Nested array non-circular SPFLOM-DOA estimation method under impulse noise

Abstract

The invention discloses a nested array non-circular SPFLOM-DOA estimation method under impulse noise, and the method comprises the following steps: 1, receiving a signal through a nested array antenna, and obtaining signal information; 2, expanded signal information is constructed according to the received signal information, and an SPFLOM matrix is calculated; step 3, performing vectorization and rearrangement processing on the SPFLOM matrix to obtain a virtual array receiving signal; step 4, removing redundancy of the virtual array receiving signal to obtain a new virtual uniform linear array receiving signal; and step 5, performing spatial smoothing and splicing on continuous parts of which the array element spacing is half-wavelength in the difference array and the sum array in the virtual uniform linear array receiving signals respectively to obtain virtual array information, constructing a covariance matrix for the virtual array information, and obtaining accurate estimation of DOA by using a dimension reduction MUSIC method. According to the method, the DOA of the non-circular signal can be accurately estimated in a strong pulse noise environment.

Description

Technical Field

[0001] The invention relates to the technical field of direction of arrival estimation, and in particular to a nested array non-circular SPFLOM-DOA estimation method under impulse noise. Background Art

[0002] In recent years, a new type of sparse array has received extensive attention, namely the nested array, which is composed of two uniform linear arrays. The nested array of N1+N2 elements can obtain 2N2(N1+1)-1 virtual linear array continuous degrees of freedom (DOF), while the uniform linear array (ULA) with the same number of elements can only obtain N1+N2-1 DOF. Therefore, the nested array structure greatly increases the number of detectable sources and can improve the angle estimation performance.

[0003] However, most DOA estimation methods in sparse arrays assume that the ambient noise is Gaussian distributed. However, in the case of high impulse noise, such as atmospheric noise generated by low-frequency and ultra-low-frequency radio waves or noise generated by mechanical vibration, the assumption of Gaussian noise fails. These scenarios usually involve impulse noise, and traditional Gaussian noise models are not suitable for this type of noise. The performance of these DOA estimation methods will be significantly degraded. Therefore, a new technical solution is needed to solve the above problems. Summary of the invention

[0004] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a nested array non-circular SPFLOM-DOA estimation method under impulse noise, which realizes accurate estimation of the DOA of non-circular signals in a strong impulse noise environment.

[0005] In order to solve the above technical problems, the technical solution of the present invention is:

[0006] A nested array non-circular SPFLOM-DOA estimation method under impulse noise comprises the following steps:

[0007] Step 1: Receive signals through nested array antennas to obtain signal information;

[0008] Step 2: construct extended signal information according to the received signal information, and calculate the SPFLOM matrix;

[0009] Step 3, vectorize and rearrange the SPFLOM matrix to obtain a virtual array receiving signal;

[0010] Step 4: Remove redundancy from the virtual array receiving signal to obtain a new virtual uniform linear array receiving signal;

[0011] Step 5: Perform spatial smoothing on the continuous parts of the difference array and sum array with half-wavelength array element spacing in the virtual uniform linear array received signal, concatenate them to obtain virtual array information, construct a covariance matrix for the virtual array information, and then use the reduced-dimensional MUSIC method to obtain an accurate estimate of DOA.

[0012] Preferably, the nested array antenna includes two sub-arrays, and the number of array elements included in the two sub-arrays is respectively N1 and N2. The array element spacing of the uniform linear array with the number of array elements N1 is d0, and the array element spacing of the uniform linear array with the number of array elements N2 is (N1+1)d0, wherein d0=λ / 2, λ is the carrier wavelength.

[0013] Preferably, in step (1), the received signal information x(t) is:

[0014] x(t)=AΦs0(t)+n(t);

[0015] Where A=[a(θ1),…,a(θ k ),a(θ K )] is the direction matrix, is the direction vector, is a noncircular phase matrix, represents the non-circular phase of the kth signal, j is an imaginary unit, n(t) is an impulse noise term that obeys a symmetric α-stable distribution, and 0<α≤2; s0(t)=[s 01 (t),…,s 0k (t),…s 0K (t)] T is the signal vector, where s 0k (t) represents the kth signal.

[0016] Preferably, in step 2, the non-circular feature of the signal information x(t) is used to expand the signal information X(t) of the array, and the expression is as follows:

[0017]

[0018] in, is the expansion direction matrix, is the augmented impulse noise term; [] * is a conjugate operation. The received signal information X is composed of X(t), where X(t) is the tth time domain snapshot in X.

