High degree of freedom DOA estimation method based on mirror inter-array in pulse noise environment

Abstract

The application provides a high-degree-of-freedom DOA estimation method based on a mirror image co-prime array in a pulse noise environment, and relates to the technical field of array signal processing, and comprises the following steps: S1: obtaining an observation signal by relying on non-circular signal characteristics; S2: calculating a pseudo-covariance matrix based on the information of the observation signal and a square-based correlation entropy operator to suppress the pulse noise; S3: vectorizing the pseudo-covariance matrix to obtain a virtual vector, removing redundant rows in the virtual vector, and performing truncation and sorting according to positions corresponding to continuous virtual array elements to obtain a virtual array receiving signal; S4: performing spatial smoothing on the virtual array receiving signal to obtain a full-rank reconstructed covariance matrix; S5: obtaining a noise subspace by performing eigenvalue decomposition on the covariance matrix; and S6: obtaining an accurate DOA estimation value by performing spectral peak searching on the noise subspace by using a MUSIC algorithm. The method has a high degree of freedom, can accurately complete DOA estimation in a pulse noise environment, and has good performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of array signal processing, and in particular, especially relates to a high degree of freedom DOA estimation method based on mirror co-prime array in a pulse noise environment. BACKGROUND

[0002] The direction of arrival (DOA) estimation has attracted extensive attention in the field of intelligent wireless communication, and has been widely developed in the field of wireless communication, especially in radar detection, intelligent radio monitoring, and vehicle automatic driving. In traditional DOA, most array structures use uniform linear array (ULA), and a ULA with M array elements can only estimate M-1 signal sources. In addition, due to the restriction of array element spacing to half the wavelength of the signal source, the ULA aperture is small, which leads to low spatial resolution of DOA estimation. However, the ULA can only increase the number of estimable signal sources and the size of the aperture by increasing the number of physical sensors, which increases the cost of hardware and reduces the applicable scenarios.

[0003] In order to estimate more signal sources under the condition of limited sensors, in recent years, an underdetermined DOA estimation method based on co-prime array (CLA) has been proposed. The CLA mainly consists of two ULAs with co-prime number of array elements. By generating a difference virtual array, the array aperture can be effectively expanded to estimate the number of signal sources exceeding the number of array elements. More specifically, for the same number of array elements, the degree of freedom (DOF) of the CLA is improved from O(M) of the ULA to O(M 2 ). In addition, the array element spacing becomes Nλ / 2 and Mλ / 2, effectively reducing the coupling effect between the array elements. In order to further improve the DOF, an extended co-prime array (ECLA) is proposed, which can achieve a virtual linear array continuous DOF of 2M(N+1)-1 using only M+N-1 array elements. However, the ECLA needs to increase M physical array elements, which increases the hardware cost.

[0004] Most of the DOA estimation methods based on the coprime array are studied in the additive white Gaussian noise (AWGN) background. However, due to the influence of natural or artificial interference, the noise caused by the automobile ignition system, sea waves, the discontinuity of mountains, atmospheric lightning and the like usually presents a pulse characteristic in the real wireless scene. For such pulse noise, the Gaussian distribution model is no longer applicable, and in practice, the Alpha stable distribution is usually used for modeling. The performance of the traditional DOA estimation method under the non-Gaussian pulse noise is seriously degraded, and in view of this problem, a series of DOA estimation methods based on fractional low-order statistics are proposed. These methods can effectively suppress the pulse noise and improve the estimation accuracy, but they depend on the prior knowledge of the signal and noise which is difficult to obtain in practical application. SUMMARY

[0005] In view of this, the purpose of the present application is to propose a high degree of freedom DOA estimation method based on the mirror coprime array in the pulse noise environment, so as to solve the technical problem that the existing DOA estimation method cannot accurately estimate as many signal sources as possible under the pulse noise environment with low hardware cost.

