Single-bit single-snapshot signal direction-of-arrival estimation method based on Hankel matrix decomposition

Abstract

The invention relates to the technical field of signal processing, in particular to a single-bit single-snapshot signal direction of arrival estimation method based on Hankel matrix decomposition, and the method comprises the steps: obtaining a received single-snapshot sampling signal and a corresponding single-bit quantized signal; constructing an initial DOA estimation model based on the symbol consistency constraint between the single-snapshot sampling signal and the single-bit quantized signal and the Hankel low-rank constraint of the single-snapshot sampling signal; optimizing the initial DOA estimation model by utilizing a Hankel matrix decomposition and function smoothing method to obtain an optimized DOA estimation model; solving the optimized DOA estimation model by using a momentum gradient descent algorithm to obtain a reconstructed original signal; and the reconstructed original signal is processed by using a single-fast-beat subspace method, and finally the estimated value of the direction of arrival of each signal source is obtained. According to the method, the precision, efficiency and robustness of direction of arrival estimation are improved.

Description

Technical Field

[0001] The embodiments of this application relate to the field of signal processing technology, and in particular to a method for estimating the direction of arrival of a single-bit, single-shot signal based on Hankel matrix decomposition. Background Technology

[0002] Array signal processing is an important branch of modern signal processing technology, with wide applications in radar detection, wireless communication, underwater sonar, and other fields. Several guiding documents have explicitly stated the need to quickly overcome the key technological bottlenecks in array signal processing to promote the innovative development of information sensing technologies.

[0003] Among the many tasks in array signal processing, Direction of Arrival (DOA) estimation is one of the core problems. Its goal is to estimate the incident direction of a target based on the signal received by the sensor array.

[0004] Most current DOA estimation methods rely on multi-snap sampling and high-bit-to-digital converters. Multi-snap sampling requires covariance matrix estimation of signals from multiple time points and multiple frames, which has insufficient real-time performance in transient target detection and high-speed motion scenarios. High-bit-to-digital converters, on the other hand, have problems with hardware complexity and high power consumption, making them unsuitable for low-power or distributed sensing systems.

[0005] Single-bit sampling technology retains only the sign information (positive or negative) of the signal, which greatly reduces hardware complexity and data storage requirements. However, current single-bit single-snapshot DOA estimation methods have the following shortcomings.

[0006] First, relying on gridded spectral compression sensing results in grid mismatch error and relatively low estimation accuracy.

[0007] Second, the optimization model is often non-convex and non-smooth, which leads to slow convergence speed of related algorithms and makes them prone to getting trapped in local optima.

[0008] Therefore, there is an urgent need in this field for a DOA estimation method that can maintain high accuracy and reduce computational complexity under single-bit single-snapshot sampling conditions. Summary of the Invention

[0009] To address the aforementioned technical issues, embodiments of this application propose a single-bit, single-snapshot signal direction-of-arrival (DOA) estimation method based on Hankel matrix decomposition. This method employs a single-bit sampling approach, effectively reducing hardware complexity and power consumption. It perfectly adapts to single-snapshot observation conditions, improves the accuracy and robustness of DOA estimation, avoids getting trapped in local optima, accelerates convergence, and enhances the efficiency of DOA estimation.

[0010] To achieve the above objectives, embodiments of this application propose a method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix factorization. The method includes the following steps: acquiring a single-snapshot sampled signal received by a vehicle-mounted millimeter-wave radar array, and a single-bit quantized signal corresponding to the single-snapshot sampled signal; constructing an initial DOA estimation model based on the sign consistency constraint between the single-snapshot sampled signal and the single-bit quantized signal, and the Hankel low-rank constraint of the single-snapshot sampled signal; optimizing the initial DOA estimation model using Hankel matrix factorization and function smoothing methods to obtain an optimized DOA estimation model; solving the optimized DOA estimation model using the momentum gradient descent algorithm to reconstruct the original signal, obtaining the reconstructed original signal; and processing the reconstructed original signal using the single-snapshot subspace method to finally obtain the estimated DOA values ​​for each signal source.

[0011] To achieve the above objectives, embodiments of this application also propose a single-bit single-snapshot signal direction-of-arrival (DOA) estimation system based on Hankel matrix factorization. The system includes: an acquisition module for acquiring a single-snapshot sampled signal received by a vehicle-mounted millimeter-wave radar array, and a single-bit quantized signal corresponding to the single-snapshot sampled signal; a construction module for constructing an initial DOA estimation model based on the sign consistency constraint between the single-snapshot sampled signal and the single-bit quantized signal, and the Hankel low-rank constraint of the single-snapshot sampled signal; an optimization module for optimizing the initial DOA estimation model using Hankel matrix factorization and function smoothing methods to obtain an optimized DOA estimation model; an original signal reconstruction module for solving the optimized DOA estimation model using the momentum gradient descent algorithm to reconstruct the original signal; and an estimation execution module for processing the reconstructed original signal using a single-snapshot subspace method to finally obtain the estimated DOA values ​​for each signal source.

