阅读说明：本技术 基于单比特量化信号虚拟域统计量重建的互质阵列波达方向估计方法 (Estimation method of direction of arrival of co-prime array based on single-bit quantized signal virtual domain statistic reconstruction ) 是由 周成伟 史治国 顾宇杰 陈积明 于 2020-06-08 设计创作，主要内容包括：本发明公开了一种基于单比特量化信号虚拟域统计量重建的互质阵列波达方向估计方法,主要解决现有技术中软硬件实现难度大及自由度受限等问题,其实现步骤是：接收端布设互质阵列与单比特模数转换器；接收端布设互质阵列与单比特模数转换器；计算互质阵列单比特接收信号所对应的等价虚拟信号；构造初始化单比特量化信号虚拟域增广协方差矩阵；基于量化与非量化信号间的统计关联性分析,设计基于量化信号虚拟域统计量重建的优化问题；利用优化所得单比特量化信号所对应的虚拟域增广协方差矩阵进行波达方向估计。本发明融合了互质阵列与单比特信号处理的优势特性,对于面向新一代无线通信系统以及无源定位、目标探测等实际应用具有广阔的前景。(The invention discloses a method for estimating the direction of arrival of a co-prime array based on single-bit quantized signal virtual domain statistic reconstruction, which mainly solves the problems of high difficulty in realizing software and hardware, limited degree of freedom and the like in the prior art, and comprises the following implementation steps of: the receiving end is provided with a co-prime array and a single-bit analog-to-digital converter; the receiving end is provided with a co-prime array and a single-bit analog-to-digital converter; calculating equivalent virtual signals corresponding to the single-bit receiving signals of the relatively prime array; constructing an initialized single-bit quantized signal virtual domain augmented covariance matrix; designing an optimization problem based on quantized signal virtual domain statistic reconstruction based on statistical relevance analysis between quantized and non-quantized signals; and performing direction-of-arrival estimation by using a virtual domain augmented covariance matrix corresponding to the single-bit quantized signal obtained by optimization. The invention integrates the advantages of the co-prime array and the single-bit signal processing, and has wide prospect for the actual application of a new generation of wireless communication system, passive positioning, target detection and the like.)

1. A method for estimating the direction of arrival of a co-prime array reconstructed based on single-bit quantized signal virtual domain statistics is characterized by comprising the following steps:

(1) the receiving end uses M + N-1 antennas to arrange a co-prime array

(2) the model of the single-bit received signal of the coprime array. Suppose there are K from θ₁；θ₂；···；θ_KA far-field narrow-band incoherent signal source in the angle direction receives an incident signal by adopting the co-prime array and the single-bit analog-to-digital converter which are constructed in the step (1) to obtain a co-prime array single-bit received signal at the first momentThe modeling can be as follows:

wherein the content of the first and second substances,for single bit quantisation operators, x (l) for unquantized coprime array raw received signal, s_k(l) Is the waveform of the k-th signal,for the noise term to be independent from each signal source,to correspond to theta_kCo-prime array of directions

Wherein u is_i(ii) a i is 1; 2, ·; m + N-1 represents the actual position of the ith physical antenna element in the co-prime array, and u₁＝0，

This (·)^HRepresents a conjugate transpose;

(3) and calculating equivalent virtual signals corresponding to the single-bit receiving signals of the relatively prime array. Vectorized co-prime array single bit received signal sampling covariance matrix

Corresponding to non-uniform virtual array

Where vec (-) denotes vectorizationThe operation of stacking the columns in the matrix in sequence to form a new vector,

wherein the content of the first and second substances,

(4) and constructing an initialized single-bit quantized signal virtual domain augmented covariance matrix. Non-uniform virtual array for overcoming co-prime array

where max (·) is the set max operation. Correspondingly, the equivalent virtual signal corresponding to the virtual domain uniform linear array

wherein, Toep (·) represents that a vector is taken as a first column of the Hermite Toeplitz matrix;

