An array layout method and device based on joint sparse recovery technology

Abstract

The present application provides an array layout method and device based on the joint sparse recovery technology. The method includes: determining the array aperture size, the number of dictionary grid points, the total number of reference direction diagrams, and the number of Hermitian reference direction diagrams according to the reference multi-direction diagram for array optimization; solving the joint sparse problem to obtain the measurement vector and the observation matrix of the sparse matching task; estimating the sparse weight vector by using the relevance vector machine algorithm; and assigning weights to individual patterns to obtain the excitation vector of the direction diagram. The advantages of the present application are as follows: By using the method of the present application, only by changing the element excitation, it is possible to reconstruct the same multi-direction diagram as the uniform array with fewer elements, that is, the same element positions are shared among different direction diagrams; The array layout method based on the joint sparse recovery technology not only meets the constraints on the expected main lobe width and sidelobe level, but also matches the entire reference direction diagram with precise details.

Description

Technical Field

[0001] This application belongs to the field of array signal processing, and particularly relates to an array layout method and device based on joint sparse recovery technology. Background Art

[0002] Array optimization design is an important task in array signal processing. It uses a spatially distributed sensor array to collect spatial field data containing desired signals and interference, and then performs weighted combination processing on the collected array data to obtain a beam output. This processor is also called a beamformer. More generally, the position, amplitude, and phase parameters of the array elements can be jointly optimized to make the beam pattern of the array system meet performance requirements such as sidelobe level and main lobe width, so as to achieve a better array optimization design purpose.

[0003] Compressive sensing is a class of sparse parameter optimization algorithms extended from probability models. This algorithm first establishes a prior probability model of sparse parameters and calculates the solution of the parameter to be estimated through the expectation-maximization algorithm. Since the established prior probability model has the function of sparse constraint, the compressive sensing algorithm is applied to the optimization design of sparse linear arrays, analyzes the mapping relationship between the beam pattern and the parameter to be estimated in the real and imaginary parts, and integrates the design model into a pure real linear model of real-imaginary part combined optimization, and finally realizes the application of the BCS algorithm. However, when the reference beam pattern is a shaped beam, the compressive sensing algorithm cannot design a sparse linear array. This is because the shaped beam is synthesized by a uniformly weighted linear array with complex weights, and the real-imaginary part combined optimization model constructed by the compressive sensing algorithm cannot ensure that the solved element excitations have consistent parameter positions in the real and imaginary parts.

[0004] Traditional array optimization methods based on grid-based compressive sensing are for single beam pattern construction, and the sparse array optimization results obtained for the optimization problem matching a single beam pattern cannot reconfigure multiple patterns simultaneously. Since the array structure generated by each pattern corresponds to a statistically independent single beam pattern, even if the CS technology is repeatedly used to optimize the array, the obtained optimal array positions will vary with different patterns, which is limited in practical applications. In recent years, with the increasing demand for multifunctionalization in the system, multi-beam pattern sparse arrays, also known as sparse reconfigurable arrays, have been widely used in engineering due to their higher flexibility. Summary of the Invention

[0005] The purpose of this application is to overcome the above defects. This application proposes an array layout method based on joint sparse recovery technology, including:

[0006] Step 1: Determine the array aperture size, dictionary grid points, total number of reference beam patterns, and number of Hermitian reference beam patterns according to the reference multi-beam patterns for array optimization;

[0007] Step 2: Solve the joint sparse problem to obtain the measurement vector and the observation matrix of the sparse matching task;

[0008] Step 3: Estimate the sparse weight vector using the relevance vector machine algorithm;

[0009] Step 4: Assign weights to individual patterns to obtain the excitation vector of the radiation pattern.