[0006] The technical means adopted by the present application are as follows:

[0007] A high degree of freedom DOA estimation method based on the mirror coprime array in the pulse noise environment comprises the following steps:

[0008] S1: using the array antenna with the coprime array structure to receive signals, then performing mirror and conjugate operations on the first subarray of the coprime array according to the non-circular signal characteristics of the signals, obtaining an improved mirror coprime array structure, and then obtaining an observation signal y;

[0009] S2: calculating a pseudo-covariance matrix based on the information of the observation signal y and the square-based correlation entropy operator suppressing the pulse noise;

[0010] S3: vectorization obtaining a virtual vector z, removing the redundant rows in z, and performing truncation and sorting according to the positions corresponding to the virtual elements [-MN, MN] to obtain a virtual array receiving signal

[0011] S4: performing spatial smoothing on to obtain a full-rank reconstructed covariance matrix R o ;

[0012] S5: obtaining a noise subspace by eigenvalue decomposition R o ​

[0013] S6: Precise DOA estimation is obtained by performing spectral peak search on the noise subspace by MUSIC algorithm.

[0014] Further, in S1, the coprime array includes a subarray ULA1 with M elements and a subarray ULA2 with N elements, M and N are coprime integers, M < N, and the two subarrays only coincide at the origin point; the element spacing of the subarray ULA1 is Nd, the element spacing of the subarray ULA2 is Md, d = λ / 2, λ is the signal wavelength; the signals received by the subarrays ULA1 and ULA2 are respectively:

[0015]

[0016]

[0017] wherein s(t) = [s1(t), s2(t), …, s k (t)] T is a far-field narrow-band non-circular signal signal vector, n1(t) and n2(t) are additive noise vectors, A1 = [a1(θ1), a1(θ2), …, a1(θ K )] is a steering matrix of the ULA1, A2 = [a2(θ1), a2(θ2), …, a2(θ K )] is a steering matrix of the ULA2, and t is a time-domain snapshot.

[0018] Further, the mirror coprime array in S1 is an improved array structure based on the coprime array, according to the characteristics of the non-circular signal, M virtual elements are added to the subarray ULA1 to obtain a subarray ULA m ; the mirror coprime array includes the subarray ULA m 1 and the subarray ULA2, and the number of elements is 2M and N respectively; the signal received by the subarray ULA1 can also be written as:

[0019]

[0020] The signal received by the extended M virtual elements is represented as:

[0021]

[0022] The signal received by the subarray ULA m is:

[0023]

[0024] The actual observed signal received by the mirror coprime array is:

[0025] ​

[0026] Furthermore, the square-based correlation entropy operator described in S2 is:

[0027]

[0028] Where σ represents the kernel length, δ = PQ, and P and Q are random variables.

[0029] Furthermore, S2 specifically includes:

[0030] Using the observed signal y, and based on the square-based correlation entropy operator, the pseudo-covariance matrix is ​​calculated:

[0031]

[0032] The (i, j)th element is:

[0033]

[0034] Among them, y i and y i These represent the i-th and j-th rows of the observed data, respectively.

[0035] Estimation is performed using a finite amount of received data, i.e.:

[0036]

[0037] The corresponding pseudo-covariance matrix is ​​updated to

[0038] Furthermore, S3 specifically includes:

[0039] Vectorization get:

[0040]

[0041] in, It is the incident signal power, I = vec(I 2M+N ), The turning matrix corresponds to the long virtual array; the virtual vector z has a large number of redundant rows. These redundant rows are removed, and the vectors are truncated and sorted according to their positions corresponding to the virtual array elements [-MN, MN] to obtain the received signal of the virtual array.

[0042]

[0043] in, An array manifold equivalent to a virtual uniform linear array.

[0044] Furthermore, S4 specifically includes:

[0045] The received signal The spatial smoothing is performed to construct a spatial smoothing matrix R:

[0046]

[0047] Wherein, R v The received signal The vth sub-array decomposed from the received signal is:

[0048] L v ={(-v+c+1)d|c=0,1,...,MN}.

[0049] Further, S5 specifically comprises:

[0050] Eigenvalue decomposition matrix R o The noise subspace is obtained

[0051]

[0052] The MUSIC algorithm is adopted to perform spectrum peak search on the noise subspace, and an accurate DOA estimation value is obtained.

[0053] The application further provides a storage medium, which comprises a stored program, wherein the program runs to execute any one of the high DOF DOA estimation methods based on the mirror-coprime array in the pulse noise environment.

[0054] The application further provides an electronic device, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, and the processor runs to execute any one of the high DOF DOA estimation methods based on the mirror-coprime array in the pulse noise environment through the computer program.

