DoA Prediction Based Beamforming with Low Training Overhead for Highly-Mobile UAV Communication with Cellular Networks

Abstract

In supporting communications with unmanned aerial vehicles (UAVs) as aerial user equipments (aUEs) in cellular systems, the current beamforming schemes based on channel state estimation are facing severe challenges from the pilot contamination effect, especially in 5G and future networks where the cell size becomes small and the user density is high. Beamforming schemes based on signal direction of arrival (DoA) are regarded as a highly promising alternative to solve this problem. However, to achieve optimal performance for DoA-based beamforming, the error to DoA estimation during pilot signal intervals, caused by the high mobility of UAVs, must be addressed. In the meantime, the training overheads of traditional DoA estimation algorithms must be reduced to save the bandwidth for data communication. This paper investigates uplink beamforming performance enhancement based on signal DoA estimation to support UAV-cellular network communication. We propose a novel DoA estimation algorithm to predict angle variations during the intervals, which achieves high precision even when UAVs are at high mobility. The prediction process requires no pilot signals and enables timely adjustment of the steering vector when calculating the beamforming weight vector. The proposed algorithm contributes to the realisation of a beamforming scheme with real-time steering vector updates, which simultaneously maintains high beamforming gains and low training overheads. Simulation results show that, compared with the conventional DoA-based beamforming scheme, the proposed method yields more accurate DoA estimation output and higher gains. Furthermore, simulation experiments also suggests that applying the proposed scheme can reduce up to 100 pilot signal transmissions per second.

1. Introduction

With the rapid development of UAVs, these devices are revolutionizing a large quantity of civil application fields, including industrial construction, products inspection, safety monitoring, agriculture, rescue and search, bird-eye viewing and so on [1,2]. Some common functions of UAVs in these applications are photographing and video recording from the air, and transfering high-resolution photos or videos requires a robust and fast communication link between the UAV and the ground server. It is thus useful to incorporate UAVs into the cellular system such as aUEs, due to the large geological coverage and stable communication it provides. In wireless communications between UAVs and cellular networks, the channels are usually dominated by line-of-sight (LoS) components accounting for 90% of the total power [3,4]. The LoS channel characteristics enhance the receiving power during communications, but also cause strong inter-cell interference [5,6,7,8].

Beamforming has been given considerable attention due to its ability to suppress such interference [9,10,11] and direct power to the desired direction (in this case, the receiver), as well as its potentially significant role in current and future communication systems such as 5G networks [12,13]. However, pilot-assisted channel state information (CSI) estimation, which is the basis of most current beamforming schemes, faces severe challenges from pilot contamination effects [14,15]. In the UAV-ground link, with less blockage the inter-cell uplink pilot interference is often so strong that it could intensify interference among pilot signals [7,15]. Thus, traditional beamforming faces decreased performance to support aerial users in current and future cellular networks.

On the other hand, beamforming based on signals’ DoA estimations, as an alternative to the CSI based solution, is shown to achieve better performance in recent years [16,17]. DoA estimation algorithms can extract the channel information from nonorthogonal signals, and therefore avoid the destructive effects of pilot contamination. Designs of combined DoA estimation and beamforming schemes for cellular system are proposed in [16,18], showing performance approaching that of the corresponding CSI based scheme with perfect CSI knowledge. Therefore, applying such method has now become a hot research topic and has the potential to supplant the conventional beamforming scheme in future cellular networks.

Despite the high potential, the research on applying DoA based beamforming in cellular system and especially on UAVs are merely at the early stage. One major challenge it faces is that the target’s mobility affects the accuracy of current estimation methods. Traditionally, the beamforming weight vector is updated only when the DoA is updated by processing a pilot signal. During the intervals between the pilot signals, the high mobility of a UAV results in a difference between its true and estimated DoA values. This problem is illustrated in the upper half of Figure 1. In the figure, a timeline is shown on the left side, and the beams formed at the corresponding time points are displayed by red curves on the right. Suppose that two consecutive pilot-assisted DoA estimations are executed at $t_{p1}$ and $t_{p2}$. However, during $t_{p1}$ and $t_{p2}$, e.g., at $t_1$ and $t_2$, the UAV’s movement causes the DoA to vary. Such angle variance is further illustrated in Figure 2. The figure shows the UAV’s positions $p{r}_{p1}$ and $p{r}_1$ at $t_{p1}$ and $t_1$, respectively, with the corresponding signal arrival angles ${\eta }_{p1}$ and ${\eta }_1$. At $t_{p1}$, the BS obtains an estimated DoA ${\gamma }_{p1}$ (an estimated position $p{e}_{p1}$ is also obtained in some algorithms). It can be observed that the estimation error is increased from (${\eta }_{p1}-{\gamma }_{p1}$) at $t_{p1}$ to (${\eta }_1-{\gamma }_{p1}$) at $t_1$. The same situation applies to $t_2$, which is not implied in the figure. Hence, back in Figure 1, the optimal gain can be maintained only at $t_{p1}$, whereas at $t_1$ and $t_2$, as the angle error increases, the gain decreases. Based on the above analysis, to maintain optimum and stable gains, the problem of the target UAV’s high mobility must be addressed.

