In recent years, the rapid expansion of the Internet of Things has led to a dramatic increase in the number of wireless access devices, placing enormous pressure on conventional terrestrial communication infrastructures. As a result, the unmanned aerial vehicle has emerged as a key component in next-generation wireless networks. The unmanned aerial vehicle offers unique advantages such as high mobility, flexible deployment, low cost, and the ability to establish line-of-sight links with ground users. In particular, when terrestrial base stations are damaged or absent, the unmanned aerial vehicle can serve as an aerial base station or a relay node to provide temporary communication coverage. However, most existing unmanned aerial vehicle systems are equipped with a single antenna, which limits their capability in terms of capacity, interference suppression, and beamforming flexibility. The integration of multiple antennas on the unmanned aerial vehicle enables spatial processing techniques such as beamforming, which can significantly enhance the quality of communication links and mitigate interference from undesired directions.
In this thesis, I focus on the communication scenario where no terrestrial base station is available. A multi-antenna unmanned aerial vehicle is used to provide temporary communication services for ground users. The main contributions of this work are twofold. First, I propose a Capon beamforming algorithm based on volume integration to handle the interference and potential errors caused by the mobility of the unmanned aerial vehicle and the complexity of the propagation environment. Second, I propose an optimized deployment method for a multi-antenna unmanned aerial vehicle to minimize its transmit power while satisfying the communication rate requirements of all ground users. Throughout this work, the term “unmanned aerial vehicle” is used consistently to emphasize the core subject of the study.
1. Background and Motivation
The fifth-generation mobile communication system promises high data rates, low latency, massive connectivity, and enhanced reliability. According to market reports, global mobile data traffic has been growing exponentially, and the number of connected devices continues to increase. In this context, the unmanned aerial vehicle has been recognized as a promising platform for extending wireless coverage, offloading traffic from overloaded terrestrial base stations, and providing communication services in emergency scenarios. The unmanned aerial vehicle can operate as an aerial base station, a relay, or a data collector. Its ability to hover at a desired location and adjust its position in real time makes it superior to fixed ground infrastructure in dynamic environments.
One of the critical challenges for the practical deployment of an unmanned aerial vehicle is the limited onboard energy. The endurance of a typical low-altitude unmanned aerial vehicle is constrained by battery capacity, payload weight, and power consumption. In communication tasks, the transmit power of the unmanned aerial vehicle is a significant part of the total power budget. Therefore, optimizing the transmit power is essential to prolong the operation time. Another challenge is the vulnerability to interference. Since the unmanned aerial vehicle communicates over the air, it may receive unwanted signals from various directions. Beamforming is an effective technique to suppress interference while enhancing the desired signal. However, conventional beamforming algorithms often assume perfect knowledge of the direction of arrival, which is not always available in practice due to the mobility of the unmanned aerial vehicle and the changing propagation environment.
In this thesis, I address these challenges by proposing robust beamforming and deployment algorithms specifically designed for a multi-antenna unmanned aerial vehicle. The thesis is organized as follows. Section 2 introduces the theoretical foundations of beamforming and channel modeling for unmanned aerial vehicle communications. Section 3 presents the volume-integration-based Capon beamforming algorithm. Section 4 describes the optimized deployment method using an improved firefly algorithm. Section 5 concludes the work and discusses future directions.
2. Theoretical Foundations
2.1 Beamforming Concepts
Beamforming is a signal processing technique that combines signals received or transmitted by multiple antennas in a phased array. By adjusting the amplitude and phase weights of each antenna element, the radiation pattern can be shaped to have a main lobe directed toward the intended user and nulls directed toward interference sources. Beamforming can be implemented in the analog domain using phase shifters or in the digital domain using baseband signal processing. Digital beamforming offers higher flexibility and precision, making it suitable for unmanned aerial vehicle communication systems where the propagation environment is dynamic.