[0055] Compared with the prior art, the application has the following advantages:

[0056] The application improves the coprime array to obtain the mirror-coprime array by using the characteristics of the non-circular signal, ensures the number of physical array elements unchanged, further improves the DOF, and increases the number of estimable signal sources. The pulse noise is considered in the coprime array correlation structure, and the square-based correlation entropy operator is proposed to effectively suppress the pulse noise, and accurate DOA estimation is realized. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to make the technical solutions of the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort based on these drawings.

[0058] Figure 1 is a schematic diagram of the coprime array structure of the present application;

[0059] Figure 2 is a schematic diagram of the mirror coprime array structure of the present application;

[0060] Figure 3 is a schematic diagram of the degrees of freedom of the array structure of the present application and other different array structures under 6 physical array elements;

[0061] Figure 4 is a schematic diagram of the spatial spectrum of the array structure of the present application and the extended coprime array when the number of physical array elements is 6, the maximum number of estimable signal sources is different, and the spatial spectrum of the two array structures is incident;

[0062] Figure 5 is a schematic diagram of the spatial spectrum of the array structure of the present application and the extended coprime array when the number of physical array elements is different, but the maximum number of estimable signal sources is the same, which is 12, and the spatial spectrum of the two array structures is incident;

[0063] FIG. 6 is a comparison diagram of the DOA estimation performance of the method of the present application and other methods when the GSNR changes when there are 3 incident signal sources, wherein FIG. 6(a) is an accuracy effect diagram, and FIG. 6(b) is an RMSE effect diagram;

[0064] FIG. 7 is a comparison diagram of the DOA estimation performance of the method of the present application and other methods when the pulse noise characteristic index α changes when there are 4 incident signal sources, wherein FIG. 7(a) is an accuracy effect diagram, and FIG. 7(b) is an RMSE effect diagram;

[0065] FIG. 8 is a comparison diagram of the DOA estimation performance of the method of the present application and other methods when the number of snapshots changes when there are 4 incident signal sources, wherein FIG. 8(a) is an accuracy effect diagram, and FIG. 8(b) is an RMSE effect diagram. DETAILED DESCRIPTION

[0066] In the following, the technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort should fall within the protection scope of the present application.

[0067] It should be noted that the terms "first", "second", and the like in the specification and claims of the present application and the above-described drawings are used to distinguish similar objects, and do not necessarily indicate a specific order or a chronological sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or device including a series of steps or units does not necessarily have to be limited to the clearly listed steps or units, but can include other steps or units not clearly listed or inherent to the process, method, product, or device.

[0068] The present application provides a high degree of freedom DOA estimation method based on mirror co-prime array in pulse noise environment:

[0069] 1. Based on the non-circular characteristics of non-circular signals, a mirror co-prime array (MCA) is proposed on the basis of a co-prime array, and the MCA is used to receive signals.

[0070] 2. The pulse noise in the actual environment is considered. For the pulse noise, a square-based correntropy operator (SCO) is proposed, and the SCO estimation matrix is used to replace the covariance matrix. Then, the matrix is vectorized, and the corresponding continuous virtual array element positions are intercepted and sorted to obtain a single snapshot signal. Then, a full-rank matrix is obtained through spatial smoothing technology, and eigenvalue decomposition is performed to obtain DOA estimation values through MUSIC algorithm spectrum peak search.

[0071] Specifically, the following steps are included:

[0072] S1: Based on the characteristics of non-circular signals, an improved mirror co-prime array structure is obtained, and then an observation signal y is obtained.

[0073] S2: Based on the information of the observation signal y, a square-based correntropy operator is proposed to calculate a pseudo-covariance matrix The pulse noise is effectively suppressed;

[0074] S3: Vectorization Get z, remove the redundant rows in z, and get the virtual vector by intercepting and sorting the positions corresponding to the virtual elements [-MN, MN]

[0075] S4: Spatial smoothing is performed on to obtain the reconstructed full-rank covariance matrix R o ;

[0076] S5: Get the noise subspace by eigenvalue decomposition R o

[0077] S6: The precise DOA estimation value is obtained by performing spectral peak search through the MUSIC algorithm.

[0078] 1. Mirror-image coprime array signal model and noise model

[0079] Signal model:

[0080] The coprime array structure is shown in Figure 1 , mainly composed of sub-arrays ULA1 and ULA2, each containing M and N elements. M and N are a pair of coprime numbers and M < N, and the two sub-arrays share a physical element at the origin, with element spacings of Nd and Md, respectively, d = λ / 2, where λ is the wavelength of the received signal. The array configuration is represented as:

[0081]

[0082] where L represents the position of the physical element.