[0010] As an improvement of the above method, the step 2 includes:

[0011] Calculate the observation matrix φ of the p-th radiation pattern (p) :

[0012]

[0013] where k0 = 2π / λ, representing the spatial wave number, λ is the wavelength; d i = -(L / 2)+Δd(i - 1) represents the position of the i-th array element unit of the preset array position dictionary, Δd = D / (I - 1), D represents the array aperture, I represents the number of dictionary grid points, L represents the linear aperture; N(p) represents the number of sampling points in the p-th radiation pattern; j represents the imaginary unit; represents the steering angle of the v-th excitation under the p-th mode radiation pattern;

[0014] When p ≤ the number P of Hermitian reference radiation patterns H , the measurement vector and the observation matrix of the sparse matching task are obtained from the following formula:

[0015]

[0016] where, represents the measurement vector of the t-th sparse matching task; represents the observation matrix of the t-th sparse matching task; represents the sample reference vector sampled at different n(p) observation angles under the reference of the p-th mode radiation pattern; represents a zero-mean Gaussian random variable with variance σ 2 ; represents the noise vector of the t-th sparse matching task;

[0017] When P H < p ≤ the total number P of reference radiation patterns, the measurement vector and the observation matrix of the sparse matching task are obtained from the following formula:

[0018]

[0019]

[0020] Among them, represents the real part extraction operator; represents the imaginary part extraction operator; represents the vector transpose.

[0021] As an improvement of the above method, step 3 includes:

[0022] Iteratively estimate the maximized posterior density function value by maximizing the likelihood function L(r) using the following formula

[0023]

[0024] Among them, represents the hyperparameter vector; T represents the number of sparse recovery matching tasks; a and b are the prior parameters of the Gamma distribution; Λ = diag(r1,…,r I ) is a diagonal matrix with diagonal elements determined by r; N represents the number of array elements;

[0025] The sparse weight vector w is obtained from the following formula (t) :

[0026]

[0027] As an improvement of the above method, step 4 includes:

[0028] If p ≤ P H , set the excitation vector w of the p-th pattern (p) = w (t) ;

[0029] If P H < p ≤ P, set the excitation vector w of the p-th pattern (p) = w (t) + jw (t+1) .

[0030] As an improvement of the above method, it further includes:

[0031] Use the normalized mean square error ξ p to evaluate the above calculation performance:

[0032]

[0033] Among them, F (p) represents the sample vector of the p-th mode pattern reference sampled at different N(p) observation angles.

[0034] As an improvement of the above method, it further includes:

[0035] The sparsity of the array arrangement is evaluated using γ = M / M UNI ; where M is the number of array elements obtained by optimization, and M UNI is the number of array elements evenly arranged within the same aperture with a half-wavelength element spacing.

[0036] This application also provides an array layout device based on the joint sparse recovery technology, implemented based on the above method. The system includes:

[0037] A parameter determination module for determining the array aperture size, the number of dictionary grid points, the total number of reference direction diagrams, and the number of Hermitian reference direction diagrams according to the reference multi-direction diagram of the array optimization;

[0038] A module for calculating the measurement vector and the observation matrix, which is used to solve the joint sparse problem to obtain the measurement vector and the observation matrix of the sparse matching task;

[0039] A sparse weight vector estimation module for estimating the sparse weight vector using the relevant vector machine algorithm;

[0040] An excitation vector acquisition module for assigning weights to individual modes to obtain the excitation vector of the direction diagram.

[0041] As an improvement to the above device, the system further includes:

[0042] An evaluation module for evaluating the performance and sparsity of the array arrangement.

[0043] Compared with the prior art, the advantages of this application are:

[0044] Using the method of this application, by only changing the element excitation, it is possible to reconstruct the same multi-direction diagram as the uniform array with fewer elements, that is, the same element positions are shared among different direction diagrams; the array layout method based on the joint sparse recovery technology not only meets the constraints on the desired main lobe width and side lobe level, but also matches the entire reference direction diagram with precise details. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Shown is the flowchart of the array layout method based on the joint sparse recovery technology;

[0046] Figure 2 Shown is the schematic diagram of the sparse optimization non-uniform layout configuration;

[0047] Figure 3 Shown is the reference multi-direction beam pattern;

[0048] Figure 4 Shown is the comparison diagram of the synthesized multi-direction diagram and the reference direction diagram based on the joint sparse recovery algorithm;

[0049] Figure 5 The figure shows the excitation amplitude and phase information diagram. Specific implementation manners

[0050] The technical solutions of the present application will be described in detail below with reference to the accompanying drawings.