[0012] To achieve the above objectives, embodiments of this application also propose an electronic device, including a processor and a memory, wherein the memory stores instructions executable by the processor, and the processor is configured to execute the instructions such that the electronic device can implement the single-bit single-snapshot signal direction-of-arrival estimation method based on Hankel matrix decomposition as described above.

[0013] To achieve the above objectives, embodiments of this application also propose a computer-readable storage medium storing a computer program that, when executed by a processor, enables the implementation of a single-bit, single-snapshot signal direction-of-arrival estimation method based on Hankel matrix decomposition as described above.

[0014] The embodiments of this application propose a method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition, which brings the following beneficial effects.

[0015] First, it reduces hardware complexity and power consumption. This application uses a single-bit sampling method, which only retains the symbol information of the signal to complete the processing, avoiding dependence on high-precision analog-to-digital converters (ADCs), thereby significantly reducing hardware costs and system power consumption.

[0016] Second, it adapts to single-shot observation conditions. This application fully exploits the structural characteristics of single-shot signals by constructing a Hankel matrix and introducing low-rank constraints, effectively solving the problem that traditional methods struggle to achieve stable direction-of-arrival estimation under single-shot conditions.

[0017] Third, it improves the accuracy and robustness of direction-of-arrival estimation. This application introduces a sign consistency constraint in the model construction and combines it with Hankel matrix decomposition and function smoothing methods for optimization, which can ensure the consistency between the reconstructed signal and the observed signal, thus maintaining high estimation accuracy and robustness even in low signal-to-noise ratio environments.

[0018] Fourth, it improves computational efficiency and facilitates real-time processing. This application uses the momentum gradient descent algorithm to solve the optimization model, which can accelerate the convergence speed, avoid getting trapped in local optima, and has lower computational complexity than traditional convex optimization methods, making it more suitable for real-time signal processing scenarios.

[0019] Optionally, the vehicle-mounted millimeter-wave radar array is a uniform linear array, consisting of a total of Composed of array elements, The integer is greater than 1, and the element spacing is... The single-shot sampling signal received by the vehicle-mounted millimeter-wave radar array This can be expressed by the formula: ; ; ; in, Represents the noise vector. , The dimension is The vector space, upper right subscript This indicates the transpose operation. The first part represents the vehicle-mounted millimeter-wave radar array. The signal received by each array element This represents spectral sparsity, i.e., the number of signal sources. Indicates the first The amplitude of the echo from each signal source, Indicates the wavelength of the echo. Indicates the first The direction of arrival of the signal source, i.e., the direction of arrival of the signal source. The incident direction of each signal source; Let the sparse signal of a single snapshot spectrum be denoted as , = ,but based on Represented as: ; based on , get and The corresponding single-bit quantized signal , , This can be expressed by the formula: ; in, Indicates taking the real part, This indicates taking the imaginary part. This indicates that the sign is taken element by element.

[0020] Optionally, the sign consistency constraint between the single-shot sampled signal and the single-bit quantized signal is expressed by the formula: ; in, express conjugate, This represents the dot product operation; make The operator representing the dimension increase of the Hankel matrix. Used to Upgrade to , This represents the dimension of the vector space after the dimension increase. The Hankel low-rank constraint of a single snapshot sampled signal is expressed by the formula: ; in, express The upgraded Hankel matrix, Represents the first of the Hankel matrix OK, Represents the first of the Hankel matrix List; Based on the symbol consistency constraint between the single-snapshot sampled signal and the single-bit quantized signal, and the Hankel low-rank constraint of the single-snapshot sampled signal, an initial DOA estimation model is constructed, including: By utilizing the sign consistency constraint between the single-shot sampled signal and the single-bit quantized signal, the signal to be reconstructed... symbols and To maintain sign consistency, the Hankel low-rank constraint of the single-shot sampled signal is utilized. rank and The rank remains consistent; based on The initial DOA estimation model is constructed and expressed as follows: ; in, Indicates one side Norm, superscript Indicates taking Power of 1 This means keeping elements with negative absolute values ​​and setting elements with positive absolute values ​​to zero. For positive integers, when dealing with sparse noise including impulse noise, take When faced with dense noise, including white noise, take , express Norm, with a superscript 2 indicating that it is squared.

