Beam Tracking Method Using Unscented Kalman Filter for UAV-Enabled NR MIMO-OFDM System with Hybrid Beamforming

Abstract

Unmanned aerial vehicles (UAVs) and millimeter-wave frequencies play key roles in supporting 5G wireless communication systems. They expand the field of wireless communication by increasing the data capacities of communication systems and supporting high data rates. However, short wavelengths, owing to the high millimeter-wave frequencies can cause problems, such as signal attenuation and path loss. To address these limitations, research on high directional beamforming technologies continue to garner interest. Furthermore, owing to the mobility of the UAVs, it is essential to track the beam angle accurately to obtain full beamforming gain. This study presents a beam tracking method based on the unscented Kalman filter using hybrid beamforming. The simulation results reveal that the proposed beam tracking scheme improves the overall performance in terms of the mean-squared error and spectral efficiency. In addition, by expanding analog beamforming to hybrid beamforming, the proposed algorithm can be used even in multi-user and multi-stream environments to increase data capacity, thereby increasing utilization in new-radio multiple-input multiple-output orthogonal frequency-division multiplexing systems.

1. Introduction

In new-radio multiple-input multiple-output orthogonal frequency-division multiplexing (NR MIMO-OFDM) systems, the use of unmanned aerial vehicles (UAVs) is increasingly attracting attention as they play crucial roles in 5G NR systems because of their high-altitude, flexibility, and mobility characteristics. Various types of UAVs are currently used in different situations. For example, a high-level UAV platform can extend the range of the radio area to be serviced, whereas a relatively low-level platform can help easily access time-sensitive systems. In addition, in hotspot areas where network usage is increasing rapidly, if the data capacity can be increased using a UAV as the base station (BS), the problems of excess data traffic can be solved [1,2]. The massive multiple-input multiple-output (m-MIMO) technology, which increases data transmission and reception efficiency through multiple antennas, is also a promising approach that supports high data rates in NR MIMO-OFDM systems [3]. Moreover, if UAVs and millimeter-wave frequencies can be integrated into NR MIMO-OFDM systems, the wireless communication area coverage can be expanded by increasing the data capacity, thus enabling high transmission speeds of 5G systems.

However, short wavelengths resulting from high millimeter-wave frequencies can cause problems, such as signal attenuation and path loss. To overcome these drawbacks, researchers have increasingly focused on high-directionality beamforming techniques. Given the full beamforming gain and high mobility of UAVs, it is essential to obtain accurate beam angles. Furthermore, accurate beam tracking techniques are essential in UAV-enabled NR MIMO-OFDM systems. Therefore, in this study, we propose an unscented Kalman filter (UKF)-based beam tracking method using hybrid beamforming.

The remainder of the paper is structured as follows. Chapter II introduces the channel model that will be defined and applied with the system model. Chapter III introduces the UKF-based beam tracking method using hybrid beamforming, and Chapter IV presents performance evaluations through simulations and their results. Finally, Chapter V presents the conclusions of this study.

2. System Model and Channel Model

2.1 System Model

In this study, we considered a downlink UAV-enabled NR MIMO-OFDM system where a UAV-BS served as the ground-user equipment (G-UE).

Both the transmitter-side UAV-BS and receiver-side G-UE had antenna arrays in the form of a uniform planar array (UPA) placed evenly on the xy-plane, as shown in Fig. 1. The UAV-BS and G-UE had UPAs of 𝑀_𝑡 × 𝑁_𝑡 each. The spacing between the adjacent antennas was uniformly 𝑑 (= λ ⁄ 2), 𝑑 = 𝑑_𝐻 = 𝑑_𝑉 , with 𝑑_𝐻 being in the horizontal-axis direction and 𝑑_𝑉 being in the vertical-axis direction. The carrier wavelength is denoted by λ.

Fig. 1. Uniform planar antenna array used for the transmitter and receiver.