[0051] The present invention mainly introduces an array layout method and device based on the joint sparse recovery technology. The joint sparse recovery method is used to iteratively optimize the array structure. Based on the multi-reference mode joint sparse model, the synthesis of the multi-pattern sparse array is transformed into a synchronous sparse approximation problem. Each pattern matching can be regarded as one or two tasks in the multi-task learning model. The joint sparse recovery enforces all tasks to share the same prior according to the statistical correlation. By only changing the element excitation, it is possible to reconstruct the same multi-pattern as the uniform array with fewer elements, that is, the same element positions are shared between different patterns. The array layout method based on the joint sparse recovery technology not only satisfies the constraints on the desired main lobe width and sidelobe level, but also matches the entire reference pattern with precise details.

[0052] 1. Multi-pattern array optimization model based on grid-based compressive sensing

[0053] Assume that I candidate elements are evenly located within the span of the linear aperture L. It is desired to design an array layout method to select appropriate element positions and excitations (including phase and amplitude), and P different operating modes of the pattern-reconfigurable array can be obtained. That is, for the designed array positions, only by changing the different element excitations, P different patterns can be realized. Therefore, for this linear array, the pattern in the p-th operating mode can be described as:

[0054]

[0055] where \(k_0 = 2\pi / \lambda\) is the spatial wave number, \(\lambda\) is the wavelength, \(u = \sin\theta\), and \(\theta\) is the geometric steering angle relative to the reference direction of the linear array. \(d\) i \(= -(L / 2) + \Delta d(i - 1)\) is the position of the i-th element unit of the preset array position dictionary (the grid spacing of the dictionary is \(\Delta d = D / (I - 1)\), and the array aperture is D), and \(a_{i,p}\) is the excitation coefficient of the i-th element unit related to the p-th pattern mode. By discretization, (1) can be rewritten in the following sparse matrix form:

[0056] F (p) \(= \varPhi\) (p) w (p) , \(p = 1, \ldots, P, (2)\)

[0057] where, is the sample vector sampled at different N(p) observation angles under the reference of the p-th mode pattern, N(p) is the number of sampling points in the p-th pattern, and w (p) = is the excitation vector of the pth directional pattern, Φ (p) In the theory of compressed sensing, it is considered as the measurement matrix. In the problem of this chapter, it has the following form:

[0058]

[0059] in, represents the steering angle of the nth excitation under the pth mode pattern.

[0060] Since multiple excitation vectors in (2) need to be calculated, when N(p) < < I, formula (2) is an uncertain polynomial problem. If these excitation vectors are sparse, they can be solved by using fewer F (p) It is assumed that these excitation vectors of length N are M-sparse, which means that each vector has only M non-zero components (M<<I), so only M array elements need to be excited with feed current, and the other IM array elements with zero excitation can be considered as "off" (i.e., there are no active elements at these assumed IM positions).

[0061] Based on the joint sparse assumption of the above multi-reference pattern synthesis, the problem can be solved by Find the sparsest excitation vector, and F (p) similar, is the sample reference vector sampled at different N(p) observation angles under the reference of the p-th mode pattern (the observation angle range is defined as u=sinθ∈[-1,1]). Considering matching noise, the mathematical expression of this problem is:

[0062]

[0063] Among them, ||·||0 and ||·||2 represent norm and 2-norm, in particular, The norm refers to the number of non-zero elements in a vector. is a square with σ 2 is the zero-mean complex Gaussian error vector of . ε represents the estimation error tolerance.

