CN116047401A - Underdetermined direction of arrival estimation method based on single-bit quantization - Google Patents

Abstract

The invention provides an underdetermined direction of arrival estimation method based on single-bit quantization. The method mainly obtains larger Array aperture and higher degree of freedom based on a differential synthesis Array (Difference Co-Array), constructs a novel single-bit sample variance matrix with multiple degrees of freedom through a space smoothing method, performs characteristic decomposition on the novel single-bit sample variance matrix to obtain a novel signal subspace with the degree of freedom larger than the number of original physical Array elements, and obtains the direction of arrival estimation of multiple sources through a polynomial root finding method without spectral peak search, thereby realizing the under-determined direction of arrival estimation with the number of the sources larger than the number of the physical Array elements, and having lower computational complexity and super-resolution characteristics.

Description

Underdetermined direction of arrival estimation method based on single-bit quantization

Technical Field

The invention belongs to the technical field of information and communication, and relates to an underdetermined direction of arrival estimation method based on single-bit quantization.

Background

Direction of arrival estimation (array direction finding) is an important topic in array signal processing, which has important applications in both traditional electronic information industries (e.g., wireless communications, astronomy, radar, sonar, etc.) and modern vertical industries (e.g., intelligent driving, unmanned aerial vehicle operation, intelligent manufacturing, intelligent home, etc.). The direction of arrival estimation has been rapidly developed in recent 60 years, and advanced direction of arrival estimation methods with super resolution and low complexity have been the target sought by vast researchers. With the continuous development and progress of modern scientific technology, array antenna systems gradually tend to be integrated onto miniaturized devices or platforms, i.e., to achieve target positioning perception on the miniaturized platforms. However, miniaturized platforms (e.g., unmanned aerial vehicles, intelligent vehicles) are severely limited by platform resources and require optimization in terms of computing power, cost, power consumption, storage, etc. However, as the number of array antennas increases, the total power consumption of the high-precision quantized analog-to-digital converter of the multi-antenna array increases exponentially, making a miniaturized platform impractical or impractical due to the high hardware cost and high power consumption. As a new generation of multi-antenna array receiver, the single-bit receiver has the advantages of large instantaneous bandwidth, real-time processing, high sensitivity and small volume, and has wide application in the field of modern electronic warfare. In general, single bit quantization has significant advantages in terms of simplifying the system, saving the computing power, reducing the cost and improving the efficiency, and has great application potential in modern radars and countermeasure systems thereof which require mass data processing.

The conventional linear array-based direction of arrival estimation methods (such as the MUSIC method in Multiple emitter location and signal parameter estimation) consider received signals that are all obtained by an infinite number of bits high precision quantized receiver. In order to avoid the occurrence of the direction finding ambiguity phenomenon, the array element spacing of the linear array generally does not exceed a half wavelength corresponding to the incident signal. Then, the high-precision quantized receiver of the conventional multi-antenna array has high cost, high power consumption and complex construction, and is impractical for a large-scale antenna array system to be applied to the radio frequency front end. Thus, in the receiver data acquisition process, a tradeoff between sampling rate and quantization accuracy is typically required. In contrast, single bit quantization, which retains only the sampled data symbol bits, has proven to be promising in large-scale multi-antenna systems. This is because single bit quantization can be achieved by only a simple comparator, no automatic gain control is required, power consumption is only a few milliwatts, and a low power consumption and low complexity solution is provided for the system while ensuring certain performance. The document DOA estimation using one-bit quantized measurements carries out direction of arrival estimation by reconstructing unquantized covariance matrix, but the computational complexity of reconstructing covariance matrix is higher. The document One-bit MUSIC directly constructs a covariance matrix from single-bit measurement, does not need to reconstruct the original unquantized covariance matrix, and directly realizes the estimation of the direction of arrival under single-bit measurement. Because of the limitation of the aperture of the physical array, the methods cannot realize the underdetermined direction of arrival estimation of which the information source number is larger than the physical array element number, so a new super-resolution underdetermined direction of arrival estimation method under single-bit quantization is needed.

