A beam angle prediction method based on fusion of neural network and Kalman filter

Abstract

The application discloses a beam angle prediction method based on neural network and Kalman filtering fusion, and belongs to the technical field of millimeter wave communication.The method adopts a single-layer neural network without an activation function to learn the behavior of LSTM, extracts a weight matrix of the single-layer neural network as a state transition matrix of a Kalman filtering algorithm, and performs beam tracking by executing the Kalman filtering algorithm.The application fuses the strong robustness of the Kalman filtering algorithm on the basis of accurate prediction of the beam tracking angle; and since the LSTM has strong learning ability, dense observation of a communication target is not needed, the observation interval can be artificially set according to cost, the prediction cost is greatly reduced, and the performance of the beam tracking system is improved.

Description

Technical Field

[0001] This invention belongs to the field of millimeter-wave communication technology, and specifically relates to a beam angle prediction method based on the fusion of neural networks and Kalman filtering. Background Technology

[0002] Fifth-generation (5G) and beyond-5G (B5G) technologies have already attracted significant attention in the communications field. According to the vision for future B5G communication systems, their throughput will be approximately a thousand times faster than existing systems. Simultaneously, latency is expected to be less than milliseconds. Therefore, high-bandwidth and high-frequency communication systems are essential for the future. Numerous advanced technologies have been proposed to support these requirements, including millimeter wave (mmWave) and massive MIMO (Multiple-Input Multiple-Output) technologies. However, it is worth noting that millimeter wave signal transmission is subject to high path loss attenuation. Beamforming systems with high array gain are employed to overcome this high path loss. Therefore, a large number of antenna transmitters are deployed to form narrower beams. For this reason, continuous high-precision beam tracking is crucial for ensuring high-quality service.

[0003] Beam tracking is a challenging task due to the mobility of communication targets and the complex variations in the radio environment in real-world settings. To provide consistently high tracking accuracy, tracking errors should be minimized during communication. Therefore, existing major beam tracking techniques require additional overhead to achieve optimal beam alignment.

[0004] In light of this trend, in recent years, some scholars have applied Kalman filtering algorithms and pure neural networks to solve beam tracking problems. Beam tracking techniques based on previously estimated states have also attracted researchers' interest. Generally speaking, beam tracking using only Kalman filtering algorithms or neural networks typically has certain shortcomings in terms of the accuracy and robustness of angle prediction, respectively. For example, V.Va et al. proposed a low-complexity conditional beam tracking algorithm using an extended Kalman filter (EKF) in a mobile millimeter-wave communication system in their paper titled "Beam tracking for mobile millimeter-wave communication systems." However, simulation results from the paper show that the simple Kalman filtering algorithm leads to large accumulated errors in beam tracking AoA (Angle-of-Arrival) and AoD (Angle-of-Departure) estimation due to strong noise in low signal-to-noise ratio regions. Simply using neural networks for beam tracking prediction, for example, W. Jiang et al. proposed a predictor based on recurrent neural networks (RNNs) in their paper "Recurrent neural networks with long short-term memory for fading channel prediction". In their algorithm, past channel state information (CSI) is used as input, and the output includes the AoA and AoD for the next interval. The results of this paper show that RNNs are a potentially powerful tool in time series prediction. However, their results also show that beam tracking problems based on pure machine learning lack robustness to sudden changes in beam direction, i.e., beam path shifts. Summary of the Invention

[0005] This invention addresses the challenges of continuous and accurate tracking of narrow millimeter-wave beams, the high overhead of continuous observation, and the robustness or accuracy issues of existing beam tracking algorithms. It proposes a beam angle prediction method based on the fusion of neural networks and Kalman filtering. Unlike traditional beam tracking that relies solely on Kalman filtering or machine learning algorithms, this invention fully leverages the powerful learning capabilities of LSTM (Long Short-Term Memory) to accurately predict the angle information for the next moment by inputting changes in historical beam direction data. In this invention, a single-layer neural network (SLNN) without activation functions learns the behavior of the LSTM. The weight matrix of this SLNN is then extracted as the state transition matrix for the Kalman filtering algorithm, which is then executed for beam tracking. This invention achieves accurate beam tracking angle prediction while incorporating the strong robustness of the Kalman filtering algorithm. Furthermore, due to the powerful learning capabilities of LSTM, dense observation of the communication target is unnecessary; the observation interval can be manually set according to cost, significantly reducing prediction costs and improving the performance of the beam tracking system.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0007] A beam tracking angle prediction method based on the fusion of machine learning and Kalman filter information, characterized by the following steps:

