Sparse Channel Digital Receiving Array System Based on Dimensionality Reduction Coding and Its Working Method

Abstract

The present invention discloses a sparse channel digital receiving array system based on dimensionality reduction coding and its working method, which includes an array antenna, a dimensionality reduction coding network, a receiving channel, a signal reconstruction network, and an array signal processing module arranged in sequence; the array antenna receives the array echo signal; the dimensionality reduction coding network performs dimensionality reduction coding and merging on the array echo signal in the radio frequency part to obtain a coded signal; the receiving channel samples and receives the coded signal using a radio frequency receiving channel and an analog-to-digital conversion channel; the signal reconstruction network, according to the sparse characteristics of the array echo signal and while constraining the statistical characteristics of the noise, performs real-time snapshot-level reconstruction of the full-array signal using a signal reconstruction network implemented by a neural network; the array signal processing module performs digital beamforming on the reconstructed full-array signal to obtain a desired direction signal. The present invention can not only maximize the retention of the characteristics of the full-channel digital receiving array, but also reduce the number of channels as much as possible and lower the cost.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital phased arrays, and particularly relates to a sparse-channel digital receiving array system based on dimensionality reduction coding and its working method. Background Art

[0002] Intelligent antennas using element-level digital beamforming technology have the capabilities of flexible and controllable simultaneous independent multi-beamforming, adaptive spatial anti-jamming, and unambiguous multi-target angle estimation in the spatial domain. With the rapid development of large-scale radio frequency integrated circuit and very large-scale digital integrated circuit technologies, digital array intelligent antennas have emerged in various ground, vehicle-mounted, airborne, and missile-mounted platform high-performance early warning, detection, and fire control radar system equipment, as well as communication systems such as high-performance low-earth orbit satellite communication payloads, satellite ground user terminals, and 5G mobile communication system base stations that require high gain, low sidelobes, and large bandwidth.

[0003] Increasing the number of array elements to improve antenna gain and aperture size is the most direct and effective means to improve the sensitivity and detection accuracy of communication and detection systems. With the expansion of the array element scale, the cost and implementation complexity of the full-channel digital receiving array increase significantly, mainly reflected in the proportional increase in the number of radio frequency channels and analog-to-digital conversion channels, the increased complexity of the local oscillator power distribution network, and the increased implementation complexity brought by the half-wavelength spatial size limitation between channels. In addition, the number of high-speed physical transmission channels required for multi-channel digital signal reception, as well as the amount of data to be interacted and converged, all increase proportionally. However, cost, power consumption, and implementation complexity limit the large-scale popularization and application of full-channel digital receiving arrays in radio systems such as communication and radar.

[0004] Existing sparse-channel digital array technologies can either only retain some characteristics of the full-channel digital array, such as sparse array antennas, phased array sub-array digital array antennas, etc.; or exchange degrees of freedom in the time domain or frequency domain for an increase in degrees of freedom in the spatial domain or gain, such as nested arrays, co-prime arrays, time-modulated arrays, multi-carrier modulated arrays, and orthogonal coded modulated arrays. Therefore, how to maximize the retention of the characteristics of the full-channel digital receiving array while reducing the number of channels as much as possible and lowering costs has always been a hot issue in the field of digital phased arrays. Summary of the Invention

[0005] The purpose of the present invention is to provide a sparse-channel digital receiving array system based on dimensionality reduction coding and its working method, which can maximize the retention of the characteristics of the full-channel digital receiving array while reducing the number of channels as much as possible and lowering costs.

[0006] The technical solution for achieving the purpose of the present invention is as follows: A sparse-channel digital receiving array system based on dimensionality reduction coding includes an array antenna, a dimensionality reduction coding network, a receiving channel, a signal reconstruction network, and an array signal processing module arranged in sequence, where:

[0007] The array antenna receives the array echo signal;

[0008] The dimensionality reduction coding network performs dimensionality reduction coding and merging on the array echo signal in the radio frequency part to obtain a coded signal;

[0009] The receiving channel samples and receives the coded signal using a radio frequency receiving channel and an analog-to-digital conversion channel;

[0010] The signal reconstruction network simultaneously constrains the statistical characteristics of the noise according to the sparse characteristics of the array echo signal, and uses a signal reconstruction network implemented by a neural network to perform real-time snapshot-level reconstruction of the full array signal;

[0011] The array signal processing module performs digital beamforming on the reconstructed full array signal to obtain a desired direction signal.

