MIMO radar multi-phase waveform design driven by soft quantization model deep learning
Patent Information
- Application Number
- CN202310973253.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-08-03
- Publication Date
- 2026-10-27
- Estimated Expiration
- 2043-08-03
AI Technical Summary
[0003]采用固定阈值的硬量化的方法来设计多相波形，因其自由度受限，导致性能也受限
[0096]本申请获取更低的ISLR值，在发射方向图上也能够获得较深的零陷深度和较低的峰值旁瓣点平，更利于提高MIMO雷达对目标的探测性能。
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Figure CN117055007B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of radar technology, and in particular to a soft quantization model-driven deep learning-based MIMO radar multiphase waveform design. Background Technology
[0002] In recent years, polyphase waveform design has become a key technology in MIMO radar systems. Existing research shows that for large-scale MIMO systems with a very large number of transmit and receive antennas, the hardware cost and power consumption are exponentially related to the quantization bit depth of digital-to-analog converters (DACs). Therefore, polyphase waveform design using low-resolution DACs can minimize the power consumption, hardware cost, and system complexity of the radar system. Furthermore, using low-resolution DACs can provide faster sampling and conversion times, thereby enabling faster signal processing. Therefore, polyphase waveform design for MIMO radar has attracted widespread attention.
[0003] The hard quantization method with a fixed threshold is used to design multiphase waveforms, but its performance is limited due to the restricted degrees of freedom. Summary of the Invention
[0004] This application provides a soft quantization model-driven deep learning-based MIMO radar multiphase waveform design to address the problems in the prior art.
[0005] In a first aspect, this application provides a MIMO radar multiphase waveform design driven by a soft quantization model and deep learning, including:
[0006] Establish an optimization model that minimizes the spatial integral sidelobe level ratio of the transmitted waveform;
[0007] In a deep learning framework, a loss function for optimizing the model is constructed, and the Adam optimizer is used to optimize the loss function to obtain the waveform matrix.
[0008] Among them, a soft quantization method with an adaptive quantization threshold is used to obtain multiphase waveforms.
[0009] Furthermore, the construction of the loss function of the optimization model in the deep learning framework, and the optimization of the loss function using the Adam optimizer to obtain the waveform matrix, includes: in the model-driven layer, using the gradient descent algorithm on the complex circular manifold to process and obtain the optimized continuous waveform.
[0010] Furthermore, the optimization model for minimizing the spatial sidelobe ratio of the transmitted waveform includes:
[0011] A problem model is established for designing multiphase waveforms that minimize the spatial integral sidelobe ratio; that is, for a waveform with M... t A centralized MIMO radar with multiple transmitting antennas, each transmitting a sequence of length N in the fast time domain.
[0012] use Represents the transmitted waveform matrix.
[0013] in This represents the data sampled at the nth time, i.e., the nth column of the waveform matrix.
[0014] use This represents the result of column vectorization of the waveform matrix;
[0015] For a uniform linear array with half a wavelength, the transmit array steering vector is:
[0016]
[0017] The energy of the transmitted signal in the θ direction can be expressed as:
[0018]
[0019] in use M represents the spatial domain d An interesting angle,
[0020] use M represents the spatial domain u An angle that doesn't interest me;
[0021] The expression for the spatial integral sidelobe ratio is as follows:
[0022]
[0023] in
[0024] The problem model to be optimized is as follows:
[0025]
[0026]
[0027] Where s m,n This represents the (m,n)th element of the waveform matrix, where m = 1,...,M t n=1,...,N,
[0028]
[0029] L=2 b represents the length of the symbol constellation set, and b represents the number of bits quantized.
[0030] Furthermore, it also includes deep learning driven by soft quantization models to optimize problem models and solve problems.
[0031] Specifically: for the optimized continuous waveform; in the soft quantization layer, a multiphase waveform is obtained through a soft quantization method, and the quantization threshold is adaptively adjusted by the network.