[0019] Preferably, in step 2, the SPFLOM matrix R is calculated according to the extended signal information X(t). SPFLOM :

[0020]

[0021] where yi (t), y j (t) are the i-th and j-th rows of the signal model y(t) at time t, respectively. represents mathematical expectation, p represents the order, and * represents the complex conjugate.

[0022] Preferably, the virtual uniform linear array receives a signal z, which is expressed as follows:

[0023] z=Jvec(R SPFLOM )=J(B * ⊙B)s SPFLOM + JΓ;

[0024]

[0025] where vec(·) represents a vectorized operation, is the expansion direction matrix, is the expansion direction vector, s SPFLOM represents the signal energy, Γ represents the vector after the impulse noise term is stretched; represents Kronecker product, ⊙ represents KR product; is a row-commuting matrix, and I P represents the P×P identity matrix, 0 P represents a P×P zero matrix, Indicates 2P 2 ×2P 2 The zero matrix of , P = N1 + N2.

[0026] As a preference, the new virtual uniform linear array receiving signal obtained in step 4 is for:

[0027]

[0028] in, and is the direction vector matrix of the difference matrix, and is the direction vector matrix of the sum matrix; and yes The noise vector of the continuous element part of the corresponding difference array; and yes The noise vector corresponding to the continuous array element part of the sum array.

[0029] Preferably, in step 5, the virtual array information Y obtained by smoothing is:

[0030]

[0031] Among them, M1=N1N2+N2-1, M2=N1N2+N1+N2-1; and Yes and The smoothing matrix obtained by spatial smoothing.

[0032] Preferably, the covariance matrix R of the virtual array information Y is Y :

[0033] R Y =YY H / (M1+1).

[0034] The present invention has the following characteristics and beneficial effects:

[0035] By adopting the above technical solution and utilizing the non-circular characteristics of the signal, the DOA estimation accuracy and the number of estimable sources are improved; the present invention uses the sign function phase fractional low-order moment (SPFLOM) to suppress the outliers in the received signal, constructs the SPFLOM matrix, performs vector processing, rearranges and removes redundancy to obtain the received signal information of the virtual uniform linear array with an array element spacing of half a wavelength, and adopts the dimension reduction MUSIC method to reduce the computational complexity. Accurate estimation of the DOA of non-circular signals is achieved in a strong impulse noise environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0037] Figure 1 It is a schematic diagram of the nested array structure of the present invention;

[0038] Figure 2 It is a schematic diagram of the structure of the nested linear array virtual array of the present invention;

[0039] Figure 3 It is a schematic diagram of the spectrum peak search of DOA estimation in a single MC experiment when three signal sources are incident on the nested array, where N1=3, N2=3 and the characteristic index α=0.5 in an impulse noise environment using the method of the present invention;

[0040] Figure 4It is a schematic diagram of RMSE performance of the method of the present invention and other algorithms under different generalized signal-to-noise ratio conditions when α=0.5 when 3 signal sources are incident on the nested array, where N1=3, N2=3, and 1000 MC experiments are run;

[0041] Figure 5 It is a schematic diagram of RMSE performance of the method of the present invention and other algorithms under different snapshot numbers when α=0.5 when 3 signal sources are incident on the nested array, where N1=3, N2=3, and 1000 MC experiments are run;

[0042] Figure 6 It is a schematic diagram of the RMSE performance of the method of the present invention and other algorithms under different characteristic index α conditions when 3 signal sources are incident on the nested array, where N1=3, N2=3, and 1000 MC experiments are run;

[0043] Figure 7 It is a schematic diagram of the RMSE performance of the method of the present invention and other algorithms under different array element numbers when three signal sources are incident on the nested array and 1000 MC experiments are run. DETAILED DESCRIPTION

[0044] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0045] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0046] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0047] Example 1

[0048] It should be noted that impulse noise does not seem to be common in the field of array signal processing, and most DOA estimation methods assume that the noise is a Gaussian noise model. However, in actual situations, the noise is composed of irregular pulses or spikes with short duration and large amplitude, and the traditional second-order statistics are no longer applicable. This kind of impulse noise can usually be modeled using the α-stable distribution, which has good applicability, and its characteristic function φ(u) can be expressed as:

[0049]

[0050] Among them, u is the variable of the characteristic function, 0<α≤2 is the characteristic exponent, j is the imaginary unit, γ is the dispersion parameter, and its meaning is consistent with the variance of the Gaussian distribution; β is the skewness parameter, δ is the location parameter, and the distribution when β=δ=0 is the symmetric α-stable (SαS) distribution.

