A method for reducing dimension of a polarization array based polarization space-time adaptive processing channel

Abstract

The application discloses a dimension-reduction polarization space-time adaptive processing channel optimization method based on a polarization array and belongs to the technical field of array signal processing.The application comprises the following steps: step 1, a polarization space-time signal model is established according to array parameters; step 2, a complete polarization space-time channel is constructed; and step 3, K channels are selected according to cross-correlation energy to form a dimension-reduction matrix.Different from existing channel construction methods, when the channel is constructed, the target polarization steering vector and the channel orthogonal to the target polarization steering vector are adopted to form a polarization dimension conversion matrix, and finally the main channel is the target polarization space-time steering vector, and the channel optimization based on the target polarization space-time steering vector not only selects the channel in the space-time domain but also considers the selection of the channel in the polarization dimension, so that a higher output signal-to-noise ratio is presented.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, specifically relating to a method for optimizing the channel of a dimension-reduced polarization space-time adaptive processing based on a polarization array. Background Technology

[0002] The complex and heterogeneous distribution of strong clutter received by radar often obscures targets in practical applications, making effective target extraction impossible and posing a significant challenge to target detection. To address this challenge, some researchers have proposed using traditional spatial filtering techniques to reduce clutter components in the echo by achieving low sidelobes and narrow beams. Others have proposed introducing other domains to highlight the differences between the signal and clutter in the joint domain, such as the Space-Time Adaptive Processing (STAP) technique. Furthermore, to address issues such as excessive computational load, dimension-reduced STAP methods such as JDL, M-CAP, optimal channel method, and channel optimization based on maximum cross-correlation energy have emerged. However, space-time adaptive processing techniques still have limitations in certain scenarios.

[0003] Polarization state, as an additional dimension of information besides the time and spatial domains, is incorporated. Polarimetric Space-Time Adaptive Processing (PSTAP) combines polarization information processing with space-time adaptive processing to suppress clutter and detect weak targets, further improving the performance of radar systems. However, due to the addition of polarization dimension information, the dimension of the clutter polarimetric space-time covariance matrix further increases. Therefore, in the case of limited auxiliary data, a dimensionality-reduced PSTAP with low computational cost and near-optimal performance has emerged. How to construct the polarimetric space-time channel and how to select the optimal channel have become problems to be solved. However, in existing papers, the transformation matrix is ​​obtained by the Kronecker product of the second-order identity matrix and the space-time dimension transformation matrix. That is, the existing channel construction methods do not consider the construction of the polarimetric dimension transformation matrix (see: S. Zhang, Z. Liu, K. Zhao and Y. Xu, "Enhanced Cascaded Iteration for Polarimetric Space-Time Adaptive Processing", 2023 8th International Conference on Signal and Image Processing (ICSIP), Wuxi, China, 2023, pp. 753-757, doi:10.1109 / ICSIP57908.2023.10270966.). Summary of the Invention

[0004] This invention provides a method for optimizing channels in dimensionality-reduced polarization-space-time adaptive processing based on polarization arrays. It employs a novel channel construction method, using the target polarization vector and a vector orthogonal to it to construct a polarization-dimensional transformation matrix. The final complete channel matrix is ​​obtained by the Kronecker product of the polarization-dimensional transformation matrix and the space-time transformation matrix. The main channel is aligned with the target polarization-space-time steering vector, i.e., the main channel is aligned with the target. Then, channel optimization is performed based on the principle of maximizing the cross-correlation energy between the auxiliary channel and the main channel.

[0005] The technical solution adopted in this invention is as follows:

[0006] A method for optimizing polarization-space-time adaptive processing channels based on polarization arrays, comprising the following steps:

[0007] Step 1: Establish a polarization space-time signal model based on the array parameters;

[0008] Step 2: Construct a complete polarization spacetime channel;

[0009] Step 3: Select K (K≥2) channels based on cross-correlation energy to obtain the channel optimization result. Then, a dimensionality reduction matrix can be constructed based on the selected K channels for polarization space-time adaptive processing.