(5) based on the analysis of statistical relevance between single-bit quantized signal and original unquantized signal statistics, the optimization problem based on quantized signal virtual domain statistics reconstruction is designed to obtain the virtual uniform arrayThe signal covariance matrix is quantized with a single bit. Based on analysis of statistical properties, the invention is based on a single-bit quantized signal covariance matrixCovariance matrix with original unquantized signalThe characteristic that the maximum linear irrelevance groups of the signal are the same is found, and the fact that the single-bit quantization process of the signal does not change the rank of the covariance matrix is shown. Thus, is composed ofVirtual domain augmented covariance matrix corresponding to the derived single-bit quantized signal

wherein the content of the first and second substances,

(6) Corresponding to a virtual uniform array using optimization

2. The method for estimating direction of arrival of a co-prime array reconstructed based on single-bit quantized signal virtual domain statistics of claim 1, wherein the co-prime array in step (1) is laid out by: firstly, a pair of coprime integers M, N is selected, then a pair of sparse uniform linear sub-arrays is constructed, wherein the first sub-array comprises M antenna array elements with the distance Nd, and the positions of the M antenna array elements are

3. The method for estimating direction of arrival of a co-prime array based on single-bit quantized signal virtual domain statistic reconstruction as claimed in claim 1, wherein the optimization problem of step (5) whose optimization solution can utilize convex relaxation technique by introducing convex relaxation technique

4. The method according to claim 1, wherein the optimization problem in step (5) can be solved by ADMM, global optimization, approximate approximation, etc. to obtain the estimation result corresponding to the virtual uniform array

5. The method for estimating direction of arrival of a co-prime array reconstructed based on single-bit quantized signal virtual domain statistics of claim 1, wherein the direction of arrival estimation in step (6) is estimated by: based on the resultsCorresponding to a virtual uniform arrayThe direction of arrival estimation may be calculated by calculating the following spatial spectrum:

wherein the content of the first and second substances,

6. The method of claim 1, wherein the direction of arrival estimation of the co-prime array based on the reconstruction of the single-bit quantized signal virtual domain statistics is based on the virtual domain augmented covariance matrix corresponding to the single-bit quantized signalAnd processing by a traditional Nyquist method, such as a subspace method, a sparse method, an optimization solution method and the like, so as to realize the estimation of the direction of arrival.

Technical Field

The invention belongs to the technical field of signal processing, particularly relates to low-cost and efficient direction of arrival estimation of radar signals, acoustic signals and electromagnetic signals, and particularly relates to a method for estimating the direction of arrival of a co-prime array based on single-bit quantized signal virtual domain statistic reconstruction, which can be used for passive positioning, target detection and a new generation of wireless communication systems.

Background

Direction-of-Arrival Estimation (Direction-of-Arrival Estimation) receives airspace signals by using an array antenna, and processes the received signals by a statistical signal processing technology and various optimization methods to recover Direction-of-Arrival information contained in the signals, which is one of the basic problems in the field of array signal processing and has wide application in the fields of radar, sonar, voice, radio astronomy, seismology, wireless communication, medical imaging, and the like.

With the increasing user demand and data scale, large-scale antenna deployment at the base station end is one of the typical features in the new generation wireless communication system. Meanwhile, with the popularization and application of the angle domain channel modeling theory in a millimeter wave Massive MIMO (Massive Multiple-Input Multiple-Output, Massive MIMO) system, the traditional direction of arrival estimation faces a huge technical challenge. On one hand, the traditional direction-of-arrival estimation is limited by the limitation of Nyquist sampling rate, the degree of freedom (namely the number of incident signal sources capable of being resolved) is determined by the number of antenna array elements, but the increase of the number of users is far higher than the increase of the number of antennas at the base station end, so when the number of the incident signal sources in a certain spatial domain range is larger than or equal to the number of the antenna array elements in the array, the effective direction-of-arrival estimation cannot be carried out by the existing uniform array method; on the other hand, with the increase of the number of antennas, a large-scale antenna system faces huge pressure on the aspects of deployment cost, operation power consumption, calculation data amount and the like, and further causes huge pressure and challenge in practical application.

