Wide linear interference suppression method for satellite communication based on differential summation common array interpolation

Abstract

The present invention discloses a satellite communication wide linear interference suppression method based on differential sum common array interpolation, and belongs to the field of satellite communication signal processing technology. The method includes: obtaining an augmented coprime array receiving signal vector and an augmented coprime array covariance matrix; constructing a differential sum common array steering vector and a virtual receiving signal vector; obtaining an interpolated uniform differential sum common array and its virtual receiving signal vector; projecting the interpolated uniform differential sum common array virtual receiving signal vector to the complementary subspace of the virtual signal correlation subspace; restoring the interpolated uniform differential sum common array virtual receiving signal vector; establishing an interpolated uniform differential sum common array spatial spectrum estimator; and calculating a satellite communication coprime array augmented weight vector. The present invention can not only effectively suppress non-circular interference signals, but also increase the degree of freedom of suppressing interference when the number of antenna array elements is constant, thereby improving the robustness of the satellite communication wide linear interference suppression method to array errors.

Description

Technical Field

[0001] The invention relates to the technical field of satellite communication signal processing, and in particular to a satellite communication wide linear interference suppression method based on differential summation common array interpolation. Background Art

[0002] Satellites have been widely used in defense, military, commerce, and industry. However, satellite signals are susceptible to various intentional and unintentional interference, and with the rapid development of modern science and technology, various interference devices are becoming cheaper and cheaper, posing a serious threat to satellite communications. Therefore, the study of interference suppression methods is of great significance to the integrity and reliability of satellite communications. Adaptive antenna array algorithm is a commonly used method for satellite communication interference suppression, including spatial processing method, space-time adaptive processing method, and space-frequency adaptive processing method. Compared with space-time adaptive processing method and space-frequency adaptive processing method, spatial processing method requires less computational cost. Beamforming is a typical spatial processing method that forms a deep null in the direction of the interference signal by adjusting the array pattern. However, this method assumes that the incident signal is a circular signal, which is not optimal for non-circular signals. In the case of non-circular signals, the performance of wide linear beamforming is better than that of beamforming. In the case where there are errors in the desired satellite signal steering vector and the array covariance matrix, robust wide linear beamforming methods are proposed to deal with these errors, such as: wide linear Capon beamforming method, generalized non-circular robust Capon beamforming method, non-circular coefficient spatial spectrum wide linear beamforming method, projection constrained wide linear beamforming method, iterative quadratic constrained quadratic programming wide linear beamforming method, and augmented covariance matrix reconstruction wide linear beamforming method. The above wide linear beamforming methods use uniform linear arrays, which limit the spatial freedom of the array under the condition of a given number of antenna elements. The coprime array is a typical sparse array structure, which consists of a coprime pair of uniform linear arrays, and the spacing between adjacent array elements is greater than half the signal wavelength. It can dramatically increase the number of virtual array elements, thereby increasing the freedom of interference suppression. It is widely used in azimuth estimation, spatial spectrum estimation, filter design, adaptive beamforming, and deception interference detection. However, the coprime array algorithm is only applicable to circular signals and cannot effectively suppress non-circular interference signals in satellite communications.

[0003] In view of the above analysis, it is very necessary to study a new coprime array wide linear interference suppression method to improve the interference suppression performance of satellite communications under array error conditions. Summary of the invention

[0004] The present invention provides a satellite communication wide linear interference suppression method based on differential summation common array interpolation to solve the problem that the satellite communication uniform linear array cannot suppress all interference when the number of interference signals is greater than the number of antenna array elements.

[0005] The technical solution adopted by the present invention is a satellite communication wide linear interference suppression method based on differential summation common array interpolation, comprising the following steps:

[0006] Step S1: cascading the coprime array non-circular signal vector observed by satellite communication and its conjugate to obtain an augmented coprime array received signal vector, and further obtaining an augmented coprime array covariance matrix;

[0007] Step S2: vectorizing and amplifying the coprime array covariance matrix, constructing a differential sum co-array steering vector and a virtual received signal vector;

[0008] Step S3: interpolating the non-uniform differential sum common array into a uniform virtual linear array to obtain an interpolated uniform differential sum common array and its virtual received signal vector;

[0009] Step S4: construct a virtual signal correlation subspace, and project the interpolated uniform difference summed common array virtual received signal vector to the complementary subspace of the virtual signal correlation subspace;

[0010] Step S5: constructing an atomic norm sparse signal recovery optimization problem about the interpolated uniform difference summed common array virtual received signal vector, and solving the recovered interpolated uniform difference summed common array virtual received signal vector;

[0011] Step S6: establishing an interpolation uniform difference sum common array spatial spectrum estimator to estimate the direction of the incident signal;

[0012] Step S7: constructing a coprime array covariance matrix and a pseudo-covariance matrix to jointly optimize the problem, and solving the power of the incident signal;

[0013] Step S8: reconstructing the coprime array interference plus noise covariance matrix and estimating the amplified desired satellite signal steering vector;

[0014] Step S9: Calculate the satellite communication coprime array expansion weight vector to suppress wide linear interference.

