A single-bit quantization based underdetermined direction of arrival estimation method

Abstract

The present application provides a kind of underdetermined direction of arrival estimation method based on single-bit quantization.The present application method is mainly based on the difference co-array (Difference Co-Array) to obtain larger array aperture and higher degree of freedom, by spatial smoothing method to construct the new single-bit sample variance matrix with multiple degree of freedom characteristics, and the new single-bit sample covariance matrix is decomposed to obtain the new signal subspace with greater degree of freedom than the original physical array element number, then the direction of arrival estimation of multiple sources is obtained by polynomial root method, without spectrum peak search, both realize the underdetermined direction of arrival estimation of the number of sources greater than the physical array element number, and have lower computational complexity and super-resolution characteristics.

Description

Technical Field

[0001] This invention belongs to the field of information and communication technology, and relates to an underdetermined direction-of-arrival estimation method based on single-bit quantization. Background Technology

[0002] Direction of arrival (DOA) estimation (array direction finding) is an important topic in array signal processing, with significant applications in traditional electronic information industries (such as wireless communication, astronomy, radar, and sonar) and modern vertical industries (such as autonomous driving, drone operations, smart manufacturing, and smart homes). DOA estimation has developed rapidly over the past 60 years, and advanced DOA estimation methods with super-resolution and low complexity have always been a goal pursued by researchers. With the continuous development and progress of modern science and technology, array antenna systems are gradually being integrated into miniaturized devices or platforms, achieving target localization and sensing on miniaturized platforms. However, miniaturized platforms (such as drones and intelligent vehicles) are strictly limited by platform resources, requiring optimization in computing power, cost, power consumption, and storage. However, with the increase in the number of array antennas, the total power consumption of the high-precision quantization analog-to-digital converter in multi-antenna arrays increases exponentially. The high hardware cost and high power consumption make miniaturized platforms impractical or unusable. As a new generation of multi-antenna array receivers, single-bit receivers offer advantages such as large instantaneous bandwidth, real-time processing, high sensitivity, and small size, making them widely applicable in modern electronic warfare. In general, single-bit quantization offers significant advantages in simplifying systems, saving computing power, reducing costs, and improving efficiency, and it has immense application potential, especially in modern radar and its countermeasures systems that require massive data processing.

[0003] Traditional direction-of-arrival (DOA) estimation methods based on linear arrays (such as the MUSIC method in "Multiple emitter location and signal parameter estimation") consider signals obtained through high-precision quantization receivers with an infinite number of bits. To avoid direction-finding ambiguity, the element spacing of the linear array generally does not exceed half the wavelength of the incident signal. Furthermore, high-precision quantization receivers for traditional multi-antenna arrays are costly, power-intensive, and complex, making their application to the RF front-end of large-scale antenna array systems impractical. Therefore, a trade-off between sampling rate and quantization accuracy is often necessary during receiver data acquisition. In contrast, single-bit quantization, which retains only the symbol bits of the sampled data, has proven promising in large-scale multi-antenna systems. This is because single-bit quantization requires only a simple comparator, eliminates the need for automatic gain control, and consumes only a few milliwatts of power, providing a low-power and low-complexity solution while maintaining certain performance. The paper "DOAestimation using one-bit quantized measurements" estimates DOA by reconstructing the unquantized covariance matrix, but the computational complexity of reconstructing the covariance matrix is ​​high. The paper "One-bit MUSIC" directly constructs the covariance matrix from single-bit measurements, without reconstructing the original unquantized covariance matrix, thus directly realizing direction-of-arrival (DOA) estimation under single-bit measurements. However, due to limitations in the physical array aperture, these methods cannot achieve underdetermined DOA estimation when the number of sources exceeds the number of physical array elements. Therefore, a new super-resolution underdetermined DOA estimation method under single-bit quantization is urgently needed. Summary of the Invention

[0004] The main content of this invention is to propose an underdetermined direction-of-arrival (DOA) estimation method based on single-bit quantization. This method primarily utilizes a difference co-array to obtain a larger array aperture and higher degrees of freedom. A novel single-bit sample covariance matrix with multi-degree-of-freedom characteristics is constructed using a spatial smoothing method. Then, eigenvalue decomposition is performed on the new single-bit sample covariance matrix to obtain a novel signal subspace with degrees of freedom greater than the original physical array elements. Finally, the DOA estimation for multiple sources is obtained through polynomial root-finding, eliminating the need for spectral peak searching. This method achieves underdetermined DOA estimation with a greater number of sources than physical array elements, while also exhibiting low computational complexity and super-resolution characteristics.

[0005] The technical solution adopted in this invention includes the following steps:

[0006] S1. Suppose the array structure is a two-level linear nested array, that is, two uniform linear arrays are nested. The number of array elements of the first-level uniform linear array is M1, the number of array elements of the second-level uniform linear array is M2, and the total number of array elements is M = M1 + M2.