[0051] The present invention provides a nested array non-circular SPFLOM-DOA estimation method under impulse noise, which specifically comprises the following steps:

[0052] Step 1: Receive signals through nested array antennas to obtain received signal information x(t).

[0053] like Figure 1 As shown, the nested array antenna includes two sub-arrays, and the number of array elements included in the two sub-arrays is N1 and N2 respectively. The uniform linear array with N1 array elements has an array element spacing of d0, and the array element spacing with N2 array elements is (N1+1)d0, where d0=λ / 2, λ is the carrier wavelength. Then the array element position geometry is:

[0054]

[0055] make sort(·) is an operation to sort the array spacing from small to large using the first array element as the reference system. i is the position of the ith array element after the array element positions are sorted from small to large, and l1 = 0. Assume that the K DOAs are θ k , k=1,2,…,K, the narrowband signal s0(t) is incident on Figure 1 On the nested linear array shown, the array receiving signal can be expressed as:

[0056] x(t)=AΦs0(t)+n(t)

[0057] where A=[a(θ1),…,a(θ k ),…a(θ K )] is the direction matrix, is the direction vector, is a noncircular phase matrix, represents the non-circular phase of the kth signal, j is an imaginary unit, n(t) is an impulse noise term that obeys a symmetric α-stable distribution, and 0<α≤2; s0(t)=[s 01 (t),…,s 0k (t),…s 0K (t)] T is the signal vector, where s 0k (t) represents the kth signal.

[0058] Step 2: Construct the extended signal information X(t) based on the non-circular characteristics of the signal and calculate its SPFLOM matrix R SPFLOM .

[0059] Specifically, using the non-circular characteristics of the signal, the extended array receiving signal is:

[0060]

[0061] in, is the expansion direction matrix, is the augmented impulse noise term; [] * is a conjugate operation. The received signal information X is composed of X(t), where X(t) is the tth time domain snapshot in X.

[0062] Calculate the SPFLOM matrix R SPFLOM :

[0063] According to the array received signal X(t), calculate the SPFLOM matrix R SPFLOM :

[0064]

[0065] Among them, y i (t), y j (t) are the i-th and j-th rows of the signal model y(t) at time t, respectively. represents mathematical expectation, p represents the order, and * represents the complex conjugate.

[0066] Step 3: R SPFLOMThe matrix is ​​vectorized and rearranged to obtain a virtual array receiving signal z.

[0067] Specifically,

[0068]

[0069]

[0070] where vec(·) represents a vectorized operation, is the expansion direction matrix, is the expansion direction vector, s SPFLOM represents the signal energy, Γ represents the stretched vector of the impulse noise term, and Γ′=JΓ represents the stretched vector of the impulse noise term after Γ is rearranged. represents Kronecker product, ⊙ represents KR product; is a row-commuting matrix, and I P represents the P×P identity matrix, 0 P represents a P×P zero matrix, Indicates 2P 2 ×2P 2 The zero matrix of , P = N1 + N2; and represents the kth signal information of the difference array virtual array, and Represents the information of the kth signal of the virtual array of negative and positive arrays respectively. D , and They represent the virtual array information of the difference matrix, negative sum matrix and positive sum matrix respectively, which can be specifically expressed as:

[0071]

[0072] where Γ D , and Represent the noise vectors of difference matrix, negative sum matrix, and positive sum matrix respectively.

[0073] Since the virtual array of the nested array is composed of the sum matrix and the difference matrix, we define:

[0074] Difference:

[0075] Positive-sum array:

[0076] Negative and array:

[0077] It can be proved that the difference matrix z DThe range of continuous uniform linear arrays is [-M1, M1]d0, M1 = N1N2 + N2-1, and the positive and negative arrays The range of the continuous uniform line array is [0,M2]d0, and the negative sum array The range of the continuous uniform linear array is [-M2,0]d0, where M2 = N1N2 + N1 + N2-1, R3 = 2MN + M-1, such as Figure 2 The virtual array is shown when N1=3, N2=3.

[0078] Step 4: Rearrange the virtual array receiving signal z and remove redundancy to obtain a new virtual uniform linear array receiving signal

[0079] For the virtual array receiving signal z, according to the difference matrix D and the sum matrix S + , S _ The virtual array element positions are sorted, and the virtual array information of the continuous array elements of z is intercepted to obtain the virtual uniform linear array receiving signal with an array element spacing of half a wavelength.

[0080]

[0081]

[0082] in, and is the direction vector matrix of the difference matrix, and is the direction vector matrix of the sum matrix; and yes The noise vector of the continuous element part of the corresponding difference array; and yes The corresponding noise vector of the continuous array element part of the sum array. It can be understood that like Figure 2 As shown, this is the virtual array when M1=3, M2=3.