[0015] As a further improvement of the present invention, in step S1, the mutually prime array non-circular signal vector observed by satellite communication is cascaded with its conjugate to obtain an augmented mutually prime array received signal vector, and further obtain an augmented mutually prime array covariance matrix, which is specifically:

[0016] (1) Consider a satellite communication device equipped with a coprime antenna array. The first subarray of the coprime array contains 2M array elements and the spacing between adjacent array elements is Nd. The second subarray contains N array elements and the spacing between adjacent array elements is Md, where d is the unit array element spacing, M and N are a pair of coprime integers and M<N. The first array element is used as the common reference array element of the two subarrays. The set of physical array element positions of the coprime array is:

[0017]

[0018] Among them, p l d is the position of the lth physical array element of the coprime array and p1=0. Since M and N are coprime integers, the total number of array elements in the coprime array is L=2M+N-1.

[0019] (2) Suppose a desired satellite signal and K non-circular interference signals are incident on a coprime array from the far field. The direction of the desired satellite signal is θ0, and the direction of the kth non-circular interference signal is θ k And k = 1, 2, ..., K; at time t, the received signal vector x(t) of the coprime array is expressed as:

[0020] x(t)=As(t)+n(t)=a(θ0)s0(t)+g(t) (2)

[0021] Among them, A=[a(θ0),a(θ1),…,a(θ K )] is the coprime array steering matrix, a(θ0) is the desired satellite signal steering vector, a(θ k ) is the kth non-circular interference signal steering vector, s(t)=[s0(t),s1(t),…,s K (t)] T is the signal beam vector, s0(t) is the desired satellite signal beam, s k (t) is the kth non-circular interference signal beam, n(t) is the noise vector, is the global interference plus noise vector;

[0022] (3) In order to utilize the non-circular characteristics of the signal, x(t) and its conjugate component x * (t) can be cascaded to obtain:

[0023]

[0024] in, is the amplified coprime array received signal vector, s * (t) is the signal conjugate beam vector, is the conjugate beam of the kth non-circular interference signal. For a strictly non-circular signal, k=0,1,…,K, substituting this relation into (3), we get:

[0025]

[0026] in, To augment the coprime array guide matrix, Indicates the direction as θ kThe non-circular signal amplification guidance vector and k = 0, 1, ..., K, is the amplified noise vector. The amplified coprime array received signal covariance matrix It is expressed as:

[0027]

[0028] As a further improvement of the present invention, in step S2, the vectorization amplifies the coprime array covariance matrix, constructs the difference sum co-array steering vector and the virtual received signal vector, specifically:

[0029] Vectorization We can get:

[0030]

[0031] Where z is the virtual common array signal vector, is the power vector, i=vec(I 2L ) is the virtual common array noise vector, is the virtual co-array steering matrix, and the virtual co-array steering vector v(θ) is expressed as:

[0032]

[0033] in,

[0034] v1(θ) and v4(θ) generate a differential common array, and the set of virtual array element positions in the differential common array is v2(θ) produces a negative summation matrix and the set of virtual array element positions is v3(θ) produces a positive summation common array with virtual array element positions at Therefore, the difference sums the set of virtual array element positions in the array It is expressed as:

[0035]

[0036] Differential summation common array virtual received signal vector Expressed as is a subvector of i, is the difference sum common matrix steering matrix which is expressed as in, is the difference sum common array steering vector and is expressed as in, is a subvector of v2(θ), is a subvector of v1(θ), is a subvector of v3(θ).

[0037] As a further improvement of the present invention, in step S3, the non-uniform differential sum common array is interpolated into a uniform virtual linear array to obtain an interpolated uniform differential sum common array and its virtual received signal vector, specifically:

[0038] Since the difference sum common array is non-uniform and contains holes, the difference sum common array is interpolated into a virtual uniform linear array, called the interpolated uniform difference sum common array, and its virtual array element position set is in, Yes Subsets, the corresponding expressions are:

[0039]

[0040] Interpolation uniform difference summation common array received signal vector Initialized to:

[0041]

[0042] Among them, <·> id Represents the virtual signal value corresponding to the virtual array element at position id; defines a binary vector b and represents it as Ideal interpolation uniform difference summation common array received signal vector Expressed as in,

[0043] represents the interpolated uniform difference summed common matrix steering matrix, represents the interpolated uniform difference summed common matrix steering vector and the expression is express The corresponding virtual uniform linear array steering vector, express The corresponding virtual uniform linear array steering vector, express The corresponding virtual uniform linear array steering vector, represents the interpolated uniform difference summed common array noise vector and the expression is vector With vector The relationship between