[0010] Furthermore, in step 1, the array used is a uniform linear polarization array consisting of M antennas, which transmits N pulses within one coherent processing interval (CPI). The point target signal model of the uniform linear polarization array is as follows:

[0011]

[0012] in, Let M be the complex amplitude of the target signal, and M and N be the number of antennas and the number of pulses within a CPI, respectively. For the target power of the H channel in the horizontal direction, r t a is the ratio of the target power in the vertical V-channel to the target power in the horizontal H-channel. psdt a is the target polarization spacetime steering vector. pt a st a dt These are the polarization steering vector, the normalized spatial steering vector, and the normalized temporal steering vector, respectively.

[0013] Based on all range ring clutter data, clutter echo data x of the full range cells of the uniformly linearly polarized array is obtained. c :

[0014]

[0015] Where, N r x is the number of distance units. c,j For clutter echo data of range loop j, its expression is:

[0016]

[0017] Where, N c The number of clutter blocks, α represents the polarization space-time steering vector of the i-th clutter block in the j-th range loop. i,j The amplitude of the echo signal of the i-th clutter block in the j-th range loop;

[0018] Furthermore, clutter echo data x c,j It can be represented as:

[0019]

[0020] in, Let be the polarization steering vector of the i-th clutter block in the j-th range ring. It is a spatial guiding vector. For time-domain steering vectors, These are the normalized spatial frequency and the normalized Doppler frequency, respectively.

[0021] Furthermore, in step 2, channels are constructed. Without polarization, MN angle-Doppler channels can be obtained. With polarization, the total number of channels is 2MN.

[0022] The matrix formed by the MN angle-Doppler channels is as follows:

[0023] T st =[T1,T2,…,T MN ]

[0024]

[0025]

[0026]

[0027] Among them, T s (s=1,…,MN) represents the s-th spacetime channel, a d (f d,i ) is the time-domain steering vector, a s (f s,j ) is the spatial guiding vector.

[0028]

[0029]

[0030] Among them, f d,i To normalize the Doppler frequency, f s,j Here, e represents the normalized spatial frequency, and e is the natural base. Represents the field of complex numbers;

[0031] After adding the polarization dimension, we define r t This represents the ratio of the target signal power in the V channel to the H channel. and Let H and V be the absolute phases of the H channel and V channel, respectively. Then the amplitude ratio and phase difference of the V channel and H channel signals are respectively... and Therefore, the target polarization steering vector can be obtained as:

[0032] u=[cosγsinγe jη ] T

[0033] Based on the target polarization steering vector, channels orthogonal to it can be obtained. Therefore, the matrix formed by the polarization-dimensional channels can be represented as follows:

[0034]

[0035] When performing dimension reduction polarization space-time adaptive processing, the matrix formed by all channels is:

[0036]

[0037] There exists a master channel among all channels, which serves as the target polarization spacetime steering vector. The remaining channels besides the main channel are auxiliary channels, and the matrix formed by all the auxiliary channels is as follows:

[0038] T 1 After conjugate transpose and adjusting the channel order, the matrix formed by all channels can also be represented as:

[0039]

[0040] The auxiliary channel constructed in this way must be orthogonal to the main channel, that is:

[0041] B H s=0

[0042] Furthermore, in step 3, the channel selection algorithm used selects several channels based on the principle of maximizing cross-correlation energy (MCRE), specifically including:

[0043] The received data x is obtained after passing through all channels. T , can be represented as:

[0044]

[0045] Here, the scalar output corresponding to the main channel is represented by d. Output data vectors for auxiliary channels.

[0046] x T covariance matrix It can be represented as:

[0047]

[0048] Wherein, the covariance matrix R of the auxiliary channel output data vector is (2NM-1)×(2NM-1) dimensional. b It can be represented as:

[0049] R b =E[bb H ] = B H RB

[0050] Where R is the covariance matrix of the data x, and E represents the expected value.