Disclosure of Invention

The invention mainly provides an underdetermined direction of arrival estimation method based on single-bit quantization. The method mainly obtains larger Array aperture and higher degree of freedom based on a differential synthesis Array (Difference Co-Array), constructs a novel single-bit sample variance matrix with multiple degrees of freedom through a space smoothing method, performs characteristic decomposition on the novel single-bit sample variance matrix to obtain a novel signal subspace with the degree of freedom larger than the number of original physical Array elements, and obtains the direction of arrival estimation of multiple sources through a polynomial root finding method without spectral peak search, thereby realizing the under-determined direction of arrival estimation with the number of the sources larger than the number of the physical Array elements, and having lower computational complexity and super-resolution characteristics.

The technical scheme adopted by the invention comprises the following steps:

s1, arranging an array structure as a two-stage linear nested array, namely nesting two uniform linear arrays, wherein the array element number of the first-stage uniform linear array is M ₁ The array element number of the second-stage uniform linear array is M ₂ And the total array element number is M=M ₁ +M ₂ ；

S2, acquiring a single-bit signal, which specifically comprises the following steps:

setting the sampling snapshot number N, and carrying out N times of single-bit parallel sampling on an antenna array with M array elements to obtain M multiplied by N dimension single-bit baseband receiving signals:

Y＝[y(1),y(2),…,y(N)]

wherein, the M-dimensional column vector y (N) represents a single-bit received signal sampled by the nth snapshot, n=1, …, N;

s3, constructing a covariance matrix through a single-bit received signal:

in the ( ^H Represents the operation of conjugate transposition,

is an M x M dimensional matrix;

s4, covariance matrix of single-bit sample

Vector quantization operation is carried out, and a new virtual receiving signal is obtained as follows:

wherein vec (·) represents vector quantization operation on the matrix, i.e. column-wise straightening to form a new column vector, y is M ² A dimension column vector;

s5, performing space smoothing operation on the virtual received signal y to obtain

Dimensional space smoothing sample covariance matrix

Wherein spatial sm 0-ing represents a spatial smoothing operation,

representing the number of array elements of the new virtual uniform linear array;

s6, space smoothing covariance matrix R _ss And (3) performing eigenvalue decomposition:

in the method, in the process of the invention,

is a diagonal matrix>

Indicating +.>

The characteristic values are arranged from big to small, and Q= [ Q ] ₁ ，…，q _M ]A normalized eigenvector matrix;

s7, acquiring a signal subspace: given the number K of sources of information,

taking the first K columns of the normalized eigenvector matrix Q as the signal subspace, i.e. Q ₁ ，…，q _K ；

S8, constructing a root-finding polynomial: : structure of the device

Valien vector->

(·) ^T Representing a transpose operation and defining a root-finding polynomial:

wherein, I·| represents modulo operation, z is any unknown variable;

s9, estimating the direction of arrival: by solving K roots of equation P (z) =0, expressed as

Then let the

φ _k Is the spatial angular frequency, and phi _k ＝-πsinθ _k The estimated direction of arrival value of the kth (k=1, …, K) source is +.>

arcsin (·) represents the inverse sine.

The invention has the beneficial effects that the direction of arrival estimation is obtained by adopting the root-finding mode, the spectrum peak search is not needed, and the blue can be realized

And (possibly K is larger than or equal to M), and has lower computational complexity.

Drawings

FIG. 1 is a single bit two-level nested uniform linear array structure;

FIG. 2 is a graph showing Root Mean Square Error (RMSE) as a function of signal-to-noise ratio (SNR);

fig. 3 shows the Root Mean Square Error (RMSE) as a function of snapshot count (Number of snapshots).

Detailed Description

The technical scheme of the invention is described in detail below with reference to the accompanying drawings.