[0032] Furthermore, the steps for optimizing the problem model based on soft quantization models using deep learning include, for example... Figure 1 As shown, it includes:
[0033] Step 1: Unfold the gradient descent algorithm in the model-driven layer, including steps 1.1-1.4;
[0034] Step 1.1: Project the Euclidean gradient onto the tangent space to obtain the Riemann gradient;
[0035] Step 1.2: Search for a provisional solution by applying the Riemann gradient along the descent direction of the tangent space gradient;
[0036] Step 1.3: Revert the provisional solution obtained in the tangent space to the Riemannian complex circular manifold to obtain a feasible solution;
[0037] Step 1.4: Adaptively adjust the search step size, using the search step size as a trainable parameter for adaptive learning, and obtain the convergent gradient;
[0038] Step 2: Quantize the waveform in the soft quantization layer, including steps 2.1-2.2;
[0039] Step 2.1: Use the sum of the differentiable shifted hyperbolic tangents as a soft quantization function to approximate the traditional non-differentiable hard quantization function;
[0040] Step 2.2: Obtain the discrete waveform through the soft quantization function and construct the loss function of the optimization model;
[0041] Step 3: Minimize the loss function using a deep learning optimizer, where the search step size in the gradient descent module and the quantization threshold in the soft quantization module can be adaptively adjusted using deep learning;
[0042] Step 4: Optimize the parameters through deep learning, including the search step size and quantization threshold. Based on the optimized quantization threshold, hard quantize the continuous waveform to obtain the final optimized multiphase waveform.
[0043] Furthermore, the steps for optimizing the problem model based on soft quantization model-driven deep learning are as follows:
[0044] Step 1.1:
[0045] The Euler gradient projection at the k-th iteration can be expressed as:
[0046]
[0047] in:
[0048] It is a point The Riemann gradient at point can be expressed as:
[0049]
[0050] It is a manifold Points on The tangent space formed by all tangent vectors at a given point can be represented as:
[0051]
[0052] in It is a point The tangent vector at that point, represents the real part of a complex vector, and ⊙ represents the Hadamard element-wise product;
[0053] The projection operator can be represented as:
[0054]
[0055] It is a point The Euler gradient at point can be expressed as:
[0056]
[0057] By calculating the real and imaginary parts separately, and by representing the complex-valued variables with real values, we can obtain the equivalent representations of the Riemann gradient and the Euler gradient:
[0058] Euler gradient rewritten as:
[0059]
[0060] in
[0061] It is an operator for obtaining the real part of a complex number. It is an operator for obtaining the imaginary part of a complex number;
[0062] The Riemann gradient is rewritten as:
[0063]
[0064] in:
[0065]
[0066]
[0067]
[0068] Step 1.2: After obtaining the Riemann gradient, search along the gradient descent direction. The provisional solution obtained can be expressed as:
[0069]
[0070] Where α k The search step size for the k-th iteration is given by separating the real and imaginary parts. The provisional solution in the tangent space is then rewritten as:
[0071]
[0072] Step 1.3: By shrinking the provisional solution obtained in the tangent space back onto the Riemannian complex circular manifold, a feasible solution can be obtained, which can be expressed as:
[0073]
[0074] Where |s T | represents vector s T Modulo by element This indicates that the Hadamard element is divided.
[0075] By separating the real and imaginary parts, the feasible solution on the Riemannian complex circular manifold can be rewritten as:
[0076]
[0077] in
[0078] Step 1.4 followed by step 2.1:
[0079] The soft quantization function can be expressed as:
[0080]
[0081] The output of the soft quantization function is limited to [0, 2π), where a = π / L is the amplitude, representing the quantized phase value, and c represents the degree to which the superimposed hyperbolic tangents approximate the non-differentiable soft quantization function. The larger c is, the closer it is to the non-differentiable soft quantization function. i} represents the quantization threshold, which is adaptively adjusted through deep learning;
[0082] Discrete waveform s can be obtained through soft quantization. Q Then the loss function of the optimized model can be rewritten as:
[0083]
[0084] in
[0085] Step 3: Use the Adam optimizer to optimize the loss function and obtain the final optimized result α after training. opt ,η opt ,s k+1 ;
[0086] Step 4: Optimize the continuous waveform s k+1 Hard quantization is performed to obtain a multiphase waveform, where c = 1 × 10 20 ,
[0087] In a second aspect, this application provides a network framework system for implementing MIMO radar multiphase waveform design based on soft quantization model-driven deep learning as described in any of the first aspects. The soft quantization model-driven deep learning (SQM-DL) network framework includes: a trainable parameter module, a gradient descent module, and a soft quantization module.
