Millimeter-wave adaptive beam tracking method based on iterative extended Kalman filter

Abstract

This invention discloses a millimeter-wave adaptive beam tracking method based on an iterative extended Kalman filter (IEKF). The invention includes the following steps: 1. Determine the ratio metric of the received signal as the observation equation for the IEKF; 2. Collect the angle changes after multiple tracking operations, calculate the angle change rate based on the average angle change, and determine the maximum time slot interval between two tracking operations; 3. Determine whether tracking is necessary based on a set threshold for signal-to-noise ratio (SNR) fading after beamforming and the maximum tracking interval determined in step 2; 4. Perform tracking using the IEKF method. This invention achieves adaptive adjustment of the tracking frequency according to the rate of change of the communication channel angle while ensuring high tracking accuracy, significantly reducing the overhead in beam tracking. This method maintains excellent tracking performance even under complex channel angle changes and low SNR conditions.

Description

Technical Field

[0001] This invention belongs to the field of digital communication technology and discloses a millimeter-wave beam tracking method based on an iterative extended Kalman filter. This method solves the problem that traditional EKF requires knowledge of the noise variance of the state transition equation and the noise variance of the observation equation, and can automatically adjust the beam tracking frequency to adapt to the rate of change of the main path angle of the millimeter-wave channel. Background Technology

[0002] Millimeter wave (mmWave) offers advantages such as wide bandwidth and high directional resolution, making it a crucial technology for high-speed communication applications like wireless local area networks (WLANs), 5G, and vehicle-to-everything (V2X) communication. However, millimeter wave signals suffer from significant path loss. To address this issue, millimeter wave communication terminals typically employ beamforming technology to provide directional gain for signal transmission. To maintain this high beamforming gain during communication, the beam direction used by the millimeter wave communication terminal must always be aligned with the primary path direction of the millimeter wave channel. This accurate beam alignment is usually achieved through beam training. However, beam training requires examining all possible directions, resulting in high time and energy costs. It is only suitable for static scenarios or those where the channel changes slowly over time, where frequent beam training is not necessary. In rapidly changing mobile scenarios, frequent beam training leads to excessive resource overhead. In fact, due to the continuous nature of channel angle changes, the channel angle at a given moment is often correlated with the angle at the previous moment. This means that the channel angle information from the previous moment can be used to estimate the current channel angle. This avoids omnidirectional beam search and greatly reduces the overhead of beam training.

[0003] Commonly used beam tracking algorithms include the Auxiliary Beam Pair (ABP) algorithm and the Extended Kalman Filter (EKF) algorithm. The ABP algorithm uses a pair of auxiliary beams near the main beam to measure the pilot signal and estimates the angle by calculating the ratio between the maximum and second largest received signal strength. This method performs well at high signal-to-noise ratios (SNR), but at low SNRs, the auxiliary beam pair may be incorrectly selected, potentially leading to severe performance degradation or even loss of tracking.

[0004] The Extended Kalman Filter (EKF) is an extension of the Kalman Filter for nonlinear applications and is widely used in target tracking. The Kalman Filter's estimation of the current state relies on the previous estimate. Therefore, existing Kalman Filter beam tracking methods require real-time, high-frequency estimation of the system state to ensure beam tracking accuracy. This incurs unnecessary overhead in low-speed scenarios. Furthermore, the observation equations chosen by current EKF-based millimeter-wave communication system beam tracking methods are inherently highly nonlinear, leading to significant higher-order term losses during linearization. In addition, existing Kalman Filter methods for beam tracking require simultaneous estimation of channel gain and channel angle information, causing errors to interact and accumulate rapidly, hindering long-term effective tracking.

[0005] To address the aforementioned issues, a beam tracking algorithm needs to be designed that can adaptively adjust the tracking frequency according to different movement speed scenarios, reduce beam tracking overhead, and overcome the problems of linearization loss and error accumulation, thereby extending the effective tracking time. Summary of the Invention

[0006] This invention discloses a millimeter-wave adaptive beam tracking method based on an iterative extended Kalman filter (EPF) for millimeter-wave mobile communication systems. First, this method overcomes the information loss problem caused by the linearization of the observation equations in the EPF method, improving tracking accuracy. Second, it applies a residual-based estimation method to estimate the noise variance of the observation equations and an innovative estimation method to estimate the noise variance of the state transition equations, solving the problem of high model requirements in traditional EPF methods. Finally, this method can adjust the beam tracking frequency in real time according to the rate of change of the millimeter-wave channel angle, effectively reducing beam tracking overhead.