[0012] Furthermore, the array antenna is specifically as follows:

[0013] For an array antenna composed of N antenna elements arranged arbitrarily, there are currently K far-field echo signals incident on the antenna array surface;

[0014] The received signals of each element of the array antenna are represented by an N-dimensional vector x(t):

[0015] x(t) = [x 1 (t), x 2 (t), …, x N (t)] T

[0016] Then there is

[0017]

[0018] In the formula, s k (t) is the k-th echo signal, k = 1, 2, 3…K, and K represents the total number of echo signals; a k is the array steering vector corresponding to the k-th target, which is determined by the target angle and the specific arrangement of the array; is independent and identically distributed Gaussian white noise in the wireless channel, and ∑ e is the covariance of the channel noise e(t).

[0019] Furthermore, the dimensionality reduction coding network encodes the array echo signal according to the dimensionality reduction coding matrix Φ in the radio frequency part, encodes and merges the N-dimensional array echo signal into an M-dimensional radio frequency coded signal, N > M, realizing the many-to-many interconnection of N antenna elements and M radio frequency channels.

[0020] Further, in the receiving channel, the downsampled and encoded signal y(t) sampled by the RF receiving channel is:

[0021] y(t) = GΦx(t) + η(t)

[0022] Each variable is expressed as:

[0023] y(t) = [y 1 (t), y 2 (t), …, y m (t), …, y M (t)] T

[0024]

[0025]

[0026] e(t) = [e 1 (t), e 2 (t), …, e n (t), …, e N (t)] T

[0027] η(t) = [η 1 (t), η 2 (t), …, η m (t), …, η M (t)] T

[0028] Among them, G is the gain of the RF receiving channel; x(t) is the signal received by the array antenna, and x n (t) is the signal received by the nth array element; K is the number of targets in space; s k (t) is the kth echo signal; a k is the array steering vector corresponding to the kth target, which is determined by the target angle and the specific arrangement of the array; e(t) is the independent and identically distributed Gaussian white noise in the wireless channel, and e n (t) is the channel noise received by the nth array element; Φ is the downsampling and encoding matrix, is the connection relationship between the mth RF channel and the nth antenna element; y(t) is the downsampled and encoded signal obtained by sampling, and y m (t) is the encoded signal received by the mth RF channel, and η(t) is the Gaussian thermal noise of each RF channel, and η m (t) is the Gaussian thermal noise of the mth RF channel.

[0029] Furthermore, the signal reconstruction network selects neural networks with different structures according to hardware resources and performance requirements, meeting the following requirements: during the forward propagation process, it can recover the corresponding full matrix received signal from the dimension-reduced encoded signal y(t) in real time for each snapshot. During the reverse propagation process, it is updated and trained based on multi-snapshot batch processing of gradient descent. The network has the ability of online training and can be adaptively updated with the changes of the target and the scenario.

[0030] Furthermore, the signal reconstruction network adopts a three-layer fully connected neural network. The input layer has M nodes, corresponding to the dimension of the dimension-reduced encoded signal y(t); the hidden layer has I nodes, which are composed of non-linear activation functions. The specific form of the activation function g(t) is not limited. If the sech(·) function gives the signal flow of the neural network, then the activation function of the i-th node in the hidden layer is where v i is the N-dimensional vector corresponding to the connection relationship with the input layer, and c i is the corresponding N-dimensional bias vector; the output layer has N nodes and can recover the full matrix received signal in real time. where g(t) = [g 1 (t), g 2 (t),..., g I (t)]T, W is the N×I-dimensional matrix characterizing the connection relationship between the hidden layer and the output layer, and b is the corresponding N-dimensional bias vector.

[0031] Furthermore, the generalized loss function of the signal reconstruction network is J = J MSE+ αJ Signal +βJ Noise , where J MSE is the maximum likelihood constraint for the signal; J Signal is the sparse constraint for the signal; J Noise is the constraint for the noise power and noise correlation characteristics; α and β are hyperparameters.