[0088] (1) Trainable parameter module:
[0089] The trainable parameters module mainly contains all the parameters to be optimized, including the search step size α = [α1,...,α]. k ,…,α K ], quantization threshold η=[η1,…,η L-1 ] and waveform vector s.
[0090] (2) Gradient Descent Module:
[0091] After parameter initialization, the deep learning training process begins. As shown in steps 1.2-1.3, the deep learning network obtains a continuous optimized waveform s after passing through the gradient descent module. K+1 .
[0092] (3) Soft quantization module:
[0093] Considering that the actual radar system transmits discrete waveforms, a quantization layer is added to the network to quantize the continuous waveforms.
[0094] On the other hand, this application provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement a soft-quantization model-driven deep learning MIMO radar multiphase waveform design as described in any one of the first aspects.
[0095] This application has the following advantages and beneficial effects:
[0096] This application achieves a lower ISLR value, and also obtains a deeper null depth and a lower peak sidelobe level in the transmission pattern, which is more conducive to improving the target detection performance of MIMO radar. Attached Figure Description
[0097] The accompanying drawings, which are included to provide a further understanding of the embodiments of this application and form part of this application, do not constitute a limitation on the embodiments of this application. In the drawings:
[0098] Figure 1 This is a flowchart illustrating the steps involved in optimizing a problem model based on soft quantization models using deep learning in this application.
[0099] Figure 2 This is a graph of the soft quantization function in an embodiment of this application.
[0100] Figure 3 This is a comparison curve of the cost function output when L=8 in the embodiments of this application.
[0101] Figure 4 This is a comparison curve of the cost function output when L=4 in the embodiments of this application.
[0102] Figure 5 This is a comparison curve of the cost function output when L=2 in the embodiments of this application.
[0103] Figure 6 This is a comparison curve of the output transmission beam pattern when L=8 in the embodiments of this application.
[0104] Figure 7 This is a comparison curve of the output transmission beam pattern when L=4 in the embodiments of this application.
[0105] Figure 8 This is a comparison curve of the output transmission beam pattern when L=2 in the embodiments of this application. Detailed Implementation
[0106] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.
[0107] In recent years, polyphase waveform design has become a key technology in MIMO radar systems. Existing research shows that for large-scale MIMO systems with a very large number of transmit and receive antennas, the hardware cost and power consumption are exponentially related to the quantization bit depth of DACs / ADCs. Therefore, employing polyphase waveform design with low-resolution DACs / ADCs can minimize the power consumption, hardware cost, and system complexity of the radar system. Furthermore, using low-resolution DACs / ADCs can provide faster sampling and conversion times, thereby enabling faster signal processing. Therefore, polyphase waveform design for MIMO radar has attracted widespread attention.
[0108] Current methods all employ hard quantization with a fixed threshold, which can be broadly categorized into two types: the first type is based on semidefinite relaxation (SDR) methods, but these methods inevitably introduce approximation errors after relaxing the constraints; the second type is based on coordinate descent (CD) methods, which may introduce quantization fuzziness errors during hard quantization.
[0109] In the first category of methods, a typical example is the paper "d'Aspremont A, Boyd S. Relaxations and randomized methods for nonconvex QCQPs[J]. EE392o Class Notes, Stanford University, 2003, 1:1-16." which proposes an SDR method to relax nonconvex quadratic constrained quadratic programming (QCQP) problems and obtain an approximate solution. Based on this method, the paper "Cui G, Li H, Rangaswamy M. MIMO radarwaveform design with constant modulus and similarity constraints[J]. IEEE Transactions on signal processing, 2013, 62(2):343-353." proposes a method based on SDR and randomization, which determines feasible solutions that are arbitrarily close to the solution of the original problem by relaxing the original problem into a fractional SDR problem and then solving it. However, the use of relaxation methods inevitably introduces approximation errors.