[0007] S2. Obtain the single-bit signal, specifically:

[0008] Given a sampling snapshot number N, perform N single-bit parallel samplings on an antenna array with M elements to obtain an M×N dimensional single-bit baseband received signal:

[0009] Y = [y(1), y(2), ..., y(N)]

[0010] Wherein, the M-dimensional column vector y(n) represents the single-bit received signal of the nth snapshot, n = 1, ..., N;

[0011] S3. Construct the covariance matrix using a single-bit received signal:

[0012]

[0013] In the formula, (·) H This represents the conjugate transpose operation. It is an M×M dimensional matrix;

[0014] S4. Covariance matrix of single-bit samples After performing vector quantization, the new virtual received signal is obtained as follows:

[0015]

[0016] Where vec(·) represents the vector quantization operation on the matrix, that is, straightening it column-wise to form a new column vector, and y is M. 2 Dimensional column vector;

[0017] S5. Perform spatial smoothing operation on the virtual received signal y to obtain... 3D smoothed sample covariance matrix

[0018]

[0019] Where spatial sm0othing represents spatial smoothing operation. This represents the number of elements in the new virtual uniform linear array;

[0020] S6. For spatially smoothed covariance matrix R ss Perform eigenvalue decomposition:

[0021]

[0022] In the formula, It is a diagonal matrix. Indicate its Let Q = [q1, ..., q2] eigenvalues ​​arranged in descending order. M [ ] represents the normalized eigenvector matrix;

[0023] S7. Obtain the signal subspace: Given the number of signal sources K, The first K columns of the normalized eigenvector matrix Q are taken as the signal subspace, i.e., q1, ..., q2. K ;

[0024] S8. Constructing the root-finding polynomial: 3D column vector (·) T Let represent the transpose operation and define the root-finding polynomial:

[0025]

[0026] Where |·| represents the modulo operation, and z is any unknown variable;

[0027] S9. Direction of arrival estimation: This is achieved by solving the K roots of the equation P(z) = 0, expressed as... Then let φ k It is the spatial angular frequency, and φ k = -πsinθ k Then the estimated direction of arrival (DOA) of the k-th (k = 1, ..., K) source is... arcsin(·) represents finding the arcsine.

[0028] The beneficial effect of this invention is that it obtains the direction of arrival estimation by finding the root, eliminating the need for spectral peak search, and enabling the realization of [unclear - possibly related to a specific method or process]. An underdetermined direction-of-arrival (DOA) estimation method under the condition that (and possibly K≥M) has low computational complexity. Attached Figure Description

[0029] Figure 1 It is a single-bit, two-level nested uniformly linear array structure;

[0030] Figure 2 This represents the relationship between root mean square error (RMSE) and signal-to-noise ratio (SNR).

[0031] Figure 3 This represents the relationship between the root mean square error (RMSE) and the number of snapshots. Detailed Implementation

[0032] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0033] Let the K directions of arrival be... Narrowband source Located in the far field of M homogeneous linear arrays, propagating in a homogeneous medium. In this simulation experiment, let M = 6, and the element positions of the first-level nested array be S. inner ={md, m=1,2,3}, the element positions of the second-level nested array are S outer ={4md, m=1,2,3}, where d is the half-wavelength distance, and its single-bit uniformly linear array structure is as follows: Figure 1 As shown. Suppose there are K = 7 signal sources in space, with their incoming wave directions being -60°, -42°, -30°, -15°, 20°, 35°, and 55°, respectively. At discrete time t, the analog signal received by the antenna array can be expressed as (output signal without passing through a single-bit sampler).

[0034] x(t)=A(θ)s(t)+n(t), t=1,…,N

[0035] n(t) is the observation noise vector, where x(t) = [x1(t), x2(t), ..., x M (t)] T θ = [θ1, θ2, ..., θ K ] T N is the total number of snapshots (samples), and n(t) = [n1(t), n2(t), ..., n M (t)] T , A(θ)=[a(θ1),…,a(θ K [)] is the array manifold matrix, also known as the steering matrix. Let s(t) be a zero-mean signal vector, and each signal is a wide-range stationary process with ergodicity, meaning its second-order statistic is time-invariant and its covariance matrix can be approximated by the sample covariance matrix. Let the noise n(t) be a space-time independent cyclic complex Gaussian process, uncorrelated with the signal s(t), then

[0036]

[0037] In the formula, δ(t1-t2) is the Kronecker impulse function. The power or variance of the noise, 0 M and I M These are the M-order zero matrix and the identity matrix, respectively.

[0038] The output signal after passing through the single-bit sampler can be expressed as:

[0039] y(t)=Δ(x(t))=Δ(A(θ)s(t)+n(t)), t=1,…,N

[0040] In the formula, Δ(x(t)) represents the single-bit sampling transformation of the complex signal and

[0041]

[0042] In the formula, and This represents the operation of finding the real and imaginary parts, and sign(·) represents the sign function.

[0043]

[0044] After obtaining the single-bit sampled data Y = [y(1), y(2), ..., y(N)], the direction of arrival estimation can be performed using the following steps:

[0045] 1. Based on the set number of sampling (snapshots) N, perform N single-bit parallel samplings on an antenna array with M (M=6) array elements to obtain an M×N dimensional single-bit baseband received signal Y = [y(1), y(2), ..., y(N)], where the M-dimensional column vector y(n), n=1, ..., N represents the single-bit received signal of the nth snapshot. The signal obtained by the single-bit sampler, i.e., y(n), n=1, ..., N, has one of the following four values:

[0046] 2. Calculate the M×M dimensional sample covariance matrix of a single-bit received signal:

[0047]

[0048] In the formula, (·) H This indicates the conjugate transpose operation.

