A single-bit quantized direction-of-arrival estimation method based on multi-antenna array

Abstract

The present invention belongs to the field of information and communication technology, and relates to a single-bit quantized direction of arrival estimation method based on a multi-antenna array. The method of the present invention directly constructs a single-bit sample variance matrix through a single-bit sampled received signal, and performs eigendecomposition on the single-bit sample covariance matrix to obtain a signal subspace, and then obtains the direction of arrival estimation of multiple sources through a polynomial root-finding method, without the need for spectral peak search, and has low computational complexity.

Description

Technical Field

[0001] The invention belongs to the field of information and communication technology, and relates to a single-bit quantized direction of arrival estimation method based on a multi-antenna array. Background Art

[0002] Direction of arrival estimation (target positioning) is an important topic in array signal processing. It has important applications in traditional information industries (such as radar, sonar, navigation, communication, etc.) and modern vertical industries (such as intelligent driving, industrial drone operations, intelligent manufacturing, smart home, smart park management, etc.). Direction of arrival estimation based on multi-antenna arrays has developed rapidly in the past 50 years, and advanced positioning methods with high resolution and low complexity have always been the goal pursued by many scholars and engineers. With the development of modern society and the advancement of science and technology, array antenna systems are gradually integrated into miniaturized devices or platforms, that is, target positioning perception is realized on miniaturized platforms. However, miniaturized platforms (such as drones, smart cars, and small satellites) are strictly limited by platform resources and need to be optimized in terms of computing power, performance, cost, power consumption, storage, etc. However, with the increase in the number of antennas, especially the emerging large-scale antenna array system, the total power consumption of the high-precision quantization analog-to-digital converter of the multi-antenna array increases exponentially. The high hardware cost and high power consumption make the miniaturized platform impractical or unusable.

[0003] The received signals considered in traditional multi-antenna array DOA estimation methods (such as the multiple signal classification method based on subspace decomposition in "Multiple emitter location and signal parameter estimation") are all signals obtained by high-precision quantizers with infinite bits. The high-precision quantization of traditional multi-antenna arrays is impractical to apply to the RF front end due to its high cost, high power consumption and complex structure. Therefore, in the design process of data acquisition, it is usually necessary to trade off between sampling rate and quantization accuracy. The resolution of commercially available analog-to-digital converters (ADCs) is usually 12 bits to 16 bits, and the power consumption is several watts. In addition, single-bit quantization that only retains the sign bit of the sampled data has proven to be promising in large-scale multi-antenna systems. In contrast, single-bit quantization only requires a simple comparator to implement, does not require automatic gain control, and consumes only a few milliwatts of power, providing a low-power and low-complexity solution for the system while ensuring certain performance. The paper "DOA estimation using one-bit quantized measurements" reconstructs the original non-quantized covariance matrix, and then uses traditional methods (such as MUSIC in "Multiple emitter location and signal parameter estimation" and Capon in "High resolution frequency-wave number spectrum analysis") to estimate the direction of arrival. However, the computational complexity of reconstructing the covariance matrix is ​​relatively high, so a new single-bit direction of arrival estimation method with low complexity and low power consumption is urgently needed. Summary of the invention

[0004] In view of the above problems, the main content of the present invention is to propose a single-bit direction of arrival estimation method based on a multi-antenna array. The method of the present invention directly constructs a single-bit sample variance matrix through a single-bit sampled received signal, and performs eigendecomposition on the single-bit sample covariance matrix to obtain a signal subspace, and then obtains the direction of arrival estimation of multiple sources through a polynomial root method, without the need for spectral peak search, and has low computational complexity.

[0005] The technical solution adopted by the present invention comprises the following steps:

[0006] S1. Obtain a single-bit signal, specifically:

[0007] Set the sampling number N, perform N single-bit parallel sampling on the antenna array with M array elements, and obtain an M×N-dimensional single-bit baseband received signal:

[0008] Y = [y(1), y(2), …, y(N)]

[0009] Wherein, the M - dimensional column vector y(n) represents the single - bit received signal of the n - th sample, n = 1, …, N;

[0010] S2. Construct a covariance matrix from the single - bit received signals:

[0011]

[0012] In the formula, (·) H represents the conjugate transpose operation;

[0013] S3. Perform eigenvalue decomposition on the single - bit sample covariance matrix :