[0110] In the second category of methods, a typical example is the paper "AN D, HU J, ZHONG K, et al. RIS Assisted Multiple User Interference Mitigation via an Accelerated Coordinate Descent Method[J]. IEEE Transactions on Cognitive Communications and Networking, 2023, 9(1): 159-69." which proposes an accelerated coordinate descent (ACD) method. This method transforms the problem into multiple one-dimensional subproblems and then uses a one-dimensional search strategy to solve the discrete phase problem. However, as the number of discrete phases increases, the time complexity of the algorithm inevitably increases. To address this issue, the paper "RAEI E, ALAEE-KERAHROODI M, SHANKAR M RB. Spatial-and Range-ISLR Trade-Off in MIMO Radar Via Waveform Correlation Optimization[J]. IEEE Transactions on Signal Processing, 2021, 69: 3283-98." proposes an iterative method based on CD and a method based on DFT to solve the joint optimization problem of spatial and range-ISLR under discrete phase constraints. The results show that the proposed method can achieve a good trade-off between spatial and range-ISLR.
[0111] In summary, the above methods all employ hard quantization with a fixed threshold to design multiphase waveforms, which may lead to quantization blurring at the quantization threshold point, inevitably introducing quantization blurring errors. Noting that non-uniform adaptive soft quantization can effectively solve the quantization blurring problem, a model-driven deep learning (SQM-DL) method based on soft quantization is proposed. Specifically, firstly, the gradient descent (GD) algorithm on the complex circular manifold (CCM) is used as a model network layer to obtain an optimized continuous waveform, where the search step size is set as a trainable network parameter. Then, the multiphase waveform is obtained through a soft quantization layer, where the quantization threshold can be adaptively adjusted by the network.
[0112] Other definitions of terms used in this application:
[0113] Integrated Sidelobe Level Ratio (ISLR)
[0114] Example:
[0115] For ease of description, let's define it as follows:
[0116] Modeling the problem of multiphase waveform design for minimizing spatial ISLR:
[0117] Consider a given M t A centralized MIMO radar with multiple transmitting antennas, each transmitting a sequence of length N in the fast time domain.
[0118] use Represents the transmitted waveform matrix.
[0119] in This represents the data sampled at the nth time (the nth column of the waveform matrix).
[0120] use This represents the result of column vectorization of the waveform matrix.
[0121] For a uniform linear array (ULA) with half a wavelength, the transmit array steering vector can be expressed as:
[0122]
[0123] The energy of the transmitted signal in the θ direction can be expressed as:
[0124]
[0125] in use M represents the spatial domain d From an interesting angle, using M represents the spatial domain u An angle that I'm not interested in.
[0126] The expression for spatial domain-ISLR is as follows:
[0127]
[0128] in
[0129] This application designs a transmission sequence set with good spatial-ISLR characteristics under discrete phase constraints. Furthermore, the objective of this application's technical solution is to minimize spatial-ISLR. Therefore, the optimization problem can be expressed as:
[0130]
[0131] Where s m,n This represents the (m,n)th element of the waveform matrix, where m = 1, ..., M. t n=1,…,N.
[0132] L=2 b represents the length of the symbol constellation set, and b represents the number of bits quantized.
[0133] Using the SQM-DL network framework described in the above manual, the steps to implement a deep learning method driven by a soft quantization model are as follows:
[0134] Step 1: Unfold the gradient descent algorithm in the model-driven layer
[0135] In the model-driven layer, we utilize the gradient descent algorithm on the Riemannian complex circular manifold. This algorithm mainly consists of four steps: Euler gradient projection, tangent space gradient descent, shrinking back to the Riemannian complex circular manifold, and adaptive learning step size.
[0136] (1) Euler gradient projection:
[0137] The Riemann gradient is obtained by projecting the Euclidean gradient onto the tangent space. At the k-th iteration, it can be expressed as:
[0138]
[0139] in:
[0140] · It is a point The Riemann gradient at point can be expressed as:
[0141]
[0142] · It is a manifold Points on The tangent space formed by all tangent vectors at a given point can be represented as:
[0143]
[0144] in It is a point The tangent vector at that point, represents the real part of a complex vector, and ⊙ represents the Hadamard element-wise product.