In order to solve the above problems, the proposed sparse array makes effective direction of arrival estimation possible under the condition of under-sampling, and as a sparse array with a systematic structure, a co-prime array can obtain more degrees of freedom by using the same number of antenna array elements, so as to break through the performance bottleneck in the aspect of degrees of freedom, and has received unprecedented attention in the field of direction of arrival estimation. However, the existing estimation method for the direction of arrival of the co-prime array generally presupposes an idealized signal sampling quantization process, which is obviously impossible in practical system application, and quantization errors caused by the limited-precision quantization process are inevitable. On the other hand, with the development of the large-scale MIMO technology, the deployment of a low-bit Analog-to-Digital Converter (ADC) at the antenna end of the base station achieves the reduction of system cost, operation power consumption, data scale and calculation complexity on the premise of sacrificing part of performance, and single-bit quantization is the lowest precision sample in the above method. However, the existing single-ratio super-large scale MIMO system generally adopts a uniform array, and has the bottleneck problem of limited freedom degree.

In summary, the fusion of the sparse array and the single-bit quantization technology is an effective method for solving the problems of limited degree of freedom, high deployment cost, large operation power consumption, large data volume scale, high calculation complexity and the like in the existing large-scale MIMO system. Although scholars at home and abroad have initially explored relevant core technologies for fusion of sparse arrays and single-bit quantization technologies, research on estimation of single-bit direction of arrival for co-prime arrays is still in the beginning, and the statistical characteristics and technical characteristics of signal processing in the virtual domain of the co-prime arrays are not completely explored and applied. Therefore, how to fully utilize the advantages of the virtual domain signal processing of the co-prime array, overcome the performance loss and the model mismatch problem caused by the discontinuity of the virtual array, realize the efficient direction of arrival estimation of the single-bit quantized signal, reduce the performance loss relative to the original unquantized signal as much as possible, and even utilize the sparse characteristic to realize the performance level exceeding is an important problem to be solved at present.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a method for estimating the direction of arrival of a co-prime array reconstructed based on single-bit quantized signal virtual domain statistics, which explores the association relation between the virtual domain statistics and the traditional unquantized signal virtual domain statistics through modeling of the co-prime array single-bit quantized signal and the second-order statistics thereof; an optimization method based on quantized signal virtual domain statistic reconstruction is further provided to realize effective utilization of all signals of the non-uniform virtual array; and finally, estimating the direction of arrival based on the reconstructed single-bit quantized signal amplification virtual domain covariance matrix, thereby realizing the combination of the advantages and the characteristics of the co-prime array signal processing and the single-bit quantized signal processing, further fundamentally improving the comprehensive performance of the direction of arrival estimation, and providing technical support for the application of the direction of arrival estimation in the fields of new-generation large-scale MIMO systems and the like.

The purpose of the invention is realized by the following technical scheme: a method for estimating the direction of arrival of a co-prime array based on single-bit quantized signal virtual domain statistic reconstruction comprises the following steps:

(1) the receiving end uses M + N-1 antennas to arrange a co-prime arrayEach array element of the co-prime array is connected with a single-bit analog-to-digital converter for single-bit quantization of a received signal, wherein M and N are co-prime integers;

(2) the model of the single-bit received signal of the coprime array. Suppose there are K from θ₁，θ₂，···，θ_KA far-field narrow-band incoherent signal source in the angle direction receives an incident signal by adopting the co-prime array and the single-bit analog-to-digital converter which are constructed in the step (1) to obtain a co-prime array single-bit received signal at the first moment