In [14,19], DoA estimation methods are proposed to exploit multi-path signals. To further distinguish the LoS signals from the multi-path components, an estimation method is proposed in [20], which explores the strongest line-of-sight channel. The algorithms in [14,16,19,20] adopt the same eigen-decomposition method, which is applied in the traditional Multiple Signal Classification (MUSIC) algorithms. The computational complexity of these algorithms is generally high and their accuracy can be severely affected when the noise is intense. Therefore, in [17,21], DoA estimation methods of lower complexity and higher accuracy have been proposed.

The methods introduced above cannot maintain highly accurate estimations for fast-moving UAVs without incurring a high system training overhead, because they focus on a single time’s connection via beamforming, without giving enough attention to the realistic mechanism of the cellular system. In these schemes, the typical solution to the UAV’s high mobility problem is to shorten the pilot signal interval ($t_{p2}-t_{p1}$), so that the DoA information is updated frequently to avoid large decrease in gain. However, this solution also requires a higher number of pilot signals to be transmitted for each user in the network. The work in [14,20] have reduced the required number of pilot signals in each beamforming training, however, these methods still heavily rely on training sequences because each DoA estimation at least requires one pilot signal. In future cellular networks, the number of users is expected to be increased by a factor on the order of tens [22], and if each individual user requires a large number of pilot signals, the total training overhead will be greatly increased and occupy an excessive amount of the bandwidth originally allocated for data transmission. Furthermore, most real-world deployment of the cellular system will set a minimum interval for transmitting pilot signals, which restricts the frequency for DoA estimation. In [23,24], position-aided beamforming methods are proposed for high-speed train communications. Since the track of the train is known to the BS processor, beamforming can be optimised by casting the highest gain to the train’s antenna at any moment, without the assistance of pilot signals. However, these methods are not applicable in UAV communications, since most UAVs do not have pre-defined trajectories. Even if trajectories of UAVs are known in some application fields, such tracks are far less precise than the ground rail way case.

In this paper, we propose an algorithm for evaluating the DoA of a UAV by utilizing position information obtained from the UAV’s flight status information (FSI). The algorithm incorporates a prediction method for tracking the angle variations during intervals between the reception of FSI update messages. Since the prediction process does not require the transmission of pilot signals, it can be executed frequently without increasing the training overhead. In this way, a steady and accurate output of DoA estimations is obtained. The proposed algorithm enables the realization of a novel beamforming scheme. As illustrated in the lower half of Figure 1, instead of using the DoA calculated at $t_{p1}$, this scheme allows the weight vector to be obtained using up-to-date DoA values generated via prediction at times between $t_{p1}$ and $t_{p2}$. Thus, high gains can be maintained for highly-mobile UAVs. Furthermore, instead of requiring a shorter ($t_{p2}-t_{p1}$), the proposed scheme can simply generate more predictions to maintain accurate DoA information, resulting in low training overhead.

Simulation experiments carried out to verify the proposed method are presented. Compared with the conventional DoA-based beamforming scheme using an improved variant of the MUSIC algorithm [17], the proposed method yields more accurate DoA estimations and higher gains. The performance margin is especially remarkable when the UAV is flying fast or the DoA estimation interval is large. Besides, simulation experiments also suggests that applying the proposed scheme can reduce up to 100 pilot signal transmissions per second.

The rest of the paper is organized as follows: Section 2 describes the sources of DoA errors and their impact on beamforming methods. Section 3 introduces the proposed algorithm and the method for the real-time steering vector update beamforming scheme. Simulation experiments and results are given in Section 4 to verify their performance. Section 5 concludes this paper.

Notations: We employ boldface for vectors and bold capital lettes for matrices; the superscript ${(·)}^{\mathrm{T}}$ denotes the transpose of a vector or matrix; the superscript ${(·)}^{\mathrm{H}}$ denotes the Hermitian transpose of a vector or matrix; the superscript ${(·)}^{-1}$ denotes the inverse of a matrix; $\mathbf{I}$ is the identity matrix; $\exp \left(x\right)$ denotes exponentia; $|·|$ denotes absolute value; the superscript ${(·)}^{\circ }$ denotes angle in degrees. The acronym list is shown in

Table 1. Acronym list.

Acronym	Explanation
UAV	unmanned aerial vehicle
DoA	direction of arrival
BS	base station
aUE	aerial user equipment
LoS	line-of-sight
CSI	channel state information
SNR	signal-to-noise ratio
SINR	signal-to-interference-plus-noise ratio
SIR	signal-to-interference ratio
MUSIC	multiple signal classification
FSI	flight status information
DL	diagonal loading
LCMV	linearly constrained minimum variance
GPS	global positioning system
IMU	inertial measurement unit
QoS	quality of service
NED	north-east-down
ECEF	earth-centered-earth-fixed
2-D	2-dimensional
3-D	3-dimensional

.