[0021] Optionally, the initial DOA estimation model is optimized using Hankel matrix factorization and function smoothing methods to obtain an optimized DOA estimation model, including: Using Hankel matrix decomposition Decompose, Decomposed into upper right corner mark This indicates the operation of taking the conjugate matrix. and All are iteration variables. , ; To ensure Having a Hankel low-rank structure, add operator constraints, which are expressed as follows: ; ; in, Represents the unit operator. Represents a linear operator, express The inverse operator of express The adjoint operator; Based on operator constraints, the initial DOA estimation model is transformed into an intermediate DOA estimation model, which is expressed as follows: ; Use function smoothing methods to Smooth to For variables , satisfy: ; in, For smoothing parameters, ; Based on the intermediate DOA estimation model, the Hankel low-rank constraint of the single-shot sampled signal is transformed into a penalty term, resulting in the optimized DOA estimation model, which is expressed as: ; in, For penalty parameters, , It indicates an identity relationship.

[0022] Optionally, the momentum gradient descent algorithm is used to solve the optimized DOA estimation model to reconstruct the original signal, resulting in the reconstructed original signal, including: right and Perform normalized spectral initialization to obtain the initialized spectrum. and ; A momentum gradient descent algorithm is designed by combining momentum acceleration methods, and the momentum gradient descent algorithm is based on... and The optimized DOA estimation model was solved, and a total of [number] steps were performed. Round iteration, It is an integer greater than 1; based on The output results after each iteration are used to reconstruct the original signal, resulting in the reconstructed original signal.

[0023] Optionally, for and Perform normalized spectral initialization to obtain the initialized spectrum. and ,include: Using the following formula, Upgraded Hankel matrix Perform truncated singular value decomposition: ; in, express The rank approximation, , , ; Based on the following formula, , , right and Perform normalized spectral initialization to obtain the initialized spectrum. and : ; ; in, This represents the Frobenius norm normalization operator; A momentum gradient descent algorithm is designed by combining momentum acceleration methods, and the momentum gradient descent algorithm is based on... and The optimized DOA estimation model is solved using the following formula: ; ; ; ; in, Represents the momentum parameter. Indicates the step size. Indicates the first Round iteration, and They represent the methods to obtain... gradient in direction and its calculation Gradient in direction; based on Output results after round iteration and Reconstruct the original signal to obtain the reconstructed original signal. , This can be expressed by the formula: .

[0024] Optionally, set ; when At that time, the following formula is used to... and Update: ; ; when At that time, the following formula is used to... and Update: ; . Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies of this application will be briefly introduced below. Obviously, the following drawings are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The drawings described herein are only used to explain this application and are not intended to limit this application.

[0026] Figure 1 This is a flowchart of a method for estimating the direction of arrival of a single-bit, single-snapshot signal based on Hankel matrix decomposition, provided in one embodiment of this application; Figure 2 This is a schematic diagram of a vehicle-mounted millimeter-wave radar array receiving signals according to an embodiment of this application; Figure 3 This is provided by one embodiment of the present application, with different smoothing parameters. In this case, and A diagram illustrating the comparison results; Figure 4 This is one embodiment provided in this application; different algorithms are available in... and A schematic diagram illustrating the relationship between success rate and signal-to-noise ratio under certain conditions; Figure 5 This is one embodiment provided in this application; different algorithms are available in... and A schematic diagram illustrating the relationship between root mean square error (RMSE) and signal-to-noise ratio under certain conditions; Figure 6 This is a schematic diagram of the structure of a single-bit single-snapshot signal direction-of-arrival estimation system based on Hankel matrix decomposition, provided in another embodiment of this application; Figure 7 This is a schematic diagram of the structure of an electronic device provided in another embodiment of this application. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. Those skilled in the art will understand that many technical details have been presented in the embodiments of this application to facilitate better understanding. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of this application. The following embodiments can be combined with and referenced by each other without contradiction.

[0028] One embodiment of this application proposes a direction-of-arrival (DOA) estimation method for single-bit, single-snapshot signals based on Hankel matrix decomposition, applied to a server. The implementation details of this embodiment's DOA estimation method are described below. These details are provided for ease of understanding and are not essential for implementing this solution.

[0029] The specific process of the single-bit, single-snapshot signal direction-of-arrival estimation method based on Hankel matrix decomposition proposed in this embodiment can be described as follows: Figure 1 As shown, it includes: Step 11: Obtain the single-shot sampling signal received by the vehicle-mounted millimeter-wave radar array, and the single-bit quantization signal corresponding to the single-shot sampling signal.