[0044] As a further improvement of the present invention, in step S4, the virtual signal correlation subspace is constructed, and the interpolated uniform difference summation common array virtual received signal vector is projected to the complementary subspace of the virtual signal correlation subspace, specifically:

[0045] Define the transformation vector as Using the transformation vector τ, the vector Translates to:

[0046]

[0047] in, is the transformed interpolated uniform difference summed common array received signal vector, at this time is called the correlation vector, and in (11) It is called the correlation subspace;

[0048] The correlation subspace matrix S is constructed as:

[0049]

[0050] Performing eigendecomposition on the correlation subspace matrix S yields:

[0051]

[0052] Among them, Λ s is a diagonal matrix consisting of positive eigenvalues, U s is a matrix consisting of eigenvectors corresponding to positive eigenvalues, U n is a matrix consisting of the eigenvectors corresponding to the remaining eigenvalues. Combining (11) and (13), we can obtain:

[0053]

[0054] As a further improvement of the present invention, in step S5, the atomic norm sparse signal recovery optimization problem about the interpolated uniform difference summed common array virtual received signal vector is constructed to solve the recovered interpolated uniform difference summed common array virtual received signal vector, specifically:

[0055] Using Vectors Construct the atomic set Ω as:

[0056]

[0057] definition The atomic norm of for:

[0058]

[0059] The atomic norm minimization optimization problem is constructed as follows:

[0060]

[0061] Among them, δ is the threshold, express is a positive semidefinite Toeplitz matrix and the vector As The first column of

[0062] The optimization problem (17) is further transformed into:

[0063]

[0064] if Available matrix The trace of is calculated as:

[0065]

[0066] Where Tr(·) represents the trace operation of the matrix. Combining equations (16) and (19), we can obtain:

[0067]

[0068] Substituting equation (20) into the optimization problem (18) yields:

[0069]

[0070] in, The optimization problem (21) is a convex optimization problem, so the optimal solution is obtained using CVX software:

[0071] As a further improvement of the present invention, in step S6, the establishment of an interpolation uniform difference sum common array spatial spectrum estimator to estimate the direction of the incident signal is specifically as follows:

[0072] The optimal solution obtained by using the optimization problem (21) Construct the Toeplitz matrix as right Performing feature decomposition yields:

[0073]

[0074] Among them, E s represents the signal subspace projection matrix, E n represents the noise subspace projection matrix, the diagonal matrix Γ s =diag{ω0,ω1,…,ω K The diagonal elements ω0,ω1,…,ω K yes The K+1 large eigenvalues ​​of the diagonal matrix The diagonal elements of yes The remaining eigenvalues;

[0075] According to the orthogonality of the subspace, we can get:

[0076]

[0077] The spatial spectrum estimator of the interpolation uniform difference summation common array is established as:

[0078]

[0079] By searching for the peak values ​​of f(θ) in the entire angular space region [-90°, 90°], the angles corresponding to these peak values ​​are expressed as These angles are the directions from which the signal is incident.

[0080] As a further improvement of the present invention, in step S7, the coprime array covariance matrix and the pseudo-covariance matrix are jointly optimized to solve the power of the incident signal, specifically:

[0081] The covariance matrix and pseudo-covariance matrix of coprime arrays are constructed to jointly optimize the problem as follows:

[0082]

[0083] in, represents the use of a coprime array steering matrix to estimate the signal direction, represents the signal power diagonal matrix, represents the estimated noise variance and is equal to The minimum eigenvalue of This shows that the power of each signal must be non-negative;

[0084] The optimization problem (25) is a least squares problem with inequality constraints, and its solution is:

[0085]

[0086] in,

[0087]

[0088]

[0089] As a further improvement of the present invention, in step S8, the reconstructing the coprime array interference plus noise covariance matrix and estimating the amplified desired signal steering vector are specifically:

[0090] The reconstructed coprime array interference plus noise covariance matrix is ​​as follows:

[0091]

[0092] Using the estimated desired satellite signal direction Calculate the amplified steering vector of the desired satellite signal in a coprime array for:

[0093]

[0094] As a further improvement of the present invention, in step S9, the calculation of the satellite communication coprime array expansion weight vector to suppress wide linear interference is specifically as follows:

[0095] Using the coprime array interference plus noise covariance matrix reconstructed in (29) and the expected signal amplification guidance vector estimated in (30) The satellite communication coprime array expansion weight vector is calculated as:

[0096]

[0097] The beneficial effects of the present invention are:

[0098] (1) Combining the advantages of coprime arrays and wide linear beamforming, it can not only suppress non-circular interference signals but also increase the freedom of interference suppression;

[0099] (2) The non-uniform difference summation common array is interpolated into a uniform virtual linear array, which not only utilizes the information of uniform virtual array elements, but also utilizes the information of non-uniform virtual array elements;