[0064] It can be expanded according to the real and imaginary parts as follows:

[0065]

[0066] If w (p) The real and imaginary parts of are represented as two real weight vectors, then is represented in the form of a real number matrix:

[0067]

[0068] where In particular, if we let then can be represented in a more simplified form:

[0069]

[0070] In particular, when the p-th reference pattern is a Hermitian pattern, we have The reference pattern vector can be further simplified to:

[0071]

[0072] By setting

[0073]

[0074] In this case, the reference pattern corresponding to the constructed Hermitian pattern is equivalently simplified to

[0075]

[0076] To sum up, the synthesis of the multi-pattern sparse array can be reconstructed as a sparse approximation problem. In order to obtain multiple sparse excitation vectors with the same zero terms from the joint sparse model (4), the algorithm principle and implementation method are introduced in detail below.

[0077] 2. Array layout method based on joint sparse recovery technology

[0078] According to the theory of joint sparse recovery learning, the statistical correlation between different tasks can be utilized to improve the performance of simultaneous inversion. Then, applying multi-task learning to compressive sensing can solve the above-mentioned simultaneous sparse approximation problem. Joint sparse recovery estimates the sparse weight vector by using the prior knowledge of the observation matrix and the measurement vector, and designs a multi-directional pattern sparse array. For different weight vectors, by making these vectors have the same prior probability, their zero terms can be kept in the same positions. Therefore, by finding the sparsest weight vector, the shared element positions and different element excitations can be obtained simultaneously. In the framework of joint sparse recovery, the M different matching patterns synthesized for the reconfigurable array can be regarded as T sparse recovery matching tasks. For non-Hermitian reference patterns, usually two tasks are required to calculate the real and imaginary parts of the complex-valued excitation, while for Hermitian reference patterns, only one task can meet the requirements of the above model description (10). Therefore, the total number of sensing tasks is T = P H + 2(P - P H )(P H is the number of Hermitian reference patterns). The corresponding sparse representation can be written as:

[0079]

[0080] where represent the measurement vector and the observation matrix of the t-th sparse matching task respectively, and N t represents the dimension of the reference vector given for the t-th sparse matching task in joint sparse recovery. is the sparse weight vector to be determined, is a zero-mean Gaussian random variable with variance σ 2 .

[0081] Based on the measurement vector parameter w (t) and σ 2 , the Gaussian likelihood function is:[[]]

[0082]

[0083] where represents the Gaussian likelihood function.

[0084] Define the parameter r0 = 1 / σ 2 . Arbitrarily obtaining the value of σ 2 , that is, r0, will affect the performance of the maximum a posteriori probability (MAP) method. Therefore, the algorithm chooses to integrate out r0 instead of finding the point estimate of r0. In the Bayesian framework, the sparsity of w (t) is achieved by imposing a prior on w (t)A sparsity-promoting prior is placed on it for regularization. According to this idea, for w of each channel (t) , a zero-mean Gaussian hierarchical prior is defined:

[0085]

[0086] where is the Gaussian density function, r = [r1, …, r I T is a shared hyperparameter vector, and the real number r i -1 (i = 1, …, I) represents the nth independent noise variance, which determines the strength of the prior of the array element excitation w (t) It can be seen from (13) that r and r0 follow the Gamma distribution, so there is a conditional distribution density function:

[0087] p(r0|a,b) = G(r0|a,b) = b a r0 a-1 exp(-br0) / Γ(a), (14)

[0088]

[0089] where and a, b, c, d are the prior parameters of the Gamma distribution. Therefore, equation (15) corresponds to the Student-t distribution, and its analytical evaluation can be carried out. By appropriately choosing the prior parameters c and d, the Student-t distribution can promote the sparsity of w by making most (t) values zero. Then, the original sparse array optimization problem can be transformed into a Bayesian linear regression problem with a known sparse prior, that is, the prior MAP estimator can be used to solve this problem. To obtain the sparse solution efficiently and accurately, the posterior of all unknown parameters can be divided into two parts:

