An anti-interference adaptive processing array reconstruction method

Abstract

The present invention provides an anti-interference adaptive processing array reconstruction method, which belongs to the field of array reconstruction technology and solves the problem that existing methods limit the improvement of anti-interference performance and cannot be applied to space-time adaptive processing array reconstruction. The method comprises the following steps: calculating the steering vector, space-time correlation coefficient and spatial correlation vector of satellite signals and interference signals, calculating the square lower bound of the space-time correlation coefficient of the space-time adaptive processing array, and calculating the optimal output upper bound of the space-time adaptive processing array; drawing a performance-cost trade-off curve, and based on the curve, selecting the optimal number of antenna-delay tap pairs used for reconstructing the space-time adaptive processing array and determining the positions of the antenna-delay tap pairs of the reconstructed space-time adaptive processing array; completing the reconstruction of the space-time adaptive processing array and forming an adaptive beam. The present invention reduces the computational cost of adaptive processing by selecting the antenna-delay tap pairs, and also maximizes the retention of anti-interference performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of array reconstruction, is applied to a satellite navigation system, and specifically relates to an anti-interference adaptive processing array reconstruction method. Background Art

[0002] Satellite navigation systems provide users with real-time positioning, navigation, and timing services and are widely used in both military and civilian applications. However, after long-distance transmission, the satellite signals reaching ground users are extremely weak, with an actual power of approximately -160dBW, far less than the noise power. Consequently, satellite signals are highly susceptible to high-power jamming attacks from the same frequency band, which can prevent ground users from properly receiving satellite signals and resulting in loss of navigation and positioning capabilities. Researching anti-jamming technologies to enhance the anti-jamming capabilities of satellite navigation signals is a key goal in the current development of satellite navigation systems.

[0003] Space-time adaptive processing technology uses the differences between satellite signals and interference in the space-time domain to perform joint space-time filtering, and is a commonly used anti-interference technology. The space-time adaptive processing array consists of multiple array elements. Corresponding to each array element channel, there are multiple levels of delay taps, thus forming a space-time two-dimensional processing structure. The anti-interference performance and computational cost of the space-time adaptive processing array are related to the number of antennas and delay taps. Using more antennas and delay taps can improve the signal-to-interference-and-noise ratio (SINR) of the array output, but it will also greatly increase the dimension of adaptive processing, thereby increasing the computational cost. How to reduce the computational cost while maintaining high anti-interference performance is an important issue in the current research of space-time adaptive processing technology. Given that array reconstruction technology can effectively reduce the data dimension of adaptive processing, studying space-time adaptive processing array reconstruction technology has become the key to solving the above problems.

[0004] The existing array reconstruction technology is an array reconstruction technology based on antenna selection, which usually aims to maximize the output SINR. It uses RF switches to select only a portion of array elements to connect to the RF channel to form a reconstructed array. Compared with the original array, the reconstructed array uses fewer array elements and RF channels, thereby reducing the dimension and computational complexity of the adaptive processing. However, the array reconstruction technology based on antenna selection is mainly applicable to the reconstruction of spatial domain adaptive processing arrays. It only considers the optimization of the number of antennas and does not optimize the number of delay taps. The degree of freedom of the space-time adaptive processing array reconstructed by this technology will be greatly reduced, which reduces the computational cost while also limiting the improvement of anti-interference performance. Therefore, in practical applications, this technology cannot be effectively applied to the reconstruction of space-time adaptive processing arrays. Summary of the Invention

[0005] In order to solve or at least partially solve the problems mentioned in the background technology, in order to reduce the computational cost while maximizing the anti-interference performance of the reconstructed array, the present invention proposes an anti-interference adaptive processing array reconstruction method; this method uses radio frequency switches and digital switches to jointly select the antenna-delay tap pairs that are used the least, thereby efficiently realizing the reconstruction process of the space-time adaptive processing array.