[0100] (3) While constructing the atomic norm minimization optimization problem, signal vector element difference, positive semidefinite matrix and orthogonal subspace constraints are imposed to improve the accuracy of signal vector recovery and signal direction estimation;

[0101] (4) Construct the optimization problem of the common coprime array covariance matrix and pseudo-covariance matrix, make full use of the information of these two matrices, and improve the accuracy of signal power estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0103] Figure 1 It is a flow chart of a satellite communication wide linear interference suppression method based on differential summation common array interpolation of the present invention;

[0104] Figure 2 Schematic diagram of the coprime array structure used in the present invention;

[0105] Figure 3 is a schematic diagram of the virtual array structure generated by the present invention;

[0106] Figure 4 Schematic diagram of the relationship between the output signal-to-interference-noise ratio and the input signal-to-noise ratio when the array information is accurately known in an embodiment of the present invention;

[0107] Figure 5is a schematic diagram of the relationship between the output signal-to-interference-noise ratio and the number of sampling snapshots when the array information is accurately known in an embodiment of the present invention;

[0108] Figure 6 Schematic diagram of the relationship between the output signal-to-interference-noise ratio and the input signal-to-noise ratio when the signal direction error is fixed in an embodiment of the present invention;

[0109] Figure 7 is a schematic diagram of the relationship between the output signal-to-interference-noise ratio and the number of sampling snapshots when the signal direction error is fixed in an embodiment of the present invention;

[0110] Figure 8 Schematic diagram of the relationship between the output signal-to-interference-noise ratio and the input signal-to-noise ratio in the case of random signal directional error in an embodiment of the present invention;

[0111] Fig. 9 Schematic diagram of the relationship between the output signal to interference noise ratio and the number of sampling snapshots in the case of random signal directional error in an embodiment of the present invention. DETAILED DESCRIPTION

[0112] like Figures 1 to 3 As shown, the satellite communication wide linear interference suppression method based on differential summation common array interpolation of the present invention comprises the following steps:

[0113] Step S1, cascading the coprime array non-circular signal vector observed by satellite communication and its conjugate to obtain an augmented coprime array received signal vector, and further obtaining an augmented coprime array covariance matrix.

[0114] Consider a satellite communication device equipped with a coprime antenna array. The first subarray of the coprime array contains 2M array elements and the spacing between adjacent array elements is Nd. The second subarray contains N array elements and the spacing between adjacent array elements is Md, where d is the unit array element spacing, M and N are a pair of coprime integers and M < N. The first array element is used as the common reference array element of the two subarrays, and the physical array element position set of the coprime array is:

[0115]

[0116] Among them, p l d is the position of the lth physical element of the coprime array and p1 = 0. Since M and N are coprime integers, the total number of elements in the coprime array is L = 2M + N-1. Suppose a desired satellite signal and K non-circular interference signals are incident on the coprime array from the far field. The direction of the desired satellite signal is θ0, and the direction of the kth non-circular interference signal is θ k And k = 1, 2, ..., K. At time t, the received signal vector x(t) of the coprime array can be expressed as:

[0117] x(t)=As(t)+n(t)=a(θ0)s0(t)+g(t) (2)

[0118] Among them, A=[a(θ0),a(θ1),…,a(θ K )] is the coprime array steering matrix, a(θ0) is the desired satellite signal steering vector, a(θ k ) is the kth non-circular interference signal steering vector, s(t)=[s0(t),s1(t),…,s K (t)] T is the signal beam vector, s0(t) is the desired satellite signal beam, s k (t) is the kth non-circular interference signal beam, n(t) is the noise vector, is the global interference plus noise vector. In order to utilize the non-circular characteristics of the signal, x(t) and its conjugate component x * (t) can be cascaded to obtain:

[0119]

[0120] in, is the amplified coprime array received signal vector, s * (t) is the signal conjugate beam vector, is the conjugate beam of the kth non-circular interference signal. For a strictly non-circular signal, Substituting this relation into (3), we can obtain:

[0121]

[0122] in, To augment the coprime array guide matrix, Indicates the direction as θ k The non-circular signal amplification guidance vector and k = 0, 1, ..., K, is the amplified noise vector. The amplified coprime array received signal covariance matrix It can be expressed as:

[0123]

[0124] Step S2: vector-enlarge the coprime array covariance matrix, and construct a differential sum co-array steering vector and a virtual received signal vector.