The modeling can be as follows:

wherein the content of the first and second substances,for single bit quantisation operators, x (l) for unquantized coprime array raw received signal, s_k(l) Is the waveform of the k-th signal,

for the noise term to be independent from each signal source,

to correspond to theta_kCo-prime array of directionsIs expressed as

Wherein u is_iI 1, 2, M + N-1 denotes the actual position of the ith physical antenna element in the co-prime array, and u₁＝0，[·]^TRepresenting a transpose operation. Obtaining a sampling covariance matrix of the co-prime array single-bit receiving signal by using the acquired L sampling snapshots

This (·)^HRepresents a conjugate transpose;

(3) and calculating equivalent virtual signals corresponding to the single-bit receiving signals of the relatively prime array. Vectorized co-prime array single bit received signal sampling covariance matrix

Obtaining a virtual array equivalent received signal corresponding to the single-bit quantized signal

Corresponding to non-uniform virtual array

Where vec (-) denotes a vectorization operation, i.e. stacking columns in the matrix in sequence to form a new vector,for the covariance matrix of the unquantized original co-prime array received signal, diag (a) represents the diagonal elements taken to form the diagonalized matrix operation, E [. cndot]In order to take the desired action,which represents the kronecker product of,in order to carry out the operation of the solid-obtaining part,in order to take the imaginary part of the operation,

wherein the content of the first and second substances,represents the power of the k-th signal source,

representing the noise power, I is the identity matrix,to correspond to theta_kDirectionally non-uniform virtual array

The steering vector of (a) can be calculated as:wherein, (.)^*Is a conjugation operation;

(4) and constructing an initialized single-bit quantized signal virtual domain augmented covariance matrix. Non-uniform virtual array for overcoming co-prime array

The problem of signal model mismatch is brought, and a non-uniform virtual array is constructed

Virtual domain uniform linear array with same positive half shaft aperture and distance of dWhere the unit spacing d is half the wavelength of the incident narrowband signal:

where max (·) is the set max operation. Correspondingly, the equivalent virtual signal corresponding to the virtual domain uniform linear array

Can be obtained by the following steps: to is directed atEquivalent virtual signals corresponding to each corresponding virtual array element position if the virtual array element position is included in the non-uniform virtual array

In (3), the equivalent virtual of that positionAnalog signal andthe virtual signals corresponding to the positions of the corresponding virtual array elements are the same; remaining non-uniform virtual arrays

And setting the equivalent virtual signal corresponding to the middle discontinuous virtual array element part to zero. Then, initializing a single-bit quantized signal virtual domain augmented covariance matrix may be constructed as:

wherein, Toep (·) represents that a vector is taken as a first column of the Hermite Toeplitz matrix;

(5) based on the analysis of statistical relevance between single-bit quantized signal and original unquantized signal statistics, the optimization problem based on quantized signal virtual domain statistics reconstruction is designed to obtain the virtual uniform array

The signal covariance matrix is quantized with a single bit. Based on analysis of statistical properties, the invention is based on a single-bit quantized signal covariance matrixCovariance matrix with original unquantized signal

The characteristic that the maximum linear irrelevance groups of the signal are the same is found, and the fact that the single-bit quantization process of the signal does not change the rank of the covariance matrix is shown. Thus, is composed ofVirtual domain augmented covariance matrix corresponding to the derived single-bit quantized signal

Can be viewed as a virtual uniform array

But there are some missing elements (i.e., where the zero element is located), which would still retain the matrix rank information associated with the incident signal source in the ideal case where all elements are known. Based on the statistical relevance analysis among the statistics, the reconstruction problem of the augmented covariance matrix can be restricted and optimized by utilizing the low-rank characteristic of the augmented covariance matrix, and then the following is constructed to

The method comprises the following steps of (1) reconstructing and optimizing a single-bit quantized signal virtual domain statistic for an optimization target:

wherein the content of the first and second substances,representing projection operations for selecting

Neutralization ofFitting the elements at the positions corresponding to the nonzero elements, wherein lambda is a user adjustment parameter,determining a matrix constraint term for semi-positive, | ·| non-woven vision_FRepresenting the Frobenius norm and rank (·) representing the rank of the matrix. Solving the optimization problem described above yields a virtual uniform array

Single bit quantized signal covariance matrix of

(6) Corresponding to a virtual uniform array using optimization

Single bit quantized signal covariance matrix ofAnd estimating the direction of arrival.