[0090]

[0091] Using the δ function approximation to simulate the hyperparameter posterior, we have:

[0092]

[0093] Then, the value of r can be estimated by maximizing the posterior density function , that is:

[0094]

[0095] In addition, obviously then maximizing ​Equivalent to maximizing where the logarithm can be analytically expressed as:

[0096]

[0097] where A = diag(r1, …, r I ) is a diagonal matrix with diagonal elements determined by r. It is worth noting that a numerical solution can be obtained from Equation (19).

[0098] Given r, and σ 2 in the case of, in the second term on the right side of Equation (16), the posterior probability density function on w (t) is a multivariate Student-t distribution with mean μ (t) , and covariance ∑ (t) , that is

[0099]

[0100] where the mean is and the covariance is

[0101] Since the mode of the multivariate Student-t distribution is equal to its mean, by substituting Equations (20) and (17) into Equation (16), the following expression can be obtained

[0102]

[0103] In summary, as Figure 1 shown, the implementation steps of the array layout method based on the joint sparse recovery technique can be summarized as follows:

[0104] Step (1): According to the reference multi-direction pattern for array optimization, determine the array aperture size D, the number of dictionary grid points I, the total number of reference direction patterns P, and the number of Hermitian reference direction patterns P H , and initialize the iterative optimization variables σ 2 , a, b.

[0105] Step (2): Construct and solve the aforementioned joint sparse problem. Specifically, when matching the p-th reference direction pattern , first determine its direction pattern sampling points n = 1, …, N(p), and substitute and d i , i = 1, …, I into Equation (3) to form the observation matrix Φ of the dictionary (p). Without loss of generality, the Hermitian reference pattern in the reference pattern to be synthesized is given priority, and it is specifically divided into the following situations: a). When p ≤ P H , the obtained Φ (p) , e (p) is substituted into Equation (9) to obtain and ( represents the noise vector of the t-th sparse matching task). Set t = t + 1, p = p + 1. b). When P H < p ≤ P, the obtained e (p) is substituted into Equations (7) and (8) to obtain and Set t = t + 2, p = p + 1.

[0106] Step (3): Estimate the sparse weight vector using the Relevance Vector Machine (RVM) algorithm. Substitute (t = 1, λ, T), a, b, N (N represents the number of array elements) into (19), and iteratively estimate by maximizing the likelihood function L(r). Substitute Equation (21) into to obtain the sparse weight vector w (t) , (t = 1, 2,..., T), and set p = t = 1 again for the initialization of the next weight allocation.

[0107] Step (4): Allocate weights for a single mode: If p ≤ P H , w (p) = w (t) can be obtained, and set t = t + 1, p = p + 1, and repeat Step (4). Conversely, if P H < p ≤ P, w (p) = w (t) + jw (t+1) can be obtained, and set t = t + 2, p = p + 1, and then repeat Step (4). If p > P, proceed to the next step.

[0108] Step (5): Use the normalized mean square error ξ p for performance evaluation:

[0109]

[0110] In addition, the sparsity of the array arrangement can be evaluated as γ = M / M UNI . Where M is the number of array elements obtained by optimization, M UNIis the number of array elements evenly arranged within the same aperture with a half-wavelength element spacing.

[0111] 3. Simulation Experiments

[0112] This section aims to conduct numerical experiments and parameter setting analysis on the algorithms introduced above. This experiment hopes to reconstruct a multi-directional beam with an array aperture of 14.5λ, which means that the performance of the reconstructed sparse array is equivalent to that of a uniform linear array with an element spacing of λ / 2 and consisting of 30 elements. Among them, the hyperparameters σ 2 , a, b, I, N all need to be reasonably selected so that the array layout method based on the joint sparse recovery technology can effectively achieve the overall optimal design of the multi-directional pattern sparse array. In terms of indicators, the normalized mean square error ξ p and the sparsity of the array arrangement γ = M / M UNI are used as performance evaluation indicators.