[0083] Suppose K unrelated far-field narrow-band non-circular signals are incident on the CLA as shown in Figure 1 , θ k (k = 1, 2, …, K) represents the kth signal source, then the observed signals received by the sub-arrays ULA1 and ULA2 are represented as:

[0084]

[0085]

[0086] where s(t) = [s1(t), s2(t), …, s k (t)] T is the signal vector, n1(t) and n2(t) are additive noise vectors, A1 = [a1(θ1), a1(θ2), …, a1(θ K )] and A2 = [a2(θ1), a2(θ2), …, a2(θ K )] are the steering matrices of the two sub-arrays. a1(θ​k ) and a2(0 k ) represent the steering vectors of the kth signal of the two subarrays, respectively:

[0087]

[0088]

[0089] Therefore, the received signal by CLA can be expressed as:

[0090] x(t) = As(t) + n(t) (6)

[0091] where, is the array flow matrix of CLA.

[0092] The received signal by subarray ULA1 can be re-expressed as:

[0093]

[0094] Since the received signal x1(t) is a complex number and its conjugate form also contains valid information, we construct a new mirror conjugate form of the received signal to effectively unfold. The extended mirror conjugate signal x 1m (t) is expressed as:

[0095]

[0096] where, (·) * represents the conjugate operation.

[0097] Stacking x1(t) and x 1m (t) gives a new mirror signal vector x m (t), which is specifically:

[0098]

[0099] Therefore, the MCA received signal is:

[0100]

[0101] Noise model:

[0102] In the actual wireless channel environment, for natural or artificial source interference, channel noise is always accompanied by sharp spikes, and is more suitable to be described by impulse noise. In practical applications, impulse noise is usually modeled by Alpha stable distribution, whose characteristic function is defined as:

[0103]

[0104] where,

[0105]

[0106]

[0107] From equation (11), it can be seen that the Alpha stable distribution is determined by four variables. In equation (10), a is the characteristic exponent and 0 < a < 2, which determines the degree of impulse response; β is the symmetry parameter, and its value range is -1 < β < 1, which is used to describe the slope. When β = 0, the distribution is a symmetric Alpha stable (SαS) distribution; γ > 0 is the dispersion parameter, which determines the dispersion degree of the sample at the median or mean, and its role is equivalent to the variance of the Gaussian distribution; μ is the location parameter, which represents the center of the probability density function, and satisfies -∞ < μ < +∞. e jμt Reflects the shift of the probability density function. When a < 2, the Alpha stable distribution no longer has a second-order or higher-order statistic. Therefore, the traditional DOA estimation method based on second-order and higher-order statistics will have a serious performance decline under such non-Gaussian impulse noise.

[0108] 2. Angle estimation method

[0109] In this embodiment, the above signal model and noise model are applied to the DOA estimation method of the application. For impulse noise, the square-based correlation entropy operator is proposed by using the properties that the correlation entropy does not depend on the prior knowledge of the signal and noise and can effectively suppress the impulse noise, and the estimation matrix thereof is defined, thereby solving the problem that the traditional DOA estimation method is no longer applicable under the impulse noise, and specifically comprising the following steps:

[0110] Step 1, calculate the SCO estimation matrix, and construct a pseudo-covariance matrix to replace the covariance matrix.

[0111] According to the SCO, the estimation matrix thereof, i.e., the pseudo-covariance matrix D, is calculated to replace the covariance matrix. D is expressed as:

[0112]

[0113] According to the signal model, the received signal is y(t), and the (i, j) term of D is expressed as:

[0114]

[0115] Wherein, y i and y j represent the i-th row and the j-th row of the observation data, respectively.

[0116] In fact, D cannot be accurately obtained, and it is usually estimated by using limited received data, and its expression is:

[0117]

[0118] Accordingly, the actual used pseudo-covariance matrix D is updated as

[0119] Step 2, virtualization operation.

[0120] Vectorization It can be obtained that:

[0121]

[0122] wherein, is the incident signal power, I = vec(I 2M+N ), corresponding to the steering vector of the long virtual array.

[0123] However, z contains repeated information, and its corresponding sensors are discontinuous in position. By selecting the elements corresponding to the continuous virtual array element [-MN, MN] position, the virtual signal z is de-redundant and sorted, and the actual continuous virtual uniform linear array receiving signal is obtained:

[0124]

[0125] wherein, is equivalent to the manifold matrix of the continuous virtual uniform linear array.