2. Problem Formulation

We consider a UAV-cellular communication scenario in which a UAV, as an aUE, transfers data over the uplink, while other UAVs simultaneously communicating with their serving BSs introduce interference with the target received uplink signal. The UAV’s altitude is assumed to be above 40 m, in which case, according to 3GPP Release 15, it has a LoS probability of 1 with the BS. To improve the received signal-to-interference-plus-noise ratio (SINR), the BS applies beamforming based on DoA estimation by first estimating the angle of arrival of the target signal and then executing beamforming.

Here, we illustrate the sources of DoA estimation errors due to the UAV’s mobility and the influence of these errors on the performance of beamforming algorithms. A brief discussion on such error has already been provided in Section 1. Here, we present a general introduction to DoA estimation errors. In a typical UAV-cellular communication scenario, multiple factors, including the angular resolution of the algorithms, the signal-to-noise ratio (SNR) and the angular spread effect, can affect the error range of DoA estimation algorithms. Moreover, additional DoA errors are caused by the UAV’s mobility during the time interval between two DOA estimations. Suppose that two consecutive DoA estimations are performed at time instants $t_{p_{n-1}}$ and $t_{p_n}$, with an interval $\mathsf{\Delta }t=t_{p_n}-t_{p_{n-1}}$. During $\mathsf{\Delta }t$, the actual DoA of the incoming signal continuously varies, while the estimated DoA remains the same. Thus, at any time instant $t_m,t_{p_{n-1}}\le t_m\le t_{p_n}$, a DoA estimation error exists, which is equal to the difference between the estimated angle and the actual angle:

$$e\left(t_m\right)=|{\gamma }_e-\eta \left(t_m\right)|,$$

(1)

where $e\left(t_m\right)$ denotes the estimation error at $t_m$ and $\eta \left(t_m\right)$ and ${\gamma }_e$ are the corresponding actual and estimated DoA values, respectively. In addition to a longer DoA estimation interval, a higher UAV speed or a reduced cell radius in the 5G system will also cause this DoA estimation error to increase [20,25].

The gain achieved with classical nonrobust beamforming decreases dramatically with even a minor DoA error [26,27]. Although robust beamforming methods have been developed to suppress such sensitivity, the optimal gains of all these algorithms degrade to various extents as the DoA error increases. We take the widely studied diagonal loading (DL) algorithm for robust beamforming as an example to illustrate this effect. In this algorithm, the beamforming weight vector, w, is obtained as follows:

$$\mathbf{w}=\frac{{(\mathbf{R}+\sigma {\mathbf{I}}_L)}^{-1}\mathbf{s}\left(\theta \right)}{{\mathbf{s}}^{\mathrm{H}}\left(\theta \right){(\mathbf{R}+\sigma {\mathbf{I}}_L)}^{-1}\mathbf{s}\left(\theta \right)},$$

(2)

where ${\mathbf{I}}_L$ is an identity matrix; $\mathbf{s}\left(\theta \right)$ denotes the steering vector of the target signal and $\theta$ is the estimated DoA value; $\mathbf{R}$ is an $L\times L$ array correlation matrix, the elements of which represent the correlations between the received signals of the array antennas. The coefficient $\sigma$, known as the DL factor, modifies $\mathbf{R}$ by enhancing the effect of noise, forcing the beamformer to mitigate noise and thus weakening its ability to suppress interference. In this way, the beamformer is made less sensitive to DoA errors.

Over a span of many years and up through recent times, a large number of algorithms have been proposed for mapping the DL factor with a certain DoA error range to achieve optimal performance [26,28,29,30]. However, simply finding the most suitable DL factor will not result in optimal gains since the DoA error range places an upper limit on the achievable gain. A plot of the SINR output of a DL beamformer versus the DL factor is shown in Figure 3, where the input SNR is 10 dB and the number of antenna elements is 8. The blue, red and orange curves represent the outputs for DoA estimation errors of 1${}^{\circ }$, 3${}^{\circ }$, and 5${}^{\circ }$, respectively. In this figure, 3.93 dB and 3.54 dB differences in the maximum gains are observed between the blue and red curves and the red and orange curves, respectively, suggesting that a large DoA error inevitably leads to a low gain. Thus, precise DoA estimation is crucial for proper beamforming performance.

3. The Proposed DoA Estimation Algorithm and Beamforming Scheme

The proposed algorithm derives real-time DoA information of the UAV from its FSI, and then the calculated DoA values are supplied to the beamformer and used to obtain the optimum beamforming weight vector. Considering the size and power consumption limitation of most commercial UAVs, we assume the target UAV carries a single omni-directional antenna.