[0030] In its specific implementation, the direction-of-arrival estimation method proposed in this embodiment is designed for vehicle-mounted millimeter-wave radar arrays. Therefore, when performing direction-of-arrival estimation, it is first necessary to obtain the single-snapshot sampling signal received by the vehicle-mounted millimeter-wave radar array, as well as the single-bit quantization signal corresponding to the single-snapshot sampling signal.

[0031] In one example, such as Figure 2 As shown, in the onboard millimeter-wave radar system of intelligent driving vehicles, the vehicle needs to detect and locate surrounding targets (such as pedestrians, vehicles, or obstacles) in real time in complex road environments. By estimating the incident direction of the target's echo signal, the target's specific location in space can be further calculated, thus providing key support for environmental perception and path decision-making.

[0032] The vehicle-mounted millimeter-wave radar array is a uniform linear array (ULA), consisting of a total of [number of components]. Composed of array elements, The integer is greater than 1, and the element spacing is... The single-shot sampling signal received by the vehicle-mounted millimeter-wave radar array This can be expressed by the formula: ; ; ; in, Represents the noise vector. , The dimension is The vector space, upper right subscript This indicates the transpose operation. The first part represents the vehicle-mounted millimeter-wave radar array. The signal received by each array element This represents spectral sparsity, i.e., the number of signal sources. Indicates the first The amplitude of the echo from each signal source, Indicates the wavelength of the echo. Indicates the first The direction of arrival of the signal source, i.e., the direction of arrival of the signal source. The incident direction of each signal source, .

[0033] To reduce the requirements for power consumption, cost, and size of in-vehicle equipment, this embodiment chooses to implement single-bit sampling using a comparator, denoted as the single-shot spectral sparse signal. , = ,but based on Represented as ,based on You can get the same as The corresponding single-bit quantized signal , , This can be expressed by the formula: ; in, Indicates taking the real part, This indicates taking the imaginary part. This indicates that the sign is taken element by element.

[0034] For variables , The specific meaning can be expressed as: .

[0035] based on It can be determined that the target of the direction-of-arrival estimation in this embodiment is to utilize the ULA received... Estimate the direction of arrival of each signal source .

[0036] Step 12: Based on the symbol consistency constraint between the single-snapshot sampled signal and the single-bit quantized signal and the Hankel low-rank constraint of the single-snapshot sampled signal, construct the initial DOA estimation model.

[0037] In the specific implementation, after obtaining the single-snapshot sampling signal and its corresponding single-bit quantized signal, an initial DOA estimation model can be constructed based on the symbol consistency constraint between the single-snapshot sampling signal and the single-bit quantized signal and the Hankel low-rank constraint of the single-snapshot sampling signal.

[0038] First, we introduce the sign consistency between single-shot sampled signals and single-bit quantized signals, also known as the sign consistency constraint. When the signal-to-noise ratio is relatively high, noise... right The symbol has less influence, which makes it and The symbols are basically the same. Therefore, using and From the sign consistency, we can obtain the sign consistency constraint as follows: ; in, express conjugate, This indicates the dot product operation.

[0039] Next, we will introduce the Hankel low-rank constraint for single-shot sampled signals, i.e., the Hankel low-rank constraint. Let... The operator representing the dimension increase of the Hankel matrix. Used to Upgrade to , This represents the dimension of the vector space after the dimension increase. The Hankel low-rank constraint of a single snapshot sampled signal is expressed by the formula: ; in, express The upgraded Hankel matrix, Represents the first of the Hankel matrix OK, Represents the first of the Hankel matrix List.

[0040] Using symbolic consistency constraints, the signal to be reconstructed is made symbols and The signs of elements should be kept as consistent as possible, i.e., the number of elements with opposite signs should be minimized. This can be achieved using the Hankel low-rank constraint. rank and The rank remains consistent, that is, it ensures The rank is also , .

[0041] based on Based on the above two constraints, the initial DOA estimation model can be constructed as follows: ; in, Indicates one side Norm, superscript Indicates taking Power of 1 This means keeping elements with negative absolute values ​​and setting elements with positive absolute values ​​to zero. For positive integers, when dealing with sparse noise including impulse noise, take When faced with dense noise, including white noise, take , express Norm, with a superscript 2 indicating the square. The introduction of this is intended to limit The size of the signal can be adjusted to effectively control the range of the reconstructed signal.