[0126] Step 3, spatial smoothing processing is performed on the virtual receiving signal .

[0127] Decompose into MN+1 overlapping sub-arrays, each sub-array containing MN+1 array elements. The vth sub-array includes array elements in the position:

[0128]

[0129] Calculate the autocorrelation matrix of all sub-arrays, and then perform average processing to obtain the spatially smoothed reconstructed covariance matrix R o :

[0130]

[0131] wherein, R v is the autocorrelation matrix of the vth sub-array.

[0132] Step 4, after the eigenvalue decomposition of the spatially smoothed reconstructed covariance matrix, the noise subspace is obtained, and the DOA estimation value is obtained by applying the MUSIC algorithm spectrum peak search.

[0133] III. Simulation results and analysis

[0134] 1. Spatial DOF analysis

[0135] ULA of MCA m , ULA2 contains M = 3, N = 4 physical elements respectively, the maximum number of signal sources that can be estimated in theory is 12 (= MN), considering 12 incoherent and same power binary phase-shift keying (BPSK) signals incident to the array, the incident angle θ = {60°, -46°, -35°, -23°, -10°, 0°, 11°, 22°, 33°, 45°, 54°, 71°}.

[0136] 1) Same number of physical sensors

[0137] Suppose that the two groups of co-prime arrays (CLA and ECLA) also have 6 physical sensors. The CLA configuration is the same as the MCA, and the ECLA configuration is 2M = 4, N = 3.

[0138] Figure 3 is the element position of the difference array generated by the three arrays. It can be seen that the DOF of CLA and ECLA is 17, and the DOF of MCA is improved to 35. In practical applications, we generally use consecutive DOF (cDOF). It can be known from Figure 3 that the cDOF of MCA reaches 29, which is much higher than the 13 of CLA and the 15 of ECLA. These results show that, under the same physical elements, MCA has higher spatial DOF than the other two arrays, so it can estimate more DOA.

[0139] The maximum number of signal sources that can be estimated by the ECLA established in the simulation is 6, and 6 signal sources are incident to the ECLA from the DOA incident to the MCA. Figure 4 is the spatial spectrum diagram obtained by using the method of the present application and the traditional ECLA based on the traditional ECLA, it can be seen that MCA can correctly separate 12 DOA, and ECLA can only distinguish 6 of them. Further verify that when using the same physical elements, MCA has higher DOF than ECLA.

[0140] 2) Same number of estimable DOA

[0141] For comparison, an ECLA is reconfigured as 2M = 6, N = 4. At this time, the DOF and cDOF of MCA and ECLA are the same, and 12 signal sources incident to MCA are incident to ECLA. Figure 5The spatial spectrum obtained by the method of the application and the spatial spectrum obtained by the traditional ECLA can be seen to show that the MCA and the ECLA can accurately estimate 12 incident signals, and the estimation errors are not much different. The results show that, compared with the ECLA, the MCA uses less M physical array elements but achieves the same DOF as the ECLA, and has higher DOF.

[0142] 2. Complexity analysis

[0143] The computational complexity is measured by the number of complex multiplications. In addition to the method proposed in the application, the algorithms using fractional low-order statistics (robust covariation (ROC), fractional lower order moment (FLOM), and phased fractional lower order moment (PFLOM)) are analyzed for comparison. The steps of each algorithm mainly include pseudo-covariance matrix construction, eigenvalue decomposition, and spectral peak search.

[0144] The main difference in the computational complexity of the algorithms is the construction of the pseudo-covariance matrix. We define G = 2M + N. The complexity of constructing the pseudo-covariance matrix for each type of algorithm is shown in Table 1. The computational complexity of eigenvalue decomposition and spectral peak search for all algorithms is the same. Let H = MN + 1, then the computational complexity of eigenvalue decomposition is O{2 3}, and the computational complexity of spectral peak search is O{[2H(H-K)+H](π / ω+1)}, where ω is the step size of spectral peak search.

[0145] Table 1 Computational complexity of constructing pseudo-covariance matrix

[0146]

[0147] 3. Performance analysis of DOA estimation

[0148] 1) Performance evaluation index

[0149] In order to effectively measure the estimation performance of the method, accuracy and root mean square error (RMSE) are selected as the judgment criteria.