[0006] The present invention adopts the following technical solutions to achieve the purpose:

[0007] An anti-interference adaptive processing array reconstruction method includes the following steps:

[0008] S1. Calculate the steering vector of the satellite signal and the interference signal;

[0009] S2. Calculate the space-time correlation coefficient and space correlation vector between the satellite signal and the interference signal;

[0010] S3. Calculate the square of the spatiotemporal correlation coefficient of the spatiotemporal adaptive processing array |β| 2 The lower bound of

[0011] S4. Calculate the upper bound of the optimal output SINR of the space-time adaptive processing array;

[0012] S5. Draw the performance-cost trade-off curve;

[0013] S6. Selecting the optimal number of antenna-delay tap pairs used to reconstruct the space-time adaptive processing array according to the performance-cost trade-off curve;

[0014] S7, determining the positions of antenna-delay tap pairs for reconstructing the space-time adaptive processing array;

[0015] S8. Complete the reconstruction process of the space-time adaptive processing array, and perform adaptive beamforming of the reconstructed space-time adaptive processing array.

[0016] Furthermore, in step S1, the steering vector includes a spatial steering vector s s and s i , time domain steering vector v s and v i , space-time joint steering vector y s and y i The specific steps of calculating the steering vector of the satellite signal and the interference signal include:

[0017] S11, obtaining the position coordinates of all antennas in the space-time adaptive processing array to obtain the antenna position coordinate matrix;

[0018] S12. Obtain prior information of satellite signals and interference signals, including elevation angle and azimuth angle, and obtain the DOA vector α of satellite signals and interference signals.s and α i ;

[0019] S13. Calculate all steering vectors of satellite signals and interference signals based on the antenna position coordinate matrix, the priori information, and the DOA vector.

[0020] Furthermore, based on the steering vector obtained in step S1, in step S2, the space-time correlation coefficient STCC between the satellite signal and the interference signal is defined as follows:

[0021]

[0022] Where, ‖...‖2 represents the L2 norm,

[0023] After expressing the STCC of the space-time adaptive processing array using M antenna-delay tap pairs, i.e., |β|, the square value of STCC is expressed as:

[0024]

[0025] Where W si is the calculated spatial correlation vector, Real means taking the real part, and Trace means the trace of the matrix.

[0026] Furthermore, in step S3, the square of the space-time correlation coefficient STCC of the space-time adaptive processing array |β| is solved by the SDP method. 2 The lower bound of the maximum output SINR of the space-time adaptive processing array with M antenna-delay tap pairs is rewritten as a semidefinite programming problem, which is as follows:

[0027]

[0028]

[0029] diag(Y)=y

[0030] Trace(Y)=M

[0031] The convex optimization method interior point method is used to solve the problem and the optimal solution (y opt ,Y opt ) and the objective function value Then the lower bound of the square of STCC is:

[0032]

[0033] Furthermore, based on the lower bound of the square of the STCC obtained in step S3, the upper bound of the optimal output SINR of the array after adaptive processing under different numbers of antenna-delay tap pairs M is calculated in step S4. opt (M), SINR opt (M) is represented as follows:

[0034]

[0035] Further, according to the calculation process of steps S1 to S4, in step S5, the SINR loss function SINR under different antenna-delay tap pairs M is calculated in sequence. loss (M), where M = 5, 6, ..., 27, as follows:

[0036]

[0037] Then calculate the normalized computational complexity G(M) under different M values ​​as follows:

[0038]

[0039] Take G(M) as the x-axis coordinate value and SINR loss (M) is used as the y-axis coordinate value to complete the drawing of the performance-cost trade-off curve under different numbers M of antenna-delay tap pairs.

[0040] Furthermore, in step S6, based on the performance-cost trade-off curve obtained, the SINR loss (M)|≤η and the minimum number of antenna-delay tap pairs M min , as the number of antenna-delay tap pairs used for space-time adaptive processing array reconstruction, where η is the set SINR loss (M) threshold value.

[0041] Furthermore, after determining the number of antenna-delay tap pairs used for space-time adaptive processing array reconstruction in step S6, in step S7, according to the number of antenna-delay tap pairs, the maximum output SINR of the space-time adaptive processing array in step S3 is substituted into the semidefinite programming problem, and the optimal solution y corresponding to y is solved using the SDP method. opt , for y opt All elements in are rounded to the nearest integer, and the M corresponding to the non-zero elements is min The antenna-delay tap pairs constitute the reconstructed space-time adaptive processing array, and then the positions of the antenna-delay tap pairs are determined.