The zenith and azimuth angles in the transmitter are denoted by 𝜃_𝑡 (zenith angle of departure, ZOD) and 𝜙_𝑡 (azimuth angle of departure, AOD), respectively, and the corresponding angles in the receiver are denoted by 𝜃_𝑟 (zenith angle of arrival, ZOA) and 𝜙_𝑟 (azimuth angle of arrival, AOA), respectively. The angle notations follow the definitions specified in the 3GPP TR 38.901 v16.1.0 [4].

The beamformer and combiner vectors are given by 𝒗_𝑘 (𝒗_𝑘 ∈ 𝐶^{(𝑀_𝑡𝑁_𝑡)×1}) and 𝒘_𝑘 (𝒘_𝑘 ∈ 𝐶^{(𝑀_𝑟𝑁_𝑟)×1}), respectively. When a transmission signal 𝑥_𝑘 is transmitted, the received signal is given by (1). The notation 𝒉_𝑘 (𝒉_𝑘 ∈ 𝐶^{(𝑀_𝑡𝑁_𝑡)×(𝑀_𝑟𝑁_𝑟)}) represents a 3D channel between the UAV-BS and G-UE in the 𝑘^𝑡ℎ transmission time interval (TTI). Moreover, 𝑛_𝑘 is additive white Gaussian noise that follows a normal distribution given by 𝑛_𝑘~𝑁(0, 𝜎_𝑛²) and is applied in the 𝑘^𝑡ℎ TTI.

𝑦_𝑘 = 𝒘_𝑘^𝐻𝒉_𝑘^𝐻𝒗_𝑘𝑥_𝑘 + 𝑛_𝑘.       (1)

2.2 Channel Model

In the NR MIMO-OFDM communication system proposed herein, we considered a slow-varying channel model where the channels did not change within a given TTI but did between TTIs [5]. However, this cannot explain the rapid movement of the UAV, so finding another beam tracking method by considering this characteristic will be a future research task. We express the 𝐿_𝑘-scatterer channel model in (2) by applying the antenna array response vector (𝒂(𝜃_𝑙,𝑘, 𝜙_𝑙,𝑘)) at the transmitter and receiver sides. Here, the path gain is represented by 𝜂_𝑙,𝑘 and is calculated using (3). Further, the attenuation degree of the signal is 𝜌_𝑙,𝑘, and 𝑑_𝑙 represents the distance between the transmit antenna and receive antenna along the path l, as shown in Fig. 1. The antenna array response vectors of the uniform square planar array configurations of both the transmitter and receiver can be modeled as shown in (4) [6]. Here, the antenna indexes of the elements along the horizontal and vertical axes in the antenna array are represented as 𝑚 (0 < 𝑚 < 𝑀 − 1) and 𝑛 (0 < 𝑛 < 𝑁 − 1), respectively, and the total number of antennas is MN.

\(\begin{aligned}\boldsymbol{h}_{k}=\sum_{l=1}^{L_{k}} \eta_{l, k} \boldsymbol{a}_{r}^{H}\left(\theta_{l, k}^{r}, \phi_{l, k}^{r}\right) \boldsymbol{a}_{t}\left(\theta_{l, k}^{t}, \phi_{l, k}^{t}\right)\end{aligned}\),       (2)

\(\begin{aligned}\eta_{l, k}=\rho_{l, k} \sqrt{M_{r} N_{r} M_{t} N_{t}} e^{-j \frac{2 \pi d_{l}}{\lambda}}\end{aligned}\),       (3)

\(\begin{aligned}\begin{array}{l} a(\theta, \phi)=\frac{1}{\sqrt{M N}}( {\left[1, \ldots, e^{j k d(m \sin (\theta) \sin (\phi)+n \sin (\theta) \cos (\phi)},\right.} \\ \left.\left.\ldots, e^{j k d((M-1) \sin (\theta) \sin (\phi)+(N-1) \sin (\theta) \cos (\phi)}\right]\right)^{T} .\end{array}\end{aligned}\)       (4)

However, most millimeter-wave frequency signals cause signal losses owing to obstacles, such as buildings and people. Consequently, most of the signal power transmitted from the UAV-BS to the G-UE is from the line-of-sight (LOS) path [7, 8]. Therefore, in the UAV-enabled NR MIMO-OFDM proposed in this study, only the LOS path was considered. The channel vector can be expressed as in (5), where the variables have the same meanings as noted previously.