[0007] This invention adopts the following technical solution: the millimeter-wave communication receiver Rx receives the pilot signal transmitted by the millimeter-wave communication transmitter Tx, and calculates in real time the signal-to-noise ratio ε of the pilot signal measured after beamforming in the current time slot t. t If ε t If the value decreases by more than a certain threshold compared to the value after the last tracking, then an iterative extended Kalman filter is used to estimate the Angle of Arrival (AoA) and Angle of Departure (AOD). If the time slot interval since the last tracking reaches the maximum tracking interval, and the value is still not estimated due to ε... t If the beam is updated when the attenuation reaches a threshold, an update is forced to ensure that the channel angle is still within the beam's coverage area, reducing the possibility of lost tracking.

[0008] The millimeter-wave adaptive beam tracking method based on iterative extended Kalman filters proceeds as follows:

[0009] Step 1: Determine the ratio of the received signal as the observation equation for IEKF;

[0010] Step 2: Collect the angle changes after multiple tracking operations, calculate the angle change rate based on the average angle change, and determine the maximum tracking interval between two tracking operations.

[0011] Step 3: Determine whether tracking is required based on the set threshold for signal-to-noise ratio fading after beamforming and the maximum tracking interval determined in Step 2.

[0012] Step 4: Perform tracing using the IEKF method.

[0013] Preferably, the received signal ratio metric in step 1 is the ratio of the strength of the received signal to that of a pair of auxiliary beams near the received beam.

[0014] Preferably, the interval between the two tracking operations to be determined in step 2 is calculated by dividing the specified beamwidth by the average value of each collected angle change. The tracking rate can be adjusted by changing the beamwidth.

[0015] Preferably, the iterative extended Kalman filter (IEKF) method described in step 4 has the advantage over the traditional iterative extended Kalman filter (IEKF) method in that it does not require knowledge of the noise variance of the state transition equation and the noise variance of the observation equation, but instead uses an iterative approximation method to estimate them. This greatly improves the robustness of the IEKF method to different motion models.

[0016] The beneficial effects of this invention are as follows:

[0017] The adaptive millimeter-wave beam tracking algorithm disclosed in this invention primarily monitors the change in signal-to-noise ratio after beamforming, supplemented by collecting angle change information between multiple tracking operations to determine the maximum tracking interval. While ensuring high tracking accuracy, it adaptively adjusts the tracking frequency according to the rate of change of the communication channel angle, significantly reducing the overhead in beam tracking. This method maintains excellent tracking performance even under conditions of complex channel angle changes and low signal-to-noise ratio. Attached Figure Description

[0018] Figure 1 This is a flowchart of the adaptive beam tracking algorithm of the present invention;

[0019] Figure 2 The tracking results of 500 time slots provided by the method of the present invention in the case of the first embodiment;

[0020] Figure 3In the case of the first embodiment, the accuracy of the method provided by the present invention is compared with that of other commonly used methods. Figure 4 It is a comparison of their expenses.

[0021] Figure 5 The tracking results of the method provided by the present invention in the case of the second embodiment.

[0022] Figure 6 In the second embodiment, the method provided by the present invention re-aligns the current time slot; Table 2 is a comparison of its overhead with the ATSC algorithm. Specific Implementation

[0023] The technical content of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0024] <First Embodiment>

[0025] In the first embodiment of the invention, beam tracking between a millimeter-wave communication base station, Tx, and a millimeter-wave communication mobile terminal, Rx, is considered. φ is defined as the channel angle of arrival at the Rx end. This is an estimate of φ. Let Rx be the beamforming direction at the Rx end, and ψ be the channel departure angle at the Tx end. Let ψ be an estimated value. This refers to the beamforming direction at the Tx end. In this embodiment, only the beam tracking of the mobile terminal is considered, that is, it is assumed that the base station's beam is always aligned with the channel's starting angle direction during beam training. A state evolution equation is used to simulate the angle change of the mobile terminal in the channel. The state evolution equation is described as follows:

[0026] φ t =φ t-1 +Ω t-1 +n t-1 (1)

[0027] The subscript t represents the t-th time slot. Where Ω t The channel angle is a fixed value for each change, and is a constant, n. t It follows a mean of 0 and a variance of . The Gaussian distribution, i.e.