[0014]

[0015] In the formula, Λ = diag(λ1, …, λ M ) is a diagonal matrix, λ1, …, λ M represent its M eigenvalues and are arranged from large to small, Q = [q1, …, q M is a normalized eigenvector matrix;

[0016] S4. Obtain the signal subspace: Given the number of signal sources K, K < M, take the first K columns of the normalized eigenvector matrix Q as the signal subspace, that is, q1, …, q K ;

[0017] S5. Construct a root - finding polynomial: Construct an M - dimensional column vector b(z) = [1, z -1 , …, z -(M-1) T , (·) T represents the transpose operation, and define the root - finding polynomial:

[0018]

[0019] Wherein, |·| represents the modulus operation, z is an arbitrary unknown variable (the root of the equation P(z) = 0 with respect to z in S6);

[0020] S6. Direction - of - arrival estimation: By solving the K roots of the equation P(z) = 0, denoted as Then let k = 1, …, K, φ k is the spatial angular frequency, and φ k = - πsinθ k , then the estimated value of the direction of arrival of the k - th (k = 1, …, K) signal source is arcsin(·) represents the arcsine operation. ​

[0021] The beneficial effect of the present invention is that there is no need to perform spectrum peak search and the calculation complexity is low. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a single-bit linear array receiving model;

[0023] Figure 2 is the relationship between the root mean square error (RMSE) and the signal-to-noise ratio (SNR);

[0024] Figure 3 is the relationship between the root mean square error (RMSE) and the number of snapshots;

[0025] Figure 4 is the relationship between the root mean square error (RMSE) and the number of array antennas (Number of sensors). DETAILED DESCRIPTION

[0026] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0027] Assume that K wave direction of arrival angles are Narrowband point source Located in the far field of M (M>K) unidirectional uniform linear array structures and propagating in a uniform medium, the single-bit uniform linear array structure is as follows Figure 1 Assume that the first array element is the reference array element and is located at the origin of the coordinate system, that is, d1 = 0, then d m =(m-1)d,d m =λ / 2 is the array element spacing, λ is the wavelength of the signal. It can be obtained that at discrete time t, the analog signal received by the antenna array can be expressed as (the output signal without single-bit sampler)

[0028] x(t)=A(θ)s(t)+n(t), t=1,…,Nn(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), n(t) = [n1(t), n2(t), …, n M (t)] T , A(θ)=[a(θ1),…,a(θ K )] is the array flow matrix or steering matrix, and the kth steering vector is

[0029]

[0030] In the formula is an imaginary unit. Let s(t) be a zero-mean signal vector, and each signal is a wide stationary process with ergodicity, that is, its second-order statistics are time-invariant and its covariance matrix can be approximated by the sample covariance matrix. Let the noise n(t) be a circular complex Gaussian process that is independent in space and time and is uncorrelated with the signal s(t), then

[0031]

[0032] Where d(t1-t2) is the Kronecker impulse function, is the power or variance of the noise, 0 M and I M are the M-order zero matrix and the unit matrix respectively.

[0033] The output signal after the single-bit sampler can be expressed as

[0034] y(t)=Δ(x(t))=Δ(A(θ)s(t)+n(t)),t=1,…,N

[0035] Where Δ(x(t)) represents the single-bit sampling transformation of the complex signal and

[0036]

[0037] In the formula, and represents the operation of obtaining the real and imaginary parts, sign(·) represents the sign function and

[0038]

[0039] After obtaining the single-bit sampled data Y=[y(1), y(2), ..., y(N)], the following steps can be used to estimate the direction of arrival:

[0040] 1. According to the set sampling (snapshot) number N, perform N single-bit parallel sampling on the antenna array with M 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, that is, the value of each element in y(n), n=1,…, N, is one of the following four cases:

[0041] 2. Calculate the M×M dimensional sample covariance matrix of the single-bit received signal:

[0042]

[0043] where (·) H represents the conjugate transpose operation.

[0044] 3. Perform eigenvalue decomposition on the single-bit sample covariance matrix :

[0045]

[0046] where Λ = diag(λ1,…,λ M ) is a diagonal matrix, λ1,…,λ M represent its M eigenvalues and are arranged from largest to smallest, and Q = [q1,…,q M is the normalized eigenvector matrix.