[0051] The cross-correlation r between the auxiliary channel output data vector b and the reference channel output d bd It can be represented as:

[0052] r bd =E[bd * ] = B H Rs

[0053] The MCRE-based auxiliary channel selection algorithm compares the calculated cross-correlation energy of each channel when selecting the optimal channel, and selects the channel with the highest cross-correlation energy as the current optimal channel. The expression for cross-correlation energy is:

[0054]

[0055] To select a suitable auxiliary channel, a channel selection matrix is ​​introduced. Where J = 2NM-1, and L is the number of auxiliary channels selected;

[0056] The reduced auxiliary channel output data vector z is:

[0057] z = V H b

[0058] The data vector in the reduced-dimensional clutter subspace is called the clutter subspace data vector, and the corresponding L×L clutter covariance matrix is:

[0059] R z =V H R b V

[0060] The cross-correlation between the reduced-dimensional clutter subspace data vector z and the reference channel output d can be expressed as:

[0061] r zd =E[zd * ] = V H r bd

[0062] Similarly, according to Wiener filtering theory, its optimal weights can be determined as follows:

[0063]

[0064] Using all k currently selected channels to cancel clutter in the reference channel, the output after cancellation is... for:

[0065]

[0066] Where, l1, l2, ..., l k Used to indicate the selected optimal channel number. Let q represent the q-th element in vector b, so vector b can be represented as b = [b1, b2, ..., bq]. J ] T , It is the residual after the main channel output d is canceled by the currently selected k channels;

[0067] The loop proceeds to the next step, where an optimal channel will be selected; this next channel will maximize the cancellation of remaining clutter components. To remove canceled clutter components from the currently selected channel, the cross-correlation should be updated as follows:

[0068]

[0069] in, This indicates that after k selected channels are used to cancel clutter from the reference channel, b and The cross-correlation, Rb(:,[l1,l2,...,lk]) represents R b The l1, l2, ..., l-th elements of the matrix k List.

[0070] The technical solution provided by this invention brings at least the following beneficial effects:

[0071] This invention fully utilizes polarization-dimensional information to construct channels. A polarization-dimensional transformation matrix is ​​constructed using the target polarization vector and vectors orthogonal to it. The final complete channel matrix is ​​obtained by the Kronecker product of the polarization-dimensional transformation matrix and the space-time transformation matrix. The main channel is aligned with the target polarization-space-time steering vector, meaning the main channel is aligned with the target. Channel optimization is then performed based on this alignment, using several auxiliary channels with the highest cross-correlation energy with the main channel to construct a dimension reduction matrix. Compared to existing methods, this method constructs channels using the target's polarization steering vector, constructs a polarization-dimensional transformation matrix, and uses the target polarization-space-time steering vector as the main channel. Furthermore, the channel optimization process considers not only space-time channels but also polarization-dimensional channels, thus the selected auxiliary channels provide superior performance. Attached Figure Description

[0072] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0073] Figure 1 This is a schematic diagram of the processing flow of the method according to an embodiment of the present invention;

[0074] Figure 2 This is a diagram illustrating the channel selection steps in an embodiment of the present invention;

[0075] Figure 3 The signal power ratio is α t =1, polarization correlation coefficient ρ c =0.3, the method of the present invention and the existing channel construction method and the full-dimensional PSTAP output signal-to-noise ratio curve.

[0076] Figure 4 The signal power ratio is α t =100, polarization correlation coefficient ρ c =0.3, the method of the present invention and the existing channel construction method and the full-dimensional PSTAP output signal-to-noise ratio curve.

[0077] Figure 5 Let α be the signal power ratio. t =100, polarization correlation coefficient ρ c =0.9, the method of the present invention and the existing channel construction method and the full-dimensional PSTAP output signal-to-noise ratio curve. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be described in detail and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Generally, the components of the embodiments of the present invention described and shown in the accompanying drawings can be arranged and designed using different configurations. 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 claimed application, but merely represents selected embodiments of the present invention.

[0079] like Figure 1 As shown, this embodiment of the invention provides a method for optimizing channels in a dimension-reduced polarization-space-time adaptive processing system based on a polarization array. The specific implementation steps include:

[0080] Step 1: Consider a uniform linear polarization array consisting of M antennas, transmitting N pulses within one coherent processing interval (CPI). The point target signal model of the polarization array is as follows:

[0081]

[0082] in, Let M be the complex amplitude of the target signal, and M and N be the number of antennas and the number of pulses within a CPI, respectively. For the target power of channel H, r t a is the ratio of the target power of the V channel to the target power of the H channel. pt a st a dt These are the polarization steering vector, the normalized spatial steering vector, and the normalized temporal steering vector, respectively.