[0083] Step 5: The difference array and the continuous part of the array element spacing of the half wavelength (i.e. and ) are spatially smoothed respectively, and the virtual array information Y is obtained by splicing, and the covariance matrix R is constructed for Y Y , and then use the dimension-reduced MUSIC method to obtain an accurate estimate of DOA.

[0084] right and Perform spatial smoothing algorithm:

[0085]

[0086] Among them, M1+1=N1N2+N2 is the number of times the sum matrix is ​​smoothed, and is also the number of sub-matrices and the number of smoothing times of the difference matrix. Represents the difference matrix The M1+2-mth to 2M1+2-mth elements in; Represents the sum matrix The M1+2-mth to M2+2-mth elements in; Represents the sum matrix Integrate the new difference matrix and sum matrix to construct a larger virtual array information The corresponding covariance matrix is:

[0087] R Y =YY H / (M1+1)

[0088] Therefore, the above formula can be regarded as a covariance matrix of a uniform linear array (ULA) consisting of M1+1 elements, which can be directly used in the reduced-dimensional MUSIC estimation algorithm, and 2M2-M1+3 signal sources can be estimated. Compared with the traditional circular signal DOA estimation algorithm, it improves a certain degree of freedom and estimation accuracy.

[0089] The smoothed covariance matrix R is obtained Y , after eigenvalue decomposition, the noise subspace U is obtained N , the accurate estimation of the DOA of the signal can be obtained by the following spectrum peak search function: RD-MUSIC :

[0090]

[0091] Where e =

[010] T , bikdiag{·} represents the matrix block diagonalization operation. T is the matrix transpose, and θ is the DOA grid value for the spectrum peak search.

[0092] Comparative Example

[0093] In order to verify the effect of the above method, multiple simulation experiments were conducted in this embodiment, and the experimental performance was analyzed. In an impulse noise environment, the generalized signal-to-noise ratio is defined as:

[0094]

[0095] The performance estimation criterion is the joint root mean square error (RMSE) defined as:

[0096]

[0097] in, is the accurate estimate of the DOA of the kth source in the jth Monte Carlo process, K represents the number of sources, and MC represents the number of Monte Carlo trials.

[0098] The present invention is compared with the existing methods, the existing methods: a uniform linear array non-circular DOA estimation method and a nested array non-circular conjugate augmented DOA estimation method, both of which are based on phase fractional low-order moments.

[0099] Figure 3 When K=3 sources are incident on the nested array, the DOA is [-10°, 30°, 60°]. Using the spectrum peak search diagram obtained by the present invention, this embodiment only runs one MC experiment. At this time, the number of sub-array elements of the nested array is N1=3, N2=3, the number of snapshots is L=500, and the GSNR=0dB. The impulse noise characteristic index α=0.5, it can be seen that the present invention can obtain accurate DOA estimation.

[0100] Figure 4 The algorithm performance comparison under different GSNR is shown in the case of α=0.5 and snapshot L=500. 1000 MC experiments are run, and the azimuth angles of the three signal sources are [-10°, 30°, 60°]. It can be seen that under the same generalized signal-to-noise ratio condition, the present invention has better DOA estimation performance.

[0101] Figure 5 The algorithm performance comparison under different snapshot numbers is shown in the case of GSNR = 0dB and α = 0.5. 1000 MC experiments are run, and the azimuth angles of the three signal sources are [-10°, 30°, 60°]. It can be seen that the performance of the present invention improves with the increase of snapshot numbers. Under the same snapshot conditions, the estimation performance of the present invention is better than other estimation methods.

[0102] Figure 6 The performance of the algorithms under different characteristic index conditions is compared when GSNR = -2dB and snapshot L = 500. 1000 MC experiments are run, and the azimuth angles of the three signal sources are [-10°, 30°, 60°]. It can be seen that the performance of the present invention improves with the increase of the characteristic index α. Under the same α condition, the estimation performance of the method of the present invention is better.

[0103] Figure 7 In the case of α=0.5 and snapshot L=500, the algorithm performance of the present invention is compared with the change of GSNR under different numbers of array elements. 1000 MC experiments are run, and the azimuth angles of the three signal sources are [-10°, 30°, 60°]. It can be seen that under the same generalized signal-to-noise ratio condition, the present invention has better DOA estimation performance as the number of array elements increases.