Further, the relatively prime array in step (1) can be arranged by: firstly, a pair of coprime integers M, N is selected, then a pair of sparse uniform linear sub-arrays is constructed, wherein the first sub-array comprises M antenna array elements with the distance Nd, and the positions of the M antenna array elements are

The second sub-array comprises N antenna elements with Md spacing and at the positionThen, the two sub-arrays are combined according to the mode that the first array element is overlapped, and the non-uniform co-prime array actually containing M + N-1 physical antenna array elements is obtained

Further, the optimization problem of step (5), the optimization solution of which can utilize convex relaxation technique by introducingIn the convex function term substitution optimization problemThe penalty term is used, wherein trace (·) represents the trace of the matrix, and then various interior point method tools such as CVX are used for carrying out efficient solutionAnd (5) solving.

Further, the optimization problem in step (5) can be solved by ADMM, global optimization, approximate approximation, etc. to obtain the virtual uniform array

Single bit quantized signal covariance matrix of

Further, the direction of arrival estimation in step (6) may be estimated by: based on the results

Corresponding to a virtual uniform arrayThe direction of arrival estimation may be calculated by calculating the following spatial spectrum:

wherein the content of the first and second substances,

as a virtual uniform array corresponding to the angle thetaThe span operation is used for collecting the eigenvectors corresponding to all eigenvalues except the maximum K eigenvalues of the corresponding matrix, | | | | represents the Euclidean norm, searching the space spectrum f (theta) | ∈ [ -90 DEG; 90 DEG)]And sequencing all the maximum value points according to the magnitude of the response value f (theta), and taking the angle value theta corresponding to the K maximum value points with the maximum response value, namely the estimation result of the direction of arrival.

Further, the direction of arrival estimation in step (6) may be based on the virtual domain augmented covariance matrix corresponding to the obtained single-bit quantized signalMatrix ofAnd processing by a traditional Nyquist method, such as a subspace method, a sparse method, an optimization solution method and the like, so as to realize the estimation of the direction of arrival.

Compared with the prior art, the invention has the following advantages:

(1) the method fully utilizes the advantage that the co-prime array can increase the degree of freedom of the estimation of the direction of arrival, deduces the single-bit co-prime array received signal to the virtual domain, designs the optimization problem based on the virtual domain signal processing on the basis of constructing the statistic characteristics of the co-prime array and the unqualified virtual domain, realizes that the number of incident signal sources distinguishable by the estimation of the direction of arrival is larger than the number of physical antenna array elements, improves the degree of freedom and reduces the calculation complexity;

(2) the method is designed based on the signal model modeling of the single-bit quantized signal to estimate the direction of arrival, combines the performance advantages of the co-prime array signal processing, and has important significance in the aspects of antenna deployment cost, system operation power consumption, data processing efficiency and the like in practical application.

(3) The method specially designs the estimation method of the direction of arrival aiming at the co-prime array, fully considers the characteristic that the virtual array corresponding to the co-prime array is a non-uniform array, realizes the effective utilization of all non-uniform virtual array elements by the quantitative signal virtual domain statistic reconstruction, and avoids the problems of performance loss, model mismatch and the like caused by the non-uniformity of the virtual array.

Drawings

FIG. 1 is a general flow diagram of the present invention.

FIG. 2 is a schematic diagram of a pair of sparse uniform subarrays constituting a co-prime array according to the present invention.

FIG. 3 is a schematic diagram of the structure of the co-prime array of the present invention.