[0008] Step 1: Set the initial time to k = 0, and obtain the initial angle [θ] through beamforming from time 0 to time m. l (0),…,θ l (m)], m∈[ξ,K]; where l is the number of paths in the actual environment, ξ is the minimum angle set when calculating acceleration, m is the initialization termination time, and K is the system termination time. Therefore, the angular velocity ω at time m is... l (m), angular acceleration at time m The derivative of acceleration The initial state vector x is obtained through difference calculation. l (m) is represented as:

[0009]

[0010] The uncertainty Σ(0|0) of the initial estimate in the Kalman filter algorithm is set to a random constant; the observation matrix C is set to an N×N identity matrix, where N is the number of antennas on the base station used for beam speed tracking.

[0011] Step 2: In practice, intensive observation operations can lead to significant time consumption. Therefore, performing observations at every time step will result in high overhead. When the time variable k is an integer multiple of τ, noisy observations will occur. As the observed variable z; when the time variable k is not an integer multiple of τ, the LSTM network f is used. N2 Output angle estimate As the observed variable z:

[0012]

[0013] Where τ is the set interval, and n is a positive integer.

[0014] Step 3: Convert the state vector estimated at time k-1 to the state vector estimated at time k-1. Input into a single-layer neural network (SLNN) f without an activation function N1 Generate the state vector from time k-1 to time k. At the initial moment, the single-layer neural network f N1 The input is the initial state vector x l (m). Extract the single-layer neural network f. N1 The weight matrix is ​​used as the state transition matrix F(k):

[0015]

[0016] Among them, w N1 The weights of the neural network are set by the user.

[0017] Step 4: Substitute the state transition matrix F(k) into formula (4) to calculate the covariance extrapolation:

[0018] Σ(k+1|k)=F(k)Σ(k|k)F(k) T +n(k) (4)

[0019] Where n(k) represents process noise.

[0020] Step 5: Substitute the observation matrix C and the calculation result of formula (4) into formula (5) to calculate the Kalman gain K(k):

[0021] K(k)=Σ(k|k-1)C H (CΣ(k|k-1)C H +R(k)) -1 (5)

[0022] Where R(k) is the measurement uncertainty set manually.

[0023] Step 6: Substitute the observed variable z into formula (6) to update the state vector at time k.

[0024]

[0025] Step 7: Update the uncertainty estimated at time k using formula (7):

[0026] Σ(k|k)=(IK(k)C)Σ(k|k-1)(IK(k)C) H +K(k)R(k)K(k) H (7)

[0027] Where I represents the identity matrix.

[0028] Step 8: Extract the state vector at time k. Angle estimates in And input into the LSTM network f N2 At the initial time, the LSTM network f N2 The input is the initial angle [θ] l (0),…,θ l [m]; The output is the angle estimate at time k+1.

[0029]

[0030] At the initial time, the LSTM network f N2 The input is the initial angle [θ] l (0),…,θ l (m)],w N2 These are the weight parameters of the neural network.

[0031] Step 9: Repeat steps 2 to 8 to obtain the predicted angle value of beam tracking at each cycle time.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] 1. This invention transforms the state transition equation into an equivalent data-driven problem. To enable the Kalman filter algorithm to obtain the appropriate state transition equation, this invention employs a single-layer neural network without activation functions to learn the behavior of the LSTM. Therefore, this single-layer neural network acts as the end-to-end learning process for the model embedded in the LSTM network.

[0034] 2. This invention combines the robustness of the Kalman filter algorithm with the predictive accuracy of machine learning. In practical applications, beam direction changes exhibit certain regularities in each specific scenario; therefore, learning from the historical changes in beam direction data to study these changes enables machine learning-based beam tracking algorithms to demonstrate high prediction accuracy. However, a current problem with machine learning-based beam tracking algorithms is that beam path changes can be random and abrupt at certain times, significantly weakening their robustness. On the other hand, Kalman filter-based beam tracking algorithms, due to their inherent characteristics, possess a strong ability to balance the predicted results obtained through algorithmic computation with directly acquired observations. This trade-off makes Kalman filter-based beam tracking algorithms more robust than purely machine learning-based beam tracking algorithms. Therefore, this invention inherits the advantages of both machine learning and Kalman filter algorithms in terms of accurate prediction and strong robustness. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the algorithm steps of the beam tracking angle prediction system based on LSTM and single-layer neural network machine learning and Kalman filter information fusion.