[0113] Obviously, the normalized mean square error ξ p will decrease as a increases and increase as b increases. Compared with ξ p , the change trend of M is exactly the opposite. First, set a ∈ [1×10 2 , 1×10 3 and b ∈ [4×10 1 , 2×10 2 to achieve a trade-off between sparsity and accuracy. A smaller σ 2 value produces higher pattern matching accuracy and a sparser filling arrangement. Therefore, the value range of σ 2 is set to σ 2 ∈ (1×10 -5 , 1×10 -2 ). The larger the N value, the more obvious the increase in P and the higher the computational complexity. If N ∈ [1×10 2 , 1×10 3 , then both ξ p and P can be maintained within the desired range. For the number of sample points N, after increasing K to 30, ξp decreases rapidly, and then ξ p fluctuates below 1×10 -3 . By considering the sparsity and accuracy of the reconfigurable array, it is recommended to select a trade-off value K within [50, 80]. Since the analytical expressions of the performance indicators and these control parameters have not been obtained, it is still an open question to conduct a strict theoretical analysis of the behavior of the performance indicators P and ξ p with respect to a certain parameter. The explanation given by the author is that the influence of a and b on the above two performance indicators can be explained from the process of solving the sparse weight vector. In addition, a and b are the priors of the Gamma distribution, and increasing a or decreasing b will help increase w (t)The values of the coefficients and, to a certain extent, reduce the estimation error. For a sparse weight vector w (t) , an increase in the coefficient value is equivalent to reducing the number of zero terms, as the values of some terms can be converted from zero to non-zero. This ultimately means that M increases and ξ p decreases.

[0114] For fire 2 speaking, fire 2 represents the user-defined variance. σ 2 The smaller it is, the less interference there is on the performance index. When σ 2 <1×10 -2 , the value of the performance index remains the ideal value. Conversely, the larger the value of σ 2 , the lower the accuracy and the sparser the filling, indicating that the values of M and ξ p increase continuously as σ 2 increases.

[0115] Finally, regarding the dependence of the above two performance indices on I and N, when I < 2D / λ, the number of candidate element positions is limited, making it difficult to select suitable element positions for all synthesized beams, resulting in a significant increase in ξ p . When I ≥ 2D / λ, the value of ξ p remains almost unchanged. Due to the relatively constant sparsity rate of this algorithm, a larger value of I usually leads to a more obvious increase in P, resulting in a higher computational complexity.

[0116] To verify the specific performance of joint sparse recovery in designing a multi-pattern sparse array with multiple reference patterns, simulation experiments are carried out in this section, and the schematic diagram of its array configuration is as Figure 2 shown. Taking an array with an aperture D = 9.5λ and 20 isotropic elements with a spacing of λ / 2 as a comparison reference, where the wavelength is λ = 1m.

[0117] In the simulation experiment, three required patterns (multi-patterns) are considered, as Figure 3 shown, including a pencil beam pattern, a flat-top beam pattern, and a cosecant squared beam pattern.

[0118] By determining the optimal element positions and single excitation coefficients through the method introduced in the present invention, the designed multi-pattern sparse arrays can all well match the required beam shapes. Figure 4The radiation patterns of a multi - pattern sparse array are compared with those of a uniform reconfigurable array. It can be observed that, on the premise of a determined sparse array structure, different radiation pattern modes with precise details can be dynamically reconfigured by changing the element excitations. Table 1 shows the array structure information of the synthesized multi - pattern sparse array, including the element excitations in different modes. The maximum element - to - element spacing is 0.7790 m, and the minimum is 0.0570 m. The uniform reference array consists of 20 isotropic elements with a spacing of 0.5 m, while only 14 elements arranged in the sparse array layout can reconfigure the above three radiation patterns without grating lobes. In other words, compared with the fully - filled layout, the number of elements is saved by 30%. Additionally, the differences in peak sidelobe levels between the reference uniform array and the sparse reconfigurable array are compared, and the results are shown in Table 2. The results indicate that, under this index, the layout obtained by the joint sparse recovery algorithm can still achieve the required peak sidelobe level effect with fewer elements used, and the gap compared with the fully - filled layout is within 5 dB. The excitation amplitudes and phases corresponding to the multi - pattern sparse array are as Figure 5 shown.