Fig. 4 is a schematic diagram of a spatial spectrum of the method of the present invention, where K is 8.

Fig. 5 is a schematic diagram of a spatial spectrum of the method of the present invention, where K is 11.

Fig. 6 is a graph showing the comparison of the rms error versus the snr for the proposed method.

Detailed Description

The technical means and effects of the present invention will be described in further detail below with reference to the accompanying drawings.

The existing direction-of-arrival estimation methods face a series of challenges such as limited degree of freedom, high system deployment cost and operation power consumption, large data volume, complex calculation and the like. In order to solve the above challenges, the present invention provides a method for estimating a direction of arrival of a co-prime array reconstructed based on single-bit quantized signal virtual domain statistics by fusing the advantageous features of co-prime array signal processing and single-bit signal processing, and referring to fig. 1, the implementation steps of the present invention are as follows:

the method comprises the following steps: m + N-1 physical antenna array elements are used for constructing a co-prime array at a receiving end, and each receiving end antenna is matched with a single-bit analog-to-digital converter for signal receiving. Firstly, selecting a pair of relatively prime integers M, N; then, referring to fig. 2, a pair of sparse uniform linear sub-arrays is constructed, wherein the first sub-array comprises M antenna elements with a spacing Nd and is located at

The second sub-array comprises N antenna elements with Md spacing and at the position

The unit interval d is half of the wavelength of the incident narrowband signal; then, the two sub-arrays are combined according to the way of overlapping the first array element, referring to fig. 3, the non-uniform co-prime array actually containing M + N-1 physical antenna array elements is obtained

Each receiving end antenna is matched with a single-bit analog-to-digital converter for carrying out binary quantization on received signals.

Step two: the model of the single-bit received signal of the coprime array. Suppose there are K from θ₁，θ₂；···；θ_KA far-field narrow-band incoherent signal source in the angle direction receives an incident signal by adopting a co-prime array and a single-bit analog-to-digital converter which are constructed in the step one to obtain a co-prime array single-bit received signal at the first momentThe modeling can be as follows:

wherein the content of the first and second substances,for single bit quantisation operators, x (l) for unquantized coprime array raw received signal, s_k(l) Is the waveform of the k-th signal,

for the noise term to be independent from each signal source,to correspond to theta_kA guiding vector of a relatively prime array of directions, expressed as

Wherein u is_i(ii) a i is 1; 2; m + N-1 denotes the actual position of the ith physical antenna element in the co-prime array, and u₁＝0，[·]^TRepresenting a transpose operation. Obtaining a sampling covariance matrix of the co-prime array single-bit receiving signal by using the acquired L sampling snapshots

This (·)^HRepresenting a conjugate transpose.

Step three: and calculating equivalent virtual signals corresponding to the single-bit receiving signals of the relatively prime array. Vectorized co-prime array single bit received signal sampling covariance matrixObtaining a virtual array equivalent received signal corresponding to the single-bit quantized signal

Corresponding to non-uniform virtual array

Where vec (-) denotes a vectorization operation, i.e. stacking columns in the matrix in sequence to form a new vector,for the covariance matrix of the unquantized original co-prime array received signal, diag (a) represents the diagonal elements taken to form the diagonalized matrix operation, E [. cndot]In order to take the desired action,which represents the kronecker product of,

in order to carry out the operation of the solid-obtaining part,

in order to take the imaginary part of the operation,

wherein the content of the first and second substances,represents the power of the k-th signal source,

representing the noise power, I is the identity matrix,to correspond to theta_kDirectionally non-uniform virtual arrayThe steering vector of (a) can be calculated as:

wherein, (.)^*Is a conjugate operation.