[0042] Further, in step S8, according to the determined position information of the antenna-delay tap pair, the Mmin The antennas corresponding to the antenna-delay tap pairs are connected to the RF front end, and the channels of the corresponding delay taps are connected for subsequent adaptive processing, thereby completing the reconstruction of the space-time adaptive processing array.

[0043] Furthermore, in step S8, the reconstructed space-time adaptive processing array is used to receive the signal; based on the MVDR algorithm, the adaptive processing weight of the reconstructed space-time adaptive processing array is calculated as:

[0044]

[0045] Where, is the interference plus noise covariance matrix R of the reconstructed space-time adaptive processing array i+n The inverse matrix of

[0046] The adaptive processing weight W is used to perform weighted processing on the received channel data. The array output after weighted processing is as follows:

[0047] z(t)=W H x(t)

[0048] Where x(t) is the M selected after array reconstruction min Data received by antenna-delay tap pairs;

[0049] This achieves adaptive beamforming of the reconstructed space-time adaptive processing array.

[0050] In summary, due to the adoption of this technical solution, the beneficial effects of the present invention are as follows:

[0051] The present invention uses an antenna-delay tap pair selection strategy and method to efficiently and accurately calculate the maximum output SINR of the space-time adaptive processing array when using different numbers of antenna-delay tap pairs, and then selects the optimal antenna-delay tap pair combination to form the reconstructed space-time adaptive processing array, thereby realizing the process of reconstructing the space-time adaptive processing array.

[0052] Compared with the unreconstructed space-time adaptive processing array, the reconstructed array uses fewer antennas and delay taps, which greatly reduces the computational cost of adaptive processing while maximally retaining the anti-interference performance.

[0053] Compared with the traditional array reconstruction technology based on antenna selection, the space-time adaptive processing array reconstructed using the method of the present invention can output a higher SINR and has stronger anti-interference performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1Flowchart for realizing the method of the present invention;

[0055] Figure 2 Schematic diagram of a space-time adaptive processing array reconstruction model of the method of the present invention;

[0056] Figure 3 : is a comparison diagram of the upper bound of the optimal SINR obtained by the method of the present invention and the traditional method when N=9 and L=3;

[0057] Figure 4 The performance-cost trade-off curve is shown when N=9 and L=3.

[0058] Figure 5 When N=9, L=3, M min =17, schematic diagram of antenna-delay tap pair selection of the space-time adaptive processing array after reconstruction;

[0059] Figure 6 When N=9, L=3, M min =17, the beam pattern of the space-time adaptive processing array after reconstruction. DETAILED DESCRIPTION

[0060] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0061] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0062] Example 1

[0063] Please see Figure 1 To understand the schematic diagram, an anti-interference adaptive processing array reconstruction method includes the following steps:

[0064] S1. Calculate the steering vector of the satellite signal and the interference signal;

[0065] S2. Calculate the space-time correlation coefficient and space correlation vector between the satellite signal and the interference signal;

[0066] S3. Calculate the lower bound of the square of the space-time correlation coefficient of the space-time adaptive processing array;

[0067] S4. Calculate the upper bound of the optimal output SINR of the space-time adaptive processing array;

[0068] S5. Draw the performance-cost trade-off curve;

[0069] S6. Selecting the optimal number of antenna-delay tap pairs used to reconstruct the space-time adaptive processing array according to the performance-cost trade-off curve;

[0070] S7, determining the positions of antenna-delay tap pairs for reconstructing the space-time adaptive processing array;

[0071] S8. Complete the reconstruction process of the space-time adaptive processing array, and perform adaptive beamforming of the reconstructed space-time adaptive processing array.

[0072] This embodiment will describe the method in detail based on the detailed calculation formulas required for the implementation of the method. The specific calculation formulas used in this embodiment are numbered in sequence to facilitate better explanation.

[0073] Corresponding to step S1 in the method of this embodiment, the calculation content is as follows.