[0036] Figure 2 The working environment of the beam tracking angle prediction system based on LSTM and single-layer neural network machine learning and Kalman filter information fusion, which is an exemplary embodiment of the present invention.

[0037] Figure 3 This is a flowchart illustrating an exemplary embodiment of the present invention: a beam tracking angle prediction system based on LSTM and single-layer neural network machine learning and Kalman filter information fusion.

[0038] Figure 4 The mean square error (MSE) of the predicted angle, as shown in the exemplary embodiment of the present invention, varies with the signal-to-noise ratio (SNR) compared to other beam tracking methods. Detailed Implementation

[0039] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention. Figure 2The working environment of the beam angle prediction method based on the fusion of neural networks and Kalman filtering, as described in this invention, is presented. The static base station periodically observes the user-end mobile device using an exhaustive search method to obtain information including its angle, angular velocity, angular acceleration, and angular acceleration derivative. Between the intervals of two exhaustive search operations, the static base station executes the beam angle prediction method based on the fusion of neural networks and Kalman filtering of this invention to perform non-observational prediction of the user-end device's angle information. The user-end device can move freely within the operating range of the static base station under normal power conditions.

[0040] This embodiment presents a beam angle prediction method based on the fusion of neural networks and Kalman filtering, the flowchart of which is shown below. Figure 3 As shown.

[0041] This embodiment demonstrates beam tracking prediction in a campus environment, presenting a beam tracking angle prediction method based on the fusion of machine learning and Kalman filter information, including the following steps:

[0042] Step 1: Set the initial time to k = 0, and obtain the initial angle [θ] through beamforming from time 0 to time m. l (0),…,θ l (m)], m∈[ξ,K]; where l is the number of paths in the actual environment, l=1 in this embodiment; ξ is the minimum angle set when calculating acceleration, ξ=1 in this embodiment; m is the initialization termination time, m=4 in this embodiment; K is the system termination time, K=1000 in this embodiment. Therefore, the angular velocity ω at time m is... l (m), angular acceleration at time m The derivative of acceleration The initial state vector x is obtained through difference calculation. l (m) is represented as:

[0043]

[0044] The uncertainty Σ(0|0) of the initial estimate in the Kalman filter algorithm is set to a random constant, which is set to 1 in this embodiment; the observation matrix C is set to an identity matrix of dimension N×N, where N is the number of antennas on the base station used for beam speed tracking.

[0045] Step 2: In practice, intensive observation operations can lead to significant time consumption. Therefore, performing observations at every time step will result in high overhead. When the time variable k is an integer multiple of τ, noisy observations will occur. As the observed variable z; when the time variable k is not an integer multiple of τ, the LSTM network f is used. N2 Output angle estimate As the observed variable z:

[0046]

[0047] Where τ is the set interval, and in this embodiment, τ takes values ​​of 1, 2, 3, and 4 in the 4 simulation experiments respectively; n is a positive integer.

[0048] Step 3: Convert the state vector estimated at time k-1 to the state vector estimated at time k-1. Input into a single-layer neural network (SLNN) f without an activation function N1 Generate the state vector from time k-1 to time k. At the initial moment, the single-layer neural network f N1 The input is the initial state vector x l (m). Extract the single-layer neural network f. N1 The weight matrix is ​​used as the state transition matrix F(k):

[0049]

[0050] Among them, w N1 The weights of the neural network are set by the user.

[0051] Step 4: Substitute the state transition matrix F(k) into formula (4) to calculate the covariance extrapolation:

[0052] Σ(k|k-1)=F(k)Σ(k-1|k-1)F(k) T +n(k) (4)

[0053] Where n(k) represents process noise.

[0054] Step 5: Substitute the observation matrix C and the calculation result of formula (4) into formula (5) to calculate the Kalman gain K(k):

[0055] K(k)=Σ(k|k-1)C H (CΣ(k|k-1)C H +R(k)) -1 (5)

[0056] Where R(k) is the measurement uncertainty set manually.

[0057] Step 6: Substitute the observed variable z into formula (6) to update the state vector at time k.