Step four: and constructing an initialized single-bit quantized signal virtual domain augmented covariance matrix. Non-uniform virtual array for overcoming co-prime arrayThe problem of signal model mismatch is brought, and a non-uniform virtual array is constructed

Virtual domain uniform linear array with same positive half shaft aperture and distance of d

Where max (·) is the set max operation. Accordingly, theEquivalent virtual signal corresponding to the virtual domain uniform linear array

Can be obtained by the following steps: to is directed at

Equivalent virtual signals corresponding to each corresponding virtual array element position if the virtual array element position is included in the non-uniform virtual array

Then the equivalent virtual signal at that location isThe virtual signals corresponding to the positions of the corresponding virtual array elements are the same; remaining non-uniform virtual arrays

And setting the equivalent virtual signal corresponding to the middle discontinuous virtual array element part to zero. Then, initializing a single-bit quantized signal virtual domain augmented covariance matrix may be constructed as:

wherein Toep (-) denotes the first column of the Hermite Toeplitz matrix as the vector.

Step five: based on the analysis of statistical relevance between single-bit quantized signal and original unquantized signal statistics, the optimization problem based on quantized signal virtual domain statistics reconstruction is designed to obtain the virtual uniform arrayThe signal covariance matrix is quantized with a single bit.

Based on analysis of statistical properties, the invention is based on a single-bit quantized signal covariance matrixCovariance matrix with original unquantized signalThe characteristic that the maximum linear irrelevance groups of the signal are the same is found, and the fact that the single-bit quantization process of the signal does not change the rank of the covariance matrix is shown. Thus, is composed ofVirtual domain augmented covariance matrix corresponding to the derived single-bit quantized signal

Can be viewed as a virtual uniform array

But there are some missing elements (i.e., where the zero element is located), which would still retain the matrix rank information associated with the incident signal source in the ideal case where all elements are known.

Based on the statistical relevance analysis among the statistics, the reconstruction problem of the augmented covariance matrix can be restricted and optimized by utilizing the low-rank characteristic of the augmented covariance matrix, and then the following is constructed to

The method comprises the following steps of (1) reconstructing and optimizing a single-bit quantized signal virtual domain statistic for an optimization target:

wherein the content of the first and second substances,representing projection operations for selectingNeutralization ofFitting the elements at the positions corresponding to the nonzero elements, wherein lambda is a user adjustment parameter,determining a matrix constraint term for semi-positive, | ·| non-woven vision_FRepresenting the Frobenius norm and rank (·) representing the rank of the matrix.

The above optimization problem can be solved by introducing various convex relaxation techniques, such as: by optimizing the above

The penalty term is usedThe convex function term is substituted, wherein trace (·) represents the trace of the matrix, and the trace can be solved through various interior point method tools such as CVX. In addition, the optimization problem can be solved by ADMM, global optimization, approximate approximation and the like to obtain the virtual uniform array

Single bit quantized signal covariance matrix of

Step six: utilizing the optimized single-bit quantized signal corresponding virtual domain augmented covariance matrix

And estimating the direction of arrival. Due to the obtained

Corresponding to a virtual uniform arrayThe direction of arrival estimation may be calculated by calculating the following spatial spectrum:

wherein the content of the first and second substances,

as a virtual uniform array corresponding to the angle theta

The span operation is used for collecting the eigenvectors corresponding to all eigenvalues except the maximum K eigenvalues of the corresponding matrix, | | · | | represents the Euclidean norm, searching the space spectrum f (theta), theta ∈ [ -90 degrees, 90 degrees]And sequencing all the maximum value points according to the magnitude of the response value f (theta), and taking the angle value theta corresponding to the K maximum value points with the maximum response value, namely the estimation result of the direction of arrival.

In addition, based on the virtual domain augmented covariance matrix corresponding to the single-bit quantized signalThe estimation of the direction of arrival can also be realized by processing through a traditional Nyquist method, such as a subspace method, a sparse method, an optimization solution method and the like.