Let K direction of arrival angles be

Is a narrowband point source->

Is positioned in the far field of M homodromous uniform linear array structures and propagates in a uniform medium. In the simulation experiment, M=6 is set, and the array element position of the first-stage nested array is S _inner = { md, m=1, 2,3}, the array element position of the second level nested array is S _outer = {4md, m=1, 2,3}, where d is a half-wave long distance, and its single-bit uniform linear array structure is shown in fig. 1. K=7 sources exist in the space, and the incoming wave directions are-60 °, -42 °, -30 °, -15 °,20 °,35 °,55 °, respectively. At discrete time t, the analog signal received by the antenna array may be represented as (output signal without going through a single bit sampler)

x(t)＝A(θ)s(t)+n(t)，t＝1，…，N

n (t) is an observation noise vector, where x (t) = [ x ] ₁ (t)，x ₂ (t)，…，x _M (t)] ^T ，θ＝[θ ₁ ，θ ₂ ，…，θ _K ] ^T N is the total snapshot (sample) number, N (t) = [ N ₁ (t)，n ₂ (t)，…，n _M (t)] ^T ，A(θ)＝[a(θ ₁ )，…，a(θ _K )]For an array flow pattern matrix or steering matrix. Let s (t) be the zero mean signal vector and each signal be a broad stationary process and have each state history, i.e. its second order statistics are time-invariant and the covariance matrix can be approximated by a sample covariance matrix. Assuming that the noise n (t) is a space-time independent cyclic complex Gaussian (circular complex Gaussian) process and is uncorrelated with the signal s (t), then

Wherein delta (t) ₁ -t ₂ ) Is a kronecker impulse function,

is the power or variance of the noise, 0 _M And I _M The zero matrix and the unit matrix are respectively M-order.

The output signal through the single bit sampler can be expressed as

y(t)＝Δ(x(t))＝Δ(A(θ)s(t)+n(t))，t＝1，…，N

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

in the method, in the process of the invention,

and->

Representing the operation of taking the real and imaginary parts, sign (& gt) representing the sign function and +.>

After obtaining the single bit sample data y= [ Y (1), Y (2), …, Y (N) ] the direction of arrival estimation may be performed as follows:

1. according to the set sampling (snapshot) number N, N times of single-bit parallel sampling is carried out on an antenna array with M (M=6) array elements, and M multiplied by N dimension single-bit baseband receiving signals Y= [ Y (1), Y (2), … and Y (N) are obtained]Where 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. the value of each element in y (N), n=1, …, N, is one of the following 4 cases:

2. calculating an M x M dimension sample covariance matrix of the single-bit received signal:

in the ( ^H Representing a conjugate transpose operation.

3. Covariance matrix for single bit samples

Vector quantization operation is carried out, and a new virtual receiving signal is obtained as follows:

wherein vec (·) represents vector quantization operation on the matrix, i.e., forming a new column vector by column-wise straightening;

4. performing space smoothing operation on the virtual receiving signal y to obtain

Dimensional space smoothing sample covariance matrix

Wherein spatial smoothing represents a spatial smoothing operation,

representing the number of array elements of the new virtual uniform linear array;

5. for space smoothing covariance matrix R _ss And (3) performing eigenvalue decomposition:

in the method, in the process of the invention,

is a diagonal matrix>

Indicating +.>

The characteristic values are arranged from big to small, and Q= [ Q ] ₁ ，…，q _M ]A normalized eigenvector matrix;

6. acquiring a signal subspace: given that the number of sources k=7,

taking the first K columns of the normalized eigenvector matrix Q as the signal subspace, i.e. Q ₁ ，…，q _K ；

7. Constructing a root-finding polynomial: : structure of the device

Valien vector->

(·) ^T Representing transpose operations and definingRoot-finding polynomials:

wherein, I·| represents modulo operation, z is any unknown variable;

9. estimating the direction of arrival: by solving K roots of equation P (z) =0, expressed as

Then let->

φ _k Is the spatial angular frequency, and phi _k ＝-πsinθ _k The estimated direction of arrival value of the kth (k=1, …, K) source is +.>

arcsin (·) represents the inverse sine.