[0125] Vectorization We can get:

[0126]

[0127] Where z is the virtual common array signal vector, is the power vector, i=vec(I 2L ) is the virtual common array noise vector, is the virtual co-array steering matrix, and the virtual co-array steering vector v(θ) can be expressed as:

[0128]

[0129] in, Obviously, v1(θ) and v4(θ) generate a differential common array, and the set of virtual array element positions in the differential common array is Generate a negative sum common array and the set of virtual array element positions is Generate a positive summation common array with virtual array element positions at Therefore, the difference sums the set of virtual array element positions in the array It can be expressed as:

[0130]

[0131] Differential summation common array virtual received signal vector It can be expressed as is a subvector of i, is the difference sum common matrix steering matrix which can be expressed as in, is the difference sum common array steering vector and can be expressed as in, is a subvector of v2(θ), is a subvector of v1(θ), is a subvector of v3(θ).

[0132] Step S3: interpolate the non-uniform difference sum common array into a uniform virtual linear array to obtain an interpolated uniform difference sum common array and its virtual received signal vector.

[0133] Since the difference sum common array is non-uniform and contains holes, the difference sum common array is interpolated into a virtual uniform linear array, called the interpolated uniform difference sum common array, and its virtual array element position set is in, Yes Subsets, the corresponding expressions are:

[0134]

[0135] Interpolation uniform difference summation common array received signal vector Can be initialized as:

[0136]

[0137] Among them, <·> idRepresents the virtual signal value corresponding to the virtual array element at position id. Define the binary vector b and represent it as Ideal interpolation uniform difference summation common array received signal vector It can be expressed as in, represents the interpolated uniform difference summed common matrix steering matrix, represents the interpolated uniform difference summed common matrix steering vector and the expression is express The corresponding virtual uniform linear array steering vector, express The corresponding virtual uniform linear array steering vector, express The corresponding virtual uniform linear array steering vector, represents the interpolated uniform difference summed common array noise vector and the expression is vector With vector The relationship between can be expressed as Step S4: construct a virtual signal correlation subspace, and project the interpolated uniform difference summed co-array virtual received signal vector to the complementary subspace of the virtual signal correlation subspace.

[0138] Define the transformation vector as Using the transformation vector τ, the vector Translates to:

[0139]

[0140]

[0141] in, is the transformed interpolated uniform difference summed common array received signal vector, at this time is called the correlation vector, and in (11) It is called the correlation subspace. The correlation subspace matrix S is constructed as:

[0142]

[0143] Performing eigendecomposition on the correlation subspace matrix S yields:

[0144]

[0145] Among them, Λ s is a diagonal matrix consisting of positive eigenvalues, U s is a matrix consisting of eigenvectors corresponding to positive eigenvalues, U nis a matrix consisting of the eigenvectors corresponding to the remaining eigenvalues. Combining (11) and (13), we can obtain:

[0146]

[0147] Step S5: construct an atomic norm sparse signal recovery optimization problem for the interpolated uniform difference summed common array virtual received signal vector, and solve the recovered interpolated uniform difference summed common array virtual received signal vector.

[0148] Using Vectors Construct the atomic set Ω as:

[0149]

[0150] definition The atomic norm of for:

[0151]

[0152] The atomic norm minimization optimization problem is constructed as follows:

[0153]

[0154] Among them, δ is the threshold, express is a positive semidefinite Toeplitz matrix and the vector As The first column of . The optimization problem (17) can be further transformed into:

[0155]

[0156] if Available

[0157] matrix The trace of can be calculated as:

[0158]

[0159] Where Tr(·) represents the trace operation of the matrix. Combining equations (16) and (19), we can obtain:

[0160]

[0161] Substituting equation (20) into the optimization problem (18) yields:

[0162]

[0163] in, The optimization problem (21) is a convex optimization problem, so the optimal solution can be obtained using CVX software:

[0164] Step S6: Establish an interpolation uniform difference sum common array spatial spectrum estimator to estimate the direction of the incident signal.

[0165] The optimal solution obtained by using the optimization problem (21) Construct the Toeplitz matrix as right Performing feature decomposition yields:

[0166]

[0167] Among them, E s represents the signal subspace projection matrix, E n represents the noise subspace projection matrix, the diagonal matrix Γ s =diag{ω0,ω1,…,ω K The diagonal elements ω0,ω1,…,ω K yes The K+1 large eigenvalues ​​of the diagonal matrix The diagonal elements of yes The remaining eigenvalues. According to the orthogonality of the subspace, we can get:

[0168]

[0169] The spatial spectrum estimator of the interpolation uniform difference summation common array is established as:

[0170]

[0171] By searching for the peaks of f(θ) in the entire angular space region [-90°, 90°], the angles corresponding to these peaks can be expressed as These angles are the directions from which the signal is incident.

[0172] Step S7: construct a coprime array covariance matrix and a pseudo-covariance matrix to jointly optimize the problem and solve the power of the incident signal.