[0047] 4. Obtain the signal subspace: Given the number of signal sources K (K < M), take the first K columns of the normalized eigenvector matrix Q as the signal subspace, that is, q1,…,q K .

[0048] 5. Construct the root-finding polynomial: Construct the M-dimensional column vector b(z) = [1, z -1 ,...,z -(M-1) T , (·) T represents the transpose operation, and define the root-finding polynomial

[0049]

[0050] where |·| represents the modulus operation, and z is any unknown variable (finding the roots of the equation P(z) = 0 with respect to z in S6).

[0051] 3. Direction of arrival estimation: By solving the K roots of the equation P(z) = 0, denoted as Then let φ k is the spatial angular frequency, and φ k = -πsinθ k , then the estimated value of the direction of arrival of the k-th signal source is arcsin(·) represents the arcsine.

[0052] The core idea of the above method working is that the core idea of all methods based on eigenvalue decomposition is that the column space spanned by the array manifold vector is the same subspace as the eigenvector corresponding to the larger eigenvalue. Next, the actual effect of the present invention will be demonstrated in combination with a simulation example, and the above method is abbreviated as 1-bit Root-MUSIC. In the simulation, assume the number of antennas M = 12, the number of signal sources K = 2, and the signal source positions are θ = [-5°, 6°] T ​, and d = λ / 2, the superimposed noise is Gaussian noise, and all results are the average results obtained from 5000 independent experiments. Figure 2 The figure shows the relationship between the root mean square error (RMSE) (RMSE in degree) and the signal-to-noise ratio (SNR) (SNR in dB). It can be seen from the figure that when the number of samples is 400, both the single-bit method (1-bit Root-MUSIC) and the unquantized method (Unquantized Root-MUSIC) perform better than when the number of samples is N = 200. Although the performance of the single-bit method is slightly worse than that of the Unquantized Root-MUSIC, the hardware cost of sampling is reduced, especially for large-scale antenna arrays, and a certain estimation effect can be achieved. Figure 3 and Figure 4 The relationship between the root mean square error (RMSE) and the number of snapshots and the number of sensors is given. Figure 3 It can be seen that the single-bit estimation method has a certain performance gain as the number of fast sorts increases, but under the condition of sample number N = 1200, the RMSE under SNR = 5dB is slightly higher than the RMSE under SNR = 0dB. This is because the error between the covariance matrix of the single-bit sample and the original unquantized covariance matrix is ​​larger under high signal-to-noise ratio conditions, and the error is lower under low signal-to-noise ratio conditions (One-bit MUSIC). According to Figure 4 It can be seen that the performance of all methods increases with the increase in the number of antennas, because the increase in the number of antennas brings more degrees of freedom.

Claims

1. A single-bit quantized direction of arrival estimation method based on a multi-antenna array, characterized in that: The following steps are involved: S1. Obtain a single-bit signal, specifically: Set the sampling number N, perform N single-bit parallel sampling on the antenna array with M array elements, and obtain an M×N-dimensional single-bit baseband received signal: Y=[y(1),y(2),…,y(N)] Wherein, the M-dimensional column vector y(n) represents the single-bit received signal of the nth sample, n=1,…,N; S2. Construct a covariance matrix using a single-bit received signal: In the formula, (·) H represents the conjugate transpose operation; S3, covariance matrix for single-bit samples Perform eigenvalue decomposition: Where Λ=diag(λ1,…,λ M ) is a diagonal matrix, λ1,…,λ M It represents its M eigenvalues ​​and arranges them from large to small, Q = [q1,…,q M ] is the normalized eigenvector matrix; S4. Obtain the signal subspace: Given the number of signal sources K, where K < M, take the first K columns of the normalized eigenvector matrix Q as the signal subspace, i.e., q1, …, q K ; S5. Construct a root-finding polynomial: Construct an M-dimensional column vector b(z)=[1, z -1 ,...,z -(M-1) ] T , (·) T Represents the transpose operation and defines the root-finding polynomial: Among them, |·| represents the modulo operation, and z is the unknown variable; S6. Direction of Arrival Estimation: By solving the K roots of the equation P(z)=0, it is expressed as Then make k=1,…,K,φ k is the spatial angular frequency, and φ k = -πsinθ k , then the estimated direction of arrival of the kth source is arcsin(·) means to find the inverse sine.

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