For a uniform linear array with \(M\) elements and inter-element spacing \(d\), the steering vector for a signal arriving at angle \(\theta\) is given by:
\[
\mathbf{a}(\theta) = \left[ 1, \; e^{-j \frac{2\pi d}{\lambda} \sin\theta}, \; \ldots, \; e^{-j \frac{2\pi (M-1)d}{\lambda} \sin\theta} \right]^T,
\]
where \(\lambda\) is the wavelength of the carrier signal. The array output is expressed as \(y(k) = \mathbf{w}^H \mathbf{x}(k)\), where \(\mathbf{w}\) is the weight vector and \(\mathbf{x}(k)\) is the received signal vector at snapshot \(k\). The objective of beamforming is to choose \(\mathbf{w}\) to maximize the output signal-to-interference-plus-noise ratio (SINR).
2.2 Channel Models for Unmanned Aerial Vehicle Communications
The communication channel between the unmanned aerial vehicle and ground users is typically modeled as a Rician fading channel because of the high probability of a line-of-sight component. The channel coefficient for a single-antenna unmanned aerial vehicle can be written as:
\[
h_k = \sqrt{\beta_k} \tilde{h}_k,
\]
where \(\beta_k\) represents the large-scale fading including path loss and shadowing, and \(\tilde{h}_k\) represents the small-scale fading. The large-scale fading term is given by:
\[
\beta_k = \beta_0 d_k^{-\varphi} = \beta_0 \left( \|\mathbf{u} – \mathbf{u}_k\|^2 + h_u^2 \right)^{-\varphi/2},
\]
where \(\beta_0\) is the channel gain at a reference distance, \(d_k\) is the distance between the unmanned aerial vehicle and user \(k\), \(\varphi\) is the path loss exponent, \(\mathbf{u}\) is the horizontal coordinate of the unmanned aerial vehicle, \(\mathbf{u}_k\) is the horizontal coordinate of user \(k\), and \(h_u\) is the altitude of the unmanned aerial vehicle.
For a multi-antenna unmanned aerial vehicle with \(M\) antennas, the channel vector between the unmanned aerial vehicle and user \(k\) is:
\[
\mathbf{h}_k = \sqrt{\beta_k} \mathbf{a}(\theta_k),
\]
where \(\mathbf{a}(\theta_k)\) is the steering vector corresponding to the angle \(\theta_k\) between the unmanned aerial vehicle and user \(k\). The angle \(\theta_k\) is determined by the relative positions of the unmanned aerial vehicle and the user, and can be expressed as:
\[
\Phi_k = \frac{x_k – x_u}{\|\mathbf{u} – \mathbf{u}_k\|^2 + h_u^2}.
\]
This channel model is fundamental to the beamforming and deployment algorithms developed in this thesis.
3. Robust Volumetric Capon Beamforming for Multi-Antenna Unmanned Aerial Vehicle
3.1 System Model and Problem Formulation
I consider a relay network in which a multi-antenna unmanned aerial vehicle acts as a relay between a terrestrial base station and ground users. The unmanned aerial vehicle receives signals from the base station and other interference sources. The received signal at the unmanned aerial vehicle array can be written as:
\[
\mathbf{x}(k) = s_0(k) \mathbf{a}(\theta_0) + \sum_{l=1}^{P-1} s_l(k) \mathbf{a}(\theta_l) + \mathbf{n}(k),
\]
where \(s_0(k)\) is the desired signal from the base station, \(\theta_0\) is its direction of arrival, \(s_l(k)\) and \(\theta_l\) are the interference signals and their directions, \(P\) is the total number of signals, and \(\mathbf{n}(k)\) is the additive white Gaussian noise vector with power \(\sigma_n^2\). The array output after beamforming is:
\[
y(k) = \mathbf{w}^H \mathbf{x}(k).