[0119] Table 1 Array structure information of the multi - pattern sparse array synthesized by the algorithm

[0120]

[0121] Table 2 Comparison of peak sidelobe levels

[0122]

[0123] This application also provides an array layout device based on the joint sparse recovery technology, which is implemented based on the above - mentioned method. The system includes:

[0124] A parameter - determining module, which is used to determine the array aperture size, the number of dictionary grid points, the total number of reference radiation patterns, and the number of Hermitian reference radiation patterns according to the reference multi - pattern optimized for the array;

[0125] A module for calculating the measurement vector and the observation matrix, which is used to solve the joint sparse problem to obtain the measurement vector and the observation matrix for the sparse matching task;

[0126] A module for estimating the sparse weight vector, which is used to estimate the sparse weight vector using the relevant vector machine algorithm;

[0127] A module for obtaining the excitation vector, which is used to assign weights for a single mode to obtain the excitation vector of the radiation pattern.

[0128] An evaluation module, which is used to evaluate the performance and sparsity of the array arrangement.

[0129] The present application may also provide a computer device, including: at least one processor, a memory, at least one network interface, and a user interface. Each component in the device is coupled together through a bus system. It can be understood that the bus system is used to implement the connection and communication between these components. In addition to the data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0130] Among them, the user interface may include a display, a keyboard, or a pointing device. For example, a mouse, a trackball, a touchpad, or a touch screen, etc.

[0131] It can be understood that the memory in the disclosed embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchlink dynamic random access memory (SLDRAM), and direct rambus random access memory (DRRAM). The memory described herein is intended to include but not be limited to these and any other suitable types of memory.

[0132] In some embodiments, the memory stores the following elements, executable modules, or data structures, or subsets thereof, or extended sets thereof: an operating system and an application program.

[0133] Among them, the operating system includes various system programs, such as the framework layer, the core library layer, the driver layer, etc., which are used to implement various basic services and handle hardware-based tasks. The application programs include various application programs, such as Media Player, Browser, etc., which are used to implement various application services. The program for implementing the method of the embodiments of the present disclosure may be included in the application programs.

[0134] In the above embodiments, the program or instruction stored in the memory may also be called. Specifically, it may be the program or instruction stored in the application program. The processor is used for:

[0135] Executing the steps of the above method.

[0136] The above method may be applied to the processor or implemented by the processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, the steps of the above method may be completed by the integrated logic circuit in the hardware of the processor or the instructions in software form. The above processor may be a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed above. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. Combining the steps of the above disclosed method may be directly embodied as being executed and completed by the hardware decoding processor, or by a combination of the hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0137] It can be understood that these embodiments described in the present application can be implemented by hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in the present application, or a combination thereof.

[0138] For software implementation, the techniques of the present application can be implemented by executing the functional modules of the present application (such as procedures, functions, etc.). The software code can be stored in a memory and executed by a processor. The memory can be implemented inside or outside the processor.

[0139] The present application can also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, the various steps in the above method embodiments can be implemented.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit them. Although the present application has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present application does not depart from the spirit and scope of the technical solutions of the present application, and they should all be covered within the scope of the claims of the present application.

