-bit direction finding method for a special non-uniform linear array in an embodiment of the present invention;
[0046] Figure 2 This is a virtual uniform array position diagram derived from a special non-uniform linear array in an embodiment of the present invention;
[0047] Figure 3 When there are two independent information sources in the embodiments of the present invention Algorithms and Direction finding comparison diagram of the algorithm;
[0048] Figure 4 When there are three independent information sources in the embodiments of the present invention and Direction finding comparison diagram;
[0049] Figure 5 For direction finding of two independent signal sources under impulsive noise environment in this embodiment of the invention The curve showing the relationship between the signal-to-noise ratio and the generalized signal-to-noise ratio;
[0050] Figure 6 For direction finding of three independent signal sources under impulsive noise environment in this embodiment of the invention The curve showing the relationship between the signal-to-noise ratio and the generalized signal-to-noise ratio;
[0051] Figure 7 This is a graph showing the relationship between the success probability and the generalized signal-to-noise ratio when two independent signal sources are used for direction finding in an impact noise environment according to an embodiment of the present invention.
[0052] Figure 8 This is a graph showing the relationship between the success probability and the generalized signal-to-noise ratio when three independent signal sources are used for direction finding in an impact noise environment according to an embodiment of the present invention. Detailed Implementation
[0053] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are merely some, not all, of the embodiments or examples of the present invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of the present invention without inventive effort should fall within the scope of protection of the present invention.
[0054] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0055] Combination Figure 1 As shown, the present invention provides a single-bit direction finding method for a special non-uniform linear array, comprising the following steps:
[0056] Step 1: Set up a special non-uniform linear array, acquire snapshot sampling data of the array received signal, and quantize the signal data.
[0057] A far-field narrowband signal from the direction Incident to The array is placed on a special non-uniform linear array composed of isotropic antennas. The placement of the array satisfies the following condition: The spacing between each array element and the first array element ,and ,in If the minimum element spacing is set to Then the coordinates of the array elements ,in All are integers, and the set It is a continuous set of natural numbers.
[0058] The array received by the first wave of the signal under impulse noise conditions The sampled data of the next snapshot is represented as follows:
[0059]
[0060] In the formula, for dimensional guiding matrix, where the first... Guide vectors , ; The direction vector of the incoming wave. The wavelength of the incident signal, for 3D array snapshot data vector, where For the number of snapshots, for The independent and identically distributed dimensional satisfy Distributed impact noise vector.
[0061] The signal is quantized using a coarse quantizer, which retains only the sign characteristics of the sampled signal after quantization. This means that the received signal is quantized using a coarse quantizer. Function operations, considering that the signals from each sensor are narrowband, require individual clipping processing for each signal component. Specifically, this process is represented using complex number operators, where the first... Individual Element The single-bit quantized signal of the next snapshot is represented as:
[0062]
[0063] in, and Representing complex numbers respectively The real and imaginary parts, , Indicates two The complex-valued element-level quantization function is composed of... The imaginary unit, For variables The symbolic function is represented as:
[0064]
[0065] Then the first The single-bit quantized received signal vector of the next snapshot is .
[0066] Step 2: Obtain the fractional low-order matrix of the signal and reconstruct the fractional low-order matrix of the quantized signal.
[0067] Define the fractional low-order matrix of the signal after single-bit quantization between the received data of the array elements as follows: , of which Line number Column elements , , , , This represents the maximum number of snapshots. These are the parameters of the fractional low-order matrix; It represents conjugate.
[0068] Define the reconstruction coefficients of a fractional low-order matrix as
[0069]
[0070] in, Indicates the first Fractional low-order matrix reconstruction coefficients of each array element.
[0071] Reconstructing the quantized fractional low-order matrix yields the reconstructed fractional low-order matrix as follows:
[0072]
[0073] in, , , and These represent the real part and the imaginary part, respectively.
[0074] Step 3: Virtually transform the quantized and reconstructed special non-uniform linear array into a uniform linear array.
[0075] Based on the characteristics of a special non-uniform linear array, the non-uniform linear array is virtualized into a uniform linear array with more elements. The maximum correlation delay of the array is... The number of elements in the virtual uniform linear array is then... Integers between these values are used to better represent the relationship between the reconstructed fractional low-order matrix and the extended fractional low-order matrix of the virtual uniform linear matrix. The reconstructed fractional low-order matrix is sampled and quantized. Fractional low-order matrices for
[0076]
[0077] Among them, let , , , , To obtain the mean function: then the virtual uniform linear array dimensional extended fractional low-order matrix for
[0078]
[0079] Then the extended steering matrix of the original array of the virtual uniform linear array is: , of which The extended directional vectors are As can be seen from the properties of a uniform linear array, The maximum number of sources that can be detected by a single array element is: .