\]
The output SINR is defined as:
\[
\mathrm{SINR} = \frac{\sigma_0^2 |\mathbf{w}^H \mathbf{a}(\theta_0)|^2}{\mathbf{w}^H \left( \sum_{l=1}^{P-1} \sigma_l^2 \mathbf{a}(\theta_l) \mathbf{a}^H(\theta_l) + \sigma_n^2 \mathbf{I} \right) \mathbf{w}}.
\]
The Capon beamformer solves the following optimization problem:
\[
\min_{\mathbf{w}} \; \mathbf{w}^H \mathbf{R}_{i+n} \mathbf{w} \quad \text{subject to} \quad \mathbf{w}^H \mathbf{a}(\theta_0) = 1,
\]
where \(\mathbf{R}_{i+n}\) is the interference-plus-noise covariance matrix. The optimal solution is:
\[
\mathbf{w}_{\mathrm{opt}} = \frac{\mathbf{R}_{i+n}^{-1} \mathbf{a}(\theta_0)}{\mathbf{a}^H(\theta_0) \mathbf{R}_{i+n}^{-1} \mathbf{a}(\theta_0)}.
\]
In practice, the true covariance matrix and steering vector are unavailable. The sample covariance matrix is computed as:
\[
\hat{\mathbf{R}} = \frac{1}{L} \sum_{k=1}^{L} \mathbf{x}(k) \mathbf{x}^H(k),
\]
where \(L\) is the number of snapshots. However, the sample covariance matrix may contain the desired signal component, leading to performance degradation at high SNR. Moreover, the steering vector mismatch due to the mobility of the unmanned aerial vehicle causes severe performance loss. Therefore, I propose a robust beamforming algorithm based on volume integration.
3.2 ROOT-MUSIC Angle Estimation
To obtain accurate angle information of the desired and interference signals, I use the ROOT-MUSIC algorithm. The covariance matrix \(\mathbf{R}\) can be decomposed into signal and noise subspaces:
\[
\mathbf{R} = \mathbf{U}_s \boldsymbol{\Lambda}_s \mathbf{U}_s^H + \mathbf{U}_n \boldsymbol{\Lambda}_n \mathbf{U}_n^H,
\]
where \(\mathbf{U}_s\) contains eigenvectors corresponding to the \(P\) largest eigenvalues, and \(\mathbf{U}_n\) contains the remaining eigenvectors. Because the steering vectors are orthogonal to the noise subspace, one can construct a polynomial whose roots correspond to the signal directions. The roots closest to the unit circle yield the directions of arrival. The angle estimates are then:
\[
\hat{\theta}_i = \arcsin \left( \frac{\lambda}{2\pi d} \arg(z_i) \right).
\]
The ROOT-MUSIC algorithm provides more accurate and faster estimation than the conventional MUSIC spectral search. The estimated angles are used to define the integration intervals for the covariance matrix reconstruction.
3.3 Volume-Integration-Based Covariance Matrix Reconstruction
Conventional robust beamforming methods reconstruct the interference covariance matrix by spatial spectrum integration over a one-dimensional angular sector. However, this approach is sensitive to direction errors and spatial scattering. To improve robustness, I propose to perform a volume integration over a ring-shaped uncertainty set. The uncertainty set is constructed as:
\[
\mathcal{G}(\mathbf{a}) = \left\{ \mathbf{a} \; \middle| \; \|\mathbf{a} – \mathbf{a}(\theta)\|_2 \le \varepsilon, \; \theta \in \hat{\Theta}_i \right\},
\]
where \(\hat{\Theta}_i\) is the estimated interference angle interval and \(\varepsilon\) is the radius of the ball uncertainty set. The interference covariance matrix is reconstructed as:
\[
\hat{\mathbf{R}}_i = \int_{\mathcal{G}} \frac{\mathbf{a} \mathbf{a}^H}{\mathbf{a}^H \hat{\mathbf{R}}^{-1} \mathbf{a}} \, d\mathbf{a}.