[0032] Furthermore, in the generalized loss function, J MSE , J Siganl and J Noise are respectively expressed as:

[0033]

[0034]

[0035]

[0036] where (·) H represents the conjugate transpose, and (·) -1denotes the inverse of a matrix, L denotes the number of snapshots, is the covariance of the reconstructed signal, ||·|| F denotes l F -norm, denotes the nth eigenvalue of, K is the number of targets which is also the sparsity of the signal, δ s is the shape parameter, is the reconstructed noise covariance, δ n is the noise power suppression coefficient.

[0037] A working method of a sparse channel digital receiving array system based on dimensionality reduction coding as described above is as follows:

[0038] After the array antenna receives the echo signal in space, it encodes the array echo signal at radio frequency through a dimensionality reduction coding network, combines and encodes the N-dimensional array echo signal into an M-dimensional radio frequency coded signal, where N > M. Through M radio frequency receiving channels and analog-to-digital conversion channels in the receiving channel, sparse channel sampling and receiving of the array signal are realized;

[0039] The signal reconstruction network constructs a sparse representation of the array echo signal according to the sparse characteristics of the signal, and at the same time constrains the statistical characteristics of the noise. A signal reconstruction network implemented by a neural network is used for real-time snapshot-level reconstruction of the N-dimensional full array signal;

[0040] The array signal processing module performs digital beamforming on the reconstructed full array signal to obtain the desired direction signal.

[0041] Compared with the prior art, the significant advantages of the present invention are: (1) The sparse channel digital receiving array based on dimensionality reduction coding can approximate the performance of the full channel digital receiving array antenna as much as possible without changing the processing framework of the existing full channel digital array communication and detection system, including digital beamforming performance, angle measurement accuracy, and accumulation gain, etc.; (2) Greatly reduce the number of radio frequency receiving channels and analog-to-digital converters ADC, and reduce the cost and power consumption of the digital receiving phased array system.

[0042] The following further describes the present invention in conjunction with the accompanying drawings of the specification. Description of the Drawings

[0043] Figure 1 is a schematic diagram of the architecture of a sparse channel digital receiving array system based on dimensionality reduction coding;

[0044] Figure 2 is a signal reconstruction network model taking a three-layer fully connected neural network as an example;

[0045] Figure 3 is a schematic diagram of the signal reconstruction network training process; Detailed Embodiments

[0046] A sparse channel digital receiving array system based on dimensionality reduction coding according to the present invention includes an array antenna, a dimensionality reduction coding network, a receiving channel, a signal reconstruction network, and an array signal processing module arranged in sequence, where:

[0047] The array antenna receives the array echo signal;

[0048] The dimensionality reduction coding network performs dimensionality reduction coding and merging on the array echo signal in the radio frequency part to obtain a coded signal;

[0049] The receiving channel samples and receives the coded signal using a radio frequency receiving channel and an analog-to-digital conversion channel;

[0050] The signal reconstruction network, according to the sparse characteristics of the array echo signal, simultaneously constrains the statistical characteristics of the noise, and uses a signal reconstruction network implemented by a neural network to perform real-time snapshot-level reconstruction of the full array signal;

[0051] The array signal processing module performs digital beamforming on the reconstructed full array signal to obtain a desired direction signal.

[0052] Further, the array antenna is specifically as follows:

[0053] For an array antenna composed of N antenna elements arranged arbitrarily, there are K far-field echo signals incident on the antenna array surface;

[0054] The received signals of each element of the array antenna are represented by an N-dimensional vector x(t):

[0055] x(t) = [x 1 (t), x 2 (t), …, x N (t)] T

[0056] Then there is

[0057]

[0058] where s k (t) is the k-th echo signal, k = 1, 2, 3…K, and K represents the total number of echo signals; a k is the array steering vector corresponding to the k-th target, which is determined by the target angle and the specific arrangement of the array; is independent and identically distributed Gaussian white noise in the wireless channel, and ∑ e is the covariance of the channel noise e(t).

[0059] Furthermore, in the dimensionality reduction coding network, the array echo signal is coded according to the dimensionality reduction coding matrix Φ in the radio frequency part, and the N-dimensional array echo signal is coded and merged into an M-dimensional radio frequency coding signal, where N > M, realizing the many-to-many interconnection of N antenna elements and M radio frequency channels.