𝒉_𝑘 = 𝜂_𝑘𝒂_𝑟^𝐻(𝜃_𝑘^𝑟, 𝜙_𝑘^𝑟)𝒂_𝑡(𝜃_𝑘^𝑡, 𝜙_𝑘^𝑡),       (5)

3. UKF-Based Beam Tracking Using Hybrid Beamforming

Owing to the short wavelengths of millimeter-wave frequencies and the high mobility of the UAV, it is imperative to obtain the exact beam angle. This section presents a method for tracking the beam angle based on the UKF using hybrid beamforming.

3.1 Hybrid Beamforming

Beamforming is a technology that allows multiple antennas to be arranged at regular intervals to create an antenna beam in a specific direction by changing the amplitude and phase of the signal supplied through each antenna to transmit and receive strong signals. In particular, in the case of 5G systems that use high-frequency millimeter waves, the wavelength is small; thus, the separation between antennas can also be reduced, enabling integration of m-MIMO technology in antennas with high densities. Therefore, the application of beamforming techniques through square planar antenna arrays to the NR MIMO-OFDM system in this study can lead to expanded cell coverage and increased transmission speeds.

Beamforming technologies can be divided into analog, fully digital, and hybrid beamforming. Analog beamforming involves the application of a beam generator to the radio frequency (RF) stage. This method has a relatively low implementation complexity, but it is difficult to implement an arbitrary beamforming matrix. Further, it has the disadvantage of being limited to one user and a single transmission and reception flow. In the case of fully digital beamforming, the beamforming generators are applied to the baseband. Beamforming can be applied by allocating different frequency resources to each user in the cell, thus forming a beam for multiple users simultaneously. In addition, an arbitrary beamforming matrix can be implemented using digital signal processing to facilitate interference and power control between the users. However, implementing this method consumes extensive hardware resources. It also has the limitation of high processing complexity. Therefore, in this study, we used hybrid beamforming to apply beam generators to both the RF stage and baseband. In other words, we used analog and electronic beamforming simultaneously.

The hybrid precoding structure applied in this study is shown in Fig. 2 [9]. Digital precoding was performed using 𝑽_𝐵𝐵 (𝑽_𝐵𝐵 ∈ 𝐶^𝑵_𝑇^{RF×𝑵_𝑠}) by the data symbols, 𝑵_𝑠 in the transmitter. Thereafter, a cyclic prefix (CP) was inserted after converting to time domain through the K-point inverse fast Fourier transform (IFFT). Lastly, analog precoding was applied using 𝑽_RF (𝑽_RF ∈ 𝐶^{𝑵_𝑇×𝑵_𝑇RF}) and transmitted to the channel.

Fig. 2. Hybrid pre-coding structure.

3.2 UKF-Based Beam Tracking

This section introduces the UKF-based beam tracking scheme [10, 11]. In this study, the channel angle vector is defined as shown in (6); for convenience, this is called as a state vector. Here, the state vector variation equation follows (7), and q_k𝒒_𝑘 (𝒒_𝑘 ∈ 𝑁^4×1) represents the Gaussian noise. Additionally, 𝒒_𝑘 follows the normal distribution 𝑁(0, 𝑸), and 𝑸 (𝑸 = 𝜎²𝑰₄) is a 4 × 4 matrix of channel angle variance (𝜎²) that indicates how fast the channel changes. In a real system, the channel angle variance depends on the ZOD(𝜃_𝑘^𝑡), AOD(𝜙_𝑘^𝑡), ZOA(𝜃_𝑘^𝑟), and AOA(𝜙_𝑘^𝑟). However, for computational convenience, we assumed the same values for these in the study