[0028] In the first embodiment of the present invention, consider the following millimeter-wave communication scenario: Define N T N represents the number of antennas for base station Tx. R This represents the number of Rx antennas for the mobile terminal. T (.) and a R (.) represent the antenna array response vectors of the base station and the mobile terminal, respectively, with channel gain coefficient α. This represents the conjugate transpose of a vector. Define v = 2πd. R sin(φ) / λ and u=2πd T sin(ψ) / λ represents the spatial frequencies of the channel's angle of arrival and angle of departure, respectively, where d T and d R These represent the distances between the base station and the mobile terminal antennas, respectively, and λ is the wavelength corresponding to the carrier frequency. (Definition) and The spatial frequency of the line-of-sight angle of the main beam of the base station and mobile terminal.

[0029] In this embodiment, a pair of auxiliary beam pairs is used on the mobile terminal to measure the pilot signal, pointing respectively to η. R -δ R and η R +δ R δ R This represents the angle between the auxiliary beam pair and the line-of-sight angle η in the spatial frequency domain of the mobile terminal. Let... The channel matrix between Tx and Rx is expressed as follows:

[0030]

[0031] definition and These are the beamforming vectors for the base station and the mobile terminal, respectively.

[0032] Pilot signal, For the noise vector, the expressions for f and w are as follows:

[0033]

[0034]

[0035] The received signals corresponding to this pair of beams are as follows:

[0036] y Δ =w(η-δ) R )HfS+z Δ

[0037] y Σ =w(η+δ) R )HfS+z ∑

[0038] Among them, z Δ and z ∑ These are independent noise vectors with a mean of 0 and a variance of . The complex Gaussian distribution.

[0039] The strength of the corresponding received signal can be calculated as follows:

[0040]

[0041] Step 1. Calculate the ratio metric of the auxiliary beam pair.

[0042] The ratio metric for the auxiliary beam pair mentioned in step 1 is calculated as follows:

[0043]

[0044] This ratio metric is used as the observation equation for IEKF. When the noise effect is negligible, Therefore, the ratio ξ measured in time slot t t The model can be remodeled as follows:

[0045]

[0046] Where, v(t) = 2πd R sin(φ(t)) / λ,w t It follows a mean of 0 and a variance of . The Gaussian distribution.

[0047] Step 2. Collect angle change information between N tracking iterations, estimate the average rate of channel angle change, and determine the maximum tracking interval T. max .

[0048] Assume there is a T interval between every two tracking operations. f The set of time slots is represented as: Γ f (t)={t,t-1,t-2,…,t-(T f -1)}, then this T f The mean change in the estimated angle of each time slot can be given by the following formula:

[0049]

[0050] Therefore, the maximum tracking interval can be estimated as follows:

[0051]

[0052] in, B represents the estimated value of the angle of arrival φ. R =1 / N R It is approximately half the beamwidth of the mobile terminal.

[0053] Step 3. Calculate the signal-to-noise ratio after beamforming, and determine whether tracking is required based on the following two conditions.

[0054] Condition-(1): If the signal-to-noise ratio after beamforming decreases by more than a threshold compared to before T time slots, i.e. |ε t -ε t-T |>γ, where γ is the set threshold.

[0055] Condition-(2): The time slot interval between two tracking operations reaches the maximum tracking interval described in step 2, i.e., T = T max .

[0056] The signal-to-noise ratio ε after beamforming in each time slot t t With transmit power P T =||s(t)|| 2 Noise variance The relationship is as follows:

[0057]

[0058] Where s(t) is the pilot sequence transmitted in the t-th time slot.

[0059] Step 4. Perform beam tracking using the IEKF method.

[0060] Step 4-1 One-step prediction and angle update:

[0061]

[0062] in, This is the angle estimate from the previous tracking.