[0150] Accuracy is defined as:

[0151]

[0152] where L Acc is the number of accurate DOA estimates, and L is the number of Monte Carlo (MC) experiments. In the application, accurate DOA estimation needs to satisfy the following formula:

[0153]

[0154] wherein is the angle estimation value of the kth signal source in the lth experiment, θ k is the angle actual setting value.

[0155] RMSE is defined as:

[0156]

[0157] wherein, K is the number of incident signal sources.

[0158] The environmental noise is pulse noise satisfying SαS distribution, a generalized signal-to-noise ratio (GSNR) is used to replace the signal-to-noise ratio (SNR), and the GSNR is defined as:

[0159]

[0160] 2) Simulation effect diagram

[0161] Figure 6 is the accuracy and RMSE of the SCO algorithm based on the MCA structure and other algorithms based on the MCA and ECLA structure. The GSNR is changed from -3dB to 5dB with a step of 1dB, assuming that 4 DOAs {0°, 10°, 20°, 30°} are incident to the MCA and ECLA independently BPSK signals. The snapshot number is set to 500, and the characteristic index of SαS is fixed to α = 1.5. As can be seen from Figure 6(a), the accuracy based on the MCA structure is always higher than that based on the ECLA structure when using the same algorithm. In addition, it is easy to see that the accuracy of the method of the present application is the highest in the entire change range. As can be seen from Figure 6(b), the RMSE of each method decreases with the increase of GSNR. Among them, the RMSE of the algorithm based on the MCA structure is always lower than that of the same algorithm based on the ECLA structure. In addition, the RMSE of the method of the present application is the lowest when selecting any GSNR. The experimental results show that the method of the present application can better complete the DOA estimation under different GSNRs under pulse noise, and is superior to other methods, and has good robustness.

[0162] Fig. 7 is a simulation result of accuracy and RMSE when the feature index α changes, the feature index α changes in the range of 1.1 to 1.6, the incident signal is set as independent and uncorrelated BPSK signals with angles of {0°, 10°, 20°}, and the GSNR is fixed as 5dB. As can be seen from Fig. 7(a), the accuracy of the algorithm based on the MCA structure is generally better than that of the algorithm based on the ECLA structure. In the entire change range, the accuracy of the method of the application and the PFLOM algorithm based on the MCA structure is higher, and converges or equals to 1. As can be seen from Fig. 7(b), the RMSE of the method of the application is obviously lower than that of any other method. The results of the two figures show that the performance of the method of the application in suppressing impulse noise is better than that of other methods

[0163] Fig. 8 shows a simulation result of the influence of the number of snapshots on the performance of the method, the number of snapshots increases from 30 to 130 with a step of 20. The incident signal is set as independent and uncorrelated BPSK signals with angles of {0°, 10°, 20°}, the GSNR is fixed as 5dB, and the feature index is fixed at α = 1.1. Fig. 8(a) describes the accuracy under different snapshot numbers, and it can be seen that the performance of all methods improves with the increase of the snapshot number. Under the same algorithm, the accuracy based on the MCA structure is obviously higher than that based on the ECLA structure. In addition, the method of the application always has the highest accuracy. When the number of snapshots is greater than or equal to 50, the method of the application realizes completely successful estimation. Fig. 8(b) gives the RMSE under different snapshot numbers. It can be observed that for the same algorithm, the RMSE based on the MCA structure is lower than that based on the ECLA structure, which further verifies the superiority of the MCA structure. In addition, the method of the application has the smallest change at each snapshot number, but the RMSE is always the smallest.

[0164] In summary, the method of high DOF DOA estimation based on mirror image coprime array in an impulse noise environment provided by the application fully utilizes the non-circular characteristics of non-circular signals, effectively improves the DOF, and further improves the number of estimable signal sources, has higher estimation accuracy and excellent performance, reduces the cost, and increases the applicable scene.

[0165] The application further provides a storage medium, which comprises a stored program, wherein the program, when executed, performs the method of high DOF DOA estimation based on mirror image coprime array in an impulse noise environment.

[0166] The application further provides an electronic device, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor performs the method of high DOF DOA estimation based on mirror image coprime array in an impulse noise environment by executing the computer program.

[0167] The integrated unit, if implemented in the form of a software function unit and sold or used as an independent product, can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application, essentially or in other words, the part that contributes to the prior art or the whole or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a mobile hard disk, a magnetic disk or an optical disk, and various media that can store program codes.