[0173] The covariance matrix and pseudo-covariance matrix of coprime arrays are constructed to jointly optimize the problem as follows:

[0174]

[0175] in, represents the use of a coprime array steering matrix to estimate the signal direction, represents the signal power diagonal matrix, represents the estimated noise variance and is equal to The minimum eigenvalue of It shows that the power of each signal must be non-negative. The optimization problem (25) is a least squares problem with inequality constraints, and its solution is:

[0176]

[0177] in,

[0178]

[0179]

[0180] Step S8: reconstruct the coprime array interference plus noise covariance matrix and estimate the amplified desired signal steering vector.

[0181] The reconstructed coprime array interference plus noise covariance matrix is ​​as follows:

[0182]

[0183] Using the estimated desired satellite signal direction The amplification steering vector of the desired satellite signal of the coprime array can be calculated for:

[0184]

[0185] Step S9, calculate the satellite communication coprime array expansion weight vector to suppress wide linear interference.

[0186] Using the coprime array interference plus noise covariance matrix reconstructed in (29) and the expected signal amplification guidance vector estimated in (30) The weight vector of satellite communication coprime array expansion can be calculated as:

[0187]

[0188] [Example]

[0189] The following is the satellite communication wide linear interference suppression experiment setup based on differential summation common array interpolation using the above method:

[0190] Satellite communication equipment uses a coprime array antenna, where M = 2 and N = 3. The position set of the coprime array physical array elements is {0, 2, 3, 4, 6, 9}d. Assume that the direction of the expected satellite signal incident on the coprime array is 0° and the non-circular phase is 0°, and the directions of the two interferences incident on the coprime array are -60° and 60° respectively, and the non-circular phase is 0°. All incident signals are binary phase shift keying signals, whose pulse forming function is the Nyquist forming function and the roll-off factor is 1. In this method, the variable In the spatial angle search range [-90°, 90], uniform sampling is performed and the sampling angle interval is 0.1°.

[0191] Experiment 1: Considering the case where the array information is precisely known: test the impact of input signal-to-noise ratio and sampling snapshot number on the output signal-to-interference-noise ratio. Figure 4 The relationship between the output signal-to-noise ratio and the input signal-to-noise ratio of all test methods is shown. Figure 5 The relationship between the output signal-to-interference-to-noise ratio and the number of sampling snapshots of all test methods is shown. The results show that the performance of the method proposed in the present invention is better than that of other test methods, because the method proposed in the present invention accurately reconstructs the coprime array interference plus noise covariance matrix and accurately estimates the desired satellite signal amplification steering vector.

[0192] Experiment 2: Consider the case of fixed direction error of the signal: Assume that the expected satellite signal direction is 0° and the actual direction is 3°, so the fixed direction error is 3°. Figure 6 The relationship between the output signal-to-noise ratio and the input signal-to-noise ratio of all test methods is shown. Figure 7 The relationship between the output signal-to-interference-noise ratio and the number of sampling snapshots of all test methods is shown. It can be seen that the performance of the method proposed in the present invention is significantly better than that of other test methods, which shows that the method proposed in the present invention is not only effective for coprime arrays, but also has robust performance for signal fixed direction errors.

[0193] Experiment 3: Consider the case of random direction error of the signal: Assume that the expected satellite signal direction is 0°, and the actual direction is randomly generated from the angle interval [-4°, 4°], so the random direction error is [-4°, 4°]. Figure 8 The relationship between the output signal-to-noise ratio and the input signal-to-noise ratio of all test methods is shown. Fig. 9 The relationship between the output signal-to-noise ratio and the number of sampling snapshots of all the test methods is shown. It can be observed that the method proposed in the present invention has the best performance in the entire input signal-to-noise ratio range and the sampling snapshot number range, which means that the method proposed in the present invention is effective for coprime array non-circular signals and can handle random directional errors of signals.

[0194] The embodiments of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited thereto. Various changes that can be made within the knowledge scope of technicians in the relevant technical field without departing from the spirit of the present invention are all within the protection scope of the claims of the present invention.

Claims

1. A satellite communication wide linear interference suppression method based on differential summation common array interpolation, characterized in that: The following steps are involved: Step S1: cascading the coprime array non-circular signal vector observed by satellite communication and its conjugate to obtain an augmented coprime array received signal vector, and further obtaining an augmented coprime array covariance matrix; Step S2: vectorizing and amplifying the coprime array covariance matrix, constructing a differential sum co-array steering vector and a virtual received signal vector; Step S3: interpolating the non-uniform differential sum common array into a uniform virtual linear array to obtain an interpolated uniform differential sum common array and its virtual received signal vector; Step S4: construct a virtual signal correlation subspace, and project the interpolated uniform difference summed common array virtual received signal vector to the complementary subspace of the virtual signal correlation subspace; Step S5: constructing an atomic norm sparse signal recovery optimization problem about the interpolated uniform difference summed common array virtual received signal vector, and solving the recovered interpolated uniform difference summed common array virtual received signal vector; Step S6: establishing an interpolation uniform difference sum common array spatial spectrum estimator to estimate the direction of the incident signal; Step S7: constructing a coprime array covariance matrix and a pseudo-covariance matrix to jointly optimize the problem, and solving the power of the incident signal; Step S8: reconstructing the coprime array interference plus noise covariance matrix and estimating the amplified desired satellite signal steering vector; Step S9: Calculate the satellite communication coprime array expansion weight vector to suppress wide linear interference.

2. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 1, characterized in that: In step S1, the mutually prime array non-circular signal vector observed by satellite communication is cascaded with its conjugate to obtain an augmented mutually prime array received signal vector, and further obtain an augmented mutually prime array covariance matrix, which is specifically: (1) Consider a satellite communication device equipped with a coprime antenna array. The first subarray of the coprime array contains 2M array elements and the spacing between adjacent array elements is Nd. The second subarray contains N array elements and the spacing between adjacent array elements is Md, where d is the unit array element spacing, M and N are a pair of coprime integers and M<N. The first array element is used as the common reference array element of the two subarrays. The set of physical array element positions of the coprime array is: P={Nmd|0≤m≤2M-1}∪{Mnd|0≤n≤N-1}={p1,p2,…,p L }d (1) Where p l d is the position of the lth physical array element of the coprime array and p1=0. Since M and N are coprime integers, the total number of array elements in the coprime array is L=2M+N-1. (2) Suppose a desired satellite signal and K non-circular interference signals are incident on a coprime array from the far field. The direction of the desired satellite signal is θ0, and the direction of the kth non-circular interference signal is θ k And k = 1, 2, ..., K; at time t, the received signal vector x(t) of the coprime array is expressed as: x(t)=As(t)+n(t)=a(θ0)s0(t)+g(t) (2) Among them, A=[a(θ0),a(θ1),…,a(θ K )] is the coprime array steering matrix, a(θ0) is the desired satellite signal steering vector, a(θ k ) is the kth non-circular interference signal steering vector, s(t)=[s0(t),s1(t),…,s K (t)] T is the signal beam vector, s0(t) is the desired satellite signal beam, s k (t) is the kth non-circular interference signal beam, n(t) is the noise vector, is the global interference plus noise vector; (3) In order to utilize the non-circular characteristics of the signal, x(t) and its conjugate component x * (t) can be cascaded to obtain: in, is the amplified coprime array received signal vector, s * (t) is the signal conjugate beam vector, is the conjugate beam of the kth non-circular interference signal. For a strictly non-circular signal, Substituting this relation into (3), we can obtain: in, To augment the coprime array guide matrix, Indicates the direction as θ k The non-circular signal amplification guidance vector and k = 0, 1, ..., K, To amplify the noise vector, the covariance matrix of the coprime array received signal is amplified It is expressed as:

3. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 2, characterized in that: In step S2, the vectorization amplifies the coprime array covariance matrix to construct a differential sum co-array steering vector and a virtual received signal vector, specifically: Vectorization We can get: Where z is the virtual common array signal vector, is the power vector, i=vec(I 2L ) is the virtual common array noise vector, is the virtual co-array steering matrix, and the virtual co-array steering vector v(θ) is expressed as: in, v1(θ) and v4(θ) generate a differential common array, in which the virtual array element position set is D = {±(Mn-Nm)d|0≤m≤2M-1,0≤n≤N-1}, and v2(θ) generates a negative sum common array and the virtual array element position set is S - ={-(Mn+Nm)d|0≤m≤2M-1,0≤n≤N-1}, v3(θ) generates a positive summation matrix and the virtual array element position is S + ={(Mn+Nm)d|0≤m≤2M-1,0≤n≤N-1}, so the difference sum common array virtual element position set V is expressed as: V=D∪S - ∪S + (8) Differential summation common array virtual received signal vector z V Expressed as i V is a subvector of i, V V is the differential sum common matrix steering matrix, which is represented by V V =[v V (θ0),v V (θ1),…,v V (θ K )], where v V (θ) is the difference-sum co-array steering vector and is expressed as in, is a subvector of v2(θ), is a subvector of v1(θ), is a subvector of v3(θ).

4. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 3, characterized in that: In step S3, the non-uniform difference sum common array is interpolated into a uniform virtual linear array to obtain an interpolated uniform difference sum common array and its virtual received signal vector, specifically: Since the difference sum common array is non-uniform and contains holes, the difference sum common array is interpolated into a virtual uniform linear array, called the interpolated uniform difference sum common array, and its virtual array element position set is I = I1∪I2∪I3, where I1, I2, and I3 are all subsets of I, and the corresponding expressions are: Interpolation uniform difference summation common array received signal vector Initialized to: Among them, <·> id Indicates the element value of the vector in brackets corresponding to the virtual array element at position id; define the binary vector b and express it as Ideal interpolation uniform difference summation common array received signal vector z I Expressed as Among them, V I =[v I (θ0),v I (θ1),…,v I (θ K )] represents the interpolation uniform difference sum common matrix steering matrix, v I (θ) represents the interpolated uniform difference summed common array steering vector and the expression is represents the virtual uniform linear array steering vector corresponding to I1, represents the virtual uniform linear array steering vector corresponding to I2, represents the virtual uniform linear array steering vector corresponding to I3, i I represents the interpolated uniform difference summed common array noise vector and the expression is vector With vector z I The relationship between 5. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 4, characterized in that: In step S4, the virtual signal correlation subspace is constructed, and the interpolated uniform difference summation common array virtual received signal vector is projected to the complementary subspace of the virtual signal correlation subspace, specifically: Define the transformation vector as Using the transformation vector τ, vector z I Translates to: in, is the transformed interpolated uniform difference summed common array received signal vector, at this time v I (θ) is called the correlation vector, and span {v I (θ):-π / 2≤θ≤π / 2} is called the correlation subspace; The correlation subspace matrix S is constructed as: Performing eigendecomposition on the correlation subspace matrix S yields: Among them, Λ s is a diagonal matrix consisting of positive eigenvalues, U s is a matrix consisting of eigenvectors corresponding to positive eigenvalues, U n is a matrix consisting of eigenvectors corresponding to the remaining eigenvalues. Combining (11) and (13), we can obtain:

6. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 5, characterized in that: In step S5, the atomic norm sparse signal recovery optimization problem about the interpolated uniform difference summed common array virtual received signal vector is constructed to solve the recovered interpolated uniform difference summed common array virtual received signal vector, specifically: Using vector v I (θ), construct the atomic set Ω as: Ω={v I (θ)|-π / 2≤θ≤π / 2} (15) definition The atomic norm of for: The atomic norm minimization optimization problem is constructed as follows: Among them, δ is the threshold, toeplitz(z I )≥0 means toeplitz(z I ) is a positive semidefinite Toeplitz matrix and the vector z I As toeplitz(z I ) The optimization problem (17) is further transformed into: If rank(toeplitz(z I ))<|I|, we can get The matrix toeplitz(z I ) is calculated as: Where Tr(·) represents the trace operation of the matrix. Combining equations (16) and (19), we can obtain: Substituting equation (20) into the optimization problem (18) yields: Where η = (1 / |I|)μ; the optimization problem (21) is a convex optimization problem, so the optimal solution is obtained using CVX software:

7. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 6, characterized in that: In step S6, the interpolation uniform difference sum common array spatial spectrum estimator is established to estimate the direction of the incident signal, specifically: The optimal solution obtained by using the optimization problem (21) Construct the Toeplitz matrix as right Performing feature decomposition yields: Among them, E s represents the signal subspace projection matrix, E n represents the noise subspace projection matrix, the diagonal matrix Γ s =diag{ω0,ω1,…,ω K The diagonal elements ω0,ω1,…,ω K yes The K+1 large eigenvalues ​​of the diagonal matrix Γ n =diag{ω K+1 ,ω K+2 ,…,ω |I|-1 The diagonal elements ω of K+1 ,ω K+2 ,…,ω |I|-1 yes The remaining eigenvalues; According to the orthogonality of the subspace, we can get: The spatial spectrum estimator of the interpolation uniform difference summation common array is established as: By searching for the peak values ​​of f(θ) in the entire angular space region [-90°, 90°], the angles corresponding to these peak values ​​are expressed as These angles are the directions from which the signal is incident.

8. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 7, characterized in that: In step S7, the coprime array covariance matrix and pseudo-covariance matrix are jointly optimized to solve the power of the incident signal, specifically: The covariance matrix and pseudo-covariance matrix of coprime arrays are constructed to jointly optimize the problem as follows: in, represents the use of a coprime array steering matrix to estimate the signal direction, represents the signal power diagonal matrix, represents the estimated noise variance and is equal to The minimum eigenvalue of , the non-negative constraint Λ ≥ 0 indicates that the power of each signal must be non-negative; The optimization problem (25) is a least squares problem with inequality constraints, and its solution is: in, 9. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 8, characterized in that: In step S8, the reconstructing the coprime array interference plus noise covariance matrix and estimating the amplified desired signal steering vector are specifically: The reconstructed coprime array interference plus noise covariance matrix is ​​as follows: Using the estimated desired satellite signal direction Calculate the amplified steering vector of the desired satellite signal in a coprime array for:

10. The satellite communication wide linear interference suppression method based on differential summation common array interpolation as claimed in claim 9, characterized in that: In step S9, the calculation of the satellite communication coprime array expansion weight vector to suppress wide linear interference is specifically as follows: Using the coprime array interference plus noise covariance matrix reconstructed in (29) and the expected signal amplification guidance vector estimated in (30) The satellite communication coprime array expansion weight vector is calculated as:

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