[0063] Step 4-2 One-step prediction covariance update:

[0064] P t|t-T =P t-T|t-T +T·Q est,t-T (8)

[0065] Where T is the time slot interval between the previous tracking action and Q est P is the covariance matrix of the noise in the estimated evolution equation. t-T|t-T The covariance matrix of the previous tracking;

[0066] Step 4-3. IEKF iteration, let the maximum number of iterations be k, and i be the iteration index.

[0067] Step 4-3-1: Calculate the Kalman gain:

[0068]

[0069] Among them, R est Let be the covariance matrix of the noise in the estimated observation equation. (.) H C represents the transpose of a matrix. t,i The calculation is as follows:

[0070]

[0071] Step 4-3-2: Calculate the estimated angle value:

[0072]

[0073] in,

[0074] Step 4-3-3: Calculate the covariance matrix:

[0075] P t|t,i =(IK t,i C t,i )P t|t-T (11)

[0076] Where I is the identity matrix.

[0077] Step 4-3-4: Calculate the covariance Q of the state evolution equation for the i-th iteration. est,t,i :

[0078] Q est,t,i =K t,i ee H K t,i (12)

[0079] in

[0080] Step 4-3-5: Calculate the covariance R of the observation equation in the i-th iteration. est,t,i :

[0081]

[0082] After the IEKF iteration ends, calculate the covariance Q of the state evolution equation required for the next tracking. est,t The covariance R of the observation equation est,t The steps are as follows:

[0083] Step 4.4 Calculate the covariance Q of the state evolution equation for the next tracking iteration. est,t :

[0084]

[0085] Step 4.5 Calculate the covariance R of the observation equation for the next tracking. est,t :

[0086]

[0087] in, The number of updates is represented by b, which is a constant and typically ranges from 0.95 to 0.99. The subscript t represents the time slot index, and the subscript i represents the IEKF iteration index.

[0088] Step 4.6 After the IEKF iteration is completed, update the beam angle. The angle estimate at the last iteration of IEKF. i = N, initialize T to 0; wait for the next time slot t+T, and return to step 4.1.

[0089] <Second Embodiment>

[0090] In the second embodiment of the present invention, beam tracking of both the base station (Tx) and the mobile communication terminal (Rx) is considered. The angle changes of both the base station and the mobile terminal are simulated using high-precision Ray-Tracing software based on the motion speed of the mobile terminal relative to the base station. The simulation parameters are shown in Table 1. The specific implementation steps of this embodiment are as follows:

[0091] Step 1: Using Ray-Tracing software, generate the angle change data of the millimeter-wave mobile terminal relative to the base station (hereinafter referred to as the base station and mobile terminal) according to the parameter settings in Table 1, and use Matlab to interpolate it, setting each time slot to 0.5ms, finally generating approximately 4.1×10 4 Each time slot is used to obtain the initial angles of the base station and the mobile terminal.

[0092] Step 2: Use the method described in Step 2 of the first embodiment to determine the maximum tracking interval for the base station and the mobile terminal, respectively.

[0093] Step 3: Measure the signal-to-noise ratio (SNR) of the base station and the mobile terminal after beamforming using the method described in Step 3 of the first embodiment. If any of the following conditions are met: Condition-(1) The fading of the SNR of one side after beamforming exceeds the set threshold γ1, execute the tracking process in Step 4; Condition-(2) The time slot interval between two tracking operations on any side reaches the maximum tracking interval described in Step 2, then execute the tracking process in Step 4.

[0094] Step 4: Use the method described in Step 4 of the first embodiment to track the main path angles of the base station and the mobile terminal respectively.

[0095] Step 5: Determine whether tracking has been lost based on the signal-to-noise ratio fading after beamforming. The set threshold is γ2. If tracking is lost, beam alignment needs to be performed using a beam search method. In this embodiment, for convenience, since channel angle data is already available, the beam direction is directly aligned with the channel.

[0096] Simulation results and analysis:

[0097] First embodiment parameter settings: Set the total number of time slots N = 500, and the number of Tx antennas N T =1, the number of Rx antennas is N R =64, initial channel direction φ and beamforming direction The initial value is π / 4, the channel is a Ricean channel with only one line-of-sight path, i.e., path number l = 1. The signal-to-noise ratio loss after beamforming caused by beam angle deviation from the channel is defined as the threshold γ, in dB. B is defined as... R =1 / N R It is approximately half the beamwidth.