[0104] In summary, from the analysis of the simulation effect diagram, it can be seen that the nested array non-circular signal DOA estimation method based on SPFLOM in an impulse noise environment proposed in the present invention realizes accurate DOA estimation in a nested array strong impulse noise environment, improves the degree of freedom, and the estimation performance is better than the traditional uniform linear array DOA estimation method.

[0105] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. A nested array non-circular SPFLOM-DOA estimation method under impulse noise, characterized in that: The steps include: Step 1: Receive signals through nested array antennas to obtain signal information; Step 2: construct extended signal information according to the received signal information, and calculate the SPFLOM matrix; Step 3, vectorize and rearrange the SPFLOM matrix to obtain a virtual array receiving signal; Step 4: Remove redundancy from the virtual array receiving signal to obtain a new virtual uniform linear array receiving signal; Step 5: Perform spatial smoothing on the continuous parts of the difference array and sum array with half-wavelength array element spacing in the virtual uniform linear array received signal, concatenate them to obtain virtual array information, construct a covariance matrix for the virtual array information, and then use the reduced-dimensional MUSIC method to obtain an accurate estimate of DOA.

2. The method for estimating non-circular SPFLOM-DOA of nested arrays under impulse noise according to claim 1, characterized in that: The nested array antenna includes two sub-arrays, each of which includes array elements of N1 and N2 respectively. The array element spacing of the uniform linear array with N1 array elements is d0, and the array element spacing of N2 array elements is (N1+1)d0, where d0=λ / 2, λ is the carrier wavelength.

3. The method for estimating non-circular SPFLOM-DOA of nested arrays under impulse noise according to claim 1, characterized in that: In step (1), the received signal information x(t) is: x(t)=AΦs0(t)+n(t); where A=[a(θ1),…,a(θ k ),…a(θ K )] is the direction matrix, is the direction vector, is a noncircular phase matrix, represents the non-circular phase of the kth signal, j is an imaginary unit, n(t) is an impulse noise term that obeys a symmetric α-stable distribution, and 0<α≤2; s0(t)=[s 01 (t),…,s 0k (t),…s 0K (t)] T is the signal vector, where s 0k (t) represents the kth signal.

4. The method for estimating non-circular SPFLOM-DOA of nested arrays under impulse noise according to claim 1, characterized in that: In step 2, the non-circular feature of the signal information x(t) is used to expand the signal information X(t) of the array, and the expression is as follows: in, is the expansion direction matrix, is the augmented impulse noise term; [] * is a conjugate operation. The received signal information X is composed of X(t), where X(t) is the tth time domain snapshot in X.

5. The method for estimating non-circular SPFLOM-DOA of nested arrays under impulse noise according to claim 4, characterized in that: In step 2, the SPFLOM matrix R is calculated according to the extended signal information X(t). SPFLOM : where y i (t), y j (t) are the i-th and j-th rows of the signal model y(t) at time t, respectively. represents mathematical expectation, p represents the order, and * represents the complex conjugate.

6. The method for estimating non-circular SPFLOM-DOA of nested arrays under impulse noise according to claim 1, characterized in that: The virtual uniform linear array receives a signal z, which is expressed as follows: z=Jvec(R SPFLOM )=J(B * ⊙B)s SPFLOM +JΓ; Where vec(·) represents a vectorized operation, is the expansion direction matrix, is the expansion direction vector, s SPFLOM represents the signal energy, Γ represents the vector after the impulse noise term is stretched; represents Kronecker product, ⊙ represents KR product; is a row-commuting matrix, and I P represents the P×P identity matrix, 0 P represents a P×P zero matrix, Indicates 2P 2 ×2P 2 The zero matrix of , P = N1 + N2.

7. The method for estimating non-circular SPFLOM-DOA of nested arrays under impulse noise according to claim 6, characterized in that: In step 4, a new virtual uniform linear array receiving signal is obtained. for: in, and is the direction vector matrix of the difference matrix, and is the direction vector matrix of the sum matrix; and yes The noise vector of the continuous element part of the corresponding difference array; and yes The noise vector corresponding to the continuous array element part of the sum array.

8. The method for estimating non-circular SPFLOM-DOA of nested arrays under impulse noise according to claim 7, characterized in that: In step 5, the virtual array information Y is obtained by smoothing: Among them, M1=N1N2+N2-1, M2=N1N2+N1+N2-1; and Yes and The smoothing matrix obtained by spatial smoothing.

9. The method for estimating non-circular SPFLOM-DOA of nested arrays under impulse noise according to claim 8, characterized in that: The covariance matrix R of the virtual array information Y Y : R Y =YY H / (M1+1)。

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