3.1. UAV FSI

Positions are sourced from the UAV FSI, which incorporates the UAV navigation data. By using a Kalman filter to integrate Global Positioning System (GPS) and on-board sensors’ motion information, the UAV’s navigator maintains more accurate positions and motion vectors (velocity and acceleration) than simply using GPS systems [31,32]. UAV’s FSI is regulated to be transmitted to the ground controllers periodically, for safety concerns. This telemetry message is exchanged at a minimal frequency of 4–5 Hz [1]. Although the BS could command the UAV to report more frequently, we will demonstrate in Section 4 that this is not an actual need. FSI is a reliable information resource—as specified in the 3GPP standard, it has high quality of service (QoS) priority (up to ${10}^{-3}$ Packet Error Loss Rate) [33]. The first step to calculate the signal DoA consists of extracting flight status data from the telemetry message, which can be realized by creating an interface between the coordination information stack and the beamforming processor.

To summarize, utilizing the FSI has several benefits. First, UAV’s position is deducted from processing UAV’s on-board GPS and the inertial measurement unit (IMU) data, which obtains higher accuracy than using the GPS sensor alone, and reduces the computational load on the BS end. Second, FSI is regulated to be transmitted for any type of UAVs, so that the proposed algorithm is applicable for all civil applications. Third, by using FSI, which already exists in the Command&Control Links between UAV and cellular networks, we reduce the use of training sequences and thus reduce the training overhead.

3.2. DoA Estimation and Prediction

The DoA of the incoming signal is defined as the angle between the signal’s propagation direction and the receiver’s antenna array. To calculate DoA, the position vector from FSI needs to be first transformed to a common reference which incorporates the BS’s position vector. The universal local north-east-down (NED) frame is used to this end, where the z-axis is perpendicular to the earth surface, and x and y axes are both tangent to the earth surface. A GPS position is typically expressed in Geodetic frame as $\rho ={(\omega ,\phi ,h)}^{\mathrm{T}}$, where h is the height above the earth surface; $\omega$ and $\phi$ are longitude and latitude, respectively. Set the original UAV and BS’s GPS positions as ${\rho }_{ug}$ and ${\rho }_{bg}$, respectively. Therefore, ${\rho }_{ug}={({\omega }_u,{\phi }_u,h_u)}^{\mathrm{T}}$, and ${\rho }_{bg}={({\omega }_b,{\phi }_b,h_b)}^{\mathrm{T}}$. To perform the transformation, their equivalent positions in Earth-Centered-Earth-Fixed (ECEF) frame, ${\mathbf{p}}_{ue}$ and ${\mathbf{p}}_{be}$, are calculated first [34],

$${\mathbf{p}}_{ue}=\left(\begin{array}{c}(\frac{r_e}{\sqrt{1-e^2{\sin }^2{\phi }_u}}+h_u)\cos {\phi }_u\cos {\omega }_u\\ (\frac{r_e}{\sqrt{1-e^2{\sin }^2{\phi }_u}}+h_u)\cos {\phi }_u\sin {\omega }_u\\ (\frac{r_e}{\sqrt{1-e^2{\sin }^2{\phi }_u}}(1-e^2)+h_u)\sin {\phi }_u\end{array}\right),$$

(3)

$${\mathbf{p}}_{be}=\left(\begin{array}{c}(\frac{r_e}{\sqrt{1-e^2{\sin }^2{\phi }_b}}+h_b)\cos {\phi }_b\cos {\omega }_b\\ (\frac{r_e}{\sqrt{1-e^2{\sin }^2{\phi }_b}}+h_b)\cos {\phi }_b\sin {\omega }_b\\ (\frac{r_e}{\sqrt{1-e^2{\sin }^2{\phi }_b}}(1-e^2)+h_b)\sin {\phi }_b\end{array}\right),$$

(4)

where ${\mathbf{p}}_{ue}$ and ${\mathbf{p}}_{be}$ are the UAV and the BS’s position vectors, respectively. $r_e$ is the earth radius, and e is a constant. Then, the UAV’s position in our defined local NED frame, ${\mathbf{p}}_{ul}$, is calculated as:

$${\mathbf{p}}_{ul}={(x_{ul},y_{ul},z_{ul})}^{\mathrm{T}}={\mathbf{T}}_{en}({\mathbf{p}}_{ue}-{\mathbf{p}}_{be}).$$

(5)

where ${\mathbf{T}}_{en}$ denotes the transformation matrix from the ECEF coordinates to the local NED coordinates,

$${\mathbf{T}}_{en}=\left[\begin{array}{ccc}-\sin {\phi }_b\cos {\omega }_b& -\sin {\phi }_b\sin {\omega }_b& \cos {\phi }_b\\ -\sin {\omega }_b& \cos {\omega }_b& 0\\ -\cos {\phi }_b\cos {\omega }_b& -\cos {\phi }_b\sin {\omega }_b& -\sin {\phi }_b\end{array}\right].$$

(6)

After incorporating the UAV’s position, the DoA estimation is obtained as follows:

$$DoA=\arccos \frac{x_{ul}-x_{bl}}{\sqrt{{(x_{ul}-x_{bl})}^2+{(y_{ul}-y_{bl})}^2+{(z_{ul}-z_{bl})}^2}},$$

(7)

where $(x_{bl},y_{bl},z_{bl})$ is the BS’s position. As the BS is on the origin, Equation (7) can be simplified as follows:

$$DoA=\arccos \frac{x_{ul}}{\sqrt{x_{ul}^2+y_{ul}^2+z_{ul}^2}}.$$

(8)