[0074] a. Obtain the position coordinates of all antennas in the space-time adaptive processing array: The space-time adaptive processing array contains N antennas, and the antenna position coordinate matrix is:

[0075]

[0076] Among them, q k =[x k ,t k ,z k ](1≤k≤N) represents the position coordinates of the kth antenna.

[0077] b. Obtaining prior information of satellite signals and interference signals: In a single interference scenario, φ s and φ i Represent the elevation angles of satellite signal and interference signal respectively, θ s and θ i Denotes the azimuth of the satellite signal and the interference signal respectively, then the two-dimensional DOA vector α of the satellite signal s and the DOA vector α of the interference signal i It can be expressed as:

[0078] α s =[sinφ s cosθ s , sinφ s sinθ s , cosφ s ] TFormula (2)

[0079] α i =[sinφ i cosθ i , sinφ i sinθ i , cosφ i ] T Formula (3)

[0080] c. Generation of spatial steering vectors of satellite signals and interference signals: Combining equations (1), (2) and (3), the spatial steering vectors s of satellite signals and interference signals are: s and s i It can be expressed as:

[0081]

[0082]

[0083] Where λ s and λ i Represent the wavelengths of satellite signals and interference signals respectively.

[0084] d. Generation of time-domain steering vectors of satellite signals and interference signals: For each antenna channel, there are L-level delay taps, and the delay of each level is τ. Then the time-domain steering vector v of the satellite signal and interference signal is s and v i It can be expressed as:

[0085]

[0086]

[0087] Where, f s and f i Represent the frequencies of satellite signals and interference signals respectively.

[0088] e. Generation of joint space-time steering vector of satellite signal and interference signal: Combining equations (2), (3), (6) and (7), the joint space-time steering vector u of satellite signal and interference signal is generated. s and u i They can be expressed as:

[0089]

[0090]

[0091] Where, represents the Kronecker product.

[0092] f. The space-time correlation coefficient (STCC) of the satellite signal and the interference signal is defined as follows:

[0093]

[0094] Where, ‖...‖2 represents the L2 norm,

[0095] g. STCC of the reconstructed space-time adaptive processing array: The array contains N antennas, and each antenna channel corresponds to L levels of delay taps. Therefore, there are NL antenna-delay tap pairs in the entire array. Define the antenna-delay tap pair selection vector y∈R NL×1 , y consists of only 0 or 1, 0 means that the antenna-delay tap pair is not selected, and 1 means that the antenna-delay tap pair is selected. Then the STCC of the space-time adaptive processing array using M antenna-delay tap pairs can be expressed as:

[0096]

[0097] Where, ⊙ represents the Hadamard product, and * represents the matrix conjugate. The square value of STCC can be expressed as:

[0098]

[0099] Where, Real means taking the real part, and Trace means the trace of the matrix.

[0100] h. Use the SDP method to solve the square of STCC |β| 2 Lower bound: Based on the minimum variance distortionless response (MVDR) adaptive processing criterion, the maximum output SINR of the space-time adaptive processing array with M antenna-delay tap pairs can be expressed as:

[0101] SINR out =SNR·NL(1-|β| 2 ) Formula (13)

[0102] Where SNR represents signal-to-noise ratio, |β| 2 The smaller the value, the larger the output SINR, so the problem of space-time adaptive processing array reconstruction with the goal of maximizing SINR can be transformed into |β| 2 The objective function and constraints of the minimization problem are expressed as follows (14):

[0103]

[0104] sty j (y j-1)=0for j=1,…,NL

[0105] y T y=M

[0106] Introduce variable matrix Y=yy T , the above formula (14) is transformed into the following formula (15):

[0107]

[0108] stY=yy T

[0109] diag(Y)=y

[0110] Trace(Y)=M

[0111] Set Y=yy T Relaxation is Y-yy T ±0, written in matrix form, ± means matrix semi-positive definite, then the above formula (15) can be rewritten as the following formula (16):

[0112]

[0113]

[0114] diag(Y)=y

[0115] Trace(Y)=M

[0116] The above formula (16) is a semidefinite programming problem, namely SDP problem, which can be solved by the convex optimization method interior point method. The optimal solution (y) corresponding to (y, Y) is obtained. opt ,Y opt ) and the objective function value Then the lower bound of the square of STCC is:

[0117]

[0118] i. Solving the upper bound of the maximum output SINR: Substituting equation (17) into equation (13), we can obtain the upper bound of the maximum output SINR of the space-time adaptive processing array reconstructed with M antenna-delay tap pairs, which is expressed as:

[0119]

[0120] j. Performance-cost trade-off curve drawing: The maximum output SINR of the initial space-time adaptive processing array composed of NL antenna-delay tap pairs is calculated as:

[0121] SINR orig =SNR·NL(1-|β orig |2 ) Formula (19)

[0122] Where, β orig The SINR loss function SINR is defined as the STCC of the NL antenna-delay tap space-time adaptive processing array. loss (M) is the difference between the maximum output SINR of the space-time adaptive processing array using M antenna-delay tap pairs after reconstruction and the maximum output SINR of the space-time adaptive processing array using the initial NL antenna-delay tap pairs, that is:

[0123] SINR loss (M) = SINR opt (M)-SINR orig M=2,...,NL Formula (20)

[0124] In space-time adaptive processing, matrix inversion operation accounts for the main computational workload. For a space-time adaptive processing array containing NL antenna-delay tap pairs, its adaptive processing requires the inversion of the NL×NL dimensional matrix, and its computational complexity is O((NL) 3 ). Taking the computational complexity of the initial space-time adaptive processing array containing NL antenna-delay tap pairs as a reference, the normalized computational complexity G is defined norm for:

[0125]

[0126] Where G opt (M)=(M) 3 is the computational complexity of the space-time adaptive processing array using M antenna-delay tap pairs after reconstruction, G orig =(NL) 3 is the computational complexity of the initial space-time adaptive processing array for NL antenna-delay tap pairs. Calculate G for different antenna-delay tap pairs M. opt (M) and SINR loss (M), respectively G opt (M) and SINR loss The calculation results of (M) are the coordinates of the x-axis and y-axis, and the performance-cost trade-off curve corresponding to different numbers of antenna-delay tap pairs M is drawn.

[0127] k. Determine the number of antenna-delay tap pairs M used to reconstruct the space-time adaptive processing array: Set the SINR loss The threshold value of (M) is η, and the SINR loss of the reconstructed array shall not be higher than η, that is:

[0128] |SINR loss (M)|≤η Formula (22)

[0129] Analyze the performance-cost trade-off curve obtained in part j and select the minimum number of antenna-delay tap pairs M on the curve that can satisfy equation (22) min The number of antenna-delay tap pairs used for the final space-time adaptive processing array reconstruction.

[0130] l. Reconstructing the M of the space-time adaptive processing array min Determination of the positions of antenna-delay tap pairs: Number of antenna-delay tap pairs M min After confirmation, M min Substituting into equation (16), the optimal solution y corresponding to y can be obtained by using the SDP method in part h. opt , for y opt After all elements in y are rounded off, opt M corresponding to non-zero elements min The antenna-delay tap pairs constitute the reconstructed space-time adaptive processing array.

[0131] m. Space-time adaptive processing array reconstruction: According to the M obtained in part l min The position information of the antenna-delay tap pairs will be combined with the M min The antennas corresponding to the antenna-delay tap pairs are connected to the RF front end, and the channels of the corresponding delay taps are connected for subsequent adaptive processing to complete the reconstruction of the array.

[0132] n. Calculation of anti-interference weights of the space-time adaptive processing array after reconstruction: Based on the MVDR algorithm, the adaptive processing weights of the space-time adaptive processing array after reconstruction are calculated as follows:

[0133]

[0134] Where, is the interference plus noise covariance matrix R of the reconstructed space-time adaptive processing array i+n The inverse matrix of .

[0135] o. Adaptive beamforming of the reconstructed space-time adaptive processing array: The adaptive processing weights obtained in the n-part are used to perform weighted processing on the received channel data. The array output after weighted processing is:

[0136] z(t)=W H x(t) Equation (24)

[0137] Where x(t) is the M selected after array reconstruction min The data received by each antenna-delay tap pair.