[0080] Step 4: Decompose the single-bit subspace.
[0081] When the signal-to-noise ratio is not too low, the fractional low-order matrix reconstructed by single-bit quantization It has subspace consistency with traditional analog signal fractional low-order matrices, that is, the eigenvectors have the same direction, only the eigenvalues are scaled.
[0082] right Perform eigenvalue decomposition superscript Represents conjugate transpose. A diagonal matrix composed of eigenvalues, arranged in descending order. , This represents a diagonal matrix, and its corresponding eigenvectors are... , It is a diagonal matrix composed of large eigenvalues. The eigenvector matrix is a diagonal matrix composed of small eigenvalues. From the eigenvector matrix of the signal subspace and signal subspace eigenvector matrix Its signal subspace is composed of Then its noise subspace is represented as Due to the orthogonality of the signal subspace and the noise subspace, it can be known that , It is a matrix composed of 0s, which indicates that it is a virtual steering matrix. Each column vector in the vector is orthogonal to the single-bit noise subspace. , Based on the orthogonality between the noise eigenvector and the signal direction vector, the single-bit spatial spectrum estimation equation for the array is obtained as follows:
[0083]
[0084] in This is represented as single-bit quantization. The peak values of the spectrum obtained by the algorithm.
[0085] Step 5: Use spectral peak search to estimate the incoming wave direction angle.
[0086] Make azimuth variable Changes are estimated by finding spectral peaks to determine the direction of arrival. The direction angle of the incoming wave.
[0087] The single-bit direction finding method (algorithm) for a special non-uniform linear array proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.
[0088] Based on the method proposed in this invention, a single-bit direction finding system for a special non-uniform linear array is developed using a programming language. This system has program modules corresponding to the steps of the above-described technical solution, and executes the steps in the above-described single-bit direction finding method for a special non-uniform linear array when running.
[0089] The developed system (software) computer program is stored on a computer-readable storage medium, and the computer program is configured to implement the steps of the above-described single-bit direction-finding method for a special non-uniform linear array when called by a processor. In other words, the invention is materialized on a carrier, becoming a computer program product.
[0090] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.
[0091] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.
[0092] The effects of the present invention will be illustrated below using specific embodiments.
[0093] Example 1
[0094] Under impact noise conditions, the specific parameter settings in the simulation experiment of this embodiment are as follows:
[0095] The special non-uniform array uses a minimum redundancy linear array with 4 elements, and the positions of the elements are as follows: However, the array elements placed by this method expand the number of virtual array elements. The value is 7; the MUSIC method based on minimum redundancy linear array single-bit reconstruction of the present invention is denoted as 7. Three simulation experiments were conducted to compare the algorithm with that of a minimum redundancy linear array. Algorithm comparison, denoted as in simulation experiments The search range for the direction of incoming waves is in Degree to Between degrees, the angle search step size is The characteristics of the impulse noise are 1.6, and the number of snapshots is 1000. To verify the performance of the designed algorithm, the direction finding accuracy of the two algorithms under special non-uniform linear array conditions, the root mean square error (RMSE) under the generalized signal-to-noise ratio, and the success probability when the absolute value of the error between the estimated source angle and the estimated angle is less than 1 are given.
[0096] Figure 2 Given a minimum redundant linear array with 4 elements, the positions of the elements are: A schematic diagram of a virtual uniform linear array is shown. Figure 3 For the number of information sources At that time, the direction of the incoming wave was 50 repeated simulation experiments were conducted. Figure 4 When the number of sources At that time, the direction of the incoming wave was Perform 50 repeated simulation experiments. The generalized signal-to-noise ratio is set to 10dB. Maximum number of snapshots ;from Figure 3 , Figure 4 It can be seen that under the condition of impact noise It can achieve relatively high-precision direction finding and has stable performance. There will be deviations during direction finding.