In the prediction algorithm, position variations based on estimated UAV’s movements are first calculated, and then transformed into the new estimated DoA angles. Assume a total number of $K_0$ predictions of the DoA values are performed between two consecutive DoA estimations via FSI, and the n-th calculated UAV’s position is denoted as ${\mathbf{p}}_n={({\alpha }_n,{\beta }_n,{\lambda }_n)}^{\mathrm{T}},0\le n\le K_0$. Then, denote the n-th calculated UAV’s velocity and the acceleration as ${\mathbf{v}}_n={(u_n,v_n,w_n)}^{\mathrm{T}},0\le n\le K_0$, and $\mu ={({\mu }_x,{\mu }_y,{\mu }_z)}^{\mathrm{T}}$, respectively. The status transition matrix is then given as follows:

$$\left[\begin{array}{c}{\alpha }_n\\ u_n\\ {\beta }_n\\ v_n\\ {\lambda }_n\\ w_n\end{array}\right]=\left[\begin{array}{cccccc}1& \tau & 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& \tau & 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& \tau \\ 0& 0& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{\alpha }_{n-1}\\ u_{n-1}\\ {\beta }_{n-1}\\ v_{n-1}\\ {\lambda }_{n-1}\\ w_{n-1}\end{array}\right]+\left[\begin{array}{c}0.5{\tau }^2{\mu }_x\\ \tau {\mu }_x\\ 0.5{\tau }^2{\mu }_y\\ \tau {\mu }_y\\ 0.5{\tau }^2{\mu }_z\\ \tau {\mu }_z\end{array}\right],$$

(9)

where $\tau$ is the time step of the prediction process. Here, ${\mathbf{v}}_0$ and $\mu$ are deducted from the original velocity ${\mathbf{v}}_b$ and acceleration vectors ${\mu }_b$ which are read from FSI in UAV’s vehicle carried NED frame,

$$\begin{array}{ccc}\hfill {\mathbf{v}}_0& =& {\mathbf{T}}_{bn}{\mathbf{v}}_b,\hfill \end{array}$$

(10)

$$\begin{array}{ccc}\hfill \mu & =& {\mathbf{T}}_{bn}{\mu }_b,\hfill \end{array}$$

(11)

where ${\mathbf{T}}_{bn}$ is the transformation matrix from the vehicle carried NED frame to the local NED frame,

$$\begin{array}{cc}\hfill & {\mathbf{T}}_{bn}=\left[\begin{array}{ccc}\cos \delta \cos \psi & \cos \delta \sin \psi & -\sin \delta \\ r_a& r_b& \sin \varphi \cos \delta \\ r_c& r_d& \cos \varphi \cos \delta \end{array}\right],\hfill \\ \hfill & r_a=\sin \varphi \sin \delta \cos \psi -\cos \varphi \sin \psi ,\hfill \\ \hfill & r_b=\sin \varphi \sin \delta \sin \psi +\cos \varphi \cos \psi ,\hfill \\ \hfill & r_c=\cos \varphi \sin \delta \cos \psi +\sin \varphi \sin \psi ,\hfill \\ \hfill & r_d=\cos \varphi \sin \delta \sin \psi -\sin \varphi \cos \psi ,\hfill \end{array}$$

(12)

where, $\varphi$, $\delta$ and $\psi$ denote the Yaw, Pitch, and Roll rotational coordinates, respectively [34]. After the new position is predicted, $DoA$ could be updated using Equation (8).

Figure 4 illustrates how the prediction algorithm maintains a stable DoA estimation output. Suppose a linear array lies on the x axis and a DoA estimation is executed when the UAV is at the position ${\mathbf{pr}}_n$, with the actual DoA to be ${\eta }_n$. By applying the proposed algorithm the BS calculates the assumed DoA ${\gamma }_n$, using the UAV’s position from the FSI message, ${\mathbf{pe}}_n$. After a certain time, the UAV reaches a new position ${\mathbf{pr}}_{n+1}$, and the BS gets a new assumed position of it, ${\mathbf{pe}}_{n+1}$. Now the actual and assumed DoA values become ${\eta }_{n+1}$ and ${\gamma }_{n+1}$, respectively. Thus, the DoA error becomes ${\eta }_{n+1}-{\gamma }_{n+1}$, whereas on the estimation point it was ${\eta }_n-{\gamma }_n$. It can be seen that compared with Figure 2, the DoA error has not shown notable variations with the movement of the UAV. We use the curves ${\mathbf{c}}_r$ and ${\mathbf{c}}_e$ to denote the actual and the predicted tracks, respectively. Since the IMU keeps highly accurate UAV velocity and acceleration information during a short time, the position error remains in a limited range during the whole prediction process. ${\mathbf{c}}_r$ can be approximated by ${\mathbf{c}}_e$ with a vector:

$${\mathbf{c}}_r\doteq {\mathbf{c}}_e+({\mathbf{pr}}_n-{\mathbf{pe}}_n).$$

(13)

Although the prediction process does not obtain a significantly more accurate position information, it keeps the DoA error free from cumulative increasing without adding to the training overhead.