[0083] clutter echo data of full-range cells (x c ) is N r Range ring clutter data (x) c,j The sum of ) can be expressed as:

[0084]

[0085] Among them, the clutter echo data of range ring j is N c The sum of clutter data from each clutter block can be expressed as:

[0086]

[0087] Where, α i,j Let be the amplitude of the echo signal of the i-th clutter block in the j-th range loop. This is the polarization space-time steering vector for the i-th clutter block in the j-th range loop. a is the polarization steering vector. sc a is the spatial guiding vector. dc For time-domain steering vectors, These are the normalized spatial frequency and the normalized Doppler frequency, respectively.

[0088] Step 2: Construct the channels. The matrix formed by the angle-Doppler channels is as follows:

[0089] T st =[T1,T2,…,T MN ]

[0090]

[0091]

[0092]

[0093] Among them, T s (s=1,…,MN) represents the s-th spacetime channel, a d (f d,i ) is the time-domain steering vector, a s (f s,j ) is the spatial guiding vector, f d,i To normalize the Doppler frequency, f s,j This represents the normalized spatial frequency.

[0094] After adding the polarization dimension, we define r t This represents the ratio of the target signal power in the V channel to the H channel. and Let H and V be the absolute phases of the H channel and V channel, respectively. Then the amplitude ratio and phase difference of the V channel and H channel signals are respectively... and For the target polarization steering vector, the Jones vector u = [cosγsinγe] is used here. jη ] T We can obtain channels orthogonal to them, and the matrix formed by the polarization-dimensional channels can be represented as follows:

[0095]

[0096] Therefore, when performing dimension reduction polarization space-time adaptive processing, the matrix formed by all channels is:

[0097]

[0098] T 1 After conjugate transpose and adjusting the channel order, the matrix formed by all channels can also be represented as:

[0099]

[0100] Where s is the target polarization spacetime steering vector It is an auxiliary channel matrix consisting of the remaining channels besides the main channel. Represents the complex field.

[0101] Step 3: Select several channels based on the principle of maximizing cross-correlation energy. See below for the specific channel selection process. Figure 2 The received data x is obtained after passing through all channels. T , can be represented as:

[0102]

[0103] Here, the scalar output corresponding to the main channel is represented by d. Output data vectors for auxiliary channels.

[0104] x T covariance matrix It can be represented as:

[0105]

[0106] Where R is the covariance matrix of the data x, and R is the covariance matrix of the auxiliary channel output data vector with dimensions of (2NM-1)×(2NM-1). b It can be represented as:

[0107] R b =E[bb H ] = B H RB

[0108] The cross-correlation r between the auxiliary channel output data vector b and the reference channel output d bd It can be represented as:

[0109] r bd =E[bd * ] = B H Rs

[0110] When the loop begins, in step 1, no channel is selected, meaning k = 0. Calculate the cross-correlation energy and select the channel with the largest value as the current optimal channel. The expression for the cross-correlation energy is as follows:

[0111]

[0112] In step k+1, clutter components in the selected channel need to be removed from the reference channel; therefore, it is necessary to... Make the following updates:

[0113]

[0114] Where E is the expected value, ω L(k) The weights are l1, l2, ..., l when using K auxiliary channels. k Used to indicate the selected optimal channel number. This is called the reduced-dimensional clutter subspace data vector, R z It is the corresponding L×L dimensional clutter covariance matrix, r zd It is the cross-correlation between the reduced-dimensional clutter subspace data vector z and the reference channel output d. This completes the... After updating, the cross-correlation energy is calculated again, and the channel with the largest value is selected as the current optimal channel, until the current number of optimal channels n has been selected. b If the value is no longer less than K, the loop ends, and channel optimization is complete.