[0098] Figure 2 The tracking results over 500 time slots are displayed. The parameter is set to the number of antennas N. R =64, fixed step size Ω t-1 =0.1*Bt, perturbation n t variance SNR = -10dB, pilot signal length is 16, auxiliary beamp angle is δ R =B R Set the threshold γ = B for the signal-to-noise ratio loss after beamforming. R .

[0099] Figure 3 The accuracy comparison of the algorithm proposed in this invention with the ATSC algorithm and the EKF algorithm (with known motion equation perturbation variance, fixed step size and observation noise variance) is shown. Figure 4 This is a comparison of their costs. As can be seen from the figure, while keeping the costs basically the same, the method still has high accuracy.

[0100] Parameter settings for the second embodiment: Tx antenna number N T =32, the number of Rx antennas is N R =32, other parameter settings are shown in Table 1.

[0101] Figure 4 , Figure 5 The results of beam tracking using the method provided in this invention are shown in the Ray-Tracing simulation of real channel variations. As can be seen from the figure, up to the 0.37 × 10⁻⁶... 4 In each time slot, this method successfully tracked the main non-line-of-sight paths, and around 0.93 × 10⁻⁶ time slots... 4 Even when the user's angular velocity suddenly increases in a time slot, this method can still track quickly. And in approximately 3.5 × 10⁻⁶ time slots... 4 Even when the LOS channel disappears and the primary channel becomes the NLOS channel at a specific time slot, this method can still accurately track the channel. And at 3.75×10 4After the time slot, frequent beam recalibration occurs due to the very weak NLOS channel and the high speed of user movement. Even so, this method can still track the channel, maximizing the effective channel gain. Figure 6 As shown in Table 2, Table 2 compares the overhead of the proposed method with that of the ATSC algorithm (this algorithm can be found in the following paper: Liu, C., Li, M., Zhao, L., Whiting, P., Hanly, SV, Collings, IB, & Zhao, M. (2020). Robust adaptive beamtracking for mobile millimetre wavecommunications. IEEE Transactions on Wireless Communications, 20(3), 1918-1934.). As can be seen from the table, the method provided by the present invention can significantly reduce the beam tracking overhead.

[0102] Table 1

[0103] Base station height 5m Transmission power 30dBm User trajectory length 410m User-side height 1.5m thermal noise -99dBm Time slot interval 0.5ms Number of antennas 32 NoiseFigure 9.1dB User movement speed 72km / h

[0104] Table 2

[0105] ATSC IEKF Number of tracking 494 198 Number of realignments 12 7

[0106] In summary, while high-frequency tracking improves tracking accuracy, it inevitably increases overhead. This invention adaptively adjusts the beam tracking frequency to adapt to the rate of change in channel angle. This effectively reduces overhead while maintaining beam tracking accuracy, and it maintains tracking effectively even in complex channel variation scenarios, demonstrating excellent robustness.