3.3. Beamforming Scheme with Real-Time Steering Vector Updates

By using the proposed method, the beamforming scheme is also radically different. The traditional only updates steering vector relying on pilots, now most estimations are done without processing traning sequences, and so steerging vector updates in real-time. In the beamforming process, the steering vector $\mathbf{s}\left(\theta \right)$ is used to adjust the direction of the main beam toward the target. Furthermore, it is derived directly from the DoA value. Thus, based on the proposed DoA estimation method, we propose a beamforming scheme that is suitable for providing service to UAVs with fast and stable uplink data transmission. First, the relation between the DoA value and the steering vector is introduced. Consider an array of L omnidirectional elements. When the DoA information is acquired, the steering vector is calculated as,

$$\mathbf{s}\left(\theta \right)={[\exp \left(j2\pi f{t}_d\right),\dots ,\exp \left(j2\pi fL{t}_d\right)]}^{\mathrm{T}},$$

(14)

where $t_d$ is the arrival time difference of the transmitted signal between array elements, given by:

$$t_d=\frac{r\cos \left(\theta \right)}{c},$$

(15)

where r is the distance between the array elements and c is the speed of light.

In our proposed beamforming scheme, beamforming is applied based on DoA estimations. This scheme consists of two stages during uplink data transmission. In Stage 1, the processor receives the FSI from the telemetry messages and calculates the DoA and the beamforming weight vector; then, it proceeds to Stage 2. In Stage 2, the processor continues to update the DoA information and the steering vector via the prediction process. When new FSI is obtained, Stage 2 terminates, and the processor returns to Stage 1. Through this process, the steering vector is updated in real-time so that the main beam can be constantly adjusted to track the target UAV, thus providing high gains for the signals of highly-mobile UAVs. The proposed scheme is summarized in Algorithm 1:

Algorithm 1: Beamforming Scheme with Real-Time Steering Vector Updates.

Decide the FSI update interval: $\mathsf{\Delta }T$. Then, decide the prediction update interval: $\tau$. Set $K_P=\frac{\mathsf{\Delta }T}{\tau }$.

4. Simulation Experiments

This section presents experiments conducted to verify the proposed DoA estimation algorithm and beamforming scheme. For this purpose, we present a performance comparison with a baseline beamforming scheme using the widely studied MUSIC algorithm. Here, a recently proposed improved variant of the MUSIC algorithm [17] is used, which offers higher accuracy and lower computational complexity than the conventional MUSIC algorithm. In all experiments, the UAVs and the BS are assumed to be in the defined local NDE frame. On the BS side, there is an antenna array with 16 elements lying on the z axis. The BS height is 15 m above the ground. The spacing between the array elements is half of the wavelength, which is 0.165 m in this case. Two UAV models in addition to the target UAV are include, which fly in circles and produce uplink signals that act as interference with the receiver. The speed values of the UAVs are selected in accordance with those applied in 3GPP Release 15. The maximum speed is 160 km/h, and a moderate value of 60 km/h is chosen. The target UAV’s transmission power is 23 dBm, and the transmitted signal-to-interference ratios (SIRs) are 1 dB and 2 dB. The noise power is −95 dBm. The carrier frequency is 0.9 GHz, and the speed of light is assumed to be $3.0\times {10}^8\mathrm{m}/\mathrm{s}$. The wireless air-ground channel model is built in accordance with the specifications of 3GPP Release 15 [3]. The small-scale fading parameters of the channel are determined in accordance with the third alternative model for fast fading in that document. The number of clusters contained in a signal is 15 [35]. The sampling interval of the improved MUSIC algorithm is $0.03255\times {10}^{-9}$ s, and the number of snapshots is 3000. The symbol length is $66.7\times {10}^{-9}$ s.

The receiving power $Pr$ (in mW) of each UAV is expressed as follows:

$$Pr={10}^{(Pt-PL)/10},$$

(16)

where $P_t$ and $PL$ denote the transmission power (in dBm) and the path loss (in dB), respectively. The path loss is a function of the 3-dimensional (3-D) distance between the UAV and the BS and the UAV’s altitude [3]:

$$\begin{array}{c}\hfill PL=max(23.9-1.8{\log }_{10}\left(h\right),20){\log }_{10}\left(d_{3D}\right)+20{\log }_{10}\left(\frac{40\pi f_c}{3}\right),\end{array}$$

(17)

where $d_{3D}$ and h are the 3-D distance and the UAV’s height, respectively, and $f_c$ is the carrier frequency. The settings of the interfering UAVs are identical in all experiments. Throughout the rest of this section, ‘UAV’ refers to the target UAV unless otherwise stated. The simulation parameters are summarized in

Table 2. Simulation Parameters.