[0060] Furthermore, in the receiving channel, the dimensionality reduction coding signal y(t) sampled by the radio frequency receiving channel is:

[0061] y(t) = GΦx(t) + η(t)

[0062] Each variable is expressed as:

[0063] y(t) = [y 1 (t), y 2 (t), …, y m (t), …, y M (t)] T

[0064]

[0065]

[0066] e(t) = [e 1 (t), e 2 (t), …, e n (t), …, e N (t)] T

[0067] η(t) = [η 1 (t), η 2 (t), …, η m (t), …, η M (t)] T

[0068] Among them, G is the gain of the radio frequency receiving channel; x(t) is the signal received by the array antenna, and x n (t) is the signal received by the nth array element; K is the number of targets in space; s k (t) is the kth echo signal; a k is the array steering vector corresponding to the kth target, which is determined by the target angle and the specific arrangement of the array; e(t) is the independent and identically distributed Gaussian white noise in the wireless channel, and e n (t) is the channel noise received by the nth array element; Φ is the dimensionality reduction coding matrix, is the connection relationship between the mth radio frequency channel and the nth antenna element; y(t) is the sampled dimensionality reduction coding signal, and y m (t) is the coding signal received by the mth radio frequency channel, and η(t) is the Gaussian thermal noise of each radio frequency channel, ηm (t) is the Gaussian thermal noise of the m-th RF channel.

[0069] Furthermore, the signal reconstruction network selects neural networks with different structures according to hardware resources and performance requirements to meet the following requirements: during the forward propagation process, it can recover the corresponding full matrix received signal from the dimensionality-reduced encoded signal y(t) in real time for each snapshot. During the backward propagation process, it is updated and trained based on multi-snapshot batch processing of gradient descent. The network has the ability of online training and can be updated adaptively with the changes of the target and scene.

[0070] Furthermore, the signal reconstruction network adopts a three-layer fully connected neural network. The input layer has M nodes, corresponding to the dimension of the dimensionality-reduced encoded signal y(t); the hidden layer has I nodes, which are composed of non-linear activation functions. The specific form of the activation function g(t) is not limited. If the sech(·) function gives the signal flow of the neural network, then the activation function of the i-th node in the hidden layer is where v i is an N-dimensional vector of the connection relationship with the input layer, and c i is the corresponding N-dimensional bias vector; the output layer has N nodes and can recover the full matrix received signal in real time where g(t) = [g 1 (t), g 2 (t),..., g I (t)] T , W is an N×I-dimensional matrix depicting the connection relationship between the hidden layer and the output layer, and b is the corresponding N-dimensional bias vector.

[0071] Furthermore, the generalized loss function of the signal reconstruction network is J = J MSE + αJ Signal + βJ Noise , where J MSE is the maximum likelihood constraint for the signal; J Signal is the sparsity constraint for the signal; J Noise is the constraint for the noise power and noise correlation characteristics; α and β are hyperparameters.

[0072] Furthermore, in the generalized loss function, J MSE , J Siganl and J Noise are respectively expressed as:

[0073]

[0074]

[0075]

[0076] Among them (·) H represents conjugate transpose, (·) -1 represents the inverse of a matrix, L represents the number of snapshots, is the covariance of the reconstructed signal, ||·|| F represents l F -norm, denotes the nth eigenvalue of, K is the number of targets, i.e., the sparsity of the signal, δ s is the shape parameter, is the reconstructed noise covariance, δ n is the noise power suppression coefficient.

[0077] A working method of a sparse channel digital receiving array system based on dimensionality reduction coding as described above is as follows:

[0078] After the array antenna receives the echo signal in space, it encodes the array echo signal in the radio frequency through the dimensionality reduction coding network, combines and encodes the N-dimensional array echo signal into an M-dimensional radio frequency coded signal, where N > M. After passing through the M radio frequency receiving channels and analog-to-digital conversion channels in the receiving channel, sparse channel sampling and reception of the array signal are realized;

[0079] The signal reconstruction network constructs a sparse representation of the array echo signal according to the sparse characteristics of the signal, and at the same time constrains the statistical characteristics of the noise. A signal reconstruction network implemented by a neural network is used for real-time snapshot-level reconstruction of the N-dimensional full array signal;

[0080] The array signal processing module performs digital beamforming on the reconstructed full array signal to obtain the desired direction signal.