[0145] · The projection operator can be represented as:
[0146]
[0147] · It is a point The Euler gradient at point can be expressed as:
[0148]
[0149] To avoid computation of complex-valued variables, this embodiment uses an equivalent real-valued representation, that is, calculating the real and imaginary parts separately. The Euler gradient can then be rewritten as:
[0150]
[0151] in
[0152] It is an operator for obtaining the real part of a complex number. It is an operator for obtaining the imaginary part of a complex number.
[0153] Similarly, the Riemann gradient can be rewritten as:
[0154]
[0155] in:
[0156]
[0157]
[0158]
[0159] (2) Tangent space gradient descent:
[0160] After obtaining the Riemann gradient, a search needs to be performed along the gradient descent direction. The resulting provisional solution can be expressed as:
[0161]
[0162] Where α k It is the search step size for the k-th iteration.
[0163] By separating the real and imaginary parts, the provisional solution in the tangent space can be rewritten as:
[0164]
[0165] (3) Back to the Riemannian complex circular manifold:
[0166] The feasible solution can be obtained by shrinking the provisional solution obtained in the tangent space back onto the Riemannian complex circular manifold, and can be expressed as:
[0167]
[0168] Where |s T | represents vector s T Modulo by element This indicates that the Hadamard element is divided.
[0169] By separating the real and imaginary parts, the feasible solution on the Riemannian complex circular manifold can be rewritten as:
[0170]
[0171] in
[0172] (4) Adaptive learning step size:
[0173] Traditional gradient descent methods typically use a fixed search step size, which may lead to gradient non-convergence. To address this issue, this embodiment proposes the SQM-DL method, which uses the search step size as a trainable parameter, thereby enabling adaptive learning of the step size.
[0174] Step 2: Quantize the waveform in the soft quantization layer
[0175] Unlike traditional methods that use a fixed quantization threshold, we add a quantization layer based on soft quantization technology, using a differentiable quantization function to approximate a non-differentiable quantization function. For example... Figure 2 As shown, the superposition of differentiable shifted hyperbolic tangents is used as the soft quantization function.
[0176] To restrict the output of a function to [0, 2π), the quantization function can be expressed as:
[0177]
[0178] Where a = π / L is the amplitude, representing the quantized phase value. c represents the degree to which the superposition of shifted hyperbolic tangents approximates the non-differentiable function; the larger c is, the closer it is to the non-differentiable function. {η i} represents the threshold for quantization, which can be adaptively adjusted through deep learning.
[0179] Discrete waveform s can be obtained through soft quantization. Q Then the loss function of the original problem can be rewritten as:
[0180]
[0181] in
[0182] Step 3: Obtain the final optimization result α after training. opt ,η opt ,s k+1 Finally, in order to obtain the final optimized multiphase waveform, the optimized continuous waveform s k+1 The quantization threshold η obtained from network adaptive learning opt Hard quantization is performed using a soft quantization function, where c = 1 × 10 20 ,
[0183] Specifically, this embodiment provides a possible implementation method, including: minimizing the loss function using a deep learning Adam optimizer; after obtaining the loss function, a mainstream deep learning optimizer such as the Adam optimizer can be used to minimize the loss function. Throughout the training process, all parameters can be learned to obtain the final optimization result α. opt ,η opt ,s k+1 .
[0184] Example:
[0185] To verify the proposed scheme, the waveform was optimized using both existing and proposed schemes. In all simulation experiments, a uniform linear array with M transmit antennas was considered. t =8, number of snapshots N=32, and the regions of interest and regions of non-interest are set to Θ respectively. d = [0°, 20°] and Θ u = [-90°, -5°] ∪ [25°, 90°]. These regions can be uniformly sampled, with a sampling interval of 5°. The deep learning model network has K = 2 layers.
[0186] Existing solutions:
[0187] 1. UNIQUE method based on coordinate descent (CD): Reference: "RAEI E, ALAEE-KERAHROODI M, SHANKAR MR B. Spatial-and Range-ISLR Trade-Off in MIMO Radar Via WaveformCorrelation Optimization[J]. IEEE Transactions on Signal Processing, 2021, 69:3283-98."