[0138] The above-mentioned parts a to o, which contain a total of 24 calculation formulas, are the specific detailed calculation formula basis framework of the method of this embodiment, thereby realizing the reconstruction process of the space-time adaptive processing array through the antenna-delay tap pair selection strategy of the present invention. Compared with the unreconstructed space-time adaptive processing array, the reconstructed array uses fewer antennas and delay taps, greatly reducing the computational cost of adaptive processing, while also retaining the anti-interference performance to the maximum extent.

[0139] Example 2

[0140] This embodiment is based on the embodiment 1, quotes the calculation formula according to the framework of embodiment 1, and takes specific data as an example to provide a detailed introduction and explanation of the application of this method.

[0141] In this embodiment, the carrier center frequency of the satellite signal and the interference signal is 1575.42MHz, which is down-converted to 46.5MHz, the sampling frequency is 62MHz, and the unit tap delay is one sampling period. The satellite signal power is -130dBm, the signal-to-noise ratio SNR is -20dB, and the signal direction is θ s =124 ° ,φ s =65 ° The interference-to-noise ratio INR is 50dB, and the interference direction is θ i =130 ° ,φ i =56 ° .

[0142] like Figure 2 As shown, the reconfigurable space-time adaptive processing array used in this embodiment consists of N antennas, each antenna channel has L-level delay taps (N=9, L=3), and the N antennas are arranged into a uniform linear array with a spacing of half the signal wavelength. The total number of antenna-delay tap pairs that can be used is NL=27. Set SINR loss The threshold value is η=1dB. Figure 2 In the figure, the antennas and delay taps with dotted outlines represent unselected ones, and the antennas and delay taps with solid outlines constitute the reconstructed space-time adaptive processing array. The specific steps for reconstructing the space-time adaptive processing array are as follows:

[0143] Step S1: Calculate the steering vectors of the satellite signal and the interference signal.

[0144] Using equations (1) to (9) in Example 1, calculate the spatial steering vector s of the satellite signal and the interference signal s and s i , time domain steering vector v s and v i , space-time joint steering vector u s and ui .

[0145] Step S2: Calculate the STCC and spatial correlation vector of the satellite signal and the interference signal.

[0146] According to the steering vector obtained in step S1, the STCC of the initial unreconstructed space-time adaptive processing array with respect to the satellite signal and the interference signal is calculated using equation (10) in embodiment 1, and W in equation (12) is calculated at the same time. si .

[0147] Step S3, calculate the square of the space-time adaptive processing array STCC |β| 2 The lower bound.

[0148] W obtained in step S2 si Substitute into equation (16) in Example 1, solve the SDP problem, and calculate the square of STCC |β| under different numbers of antenna-delay tap pairs M. 2 The lower bound

[0149] Step S4: Calculate the upper bound of the optimal output SINR of the space-time adaptive processing array.

[0150] Use step S3 to obtain |β| 2 The lower bound Substituting into equation (18) in Example 1, the upper bound of the optimal output SINR of the array after adaptive processing under different numbers of antenna-delay tap pairs M can be calculated: opt (M). When selecting different numbers of antenna-delay tap pairs M, Figure 3 The upper bound of the optimal SINR obtained by using the SDP reconstruction method based on antenna-delay tap selection, the exhaustive reconstruction method based on antenna-delay tap selection, and the space-time adaptive processing array reconstruction method based on antenna selection reconstruction were compared.

[0151] It can be seen that the array reconstructed by the SDP method proposed in this embodiment has an output SINR of almost the same size as that of the reconstructed array obtained by the exhaustive method, thus proving that the SDP method proposed in this embodiment is correct and effective. The SDP method has a much lower computational complexity than the exhaustive method, requiring multiple possible antenna-delay tap pair combinations. Therefore, it can achieve array reconstruction more quickly and efficiently. Compared with the space-time adaptive processing array reconstruction method based on antenna selection, the array reconstructed using the proposed method can output a higher SINR, thus having stronger anti-interference capabilities.

[0152] Step S5: draw a performance-cost trade-off curve.