[0049] 3. For the single-bit sample covariance matrix After performing vector quantization, the new virtual received signal is obtained as follows:

[0050]

[0051] Where vec(·) represents the vector quantization operation on the matrix, that is, straightening the matrix column by column to form a new column vector;

[0052] 4. Perform spatial smoothing operation on the virtual received signal y to obtain... 3D smoothed sample covariance matrix

[0053]

[0054] Spatial smoothing refers to spatial smoothing operations. This represents the number of elements in the new virtual uniform linear array;

[0055] 5. For the spatially smoothed covariance matrix R ss Perform eigenvalue decomposition:

[0056]

[0057] In the formula, It is a diagonal matrix. Indicate its Let Q = [q1, ..., q2] eigenvalues ​​arranged in descending order. M [ ] represents the normalized eigenvector matrix;

[0058] 6. Obtain the signal subspace: Given the number of signal sources K = 7, The first K columns of the normalized eigenvector matrix Q are taken as the signal subspace, i.e., q1, ..., q2. K ;

[0059] 7. Constructing the root-finding polynomial: 3D column vector (·) T Let represent the transpose operation and define the root-finding polynomial:

[0060]

[0061] Where |·| represents the modulo operation, and z is any unknown variable;

[0062] 9. Direction of arrival estimation: This is achieved by solving the K roots of the equation P(z) = 0, expressed as... Then let φ k It is the spatial angular frequency, and φ k = -πsinθ k Then the estimated direction of arrival (DOA) of the k-th (k = 1, ..., K) source is... arcsin(·) represents finding the arcsine.

[0063] 10. Calculate the root mean square error (RMSE) based on the estimated and true values.

[0064] The following simulation examples demonstrate the practical effects of this invention, and the method described above is abbreviated as 1-bit SS-MUSIC. The superimposed noise is assumed to be Gaussian noise, and all results are the average of 20,000 independent experiments. The method used for comparison is Unquantized SS-MUSIC from the literature "Nested arrays: A novel approach to array processing with enhanced degrees of freedom". Figure 2 The figure shows the relationship between the root mean square error (RMSE) (RMSE is in degrees) and the signal-to-noise ratio (SNR) (SNR is in dB) with a sample size of 500. Figure 3 The figure shows the relationship between the root mean square error (RMSE) (RMSE is in degrees) and the number of snapshots when the SNR is 0dB. Figure 3 As can be seen, the single-bit method (1-bit SS-MUSIC) suffers a certain loss in RMSE performance compared to the unquantized method (Unquantized SS-MUSIC). This is because there is a certain error between the single-bit sample covariance matrix and the original unquantized covariance matrix. However, both methods achieve underdetermined direction-of-arrival estimation. Although the single-bit method performs slightly worse than the Unquantized SS-MUSIC method, it achieves a certain level of estimation effect while reducing sampling hardware costs and facilitating system integration and miniaturization.

Claims

1. A method for estimating underdetermined direction of arrival based on single-bit quantization, characterized in that, Includes the following steps: S1. Suppose the array structure is a two-level nested linear array, that is, two uniform linear arrays nested together. The number of elements in the first-level uniform linear array is... The number of elements in the second-level uniform linear array is The total number of array elements is ; S2. Obtain the single-bit signal, specifically: Given a sampling snapshot number N, perform N single-bit parallel samplings on an antenna array with M elements to obtain... Single-bit baseband received signal: ， in, 3D column vector This represents the single-bit received signal from the nth snapshot. ; S3. Construct the covariance matrix using a single-bit received signal: ， In the formula, This represents the conjugate transpose operation. for 3D matrix; S4. Covariance matrix of single-bit samples After performing vector quantization, the new virtual received signal is obtained as follows: ， in, This represents the vector quantization operation on a matrix, that is, straightening the matrix column by column to form a new column vector. for Dimensional column vector; S5, Virtual received signal Spatial smoothing operation is performed to obtain 3D smoothed sample covariance matrix : ， Spatial smoothing refers to spatial smoothing operations. This represents the number of elements in the new virtual uniform linear array; S6. Smoothing the spatial covariance matrix Perform eigenvalue decomposition: ， In the formula, It is a diagonal matrix. Indicate its The eigenvalues ​​are arranged in descending order. This is the normalized eigenvector matrix; S7. Obtain the signal subspace: Given the number of signal sources K, K < Take the normalized eigenvector matrix The first K columns are used as the signal subspace, i.e. ; S8. Constructing the root-finding polynomial: Constructing... 3D column vector , Let represent the transpose operation and define the root-finding polynomial: ， in, This represents the modulo operation, where z is any unknown variable; S9. Direction of arrival estimation: by solving equations The K roots are represented as Then let , , It is the spatial angular frequency, and Then the estimated direction of arrival (DOA) of the k-th source is . , This indicates the calculation of the arcsine.

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