[0115] In the simulation, a uniform linear array with half-wavelength spacing is used as an example. The number of array elements N = 16, the number of pulses M = 16, the pulse repetition frequency PRF = 2000Hz, and the wavelength λ = 0.25m are set. Considering a front-looking airborne radar, the aircraft speed is v. c =125 m / s. Consider Gaussian clutter, with the polarization correlation coefficient of each clutter block being ρ. c The signal power ratio of different polarization channels is α c =1. For a target viewed from the side, set its Doppler frequency to f. d =0, the signal power ratio of different polarization channels is α t =1. Simulation results present the output signal-to-noise ratio (SNR) curves of the proposed method and existing channel construction methods for channel optimization, with 6 channels and ρ... c α is the polarization correlation coefficient. t This represents the signal power ratio of different polarization channels. Figure 3 , Figure 4 , Figure 5 ρ were presented respectively c =0.3, α t =1, ρ c =0.3, α t When = 100, and ρ c =0.9, α t When the clutter covariance matrix is ​​100, the output signal-to-clutter ratio (SNR) curves of full-dimensional polarization-space-time adaptive processing based on the ideal clutter covariance matrix and reduced-dimensional polarization-space-time adaptive processing with different channel construction methods are shown. The simulation results demonstrate that, under different polarization correlation coefficients and target signal power ratios, the output SNR of this invention is higher than that of existing channel construction methods. This simulation is based on the ideal clutter covariance matrix; when using an estimated covariance matrix, inaccurate covariance matrix results in a diminished advantage for this method.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0117] The above descriptions are merely some embodiments of the present invention. Those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for optimizing dimensionality-reduced polarization-space-time adaptive processing channels based on polarization arrays, characterized in that, Includes the following steps: Step 1: Establish a polarization space-time signal model based on the array parameters. The array used is a uniform linear polarization array consisting of M antennas, which transmits N pulses within one coherent processing interval. Step 2: Construct a complete polarization spacetime channel; Step 3: Select K channels based on the cross-correlation energy, where K is a preset value and K≥2; In step 2, when constructing a complete polarization spacetime channel, without adding polarization, MN angle-Doppler channels are obtained, and after adding polarization, the total number of channels is 2MN. The matrix formed by MN angle-Doppler channels is: in, For the s-th spacetime channel, , For time-domain steering vectors, It is a spatial guiding vector. in, To normalize the Doppler frequency, To normalize spatial frequency, The natural base, Represents the field of complex numbers; definition This represents the ratio of the target signal power in the V channel to the H channel. and Let H and V be the absolute phases of the H channel and V channel, respectively. Then the amplitude ratio and phase difference of the V channel and H channel signals are respectively... and The corresponding target polarization steering vector is: ; The matrix formed by polarization-dimensional channels is determined based on the target polarization steering vector. : Based on matrix sum matrix The matrix formed by all channels during dimensionality reduction polarization space-time adaptive processing is obtained. : matrix The matrix is ​​obtained by conjugate transpose and adjusting the channel order. Among them, the target polarization spacetime steering vector The matrix formed by all auxiliary channels ,and .

2. The method as described in claim 1, characterized in that, In step 1, the point target signal model of the uniform linear polarization array is as follows: in For the complex amplitude of the target signal, The target power for the horizontal H-channel is... This represents the ratio of the target power in the vertical V-channel to the target power in the horizontal H-channel. , , These are the polarization steering vector, the normalized spatial steering vector, and the normalized temporal steering vector, respectively. Based on all range ring clutter data, clutter echo data of the full range cells of the uniform linear polarization array are obtained. : in, The number of distance units. For distance loop The clutter echo data is expressed as follows: in, The number of clutter blocks, Indicates the first In the distance ring, the first The polarization space-time steering vector of each clutter block, For the first In the distance ring, the first The amplitude of the echo signal of the clutter block.

3. The method as described in claim 2, characterized in that, clutter echo data The expression is set as follows: in, For the first In the distance ring, the first The polarization steering vector of each clutter block. It is a spatial guiding vector. For time-domain steering vectors, , These are the normalized spatial frequency and the normalized Doppler frequency, respectively.

4. The method as described in claim 1, characterized in that, In step 3, K channels are selected based on the cross-correlation energy, specifically as follows: Received data Data obtained after passing through all channels : in, Used to represent the scalar output corresponding to the main channel, i.e., the reference channel output. Output data vectors for auxiliary channels; data covariance matrix for: in, For data The covariance matrix, The covariance matrix of the auxiliary channel output data vector. for: And the auxiliary channel output data vector With reference channel output cross-correlation for: The cross-correlation energy-based auxiliary channel selection algorithm compares the calculated cross-correlation energy of each channel when selecting the optimal channel, and selects the channel with the highest cross-correlation energy as the current optimal channel. The cross-correlation energy expression is as follows: in, Let n be a column vector with n elements equal to 1 and the rest equal to 0. for The nth element, For matrix The element in the nth row and nth column.

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