[0153] According to equations (19) and (20) in Example 1, the SINR loss function SINR is calculated in sequence when M=5, 6, ..., 27. loss (M), as shown in formula (25):

[0154]

[0155] According to formula (21) in Example 1, the normalized computational complexity G(M) when M=5, 6, ..., 27 is calculated as follows:

[0156]

[0157] G(M) and SINR loss (M) is the x-axis and y-axis coordinate values, and the performance-cost trade-off curves under different antenna-delay tap pairs M are drawn, as shown in Figure 4 shown.

[0158] Step S6: reconstructing the optimal selection of the number M of antenna-delay tap pairs of the space-time adaptive processing array.

[0159] Based on the performance-cost trade-off curve of step S5, select the curve that satisfies |SINR loss (M)|≤1dB and the minimum number of antenna-delay tap pairs M min As the number of antenna-delay tap pairs used for the final space-time adaptive processing array reconstruction. Figure 4 As shown, when M≥17, |SINR loss (M)|≤1dB, therefore, determine M min =17. In addition, Figure 4 It can be seen that compared with the initial unreconstructed space-time adaptive processing array containing 27 antenna-delay tap pairs, the computational cost of the reconstructed array is 24.96% of the computational cost of the unreconstructed array, while the SINR loss is only -0.82dB. Therefore, the array reconstructed using the proposed method greatly reduces the computational cost of adaptive processing while also retaining high anti-interference performance to the maximum extent.

[0160] Step S7: Determine the positions of the antenna-delay tap pairs for reconstructing the space-time adaptive processing array.

[0161] The M obtained in step S6 min =17 is brought into equation (16) in Example 1 to solve the SDP problem and calculate M min =17, the optimal solution y for the antenna-delay tap pair selection vector y opt , for y opt After all elements in y are rounded off, opt M corresponding to non-zero elements min= 17 antenna-delay tap pairs constitute the reconstructed space-time adaptive processing array.

[0162] Step S8: reconstructing the space-time adaptive processing array and adaptive beamforming of the reconstructed space-time adaptive processing array.

[0163] According to the M obtained in step S7 min = 17 antenna-delay tap position information, which will be combined with M min = 17 antenna-delay tap pairs. The corresponding antennas are connected to the RF front end, and the corresponding delay tap channels are connected for subsequent adaptive processing to complete the array reconstruction. Figure 5 A schematic diagram of the antenna-delay tap pair selection of the reconstructed space-time adaptive processing array is given, where the cross symbol indicates that it is discarded and the diamond symbol indicates that it is used.

[0164] The reconstructed space-time adaptive processing array is used to receive signals, and the adaptive processing weight W is calculated according to formula (23) in Example 1, and the weighted processing is performed on each received channel data using formula (24). Figure 6 The beam pattern of the reconstructed space-time adaptive processing array is given. It can be seen that a null is formed in the interference signal space and the interference is suppressed.

Claims

1. An anti-interference adaptive processing array reconstruction method, characterized in that: The steps include: S1. Calculate the steering vectors of the satellite signal and the interference signal, wherein the steering vectors include the space-time domain joint steering vectors and ; S2. Calculate the space-time correlation coefficient and spatial correlation vector between the satellite signal and the interference signal; Based on the steering vector obtained in step S1, in step S2, define the space-time correlation coefficient STCC of the satellite signal and the interference signal: Where, represents the L2 norm, ; Represents a vector The conjugate transpose of Indicates that the array contains antennas, Indicates that each antenna channel corresponds to Stage delay tap; S3. Calculate the square of the space-time correlation coefficient of the space-time adaptive processing array The lower bound of S4. Calculate the upper bound of the optimal output SINR of the space-time adaptive processing array; S5. Draw the performance-cost trade-off curve; S6. Selecting the optimal number of antenna-delay tap pairs used to reconstruct the space-time adaptive processing array according to the performance-cost trade-off curve; S7, determining the positions of antenna-delay tap pairs for reconstructing the space-time adaptive processing array; S8. Complete the reconstruction process of the space-time adaptive processing array, and perform adaptive beamforming of the reconstructed space-time adaptive processing array.