𝝍k=[𝜃^t_k𝜙^t_k𝜃^r_k𝜙^r_k]^T ,        (6)

𝝍_𝑘 = 𝝍_𝑘−1 + 𝒒_𝑘,       (7)

The signal received by the proposed UKF-based beam tracking scheme is represented through (8). Since 𝑦_𝑘 and 𝑛_𝑘 are complex forms, (8) can be redefined as (9) and (10). The nonlinear measurement function is expressed using 𝑓(𝝍_𝑘) and 𝑔(𝝍_𝑘), as shown in (11).

𝑦_𝑘 = 𝒘_𝑘^𝐻𝒉_𝑘^𝐻𝒗_𝑘𝑥_𝑘 + 𝑛_𝑘 = 𝜂_𝑘𝒘_𝑘^𝐻𝒂_𝑟(𝜃_𝑘^𝑟, 𝜙_𝑘^𝑟)𝒂_𝑡^𝐻(𝜃_𝑘^𝑡, 𝜙_𝑘^𝑡)𝒗_𝑘𝑥_𝑘 + 𝑛_𝑘,       (8)

\(\begin{aligned}y_{k}=\left[\begin{array}{l}\operatorname{Re}\left(y_{k}\right) \\ \operatorname{Im}\left(y_{k}\right)\end{array}\right]=\left[\begin{array}{l}\operatorname{Re}\left(\boldsymbol{w}_{k}^{H} \boldsymbol{h}_{k}^{H} \boldsymbol{v}_{k} x_{k}+n_{k}\right) \\ \operatorname{Im}\left(\boldsymbol{w}_{k}^{H} \boldsymbol{h}_{k}^{H} \boldsymbol{v}_{k} x_{k}+n_{k}\right)\end{array}\right],\end{aligned}\)       (9)

𝒏_𝑘 = [Re(𝑛_𝑘) Im(𝑛_𝑘)]^𝑇,

𝒏_𝑘 ~ 𝑁(0, 𝑸_𝑛),

\(\begin{aligned}\boldsymbol{Q}_{n}=\frac{\sigma_{n}^{2}}{2} \boldsymbol{I}_{2},\end{aligned}\)       (10)

𝑓(𝝍_𝑘) = Re(𝒘_𝑘^𝐻𝒉_𝑘^𝐻𝒗_𝑘𝑥_𝑘),

𝑔(𝝍_𝑘) = Re(𝒘_𝑘^𝐻𝒉_𝑘^𝐻𝒗_𝑘𝑥_𝑘),       (11)

The initial state vector and covariance were calculated using (12) and (13):

\(\begin{aligned}\widehat{\boldsymbol{\psi}}_{0}=E[\boldsymbol{\psi}]\end{aligned}\),       (12)

\(\begin{aligned}\boldsymbol{P}_{0}=E\left[\left(\boldsymbol{\psi}-\widehat{\boldsymbol{\psi}}_{0}\right)\left(\boldsymbol{\psi}-\widehat{\boldsymbol{\psi}}_{0}\right)^{T}\right],\end{aligned}\)       (13)

To predict the next state vector, the previous state vector was used. Therefore, the state vector and covariance were predicted using (14) and (15), respectively. Here, the state index is represented as 𝑘, which is an integer greater than or equal to 1.

\(\begin{aligned}\widehat{\boldsymbol{\psi}}_{k}^{f}=\widehat{\boldsymbol{\psi}}_{k-1}\end{aligned}\),       (14)

\(\begin{aligned}\overline{\boldsymbol{P}}_{k}=\boldsymbol{P}_{k-1}+\boldsymbol{Q}_{g}\end{aligned}\),       (15)

The UKF-based beam tracking method proposed herein tracks angles by estimating the motion state of the UAV as a Gaussian distribution by substituting several sample points called sigma points into a nonlinear measurement function.