[0042] Understandably, the initial DOA estimation model does not require complete sign consistency, thus it has good fault tolerance for sign flipping problems caused by noisy environments.

[0043] Step 13: Optimize the initial DOA estimation model using Hankel matrix decomposition and function smoothing methods to obtain the optimized DOA estimation model.

[0044] In the specific implementation, after the initial DOA estimation model is constructed, it is necessary to use Hankel matrix decomposition and function smoothing methods to optimize the initial DOA estimation model, thereby obtaining the optimized DOA estimation model.

[0045] The initial DOA estimation model is difficult to solve in polynomial time, so the Hankel low-rank constraint needs to be replaced with an equivalent form. To ensure the low-rank structure, this embodiment chooses to use Hankel matrix decomposition to... Decompose, Decomposed into , The top right corner mark This indicates the operation of taking the conjugate matrix. and All are iteration variables. , Through Hankel matrix decomposition, the number of parameters decreases from... Successfully descended to This effectively reduces the scale of parameter updates, thereby improving computational efficiency.

[0046] To ensure Having a Hankel low-rank structure, this embodiment adds the following operator constraints: ; ; in, Represents the unit operator. Represents a linear operator, express The inverse operator of express The adjoint operator.

[0047] For variables , satisfy , express The 1st dimension of the matrix The number of diagonal elements. .

[0048] Based on operator constraints, the initial DOA estimation model can be transformed into an intermediate DOA estimation model, which is expressed as follows: .

[0049] However, in the intermediate DOA estimation model, Since the operator is non-smooth, solving the intermediate DOA estimation model is a non-smooth and non-convex optimization problem. The lack of smoothness means that the solution algorithm for the intermediate DOA estimation model cannot be designed using momentum acceleration techniques, which seriously affects the convergence performance of the algorithm.

[0050] To address this issue, this embodiment uses a function smoothing method. Smooth to For variables , satisfy, , This demonstrates the Rectified Linear Unit (ReLU), a commonly used component in deep learning, which utilizes ReLU's smoothing operator. The smoothing design of the operator uses the negative function of the SquarePlus function. To smooth it out.

[0051] For variables , satisfy: ; in, For smoothing parameters, ,when hour, Degenerate into ,like Figure 3 As shown, Approaching from below , The smaller the value, and The smaller the gap, the better.

[0052] Based on the intermediate DOA estimation model, the Hankel low-rank constraint is transformed into a penalty term to obtain the optimized DOA estimation model, which is expressed as:

[0053] in, For penalty parameters, , It indicates an identity relationship.

[0054] Step 14: Solve the optimized DOA estimation model using the momentum gradient descent algorithm to reconstruct the original signal and obtain the reconstructed original signal.

[0055] In the specific implementation, after obtaining the optimized DOA estimation model, a non-convex optimization algorithm can be designed. The momentum gradient descent algorithm is used to solve the optimized DOA estimation model (iterative update) to reconstruct the original signal and obtain the reconstructed original signal.

[0056] During the reconstruction process, it is first necessary to use traditional spectral initialization methods to... and Perform normalized spectral initialization to obtain the initialized spectrum. and Subsequently, a momentum gradient descent algorithm was designed by combining the momentum acceleration method, and the momentum gradient descent algorithm was used based on... and The optimized DOA estimation model was solved, and a total of [number] steps were performed. Round iteration ( (Integers greater than 1). Based on... The output results after each iteration are used to reconstruct the original signal, resulting in the reconstructed original signal.

[0057] In progress and During the spectral initialization process, the following formula is first used to initialize the spectrum. Upgraded Hankel matrix Perform truncated singular value decomposition: ; in, express The rank approximation, , , .

[0058] Then, based on the following formula, , , right and Perform normalized spectral initialization to obtain the initialized spectrum. and : ; ; in, This represents the Frobenius norm normalization operator.

[0059] After completing the and After spectral initialization, the momentum gradient descent algorithm can be designed using the momentum acceleration method. The following formula utilizes the momentum gradient descent algorithm based on... and Solve the optimized DOA estimation model: ; ; ; ; in, Indicates the momentum parameter. Indicates the step size. Indicates the first Round iteration, and They represent the methods to obtain... gradient in direction and its calculation Gradient in the direction.

[0060] Finally, based on Output results after round iteration and Reconstruct the original signal to obtain the reconstructed original signal. , This can be expressed by the formula: .

[0061] In one example, let .

[0062] when At that time, the following formula is used to... and Update: ; .

[0063] when At that time, the following formula is used to... and Update: ; .