Parameter	Value
Number of array elements	16
BS height	15 m
Spacing between array elements	0.165 m (half of wavelength)
UAV speed	60 km/h, 160 km/h
Transmission power (target UAV)	23 dBm
Transmission SIR	1 dB, 2 dB
Noise power	−95 dBm
Carrier frequency	0.9 GHz
Light speed	3.0 $\times {10}^8$ m/s
Path loss model	The Rural Macro cell model in [3]
Fast fading model	The third alternative in [3]
Number of clusters	15
Sampling interval	$0.03255\times {10}^{-9}$ s
Number of snapshots	3000
Symbol length	$66.7\times {10}^{-9}$ s

.

4.1. Performance Comparison for High and Low UAV Speed Scenarios

The purpose of this group of experiments is to compare the DoA estimation and beamforming performance of the proposed and baseline methods. Here, two scenarios are studied to consider the high and moderate mobilities of the UAV, for which the UAV’s speed is set to 160 km/h and 60 km/h, respectively. Horizontally, the trajectory of the target UAV is a curve with a radius of 80 m. We set the initial distance between the UAV and the BS as 100 m. For both beamforming schemes, we adopt two widely studied beamformers, a nonrobust method and a robust method, namely, the linearly constrained minimum variance (LCMV) beamformer and the DL beamformer, respectively. Because the typical transmission frequency of FSI messages is 4–5 Hz, the pilot signal interval is set to 200 ms for the proposed algorithm. The prediction process has low complexity and thus can be executed at a high frequency. However, given the limited change in the position of the UAV within a short time duration, the prediction process is executed every 1 ms in our experiments. The improved MUSIC algorithm considered for comparison uses reference signals to perform DoA estimation; considering that the reference signals usually have a higher transmission frequency than the telemetry messages, the DoA estimation interval for the traditional beamforming scheme is set to 50 ms. The errors of both DoA estimation methods and of the beamforming output are examined every 10 ms. Each time the averaged absolute error output of 20 times DoA estimation results are obtained. The widely adopted GPS multivariate Gaussian positioning error model is applied for the proposed method. Both the vertical and horizontal errors have means of zero. Based on a review of popular commercial products [36,37,38], the standard variances of the vertical and horizontal errors are selected to be $\sqrt{3}$ m and $\sqrt{2}$ m, respectively.

We compare the computational complexity of both DoA estimation algorithms using simulation experiments in Matlab. The general setting is as follows: considering the realistic execution frequency of both algorithms, the proposed algorithm is performed once and the prediction is executed once per 1ms; the improved MUSIC algorithm is performed four times. The algorithm execution time is obtained by averaging 100 independent executions. The average time duration in executing the conventional MUSIC algorithm is 0.0540 s, while the proposed method is 0.0029 s. The MUSIC algorithm is approximately 19 times higher in computation time than the proposed method. Therefore, the proposed method is of significantly lower computational complexity.

The DoA estimation errors for the high-speed and low-speed scenarios are shown in Figure 5a,b, respectively. From these figures, it can be seen that the proposed method has obtained better DoA estimation performance. In Figure 5a, we have marked the pilot signal intervals for the proposed algorithm during the period of 400–600 ms and for the improved MUSIC algorithm during the period of 450–500 ms. For the conventional method, it can be seen that during 450–500 ms, the UAV’s mobility causes the DoA estimation errors to increase. These errors are larger in Figure 5a than in Figure 5b due to the higher speed of the UAV. The proposed prediction method, on the other hand, continues tracking the variations in the DoA value, causing the errors to remain low during the DoA estimation interval. Besides during the intervals, the proposed algorithm is also more accurate on DoA estimations via pilot signals, e.g., at 600 ms. This is because it explores LoS signals directly, thus avoiding the destructive influence of the angular spread effect. It should be noted that if no LoS paths exist, the proposed method can be less accurate. However, according to 3GPP Release 15, a major proportion of the UAVs incorporated into the cellular system are maintaining LoS connections with the BSs, and therefore the proposed algorithm can be found useful in many civil UAV application scenarios.

The timely updating of the DoA estimations directly contributes to the performance of beamforming, as seen in Figure 6c,d for the two different speed scenarios. The red and blue lines represent the outputs of the DL beamformer combined with the proposed algorithm and the improved MUSIC algorithm, respectively, and the black and yellow lines represent the outputs of the LCMV beamformer combined with the proposed algorithm and the improved MUSIC algorithm, respectively. We summarize the statistics of these results in

Table 3. Statistics of the SINR performance.