Here, \(\begin{aligned}\overline{\boldsymbol{\psi}}_{k}\end{aligned}\) represents the (2n + 1) sigma points, as shown in (16), where the value of nn is 4, the dimension of the state vector, as shown in (6).

\(\begin{aligned}\overline{\boldsymbol{\psi}}_{k}=\left[\begin{array}{llll}\overline{\boldsymbol{\psi}}_{k}^{0} & \overline{\boldsymbol{\psi}}_{k}^{1} & \ldots & \overline{\boldsymbol{\psi}}_{k}^{2 n+1}\end{array}\right]\end{aligned}\),       (16)

Each element of \(\begin{aligned}\overline{\boldsymbol{\psi}}_{k}\end{aligned}\) can be calculated through (17). Here, the 𝑖-th column vector of the matrix shown in (15) is represented as \(\begin{aligned}\left(\sqrt{\bar{P}_{k}}\right)_{(i)}\end{aligned}\), and the weights in (17) can be calculated through (18). Here, 𝑠𝑠 is a scaling variable, and α is a constant indicating the degree to which the sigma points are spread around the predicted state vector (\(\begin{aligned}\widehat{\boldsymbol{\psi}}_{k}^{f}\end{aligned}\)). Here, the constant α is usually set to a small positive value within the range 10⁻⁴ ≤ α ≤ 1 and was calculated as 10⁻³ in this study. The constant 𝜅 represents a quadratic scaling variable and was calculated as (3 − 𝑛).

\(\begin{aligned}\begin{array}{c}\overline{\boldsymbol{\psi}}_{k}^{0}=\widehat{\boldsymbol{\psi}}_{k}^{f}, \\ \overline{\boldsymbol{\psi}}_{k}^{i}=\widehat{\boldsymbol{\psi}}_{k}^{f}+\gamma\left(\sqrt{\bar{P}_{k}}\right)_{(i)}, i=1, \ldots, n, \\ \overline{\boldsymbol{\psi}}_{k}^{i}=\widehat{\boldsymbol{\psi}}_{k}^{f}-\gamma\left(\sqrt{\bar{P}_{k}}\right)_{(i)}, i = n+1, \ldots, 2n, \end{array}\end{aligned}\)       (17)

\(\begin{aligned}\begin{array}{c}\gamma=\sqrt{n+s} \\ s=\alpha^{2}(n+\kappa)-n,\end{array}\end{aligned}\)       (18)

As in the process of (19), the previously calculated sigma points were substituted into the non-linear measurement function, and the result is expressed as 𝒁_𝑘 (𝒁_𝑘 = [𝑍_𝑘⁰ 𝑍_𝑘¹ … 𝑍_𝑘^2𝑛+1]^𝑇).

\(\begin{aligned}Z_{k}^{i}=\left[f\left(\overline{\boldsymbol{\psi}}_{k}\right) g\left(\overline{\boldsymbol{\psi}}_{k}\right)\right]^{T}, i=0, \ldots, 2 n,\end{aligned}\)       (19)

The state vector and auto-covariance can be estimated from the Gaussian distribution using the output value (𝑍_𝑘^𝑖) of the nonlinear measurement function. (20) represents the process of estimating the state vector, and (21) shows the process of estimating the auto-covariance. The weights used for each calculation are expressed in (22). When estimating the distribution of the state vector (𝝍), the value 𝛽 was set to 2 because the estimated distribution followed a Gaussian distribution.