Claims

1. An array layout method based on joint sparse recovery technology, comprising: Step 1: Determine the array aperture size, the number of dictionary grid points, the total number of reference patterns, and the number of Hermitian reference patterns according to the reference multi-direction pattern for array optimization; Step 2: Solve the joint sparse problem to obtain the measurement vector and the observation matrix for the sparse matching task; Step 3: Estimate the sparse weight vector using the relevance vector machine algorithm; Step 4: Assign weights to individual modes to obtain the excitation vector of the pattern; The said Step 2 includes: Calculate the observation matrix Φ of the p-th pattern (p) : where \(k_0 = 2\pi / \lambda\) represents the spatial wave number, \(\lambda\) is the wavelength; \(d\) i \(=-(L / 2)+\Delta d(i - 1)\) represents the position of the \(i\)-th array element unit in the preset array position dictionary, \(\Delta d = D / (I - 1)\), \(D\) represents the array aperture, \(I\) represents the number of dictionary grid points, and \(L\) represents the linear aperture; \(N(p)\) represents the number of sampling points in the \(p\)-th pattern; \(j\) represents the imaginary unit; represents the steering angle of the \(n\)-th excitation under the \(p\)-th mode pattern; When p ≤ the number P of Hermitian reference patterns H the measurement vector and the observation matrix of the sparse matching task are obtained by the following formula: Among them, represents the measurement vector of the t-th sparse matching task; represents the observation matrix of the t-th sparse matching task; represents the sample reference vector sampled at different N(p) observation angles under the reference of the p-th pattern direction diagram; represents a zero-mean Gaussian random variable with variance σ 2 ; represents the noise vector of the t-th sparse matching task; When P H When p ≤ the total number of reference direction patterns P, the measurement vector and the observation matrix of the sparse matching task are obtained by the following formula: Among them, represents the real part extraction operator; represents the imaginary part extraction operator; represents the vector transpose.

2. The array layout method based on the joint sparse recovery technique according to claim 1, characterized in that The said Step 3 includes: Iteratively estimate the maximized posterior density function value by maximizing the likelihood function L(r) using the following formula Among them, represents the hyperparameter vector; T represents the number of sparse recovery matching tasks; a and b are the prior parameters of the Gamma distribution; Λ = diag(r1,…,r I ) is a diagonal matrix with diagonal elements determined by r; N represents the number of array elements; Obtain the sparse weight vector w from the following formula (t) :

3. The array layout method based on the joint sparse recovery technology according to claim 2, wherein The said Step 4 includes: If p ≤ P H , set the excitation vector w of the p-th pattern (p) = w (t) ; If P H When p ≤ P, set the excitation vector w of the p-th pattern (p) = w (t) + jw (t+1) .

4. The array layout method based on the joint sparse recovery technology according to claim 1, wherein It further includes: Use the normalized mean square error ξ p Evaluate the computational performance: where, F (p) represents the sample vector sampled at different N(p) observation angles under the reference of the p-th pattern directional diagram.

5. The method for array arrangement based on the joint sparse recovery technique according to claim 1, characterized in that It further includes: The sparsity of the array arrangement is evaluated using γ = M / M UNI ; where M is the number of array elements obtained by optimization, and M UNI is the number of array elements uniformly arranged within the same aperture with a half-wavelength element spacing.

6. An array arrangement device based on the joint sparse recovery technology, which is implemented based on the method according to any one of claims 1-5, and is characterized in that The said device includes: A parameter determination module, configured to determine the array aperture size, the number of dictionary grid points, the total number of reference patterns, and the number of Hermitian reference patterns according to the reference multi-direction pattern for array optimization; A measurement vector and observation matrix calculation module, configured to solve the joint sparse problem to obtain the measurement vector and the observation matrix for the sparse matching task; A sparse weight vector estimation module, configured to estimate the sparse weight vector using the relevance vector machine algorithm; and An excitation vector acquisition module, configured to assign weights to individual modes to obtain the excitation vector of the pattern.

7. The array arrangement device based on the joint sparse recovery technique according to claim 6, characterized in that, The said device further includes: An evaluation module, configured to evaluate the performance and sparsity of the array arrangement.

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