[0081] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0082] Embodiment

[0083] The architecture of the sparse channel digital receiving array system based on dimensionality reduction coding involved in this embodiment is as Figure 1 shown. Two modules are added on the basis of the traditional digital receiving array: a dimensionality reduction coding network and a signal reconstruction network.

[0084] Module 1: Array antenna, which receives the array echo signal;

[0085] Consider an array antenna composed of N antenna elements arranged arbitrarily. There are K far-field echo signals incident on the antenna array surface. The received signals of each element of the array antenna are represented by an N-dimensional vector x(t), x(t) = [x 1 (t), x 2 (t), …, x N(t)] T Then there is

[0086]

[0087] In formula (1), s k (t) is the k-th echo signal, and a k is the array steering vector corresponding to the k-th target, which is determined by the target angle and the specific arrangement of the array. is the independent and identically distributed Gaussian white noise in the wireless channel, and ∑ e is the covariance of the channel noise e(t).

[0088] Module 2: Dimensionality reduction coding network, which realizes the dimensionality reduction coding of the array echo signal;

[0089] The dimensionality reduction coding network encodes the array echo signal according to the dimensionality reduction coding matrix Φ in the radio frequency, and encodes and combines the N-dimensional array echo signal into an M-dimensional radio frequency coding signal (N > M) to reduce the number of subsequent receiving channels.

[0090] Module 3: Receiving channel, which realizes the sparse channel sampling and reception of the array signal;

[0091] The dimensionality reduction coding signal obtained by sampling the receiving channel can be represented by an M-dimensional vector y(t), y(t) = [y 1 (t), y 2 (t), …, y M (t)] T Then there is

[0092]

[0093] In formula (2), is an M×N-dimensional dimensionality reduction coding matrix, is the connection relationship between the m-th radio frequency channel and the n-th antenna element. The form of the dimensionality reduction coding matrix Φ is free, and different coding methods will bring different angle characteristics to the system, which can be selected and optimized according to the actual arrangement of the antenna array and the specific scenario requirements. is the independent and identically distributed Gaussian thermal noise introduced by the radio frequency channel, and ∑ η is the covariance of the channel thermal noise η(t).

[0094] Module 4: Signal reconstruction network, which realizes the snapshot-level real-time reconstruction of the N-dimensional full-array received signal;

[0095] Considering the real-time requirement of the digital phased array system and the low signal-to-noise ratio characteristic of the echo signal in the actual scenario, the present invention uses a neural network to realize the real-time snapshot-level reconstruction of the full-array received signal.

[0096] The specific implementation method of the signal reconstruction network is not fixed, and neural networks with different structures can be selected according to hardware resources and performance requirements. For convenience, the present invention takes a three-layer fully connected neural network as shown in Figure 2 as an example for description. Among them, the input layer has M nodes, corresponding to the dimension of the dimensionality reduction encoded signal y(t); the hidden layer has I nodes, which are composed of non-linear activation functions. The specific form of the activation function g(t) is not limited. Here, taking the sech(·) function as an example to give the signal flow of the neural network, the activation function of the i-th node in the hidden layer is where v i is an N-dimensional vector of the connection relationship with the input layer, and c i is the corresponding N-dimensional bias vector; the output layer has N nodes, which can recover the full matrix received signal in real time where g(t) = [g 1 (t), g 2 (t),..., g I (t)] T , W is an N×I-dimensional matrix characterizing the connection relationship between the hidden layer and the output layer, and b is the corresponding N-dimensional bias vector.

[0097] In addition, the present invention provides a generalized loss function applicable to the signal reconstruction network:

[0098] J = J MSE + αJ Signal + βJ Noise (3)

[0099] In formula (3), J MSE is the maximum likelihood estimation term of the array signal, J Signal is the sparse constraint term for the signal, J Noise is the constraint term for the power and noise correlation characteristics of the noise, and α and β are hyperparameters.