Claims

1. A millimeter-wave adaptive beam tracking method based on an iterative extended Kalman filter (IEKF), characterized in that... Includes the following steps: Step 1: Determine the ratio of the received signal as the observation equation for IEKF; The ratio metric for the auxiliary beam pair is calculated as follows: The corresponding received signal strength is calculated as follows: Among them, y Δ and y ∑ These represent the received signals using auxiliary beam pairs, respectively; χ Δ and χ ∑ y Δ and y ∑ The corresponding received signal strength; this ratio metric is used as the observation equation for IEKF; when noise effects are negligible, δ R This represents the angle between the auxiliary beam pair and the line-of-sight angle η in the spatial frequency domain of the mobile terminal, where v is the spatial frequency of the channel angle of arrival and η is the line-of-sight angle; therefore, the ratio metric ξ measured in time slot t... t The model can be remodeled as follows: Where, v(t) = 2πd R sin(φ(t)) / λ, where λ is the wavelength corresponding to the carrier frequency, φ(t) is the angle of arrival of the channel in time slot t, and w t It follows a mean of 0 and a variance of . Gaussian distribution, d R This refers to the distance between the antennas of the mobile terminal. Step 2: Collect the angle changes after multiple tracking attempts, calculate the angle change rate based on the average angle change, and determine the maximum tracking interval between two tracking attempts. Step 3: Determine whether tracking is required based on the set threshold for signal-to-noise ratio fading after beamforming and the maximum tracking interval determined in Step 2; Step 4: Perform tracing using the IEKF method; The received signal ratio metric described in step 1 is the ratio of the strength of the received signal to that of a pair of auxiliary beams near the receiving beam. The interval between the two tracking steps to be determined in step 2 is calculated by dividing the specified beamwidth by the average value of each collected angle change, wherein the tracking rate is adjusted by changing the beamwidth; Step 3, which determines whether beam tracking needs to be performed, follows two conditions: Condition (1): If the signal-to-noise ratio after beamforming decreases by more than a threshold compared to before T time slots; Condition (2): The time slot interval between two tracking operations reaches the maximum tracking interval described in step 2; Step 4, which describes using the IEKF method to perform beam tracking, is implemented as follows: Step 4-1. One-step prediction and angle update; Step 4-2. One-step prediction of covariance update; Step 4-3. IEKF iteration; Step 4-4. Calculate the covariance of the state evolution equation for the next tracking iteration; Steps 4-5. Calculate the covariance matrix of the noise in the observation equation for the next tracking iteration; Step 4-6. After the IEKF iteration is completed, update the beam angle, wait for the next time slot t+T, and return to step 4-1; Step 4-3's IEKF iteration, let the maximum number of iterations be k, and i be the iteration index, is implemented as follows: Step 4-3-1: Calculate the Kalman gain: Among them, P t|t-T The covariance matrix obtained after angle estimation for time slot tT; R est,t,i-1 Let be the covariance matrix of the noise in the observation equation obtained after the (i-1)th iteration, for time slot t; (.) H C represents the transpose of a matrix. t,i Let be the observation matrix for the i-th iteration in time slot t, calculated as follows: in, For use The noise-free observation equations are calculated. The estimated spatial frequency corresponding to the channel angle of arrival obtained in time slot t; Here is the estimated value of the channel angle of arrival obtained in time slot t; Step 4-3-2: Calculate the estimated angle value: in, For use The values ​​of the noise-free observation equations are calculated; The angle estimate of the channel angle of arrival obtained in the tT time slot; The estimated spatial frequency corresponding to the channel angle of arrival obtained in time slot tT; For time slot t, the estimated angle of arrival of the channel is obtained after the i-th IEKF iteration. Step 4-3-3: Calculate the covariance matrix: P t|t,i =(I-K t,i C t,i )P t|t-T Where I is the identity matrix; P t|t,i For time slot t, the covariance matrix obtained after the i-th IEKF iteration; Step 4-3-4: Calculate the covariance Q of the state evolution equation for the i-th iteration. est,t,i : Q est,t,i =K t,i ee H K t,i in For use The values ​​of the noise-free observation equations are calculated; Step 4-3-5: Calculate the covariance matrix R of the observation equation noise in the i-th iteration. est,t,i : After the IEKF iteration ends, calculate the covariance Q of the state evolution equation required for the next tracking. est,t The covariance matrix R of the observation equation noise est,t .

2. The millimeter-wave adaptive beam tracking method based on an iterative extended Kalman filter (IEKF) as described in claim 1, characterized in that... Step 4-4 describes calculating the covariance Q of the state evolution equation for the next tracking iteration. est,t The specific implementation is as follows: in, c represents the number of updates, b is a constant, t is the time slot index, i is the IEKF iteration index, and N represents the number of tracking steps.

3. The millimeter-wave adaptive beam tracking method based on an iterative extended Kalman filter (IEKF) as described in claim 2, characterized in that... Steps 4-5: Calculate the covariance matrix R of the noise in the observation equation for the next tracking iteration. est,t : in, c represents the number of updates, b is a constant, t is the time slot index, and i is the IEKF iteration index.

4. The millimeter-wave adaptive beam tracking method based on an iterative extended Kalman filter (IEKF) as described in claim 3, characterized in that... Steps 4-6: After the IEKF iteration is complete, update the beam angle. The angle estimate at the last iteration of IEKF. i = k, initialize T to 0; wait for the next time slot t+T, and return to step 4-1.

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