10. The Root Mean Square Error (RMSE) is calculated from the estimated and actual values.

The practical effect of the invention is demonstrated below in combination with a simulation example, and the method is abbreviated as 1-bit SS-MUSIC. Let the superimposed noise be gaussian noise and all the results be average results obtained from 20000 independent experiments. The method of participation in the comparison is Unqualited SS-MUSIC in the document "Nested arrays: A novel approach to array processing with enhanced degrees of freedom". Fig. 2 shows the variation of Root Mean Square Error (RMSE) with Signal-to-Noise Ratio (SNR) in dB for a sample number of 500. Fig. 3 shows the variation of Root Mean Square Error (RMSE) in degrees with the number of beats (Number of snapshots) for an SNR of 0 dB. As can be seen from fig. 3, the single bit method (1-bit SS-MUSIC) has a certain loss in RMSE performance than the Unquantized SS-MUSIC method (Unquantized SS-MUSIC) because there is a certain error between the single bit sample covariance matrix and the original Unquantized covariance matrix, but both achieve underdetermined direction of arrival estimation. Although the single bit method has slightly poorer performance than the Unqualited SS-MUSIC, a certain estimation effect can be achieved, and meanwhile, the cost of sampling hardware is reduced, so that the system integration and miniaturization are facilitated.

Claims (1)

1. An underdetermined direction of arrival estimation method based on single bit quantization is characterized by comprising the following steps:

s1, arranging an array structure as a two-stage linear nested array, namely nesting two uniform linear arrays, wherein the array element number of the first-stage uniform linear array is M ₁ The array element number of the second-stage uniform linear array is M ₂ The total array element number is m=m ₁ +M ₂ ；

S2, acquiring a single-bit signal, which specifically comprises the following steps:

setting the sampling snapshot number N, and carrying out N times of single-bit parallel sampling on an antenna array with M array elements to obtain M multiplied by N dimension single-bit baseband receiving signals:

Y＝[y(1),y(2),…,y(N)]

wherein, the M-dimensional column vector y (N) represents a single-bit received signal sampled by the nth snapshot, n=1, …, N;

s3, constructing a covariance matrix through a single-bit received signal:

in the ( ^H Represents the operation of conjugate transposition,

is an M x M dimensional matrix;

s4, covariance matrix of single-bit sample

Vector quantization operation is carried out to obtain newIs:

wherein vec (·) represents vector quantization operation on the matrix, i.e. column-wise straightening to form a new column vector, y is M ² A dimension column vector;

s5, performing space smoothing operation on the virtual received signal y to obtain

Dimension space smooth sample covariance matrix ++>

Wherein spatial smoothing represents a spatial smoothing operation,

representing the number of array elements of the new virtual uniform linear array;

s6, space smoothing covariance matrix R _ss And (3) performing eigenvalue decomposition:

in the method, in the process of the invention,

is a diagonal matrix>

Indicating +.>

The characteristic values are arranged from big to small, and Q= [ Q ] ₁ ,…,q _M ]A normalized eigenvector matrix;

s7, acquiring a signal subspace: given the number K of sources of information,

taking the first K columns of the normalized eigenvector matrix Q as the signal subspace, i.e. Q ₁ ,…,q _K ；

S8, constructing a root-finding polynomial: : structure of the device

Valien vector->

(·) ^T Representing a transpose operation and defining a root-finding polynomial:

wherein, I·| represents modulo operation, z is any unknown variable;

s9, estimating the direction of arrival: by solving K roots of equation P (z) =0, expressed as

Then let the

k＝1,…,K，φ _k Is the spatial angular frequency, and phi _k ＝-πsinθ _k The estimated direction of arrival value of the kth (k=1, …, K) source is +.>

arcsin (·) represents the inverse sine. />

Images