On one hand, the invention fully utilizes the advantages of the signal processing of the co-prime array virtual domain, fully utilizes all the discontinuous virtual array elements and realizes the estimation freedom degree of the direction of arrival

To

The improvement of (1) enables the proposed method to estimate more than the conventional nyquist method at the same number of antennasThe incident signal source reduces the number of radio frequency channels in hardware deployment and reduces the data scale and the calculation complexity of received signals; on the other hand, the invention realizes the sparse array virtual domain signal processing based on the single-bit quantized signal by utilizing the single-bit signal processing technology, and utilizes the single-bit quantized signal covariance rectangle corresponding to the augmented virtual array to carry out efficient direction of arrival estimation according to the statistical relevance analysis of the quantized signal statistic. Meanwhile, the single-bit direction-of-arrival estimation method provided by the invention reduces the average power consumption of a plurality of watts of a main stream 12-16 bit analog-to-digital converter in the existing system to a plurality of milliwatts, greatly reduces the power consumption of the system, and simultaneously avoids adverse effects caused by errors between idealized modeling and limited precision quantization in the traditional method.

The effect of the proposed method is further described below with reference to simulation examples.

Simulation example 1: the parameters of the co-prime array are selected to be M-3 and N-5, that is, the co-prime array of the framework comprisesAnd each antenna element. The incident directions of the incident narrow-band signals are uniformly distributed at-50 deg. and 50 deg]The signal-to-noise ratio is 0dB, the sampling fast beat number is L500, and the user adjustment parameter λ is 0.25. The estimation method of the direction of arrival of the co-prime array based on the single-bit quantized signal virtual domain statistic reconstruction is under the underdetermined conditionAnd

the lower spatial spectrum is shown in fig. 4 and 5, respectively, wherein the dashed line represents the true direction of arrival of the incident signal. The simulation result shows that the method provided by the invention can effectively distinguish all incident signal sources under the two conditions, which shows that the degree of freedom is still improved under the background of single-bit quantized signal processing. In addition, the results shown in FIG. 5 further illustrate that the present invention can effectively utilize non-uniform arraysAnd the virtual domain Nyquist signal processing is carried out by using discontinuous array elements, so that the maximization of the degree of freedom performance is realized.

Simulation example 2: the parameters of the co-prime array are selected to be M-3 and N-5, that is, the co-prime array of the framework comprises

And each antenna element. Suppose that

The incident directions of narrow band incident signals are uniformly distributed at [ -50 DEG, 50 DEG ]]The sampling fast beat number is L500, and the user adjustment parameter λ is 0.25. The performance comparison schematic diagram of the root mean square error along with the signal-to-noise ratio of the method provided by the invention and the existing sparse signal reconstruction and virtual interpolation method based on non-quantized signals is shown in fig. 6, wherein the distance between the grid points of the predefined space used for sparse reconstruction and spectral peak search in the compared method is 0.1 degrees, and for each signal-to-noise ratio simulation parameter setting, the root mean square error is obtained by averaging 1000 Monte Carlo tests. Meanwhile, the clarmero bound based on the virtual domain signal processing is also given at the same time to represent the optimal value. From the comparison result shown in fig. 6, it can be seen that when the signal-to-noise ratio is greater than 5dB, the method of the present invention can still obtain better performance than the method based on non-quantized signal processing under the condition of single-bit quantization, and maintain the same performance trend as the cramer-mero boundary of virtual domain signal processing.

In conclusion, the invention mainly solves the defects of the prior art in the aspects of the degree of freedom, the computational complexity, the system deployment cost, the power consumption, the data scale and the like, and on one hand, the virtual domain signal processing characteristics of the co-prime array are fully utilized to realize the increase of the degree of freedom; on the other hand, based on the single-bit quantitative signal modeling and the statistical relevance analysis design optimization problem, the integration of the advantages of single-bit signal processing and co-prime array signal processing is realized, and the method has wide application prospects in the actual application and passive positioning, target detection and other applications oriented to a new generation of wireless communication systems.