[0064] Step 15: The reconstructed original signal is processed using the single-fast tempo spatial method to obtain the estimated values ​​of the direction of arrival of each signal source.

[0065] In practical implementation, after obtaining the reconstructed original signal, the single-fast tempo space method can be used to process the reconstructed original signal to finally obtain the estimated values ​​of the direction of arrival of each signal source. .

[0066] The proposed method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition in this embodiment offers the following advantages.

[0067] First, it reduces hardware complexity and power consumption. This embodiment uses a single-bit sampling method, which only retains the symbol information of the signal to complete the processing, avoiding dependence on high-precision analog-to-digital converters (ADCs), thereby significantly reducing hardware costs and system power consumption.

[0068] Second, it adapts to single-shot observation conditions. This embodiment fully exploits the structural characteristics of single-shot signals by constructing a Hankel matrix and introducing low-rank constraints, effectively solving the problem that traditional methods struggle to achieve stable direction-of-arrival estimation under single-shot conditions.

[0069] Third, it improves the accuracy and robustness of direction-of-arrival estimation. This embodiment introduces a sign consistency constraint in model construction and combines it with Hankel matrix decomposition and function smoothing methods for optimization, which can ensure the consistency between the reconstructed signal and the observed signal, thus maintaining high estimation accuracy and robustness even in low signal-to-noise ratio environments.

[0070] Fourth, it improves computational efficiency and facilitates real-time processing. This embodiment uses the momentum gradient descent algorithm to solve the optimization model, which can accelerate the convergence speed, avoid getting trapped in local optima, and has lower computational complexity than traditional convex optimization methods, making it more suitable for real-time signal processing scenarios.

[0071] The steps described above are for clarity only. In implementation, they can be combined into one step, or some steps can be broken down into multiple steps, as long as they involve the same logical relationship, they are all within the scope of protection of this application. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the scope of protection of this application.

[0072] In one embodiment, to verify the effectiveness of the proposed method for estimating the direction of arrival (DOA) of a single-bit single-shot signal based on Hankel matrix decomposition (hereinafter referred to as the method or Acc-OSCAR), we conducted a corresponding simulation experiment.

[0073] This experiment demonstrates the proposed method (Acc-OSCAR-) through numerical simulation. and Acc-OSCAR- Performance of ) in single-bit direction-of-arrival estimation, and comparison with the state-of-the-art algorithm CBIHT- CBIHT- A comparison was made between iCBIHT and 1-bit-ANM. Consideration was given to... Direction of arrival estimation for a uniform linear array of sensors, setting... , The vector consisting of the direction of arrival and the direction of arrival .

[0074] Figure 4 The success rates of this method and the comparison algorithm are shown. Figure 4 As can be seen from this, this method has the best success rate compared to 1-bit-ANM. The success rate represents... The RMSE of the sub-Monte Carlo algorithm is less than the threshold. The frequency.

[0075] Figure 5 This demonstrates the RMSE of our method and the comparison algorithm under successful conditions, from Figure 5 It can be seen that this method has better RMSE than 1bit-ANM, especially when the signal-to-noise ratio is greater than 20dB.

[0076] Another embodiment of this application proposes a single-bit single-snapshot signal direction-of-arrival estimation system based on Hankel matrix decomposition. The details of the single-bit single-snapshot signal direction-of-arrival estimation system based on Hankel matrix decomposition proposed in this embodiment are described in detail below. The following content is only for the convenience of understanding and is not necessary for implementing this example.

[0077] Figure 6 This is a schematic diagram of the structure of a single-bit single-shot signal direction-of-arrival estimation system based on Hankel matrix decomposition proposed in this embodiment, including: acquisition module 21, construction module 22, optimization module 23, original signal reconstruction module 24, and estimation execution module 25.

[0078] The acquisition module 21 is used to acquire the single-shot sampling signal received by the vehicle-mounted millimeter-wave radar array, as well as the single-bit quantization signal corresponding to the single-shot sampling signal.

[0079] Module 22 is used to construct an initial DOA estimation model based on the symbol consistency constraint between the single-snapshot sampled signal and the single-bit quantized signal and the Hankel low-rank constraint of the single-snapshot sampled signal.

[0080] Optimization module 23 is used to optimize the initial DOA estimation model using Hankel matrix decomposition and function smoothing methods to obtain the optimized DOA estimation model.

[0081] The original signal reconstruction module 24 is used to solve the optimized DOA estimation model using the momentum gradient descent algorithm to reconstruct the original signal and obtain the reconstructed original signal.