\(\begin{aligned}\widehat{\boldsymbol{Z}}_{k}=\sum_{i=0}^{2 n} W_{i}^{m} Z_{k}^{i}\end{aligned}\)       (20) 

\(\begin{aligned}\boldsymbol{P}_{(Z Z) k}=\sum_{i=0}^{2 n} W_{i}^{c}\left[Z_{k}^{i}-\widehat{\boldsymbol{Z}}_{k}\right]\left[Z_{k}^{i}-\widehat{\mathbf{Z}}_{k}\right]^{T}+\boldsymbol{Q}_{n},\end{aligned}\)        (21)

\(\begin{aligned}\begin{array}{c}W_{0}^{m}=\frac{s}{n+s}, \\ W_{0}^{c}=\frac{s}{n+s}+\left(1-\alpha^{2}+\beta\right), \\ W_{i}^{m}=W_{i}^{c}=\frac{s}{2(n+s)}, i=1, \ldots, 2 n,\end{array}\end{aligned}\)       (22)

The cross-covariance between the state vector (\(\begin{aligned}\widehat{\boldsymbol{\psi}}_{k}^{f}\end{aligned}\)) previously predicted through (14) and state vector (\(\begin{aligned}\widehat{Z}_{k}\end{aligned}\)) estimated through (20) can be calculated using (23).

\(\begin{aligned}\boldsymbol{P}_{(X Z) k}=\sum_{i=0}^{2 n} W_{i}^{c}\left[\overline{\boldsymbol{\psi}}_{k}^{i}-\widehat{\boldsymbol{\psi}}_{k}^{f}\right]\left[Z_{k}^{i}-\widehat{\boldsymbol{Z}}_{k}\right]^{T},\end{aligned}\)       (23)

The UKF Kalman gain (𝜀𝑘) can be calculated using (24) with the previously calculated auto-covariance (𝑷(𝑍𝑍)𝑘) and cross-covariance (𝑷(XZ)𝑘). Additionally, using the calculated Kalman gain values, we modified the state vector (\(\begin{aligned}\widehat{\boldsymbol{\psi}}_{k}^{f}\end{aligned}\)) and covariance (\(\begin{aligned}\widehat{\boldsymbol{\psi}}_{k}^{f}\end{aligned}\)) predicted in (14) and (15). (25) denotes the final estimate of the current channel angle vector (\(\begin{aligned}\widehat{\boldsymbol{\psi}}_{k}\end{aligned}\)), and (26) represents the final covariance of the channel angle vector (𝑷𝑘). Both values were used for beam tracking in the following state. The UKF-based beam tracking scheme is summarized in the flow chart in Fig. 3.

Fig. 3. UKF-based beam tracking algorithm using hybrid beamforming.

𝜀𝑘 = 𝑷_(XZ)𝑘𝑷⁻¹_(𝑍𝑍)k,       (24)

\(\begin{aligned}\widehat{\boldsymbol{\psi}}_{k}=\widehat{\boldsymbol{\psi}}_{k}^{f}+\varepsilon_{k}\left[\boldsymbol{Z}_{k}-\widehat{\boldsymbol{Z}}_{k}\right]\end{aligned}\),       (25)

\(\begin{aligned}\boldsymbol{P}_{k}=\overline{\boldsymbol{P}}_{k}-\varepsilon_{k} \boldsymbol{P}_{(z z) k} \varepsilon_{k}^{T}\end{aligned}\) .       (26)

4. Simulation Results 

In this section, we present and analyze the simulation results. The simulation environment and results are as follows.

4.1 Simulation Setup 

Table 1 outlines the simulation system parameters. The simulations were performed based on the UAV-enabled NR downlink MIMO-OFDM system, which was configured to have a system bandwidth of 100 MHz in the frequency band of 30 GHz.

Table 1. System parameters

4.2 Performance Evaluation 

An existing work on comparative analysis proposes a UKF-based beam tracking technique using analog beamforming [11], so our study compares and analyzes the case of using analog and hybrid beamforming to evaluate the performance improvement by the proposed technique. The mean square error (MSE), frame error rate (FER), throughput, and spectral efficiency (SE) were used as the performance indicators. In addition, all the performance indicators were based on AOD. In the case of MSE, it was calculated using (26). Because the remaining ZOD, AOA, and ZOA showed similar patterns to the AOD, only the AOD components have been covered in this study.