2. The anti-interference adaptive processing array reconstruction method according to claim 1, characterized in that: In step S1, the steering vector includes a spatial steering vector and , time-domain steering vector and , space-time joint steering vector and ; The specific steps of calculating the steering vector of the satellite signal and the interference signal include: S11, obtaining the position coordinates of all antennas in the space-time adaptive processing array to obtain the antenna position coordinate matrix; S12. Obtain prior information of satellite signals and interference signals, including elevation angle and azimuth angle, and obtain the DOA vectors of satellite signals and interference signals. and ; S13. Calculate all steering vectors of satellite signals and interference signals based on the antenna position coordinate matrix, the priori information, and the DOA vector.

3. The anti-interference adaptive processing array reconstruction method according to claim 2, characterized in that: Indicates the choice of use The STCC of the space-time adaptive processing array of antenna-delay tap pairs is After that, the square value of STCC is expressed as: Where, is the calculated spatial correlation vector, , represents the real part, represents the trace of the matrix; represents the defined antenna-delay tap pair selection vector, That is, vector The transpose of .

4. The anti-interference adaptive processing array reconstruction method according to claim 3, characterized in that: In step S3, the square of the space-time correlation coefficient STCC of the space-time adaptive processing array is solved using the SDP method. The lower bound of The maximum output SINR of the space-time adaptive processing array of antenna-delay tap pairs can be rewritten as a semidefinite programming problem, which is as follows: The convex optimization method interior point method is used to solve the problem, and the solution is The corresponding optimal solution And the objective function value , then the lower bound of the square of STCC is: 。 5. The anti-interference adaptive processing array reconstruction method according to claim 4, characterized in that: According to the lower bound of the square of STCC obtained in step S3, the number of different antenna-delay tap pairs is calculated in step S4. The upper bound of the optimal output SINR of the array after adaptive processing is , is represented as follows: 。 6. The anti-interference adaptive processing array reconstruction method according to claim 5, characterized in that: According to the calculation process of steps S1 to S4, in step S5, the number of different antenna-delay tap pairs is calculated in sequence. SINR loss function under ,in ,as follows: Then calculate the different Normalized computational complexity under the value ,as follows: by As x Axis coordinate values, in As y Axis coordinate values, completed in different antenna-delay tap pairs Drawing of the performance-cost trade-off curve below.

7. The anti-interference adaptive processing array reconstruction method according to claim 6, characterized in that: In step S6, according to the performance-cost trade-off curve obtained, select The minimum number of antenna-delay tap pairs , as the number of antenna-delay tap pairs used for space-time adaptive processing array reconstruction, where For setting about threshold value.

8. The anti-interference adaptive processing array reconstruction method according to claim 7, characterized in that: After determining the number of antenna-delay tap pairs used for space-time adaptive processing array reconstruction in step S6, in step S7, the maximum output SINR of the space-time adaptive processing array in step S3 is substituted into the semidefinite programming problem and solved using the SDP method. The corresponding optimal solution ,right All elements in are rounded to the nearest integer, and the non-zero elements correspond to The antenna-delay tap pairs constitute the reconstructed space-time adaptive processing array, and then the positions of the antenna-delay tap pairs are determined.

9. The anti-interference adaptive processing array reconstruction method according to claim 8, characterized in that: In step S8, based on the determined position information of the antenna-delay tap pair, The antennas corresponding to the antenna-delay tap pairs are connected to the RF front end, and the channels of the corresponding delay taps are connected for subsequent adaptive processing, thereby completing the reconstruction of the space-time adaptive processing array.

10. The anti-interference adaptive processing array reconstruction method according to claim 9, characterized in that: In step S8, the reconstructed space-time adaptive processing array is used to receive the signal. Based on the MVDR algorithm, the adaptive processing weight of the reconstructed space-time adaptive processing array is calculated as: Where, is the interference plus noise covariance matrix of the reconstructed space-time adaptive processing array The inverse matrix of Use the obtained adaptive processing weights , perform weighted processing on each received channel data, and the array output after weighted processing is as follows: Where, The selected array after reconstruction Data received by antenna-delay tap pairs; This achieves adaptive beamforming of the reconstructed space-time adaptive processing array.

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