[0082] The estimation execution module 25 is used to process the reconstructed original signal using a single-beat spatial method to finally obtain the estimated values ​​of the direction of arrival of each signal source.

[0083] It is not difficult to see that this embodiment is a system embodiment corresponding to the above method embodiments, and this embodiment can be implemented in conjunction with the above method embodiments. The relevant technical details and technical effects mentioned in the above method embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above method embodiments.

[0084] It is worth mentioning that all modules and units involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed in this application; however, this does not mean that other units do not exist in this embodiment.

[0085] Another embodiment of this application provides an electronic device, such as Figure 7 As shown, it includes a processor 31 and a memory 32. The memory 32 stores instructions that the processor 31 can execute. When the processor 31 is configured to execute the instructions, the electronic device can implement a single-bit single-shot signal direction-of-arrival estimation method based on Hankel matrix decomposition as described in the above method embodiment.

[0086] The memory and processor are connected via a bus, which includes any number of interconnecting buses and bridges, connecting various circuits of one or more processors and the memory. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0087] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0088] Another embodiment of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, can implement a single-bit single-snapshot signal direction-of-arrival estimation method based on Hankel matrix decomposition as described in the above method embodiments.

[0089] That is, those skilled in the art will understand that all or part of the steps in the above method embodiments can be implemented by a program instructing related hardware. The program is stored in a storage medium and includes several instructions to cause a device (such as a microcontroller, chip, etc.) or processor to execute all or part of the steps of the method described in the method embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory, random access memory, magnetic disks, or optical disks.

[0090] Those skilled in the art will understand that the above embodiments are specific implementations of this application, and in practical applications, various changes can be made in form and detail without departing from the spirit and scope of this application. For those skilled in the art, several improvements and modifications can be made without departing from the principles of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition, characterized in that, The method includes: Acquire the single-snapshot sampling signal received by the vehicle-mounted millimeter-wave radar array, and the single-bit quantized signal corresponding to the single-snapshot sampling signal; An initial DOA estimation model is constructed based on the symbol consistency constraint between the single-snapshot sampled signal and the single-bit quantized signal and the Hankel low-rank constraint of the single-snapshot sampled signal. The initial DOA estimation model was optimized using Hankel matrix decomposition and function smoothing methods to obtain the optimized DOA estimation model. The momentum gradient descent algorithm is used to solve the optimized DOA estimation model to reconstruct the original signal and obtain the reconstructed original signal. The reconstructed original signal is processed using the single-fast tempo spatial method to obtain the estimated values ​​of the direction of arrival of each signal source.

2. The method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition according to claim 1, characterized in that, The vehicle-mounted millimeter-wave radar array is a uniform linear array, consisting of a total of Composed of array elements, The integer is greater than 1, and the element spacing is... The single-shot sampling signal received by the vehicle-mounted millimeter-wave radar array This can be expressed by the formula: ； ； ； in, Represents the noise vector. , Indicates dimension as The vector space, upper right subscript This indicates the transpose operation. The first part represents the vehicle-mounted millimeter-wave radar array. The signal received by each array element This represents spectral sparsity, i.e., the number of signal sources. Indicates the first The amplitude of the echo from each signal source, Indicates the wavelength of the echo. Indicates the first The direction of arrival of the signal source, i.e., the direction of arrival of the signal source. The incident direction of each signal source; Let the sparse signal of a single snapshot spectrum be... , = ,but based on Represented as: ； based on , get and The corresponding single-bit quantized signal , , This can be expressed by the formula: ； in, Indicates taking the real part, This indicates taking the imaginary part. This indicates that the sign is taken element by element.

3. The method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition according to claim 2, characterized in that, The sign consistency constraint between the single-shot sampled signal and the single-bit quantized signal is expressed by the formula: ； in, express conjugate, This represents the dot product operation; make The operator representing the dimension increase of the Hankel matrix. Used to Ascend to , This represents the dimension of the vector space after the dimension increase. The Hankel low-rank constraint of a single snapshot sampled signal is expressed by the formula: ； in, express The upgraded Hankel matrix, Represents the first of the Hankel matrix OK, Represents the first of the Hankel matrix List; Based on the symbol consistency constraint between the single-snapshot sampled signal and the single-bit quantized signal, and the Hankel low-rank constraint of the single-snapshot sampled signal, an initial DOA estimation model is constructed, including: By utilizing the sign consistency constraint between the single-shot sampled signal and the single-bit quantized signal, the signal to be reconstructed... symbols and To maintain sign consistency, the Hankel low-rank constraint of the single-shot sampled signal is utilized. Upgraded Hankel matrix rank and The rank remains consistent; based on The initial DOA estimation model is constructed and expressed as follows: ； in, Indicates one side Norm, superscript Indicates taking Power of 1 This means keeping elements with negative absolute values ​​and setting elements with positive absolute values ​​to zero. For positive integers, when dealing with sparse noise including impulse noise, take When faced with dense noise, including white noise, take , express Norm, with a superscript 2 indicating that it is squared.