\(\begin{aligned}M S E=E\left[\left|\phi_{k}^{t}-\hat{\phi}_{k}^{t}\right|^{2}\right].\end{aligned}\)       (27)

Fig. 4 shows the simulation results and comparison of the performances with respect to MSE based on the beamforming type. When the UKF-based beam tracking was performed using hybrid beamforming, it was found that the MSE improved to a greater extent than when analog beamforming was used.

Fig. 4. Comparison of beam tracking performances based on the UKF according to beamforming type (MSE).

Fig. 5 shows the simulation results for comparison of the MSE performances according to the number of RF chains when using hybrid beamforming. The simulations were conducted for 8 and 16 RF chains. As seen in Fig. 5, the performance was improved when the number of RF chains was 16 instead of 8. Thus, in the following simulations, when hybrid beamforming was used, the experiments were conducted with 16 RF chains.

Fig. 5. Comparison of beam tracking performances based on the UKF according to the number of RF chains (MSE).

Fig. 6 shows the results of analyzing the MSE performances of the UKF-based beam tracking algorithm when using hybrid beamforming at different signal-to-noise ratios (SNRs). As the SNR increased, the estimated MSE of the AOD gradually decreased. In this case, the channel angle variance (𝜎2) was set to (0.5°)2 to perform the simulations.

Fig. 6. Comparison of beam tracking performances based on the UKF according to signal-to-noise ratio (SNR) (MSE).

Fig. 7 shows the simulation results of analyzing the MSE performance of the proposed algorithm according to channel angle variance (𝜎2). As the value of the channel angle variance increased, the channel changed rapidly and beam tracking based on the UKF became difficult. Consequently, as can be seen in Fig. 7, the MSE of the AOD increased. The SNR was set to 20 dB.

Fig. 7. Comparison of beam tracking performances based on the UKF according to the channel angle variance (MSE).

Figs. 8, 9, and 10 show the FER, throughput, and SE, respectively, based on analog and hybrid beamforming. When simulating the SNR in intervals of 5 dB, from 0 dB to 40 dB, it was observed that for hybrid beamforming, the performance improved compared to that of analog beamforming.

Fig. 8. Comparison of beam tracking performances based on the UKF according to the beamforming type (FER).

Fig. 9. Comparison of beam tracking performances based on the UKF according to the beamforming type (Throughput).

Fig. 10. Comparison of beam tracking performance based on the UKF according to the beamforming type (SE).

Analog beamforming is a method of adjusting the phase by generating only one beam at a time using one RF chain. Although this approach is good in terms of hardware implementation, it has the disadvantage of being too expensive as well as limited to one user and one stream. On the other hand, hybrid beamforming is a method of simultaneously adjusting the phase of the baseband using multiple RF chains and digital signal processing of the baseband, and analog and digital beamforming are applied at the same time. Since a small number of phase regulators can be used to adjust the balance between the spectral and hardware efficiencies, we can predict better performance than with analog beamforming.

5. Conclusion 

This study proposes a UKF-based beam tracking method using hybrid beamforming in a UAV-enabled NR MIMO-OFDM system. The proposed algorithm uses a nonlinear measurement function at several sample points called sigma points to estimate the motion state of the UAV as a Gaussian distribution while tracking the beam angle. In addition, by utilizing hybrid beamforming, the proposed method can be applied to multi-user and multi-stream environments over existing algorithms that are limited to single-user and single-stream environments, thus increasing the data capacity and utilization in 5G systems. The simulation results confirm that the proposed algorithm can track channel angles accurately with high spectral efficiency at the transceiver. The future research challenges include evaluating the performance of the algorithm by applying it to multi-user and multi-stream environments [12].