Data	Value (Proposed Scheme)	Value (Conventional Scheme)
Standard variance (DL, UAV speed = 160 km/h)	0.04 dB	0.09 dB
Standard variance (LCMV, UAV speed = 160 km/h)	0.50 dB	0.92 dB
Average gain (DL, UAV speed = 160 km/h)	21.92 dB	21.31 dB
Average gain (LCMV, UAV speed = 160 km/h)	2.70 dB	−2.71 dB
Standard variance (DL, UAV speed = 60 km/h)	0.02 dB	0.05 dB
Standard variance (LCMV, UAV speed = 60 km/h)	0.16 dB	0.53 dB
Average gain (DL, UAV speed = 60 km/h)	21.95 dB	21.48 dB
Average gain (LCMV, UAV speed = 60 km/h)	3.46 dB	−0.88 dB

, where the average gains and standard variances of the DL and LCMV results are provided. In both figures, the proposed scheme using the DL beamformer exhibits the highest performance, with average gains of 21.92 dB for the scenario in Figure 6c and 21.95 dB for the scenario in Figure 7b, whereas the performance of the conventional scheme using the LCMV beamformer is the worst, with corresponding average gains of −2.71 dB and −0.88 dB, respectively. It is also observed that the DL beamformer achieves much higher gains than the LCMV beamformer. However, it should be noted that its computational complexity is also much higher. For both beamformers, there are no significant margins between the low-speed and high-speed cases in terms of the average SINR or variance, thus demonstrating the stability of the proposed beamforming scheme.

4.2. Performance Comparison for Varying Pilot Signal Intervals

In this subsection, we examine the beamforming performance of the proposed and conventional schemes considering varying pilot signal intervals. For both schemes, we consider three experiments based on scenarios with interval values of 10 ms, 50 ms and 200 ms. The UAV is flying along a curve with 80 m radius, and the speed is fixed at 160 km/h. The initial distance between the UAV and the BS is 100 m. The SINR outputs of the LCMV and DL beamformers are shown in Figure 7c,d, respectively.

It is observed that the proposed scheme maintains higher performance for both beamformers. Furthermore, the stability of the proposed method is convincingly demonstrated here since the three cases show very similar DoA estimation and beamforming performance, for both the LCMV and DL beamformers. Thus, we conclude that an FSI exchange frequency of 5 Hz is sufficient to achieve high and stable beamforming performance. In this way, the proposed algorithm can save significant training overhead. Accordingly, we compare the training overheads of the two schemes. Based on the previous analysis, we assume that the proposed method receives telemetry messages every 200 ms. Given that the telemetry information already exists on the Command&Control link for UAV-cellular communications, the corresponding overhead is incurred even if the FSI is not applied for DoA estimation; therefore, the traditional method will also require the consumption of a minimum of 5 Hz for telemetry messages. Thus, the proposed method can achieve overhead reductions of 100, 20 and 5 pilot signals per second relative to the conventional scheme when using pilot signal intervals of 10 ms, 50 ms and 200 ms, respectively.

We also note that the pilot signal transmission interval mainly affects the conventional scheme by magnifying the accumulated error of the improved MUSIC algorithm. In the traditional scheme, the DoA information cannot be updated until a new pilot signal is received and processed. Thus, this scheme suffers from large errors when the DoA estimation interval is 200 ms, and the gain also decreases dramatically.

4.3. Performance Evaluation for the Random Mobility Scenario

From the previous results, it can be concluded that DoA estimation is crucial for beamforming performance. When all other conditions remain the same, the beamformer’s SINR output is inversely proportional to the DoA error. However, the routes of UAVs are more complex than those of most traditional ground vehicles that are served in cellular networks. The varying trajectories and flexible headings of UAVs lead to constant variation in the DoA information and therefore may cause turbulent fluctuations in the output of DoA estimation algorithms.

In this subsection, we use a UAV random walk model to further verify the suitability of the proposed algorithm for UAVs with high mobility. In the model, the initial distance between the UAV and the BS is 490 $\mathrm{m}$. The amplitude of the UAV velocity is constant at 160 km/h, whereas its direction varies every 300 ms. The azimuth and polar angles of the velocity are chosen randomly between $0^{\circ }$ and ${360}^{\circ }$ and between $-{60}^{\circ }$ and ${60}^{\circ }$, respectively. The DoA estimation interval is 200 ms. The random walk process lasts 6000 ms and is executed 20 times at each point, and the average absolute errors are presented in Figure 8.

It can be seen that the proposed algorithm maintains accurate DoA estimations throughout the whole process. The overall stability is also remarkable: the average absolute errors remain between ${0.08}^{\circ }$ and ${0.36}^{\circ }$. Compared with the errors reported in the previous subsections, the output is more accurate here. This is because of the longer distance between the UAV and the BS, which causes the same position errors to correspond to smaller DoA estimation errors. Thus, the proposed DoA estimation algorithm maintains more accurate DoA estimations over longer distances.

5. Conclusions

In this paper, we investigate high performance beamforming for communications between UAVs and cellular networks. The UAV’s signal is estimated by a proposed DoA estimation algorithm and its variations are also predicted by using position information. The proposed algorithm maintains precise DoA estimations, and is of low complexity. Meanwhile, by using DoA information from the Command&Control Links instead of from pilot signals, the proposed algorithm incurs much less training overhead to the network. The algorithm is applicable to beamforming, based on which a beamforming scheme with real-time steering vector updates is also proposed. As proved by simulation results, by applying the proposed beamforming scheme higher DoA accuracy and more stable beamforming gains are obtained compared with traditional beamforming methods. In the meantime, training overhead is proved to be reduced significantly.