[0188] 2. Semi-definite relaxation (SDR) method: Reference: "Cui G, Li H, Rangaswamy M. MIMO radar waveform design with constant modulus and similarity constraints[J]. IEEE Transactions on signal processing, 2013, 62(2):343-353."
[0189] Figures 3-5Cost function curves for different phase numbers L are presented. It can be seen that, compared to the UNIQUE and SDR methods, the cost function convergence curve of the proposed method converges to a minimum value for different L values. Furthermore, the ISLR value of the proposed method decreases as the L value increases. Specifically, in Figure 3 In the study, when L=8, the proposed method achieved an ISLR of 0.0263846, which is 0.981 dB lower than the UNIQUE method and 4.971 dB lower than the SDR method. Figure 3 In the study, when L=4, the proposed method achieved an ISLR of 0.0720194, which is 0.259 dB lower than the UNIQUE method and 2.265 dB lower than the SDR method. Figure 4 In the study, when L=2, the ISLR of the proposed method converged to 0.199876, which is 0.563dB and 1.057dB lower than that of the UNIQUE and SDR methods, respectively.
[0190] Figures 6-8 Curves showing the normalized transmit beam pattern as a function of azimuth angle for different phase numbers L are presented. Figure 6 In the proposed method, when L=8, the null depth formed at the main lobe edge of the transmit beam pattern is 4.442 dB and 4.718 dB deeper than that of the UNIQUE and SDR methods, respectively. Furthermore, it exhibits lower peak sidelobe levels in the [25°, 90°] region. Figure 7 In the proposed method, when L=4, the null depth formed at the main lobe edge of the emitted beam pattern is 7.578dB deeper than that of the UNIQUE method and 7.537dB deeper than that of the SDR method, and it also exhibits lower sidelobe levels in the region [-90°, -5°] ∪ [25°, 90°]. Figure 8 In the example, when L=2, it can be seen that the transmit beam pattern is symmetrical about 0°. In fact, when the transmit waveform is a true 1-bit sequence, the transmit beam pattern is also symmetrical. The peak sidelobe level of the transmit beam pattern of the proposed method is 1.116 dB and 2.304 dB lower than that of the UNIQUE method and the SDR method, respectively.
[0191] The above simulations verify the performance advantages of the soft quantization model-driven deep learning method disclosed in this invention: it can achieve a lower ISLR value, and can also obtain a deeper null depth and a lower peak sidelobe level in the transmission pattern, which is more conducive to improving the target detection performance of MIMO radar.
[0192] Those skilled in the art will understand that embodiments of this application can be provided as methods or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0193] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.
[0194] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.
[0195] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the following claims.
[0196] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.
Claims
1. A method for designing multiphase waveforms of MIMO radar using a soft quantization model-driven deep learning approach, characterized in that, include: Establish an optimization problem model for minimizing the spatial integral sidelobe level ratio of the transmitted waveform; The problem model is based on a soft quantization model-driven deep learning optimization model, wherein the deep learning model includes a model-driven layer and a soft quantization layer. In the model-driven layer, the gradient descent algorithm on the complex circular manifold is used to process and obtain the optimized continuous waveform; for the optimized continuous waveform, in the soft quantization layer, the multiphase waveform is obtained by the soft quantization method, and the quantization threshold is adaptively adjusted by deep learning. In the model-driven layer, the gradient descent algorithm on the complex circular manifold is used to process and obtain the optimized continuous waveform, including: Step 1.1: Project the Euclidean gradient onto the tangent space to obtain the Riemann gradient; Step 1.2: Search for a provisional solution by applying the Riemann gradient along the descent direction of the tangent space gradient; Step 1.3: Revert the provisional solution obtained in the tangent space to the Riemannian complex circular manifold to obtain a feasible solution; Step 1.4: Adaptively adjust the search step size, using the search step size as a trainable parameter for adaptive learning, and obtain the convergent gradient; The optimized continuous waveform, in the soft quantization layer, obtains a multiphase waveform through a soft quantization method, and adaptively adjusts the quantization threshold through deep learning, including: Step 2.1: Use the sum of the differentiable shifted hyperbolic tangents as a soft quantization function to approximate the traditional non-differentiable hard quantization function; Step 2.2: Obtain the discrete waveform through the soft quantization function and construct the loss function of the optimization model; Step 2.3: Minimize the loss function using the Adam optimizer, where the search step size in the gradient descent module and the quantization threshold in the soft quantization module can be adaptively adjusted through deep learning; Step 2.4: Optimize the parameters through deep learning, including the search step size and quantization threshold. Based on the optimized quantization threshold, hard quantize the continuous waveform to obtain the final optimized multiphase waveform.