[0058]

[0059] Step 7: Update the uncertainty estimated at time k using formula (7):

[0060] Σ(k|k)=(IK(k)C)Σ(k|k-1)(IK(k)C) H +K(k)R(k)K(k) H (7)

[0061] Where I represents the identity matrix.

[0062] Step 8: Extract the state vector at time k. Angle estimates in And input into the LSTM network f N2 At the initial time, the LSTM network f N2 The input is the initial angle [θ] l (0),…,θ l [m]; The output is the angle estimate at time k+1.

[0063]

[0064] At the initial time, the LSTM network f N2 The input is the initial angle [θ] l (0),…,θ l (m)],w N2 These are the weight parameters of the neural network.

[0065] Step 9: Repeat steps 2 to 8 to obtain the predicted angle value of beam tracking at each cycle time.

[0066] The performance curve of the mean square value of the predicted angle as a function of the signal-to-noise ratio in the embodiments of the present invention is shown in Figure 4 The results are presented below. In a campus testing environment, compared with traditional Kalman filter-based algorithms and pure LSTM prediction schemes, the method of this invention achieves improvements of 67.21% and 33.5% in the accuracy prediction of the angle of arrival (AoA) and the angle of launch (AoD) of the moving target, respectively. Furthermore, compared with data-driven prediction schemes, the method of this invention exhibits stronger robustness when the angle state value of the moving target changes abruptly, achieving consistently and robustly high tracking accuracy with low tracking overhead.

[0067] The above description is merely a detailed illustration of specific embodiments of the present invention and is not intended to limit the invention. Various substitutions, modifications, and improvements made by those skilled in the art without departing from the principles and scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A beam tracking angle prediction method based on the fusion of machine learning and Kalman filtering information, characterized in that, Includes the following steps: Step 1: Set the initial time to k = 0, and obtain the initial angle [θ] through beamforming from time 0 to time m. l (0),…,θ l (m)], m∈[ξ,K]; where l is the number of paths in the actual environment, ξ is the minimum angle set when calculating acceleration, m is the initialization termination time, and K is the system termination time; therefore, the angular velocity ω at time m is... l (m), angular acceleration at time m The derivative of acceleration The initial state vector x is obtained through difference calculation. l (m) is represented as: The uncertainty Σ(0|0) of the initial estimate in the Kalman filter algorithm is set to a random constant; the observation matrix C is set to an identity matrix of dimension N×N, where N is the number of antennas on the base station used for beam speed tracking; Step 2: When the time variable k is an integer multiple of τ, the noisy observations... As the observed variable z; when the time variable k is not an integer multiple of τ, the LSTM network f is used. N2 Output angle estimate As the observed variable z: Where τ is the set interval, and n is a positive integer; Step 3: Convert the state vector estimated at time k-1 to the state vector estimated at time k-1. Input into a single-layer neural network (SLNN) f without an activation function N1 Generate the state vector from time k-1 to time k. At the initial moment, the single-layer neural network f N1 The input is the initial state vector x l (m); Extract the single-layer neural network f N1 The weight matrix is ​​used as the state transition matrix F(k): wherein w N1 is a human-set input neural network weight; Step 4: Substitute the state transition matrix F(k) into formula (4) to calculate the covariance extrapolation: Σ(k+1|k)=F(k)Σ(k|k)F(k) T +n(k) (4) Where n(k) represents process noise; Step 5: Substitute the observation matrix C and the calculation result of formula (4) into formula (5) to calculate the Kalman gain K(k): K(k)=Σ(k|k-1)C H (CΣ(k|k-1)C H +R(k)) -1 (5) Where R(k) is the measurement uncertainty set manually; Step 6: Substitute the observed variable z into formula (6) to update the state vector at time k. Step 7: Update the uncertainty estimated at time k using formula (7): Σ(k|k)=(IK(k)C)Σ(k|k-1)(IK(k)C) H +K(k)R(k)K(k) H (7) Where I represents the identity matrix; Step 8: Extract the state vector at time k. Angle estimates in And input into the LSTM network f N2 At the initial time, the LSTM network f N2 The input is the initial angle [θ] l (0),…,θ l [m]; The output is the angle estimate at time k+1. At the initial time, the LSTM network f N2 The input is the initial angle [θ] l (0),…,θ l (m)],w N2 These are the weight parameters of the neural network; Step 9: Repeat steps 2 to 8 to obtain the predicted angle value of beam tracking at each cycle time.

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