[0100] Next, we give a specific constraint function to more clearly describe the generalized loss function given by the present invention. J MSE , J Siganl and J Noise can be respectively expressed as:

[0101]

[0102]

[0103]

[0104] where (·) H represents conjugate transpose, (·) -1 represents the inverse of the matrix, L represents the number of snapshots, is the covariance of the reconstructed signal, ||·|| F represents the l F -norm, represents the nth eigenvalue of, K is the number of targets which is also the sparsity of the signal, δ s is the shape parameter, is the reconstructed noise covariance, δ n is the noise power suppression coefficient.

[0105] The signal reconstruction network training model involved in the present invention is as Figure 3 shown. During the forward propagation process of the signal reconstruction network, the corresponding full matrix received signal can be recovered from the dimension-reduced encoded signal y(t) snapshot by snapshot On the other hand, the backpropagation process of the signal reconstruction network is based on multi-snapshot batch processing, without the need for any database for offline training, and can be implemented for online training on a hardware platform, and can be adaptively updated with the changes of targets and scenarios.

[0106] The backpropagation process of the signal reconstruction network based on gradient descent can be expressed as:

[0107]

[0108] In formula (4), Z j is the parameter Z to be trained in the jth iteration process, including W, b, v i and c i , i = 1, 2,..., I. μ is the iteration step size of gradient descent. is the partial derivative of the generalized loss function J(Z, Z * ) with respect to Z * , (·) * represents the conjugate of the matrix.

[0109] Module 5: Array signal processing module, which performs array signal processing using the same processing method as the full-channel digital receiving array, and can retain all the advantages of the full-channel digital receiving array.

[0110] The present invention can effectively reduce the number of RF channels, reduce the system cost of the digital receiving array, and the reconstructed full matrix signal can be processed for subsequent tasks such as array signal processing and parameter estimation using the same algorithm as the full-channel digital receiving array.

Claims

1. A sparse-channel digital receiving array system based on dimensionality reduction coding, characterized in that, it includes an array antenna, a dimensionality reduction coding network, a receiving channel, a signal reconstruction network, and an array signal processing module arranged in sequence, where: The array antenna receives the array echo signal; The dimensionality reduction coding network performs dimensionality reduction coding and merging on the array echo signal in the radio frequency part to obtain a coded signal; The receiving channel samples and receives the coded signal using a radio frequency receiving channel and an analog-to-digital conversion channel; The signal reconstruction network, according to the sparse characteristics of the array echo signal, simultaneously constrains the statistical characteristics of the noise, and uses a signal reconstruction network implemented by a neural network to perform real-time snapshot-level reconstruction of the full-array signal; The array signal processing module performs digital beamforming on the reconstructed full-array signal to obtain a desired direction signal; In the receiving channel, the dimensionality reduction coded signal y(t) sampled by the radio frequency receiving channel is: y(t) = GΦx(t) + η(t) Each variable is expressed as: y(t) = [y 1 (t), y 2 (t), …, y m (t), …, y M (t)] T e(t) = [e 1 (t), e 2 (t), …, e n (t), …, e N (t)] T η(t) = [η 1 (t), η 2 (t), …, η m (t), …, η M (t)] T Among them, G is the gain of the radio frequency receiving channel; x(t) is the signal received by the array antenna, and x n (t) is the signal received by the nth array element; K is the number of targets in space; s k (t) is the kth echo signal; a k is the array steering vector corresponding to the kth target, which is determined by the target angle and the specific arrangement of the array; e(t) is the independent and identically distributed Gaussian white noise in the wireless channel, and e n (t) is the channel noise received by the nth array element; Φ is the dimensionality reduction coding matrix, is the connection relationship between the mth radio frequency channel and the nth antenna element; y(t) is the dimensionality reduction coding signal obtained by sampling, and y m (t) is the coding signal received by the mth radio frequency channel, η(t) is the Gaussian thermal noise of each radio frequency channel, and η m (t) is the Gaussian thermal noise of the mth radio frequency channel.