2. The method for designing multiphase waveforms of MIMO radar driven by soft quantization model deep learning according to claim 1, characterized in that, The optimization problem model for minimizing the spatial integral sidelobe level ratio of the transmitted waveform includes: A problem model is established for designing a multiphase waveform that minimizes the spatial integral sidelobe level ratio; that is, for a waveform with... There are _ ... Centralized MIMO radar, use Represents the transmitted waveform matrix. in Indicates the first The time-sampled data, i.e., the waveform matrix of the [number]th time sample, is [number]th [number List, use This represents the result of column vectorization of the waveform matrix; For a uniform linear array with half a wavelength, the transmit array steering vector is: ； Transmitted signal in Energy in a direction can be expressed as: ； in ,use In the airspace An interesting angle, use In the airspace An angle that doesn't interest me; The expression for the spatial integral sidelobe ratio is as follows: ； in , ; The problem model to be optimized is as follows: ； in The waveform matrix represents the first... One element, , ， This represents the number of phases in the quantization. Indicates the number of bits quantized.
3. The method for designing multiphase waveforms of MIMO radar driven by soft quantization model deep learning according to claim 2, characterized in that, Step 1.1 specifically includes: Euler gradient projection in the th In the nth iteration, it can be represented as: ； in: It is a point The Riemann gradient at point can be expressed as: ； It is a manifold Points on The tangent space formed by all tangent vectors at a given point can be represented as: ； in It is a point The tangent vector at that point, Let represent the real part of the elements of a complex vector. Represents the Hadamard element-wise product; The projection operator can be represented as: ； It is a point The Euler gradient at point can be expressed as: ； By calculating the real and imaginary parts separately, and by representing the complex-valued variables with real values, we can obtain the equivalent representations of the Riemann gradient and the Euler gradient: Euler gradient rewritten as: ； in , , , It is an operator for obtaining the real part of a complex number. It is an operator for obtaining the imaginary part of a complex number; The Riemann gradient is rewritten as: ； in: ； ； ； Step 1.2 specifically involves: after obtaining the Riemann gradient, searching along the gradient descent direction, and obtaining a provisional solution that can be expressed as: ； in It is the first The search step size for the next iteration, by separating the real and imaginary parts, is rewritten as the provisional solution in the tangent space: ； Step 1.3 specifically involves: by shrinking the provisional solution obtained in the tangent space back onto the Riemannian complex circular manifold, a feasible solution can be obtained, which can be expressed as: ； in Representing vectors Modulo by element This indicates that the Hadamard element is divided. By separating the real and imaginary parts, the feasible solution on the Riemannian complex circular manifold can be rewritten as: ； in ; Step 1.4 specifically involves: using the search step size as a trainable parameter of the network, and adaptively adjusting the search step size through deep learning; Step 2.1 specifically involves: The soft quantization function can be expressed as: ； The output of this function is ,in The amplitude represents the quantized phase value. This represents the degree to which the sum of the shifted hyperbolic tangents approximates the non-differentiable hardquantized function. The larger the value, the closer it is to the hard quantization function. This represents a quantization threshold that can be adaptively adjusted through deep learning. Step 2.2 specifically involves: Discrete waveforms can be obtained through soft quantization. Then the loss function of the optimized model can be rewritten as: ； in ; Step 2.3 specifically involves: using the Adam optimizer to optimize the loss function and obtaining the final optimization result after training. ; Step 2.4 specifically involves: optimizing the continuous waveform. Hard quantization is performed to obtain multiphase waveforms, where , .