[0097] Under the condition of a 4-element minimum redundancy linear array, utilizing Algorithms and The algorithm performs DOA estimation on the information source. Figure 5 , Figure 7 For the number of information sources At that time, the direction of the incoming wave was ; Figure 6 , Figure 8 For the number of information sources At that time, the direction of the incoming wave was The unit for the direction of incoming waves is degrees, and the number of snapshots is... To a value of 1000, conduct 1000 Monte Carlo experiments. From... Figure 5 , Figure 6 It can be seen The algorithm outperforms the standard root mean square error even at lower generalized signal-to-noise ratios. The root mean square error of the algorithm under the same generalized signal-to-noise ratio. (Explanation) The algorithm achieves relatively accurate target estimation at low generalized signal-to-noise ratios and exhibits strong resistance to noise interference. Figure 7 , Figure 8 It can be seen that special non-uniform linear arrays, under conditions of low generalized signal-to-noise ratio, The success rate of the algorithm is higher than As can be seen from the algorithm, the algorithm proposed in this invention has a good ability to estimate the direction angle.
[0098] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.
Claims
1. A single-bit direction-finding method for a special non-uniform linear array, characterized in that, Includes the following steps: Step 1: Set up a special non-uniform linear array, acquire snapshot sampling data of the array received signal, and quantize the signal data; Step 2: Obtain the fractional low-order matrix of the signal and reconstruct the fractional low-order matrix of the quantized signal; Step 3: Virtually convert the quantized and reconstructed special non-uniform linear array into a uniform linear array; Step 4: Decompose the single-bit subspace; Step 5: Use spectral peak search to estimate the incoming wave direction angle.
2. The method according to claim 1, characterized in that, Step one includes the following steps: definition A far-field narrowband signal from the direction Incident to On a special non-uniform linear array composed of isotropic antennas; the placement of the array satisfies the following condition: the first... The spacing between each array element and the first array element ,and ,in If the minimum element spacing is set to Then the coordinates of the array elements ,in All are integers, and the set It is a continuous set of natural numbers; The array received by the first wave of the signal under impulse noise conditions The sampled data from the quick snapshot is represented as follows: In the formula, for dimensional guiding matrix, where the first... Guide vectors , , The wavelength of the incident signal, for 3D array snapshot data vector, where For the number of snapshots, , The maximum number of snapshots, for The independent and identically distributed dimensional satisfy Distributed impact noise vector; Quantize the signal, the first Individual Element The single-bit quantized signal of the next snapshot is represented as: in, and They represent the real and imaginary parts, respectively. Indicates two The complex-valued element-level quantization function is composed of... The imaginary unit, For variables The symbolic function is represented as: Then the first The single-bit quantized received signal vector of the next snapshot is .
3. The method according to claim 2, characterized in that, Step two includes the following steps: Define the fractional low-order matrix of the signal after single-bit quantization between the received data of the array elements as follows: , of which Line number Column elements , , , These are the parameters of the fractional low-order matrix; Represents conjugation; Define the reconstruction coefficients of a fractional low-order matrix as: in, Indicates the first Fractional low-order matrix reconstruction coefficients of each array element; Reconstructing the quantized fractional low-order matrix yields the following reconstructed fractional low-order matrix: 。 4. The method according to claim 3, characterized in that, Step three includes the following steps: The non-uniform linear array is virtualized into a uniform linear array with more elements, and the maximum correlation delay of the array is... The number of elements in the virtual uniform linear array is then... Integers between, sampled and quantized reconstructed Fractional low-order matrices for: Among them, let , , , , To obtain the mean function: then the virtual uniform linear array dimensional extended fractional low-order matrix for: Then the extended steering matrix of the original array of the virtual uniform linear array is: , of which The extended directional vectors are .
5. The method according to claim 4, characterized in that, Step four includes the following steps: For fractional low-order matrices Perform eigenvalue decomposition ,in Represents conjugate transpose. A diagonal matrix composed of eigenvalues, arranged in descending order. , This represents a diagonal matrix, and its corresponding eigenvectors are... , It is from the front The large eigenvalues form a diagonal matrix. The eigenvector matrix is a diagonal matrix composed of small eigenvalues. From the eigenvector matrix of the signal subspace and signal subspace eigenvector matrix Its signal subspace is composed of Then its noise subspace is represented as Due to the orthogonality between the signal subspace and the noise subspace, , It is a matrix composed of 0s. Based on the orthogonality between the noise eigenvector and the signal direction vector, the single-bit spatial spectrum estimation equation of the array is obtained as follows: in Indicates that after single-bit quantization, The peak values of the spectrum obtained by the algorithm.
6. A single-bit direction-finding system for a special non-uniform linear array, characterized in that, The system has a program module corresponding to the steps of the method described in any one of claims 1 to 5, and executes the steps in the single-bit direction finding method of the special non-uniform linear array described above when running.
7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the single-bit direction-finding method for the special non-uniform linear array as described in any one of claims 1 to 5.