[0168] 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 foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A high degree of freedom (DOA) estimation method based on mirror orthogonal array in a pulse noise environment, characterized in that, Comprise the following steps: S1: receiving signals by using an array antenna of a coprime array structure, then performing mirroring and conjugation operation on a first subarray of the coprime array according to non-circular signal characteristics of the signals, obtaining an improved mirroring coprime array structure, and then obtaining observation signals ; S2: calculating a pseudo-covariance matrix based on information of the observation signal and a square-based correlation entropy operator to suppress the impulse noise;​ S3: vectorization obtain a virtual vector , remove the redundant rows in the virtual vector , and perform truncation and sorting according to the positions corresponding to the virtual array elements , to obtain a virtual array receiving signal ; is the number of array elements of the subarray , and is the number of array elements of the subarray ; S4: to spatially smooth, resulting in a fully reconstructed covariance matrix ; S5: by eigenvalue decomposition obtaining a noise subspace ; S6: Precise DOA estimation is obtained by performing spectral peak search on the noise subspace calculated by MUSIC algorithm. Precise DOA estimation is obtained by performing spectral peak search on the noise subspace calculated by MUSIC algorithm.

2. The high degree-of-freedom (DOA) estimation method based on mirror-symmetric-orthogonal-array in pulse noise environment according to claim 1, characterized in that, In S1, the coprime array includes a subarray with an array element number of and a subarray with an array element number of , , , , are coprime integers, , the two subarrays only have one physical array element coinciding at the origin; the array element spacing of the subarray is , and the array element spacing of the subarray is , , is a signal wavelength; the signals received by the subarrays and are respectively wherein is a far-field narrowband non-circular signal signal vector, and is an additive noise vector, is a steering matrix of is a steering matrix of is a steering matrix of is a steering matrix of is a number of signal sources.

3. The high degree-of-freedom (DOA) estimation method based on mirror-symmetric-orthogonal-array in pulse noise environment according to claim 2, characterized in that, The mirror-coprime array in S1 is an improved array structure based on a coprime array. According to the characteristics of a non-circular signal, sub-arrays increasing The number of virtual elements of the sub-array ; the mirror-coprime array comprises sub-arrays and sub-array , the number of elements of which are and ; the received signal of the sub-array may be written as: extended The received signal representation for the virtual array element is given by subarray The received signal is: The actual observation signal received by the mirror-symmetric array is: 。 4. The high degree-of-freedom (DOA) estimation method based on mirror-symmetric-orthogonal-array in pulse noise environment according to claim 1, characterized in that, The square-based correlation entropy operator in S2 is: wherein represents the core length, , and is a random variable.

5. The method of claim 4, wherein, S2 specifically comprises: Utilizing observation signals A pseudo-covariance matrix is calculated based on a square-based correlation entropy operator: Wherein, the (i, j) element is: wherein, and denote the i-th and j-th row of the observation data, respectively; Estimation is performed using the received limited amount of data, i.e.: The corresponding pseudo-covariance matrix is updated as .

6. The method of claim 1, wherein, S3 specifically comprises: Vectoring Obtained: wherein, is the incident signal power, is the number of signal sources, , is the steering matrix corresponding to the long virtual array; virtual vector There are a large number of redundant rows in it, remove the redundant rows in it, and intercept and sort according to the position corresponding to the virtual array element , get the virtual array receiving signal : wherein, Array flow pattern equivalent to a virtual uniform linear array.

7. The method of claim 6, wherein, S4 specifically comprises: The received signal is obtained spatial smoothing is performed to construct a spatial smoothing matrix : wherein for receiving signals decomposed into a first sub-array, the corresponding position is: ； wherein , is the signal wavelength.

8. The method of claim 1, wherein, S5 specifically comprises: Eigenvalue decomposition matrix Obtaining noise subspace : wherein, is the number of signal sources; The MUSIC algorithm is used to search for spectral peaks in the noise subspace to obtain an accurate DOA estimation value.

9. A storage medium, characterized by The storage medium comprises a stored program, wherein the program, when executed, performs the high-degree-of-freedom DOA estimation method based on the mirror-symmetric array in the pulse noise environment according to any one of claims 1 to 8.

10. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor performs the high-degree-of-freedom DOA estimation method based on the mirror-symmetric array in the pulse noise environment according to any one of claims 1 to 8 by running the computer program.

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