4. The method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition according to claim 3, characterized in that, The initial DOA estimation model is optimized using Hankel matrix factorization and function smoothing methods to obtain the optimized DOA estimation model, including: Using Hankel matrix decomposition Decompose, Decomposed into upper right corner mark This indicates the conjugate transpose operation. and All are iteration variables. , ; To ensure Having a Hankel low-rank structure, add operator constraints, which are expressed as follows: ； ； in, Represents the unit operator. Represents a linear operator, express The inverse operator of express The adjoint operator; Based on operator constraints, the initial DOA estimation model is transformed into an intermediate DOA estimation model, which is expressed as follows: ； Use function smoothing methods to Smooth to For variables , satisfy: ； in, For smoothing parameters, ; Based on the intermediate DOA estimation model, the Hankel low-rank constraint of the single-shot sampled signal is transformed into a penalty term, resulting in the optimized DOA estimation model, which is expressed as: ； in, For penalty parameters, , It indicates an identity relationship.

5. The method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition according to claim 4, characterized in that, The momentum gradient descent algorithm is used to solve the optimized DOA estimation model to reconstruct the original signal, resulting in the reconstructed original signal, including: right and Perform normalized spectral initialization to obtain the initialized spectrum. and ; A momentum gradient descent algorithm is designed by combining momentum acceleration methods, and the momentum gradient descent algorithm is based on... and The optimized DOA estimation model was solved, and a total of [number] steps were performed. Round iteration, It is an integer greater than 1; based on The output results after each iteration are used to reconstruct the original signal, resulting in the reconstructed original signal.

6. The method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition according to claim 5, characterized in that, right and Perform normalized spectral initialization to obtain the initialized spectrum. and ,include: Using the following formula, Upgraded Hankel matrix Perform truncated singular value decomposition: ； in, express The rank approximation, , , ; Based on the following formula, , , right and Perform normalized spectral initialization to obtain the initialized spectrum. and : ； ； in, This represents the Frobenius norm normalization operator; A momentum gradient descent algorithm is designed by combining momentum acceleration methods, and the momentum gradient descent algorithm is based on... and The optimized DOA estimation model is solved using the following formula: ； ； ； ； in, Represents the momentum parameter. Indicates step size, Indicates the first Round iteration, and They represent the methods to obtain... gradient in direction and its calculation Gradient in direction; based on Output results after round iteration and Reconstruct the original signal to obtain the reconstructed original signal. , This can be expressed by the formula: 。 7. The method for estimating the direction of arrival (DOA) of a single-bit, single-snapshot signal based on Hankel matrix decomposition according to claim 6, characterized in that, set up ; when At that time, the following formula is used to... and Update: ； ； when At that time, the following formula is used to... and Update: ； 。 8. A direction-of-arrival estimation system for a single-bit, single-snapshot signal based on Hankel matrix decomposition, characterized in that, The system includes: The acquisition module is used to acquire the single-snapshot sampling signal received by the vehicle-mounted millimeter-wave radar array, as well as the single-bit quantized signal corresponding to the single-snapshot sampling signal; The building module is used to construct an initial DOA estimation model based on the symbol consistency constraint between the single-snapshot sampled signal and the single-bit quantized signal and the Hankel low-rank constraint of the single-snapshot sampled signal; The optimization module is used to optimize the initial DOA estimation model using Hankel matrix decomposition and function smoothing methods to obtain the optimized DOA estimation model. The original signal reconstruction module is used to solve the optimized DOA estimation model using the momentum gradient descent algorithm to reconstruct the original signal and obtain the reconstructed original signal. The estimation execution module is used to process the reconstructed original signal using a single-beat spatial method, and finally obtain the estimated values ​​of the direction of arrival of each signal source.

9. An electronic device, characterized in that, include: The processor and memory, wherein the memory stores instructions executable by the processor, and the processor is configured to, when executing the instructions, enable the electronic device to implement a single-bit single-snapshot signal direction-of-arrival estimation method based on Hankel matrix decomposition as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it can implement a method for estimating the direction of arrival of a single-bit, single-shot signal based on Hankel matrix decomposition as described in any one of claims 1 to 7.

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