2. The sparse-channel digital receiving array system based on dimensionality reduction coding according to claim 1, characterized in that, The array antenna is specifically as follows: For an array antenna composed of N antenna elements arranged arbitrarily, there are K far-field echo signals incident on the antenna array surface; The received signals of each element of the array antenna are represented by an N-dimensional vector x(t): x(t) = [x 1 (t), x 2 (t), …, x N (t)] T Then there is where s k (t) is the k-th echo signal, k = 1, 2, 3... K, and K represents the total number of echo signals; a k is the array steering vector corresponding to the k-th target, which is determined by the target angle and the specific arrangement of the array; is independent and identically distributed Gaussian white noise in the wireless channel, and Σ e is the covariance of the channel noise e(t).

3. The sparse-channel digital receiving array system based on dimensionality reduction coding according to claim 1, characterized in that, The dimensionality reduction coding network encodes the array echo signal according to the dimensionality reduction coding matrix Φ in the radio frequency part, encodes and merges the N-dimensional array echo signal into an M-dimensional radio frequency coded signal, N > M, realizing the many-to-many interconnection of N antenna elements and M radio frequency channels.

4. The sparse-channel digital receiving array system based on dimensionality reduction coding according to claim 1, characterized in that, The signal reconstruction network selects neural networks with different structures according to hardware resources and performance requirements, meeting the following requirements: During the forward propagation process, it can recover the corresponding full-array received signal from the dimensionality-reduced encoded signal y(t) in real time and snapshot by snapshot. During the backward propagation process, it is updated and trained based on gradient descent with multi-snapshot batch processing. The network has the ability of online training and can be adaptively updated with the changes of targets and scenarios.

5. The sparse-channel digital receiving array system based on dimensionality reduction coding according to claim 4, characterized in that, The signal reconstruction network uses a three-layer fully connected neural network. The input layer has M nodes, corresponding to the dimension of the dimensionality-reduced encoded signal y(t); the hidden layer has I nodes, which are composed of non-linear activation functions. The specific form of the activation function g(t) is not limited. The sech(·) function gives the signal flow of the neural network. Then the activation function of the i-th node in the hidden layer is where v i is an N-dimensional vector of the connection relationship with the input layer, and c i is the corresponding N-dimensional bias vector; the output layer has N nodes and can recover the full matrix received signal in real time where g(t) = [g 1 (t), g 2 (t),..., g I (t)] T , W is an N×I-dimensional matrix characterizing the connection relationship between the hidden layer and the output layer, and b is the corresponding N-dimensional bias vector.

6. The sparse-channel digital receiving array system based on dimensionality reduction coding according to claim 5, characterized in that, The generalized loss function of the signal reconstruction network is \(J = J\) MSE +\(\alpha J\) Signal +\(\beta J\) Noise , where \(J\) MSE is the maximum likelihood constraint for the signal; \(J\) Signal is the sparsity constraint for the signal; \(J\) Noise is the constraint for the noise power and noise correlation characteristics; \(\alpha\) and \(\beta\) are hyperparameters.

7. The sparse-channel digital receiving array system based on dimensionality reduction coding according to claim 5, characterized in that, J in the generalized loss function MSE 、J Siganl and J Noise are respectively expressed as: Among them (·) H denotes conjugate transpose, (·) -1 denotes the inverse of a matrix, L denotes the number of snapshots, is the covariance of the reconstructed signal, ||·|| F denotes l F -norm, denotes the nth eigenvalue of, K is the number of targets, i.e., the sparsity of the signal, δ s is the shape parameter, is the reconstructed noise covariance, δ n is the noise power suppression coefficient.

8. A working method of the sparse-channel digital receiving array system based on dimensionality reduction coding according to any one of claims 1 to 7, characterized in that, specifically as follows: After the array antenna receives the echo signal in space, it encodes the array echo signal in the radio frequency through the dimensionality reduction coding network, encodes and merges the N-dimensional array echo signal into an M-dimensional radio frequency coded signal, N > M, and through the M-way radio frequency receiving channels and analog-to-digital conversion channels in the receiving channel, realizes the sparse-channel sampling and receiving of the array signal; The signal reconstruction network constructs a sparse representation of the array echo signal according to the sparse characteristics of the signal, simultaneously constrains the statistical characteristics of the noise, and uses a signal reconstruction network implemented by a neural network to perform real-time snapshot-level reconstruction of the N-dimensional full-array signal; The array signal processing module performs digital beamforming on the reconstructed full-array signal to obtain a desired direction signal.

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