\]
Because the integrand is invariant to scaling of \(\mathbf{a}\), the volume integral can be reduced to a surface integral:
\[
\hat{\mathbf{R}}_i \approx \sum_{m=1}^{M} \sum_{n=1}^{N} \frac{\mathbf{a}_{mn} \mathbf{a}_{mn}^H}{\mathbf{a}_{mn}^H \hat{\mathbf{R}}^{-1} \mathbf{a}_{mn}},
\]
where \(M\) is the number of discrete angles in \(\hat{\Theta}_i\) and \(N\) is the number of discrete points on the surface of the ball. Compared with the planar integration, this volume integration method collects the errors caused by direction mismatch and scattering, thus improving the robustness of the beamformer.
The noise covariance matrix is approximated by the minimum eigenvalue of \(\hat{\mathbf{R}}\) times the identity matrix. Therefore, the reconstructed interference-plus-noise covariance matrix is:
\[
\hat{\mathbf{R}}_{i+n} = \hat{\mathbf{R}}_i + \lambda_{\min} \mathbf{I}.
\]
Then, the steering vector is refined by maximizing the output power under the spherical uncertainty set constraint:
\[
\min_{\mathbf{e}} \; (\mathbf{a}(\hat{\theta}_s) + \mathbf{e})^H \hat{\mathbf{R}}^{-1} (\mathbf{a}(\hat{\theta}_s) + \mathbf{e}) \quad \text{subject to} \quad \|\mathbf{e}\|_2 \le \varepsilon_s.
\]
The final weight vector is computed as:
\[
\hat{\mathbf{w}} = \frac{\hat{\mathbf{R}}_{i+n}^{-1} \hat{\mathbf{a}}}{\hat{\mathbf{a}}^H \hat{\mathbf{R}}_{i+n}^{-1} \hat{\mathbf{a}}},
\]
where \(\hat{\mathbf{a}}\) is the corrected steering vector.
3.4 Simulation Results
I evaluate the proposed algorithm through computer simulations. The parameters are summarized in the table below.
| Parameter | Value |
|---|---|
| Number of antennas \(M\) | 10 |
| Inter-element spacing \(d\) | \(\lambda/2\) |
| Desired signal angle \(\theta_0\) | \(0^\circ\) |
| Interference angles | \(-30^\circ, 40^\circ\) |
| Interference-to-noise ratio | 30 dB |
| Snapshots \(L\) | 100 |
| Path loss exponent \(\varphi\) | 3.8 |
| LoS extra loss | 1 dB |
| NLoS extra loss | 20 dB |
The normalized beampatterns are shown in the figure below. The proposed algorithm and the method in [74] both steer the main lobe toward the desired direction, but the proposed algorithm yields lower sidelobes. Both the proposed algorithm and [75] place deep nulls at the interference directions, but the main lobe of [75] is biased, which may suppress the desired signal.
Figure 5 shows the output SINR versus the input SNR. At low SNR, the diagonal loading method has lower SINR due to steering vector mismatch. The proposed algorithm maintains high SINR over a wide SNR range. At high SNR, the output SINR of [74] degrades because the reconstructed covariance matrix contains the desired signal component, while the proposed algorithm still achieves near-optimal performance. The proposed algorithm also performs well with respect to the number of snapshots, as can be seen in Figure 6. It converges quickly and achieves a higher SINR than the compared methods when the number of snapshots is large. Finally, the output SINR versus the number of interference signals is shown in Figure 7. The proposed algorithm is more tolerant to an increasing number of interferers than the other methods.
4. Optimized Deployment for Multi-Antenna Unmanned Aerial Vehicle Communications
4.1 System Model and Problem Formulation
In this section, I consider the scenario where a multi-antenna unmanned aerial vehicle acts as an aerial base station for \(K\) ground users. The unmanned aerial vehicle is equipped with \(M\) antennas arranged in a uniform linear array, and each ground user has a single antenna. The channel between the unmanned aerial vehicle and user \(k\) is modeled as:
\[
\mathbf{h}_k = \frac{\sqrt{\beta_0}}{d_k^{\varphi/2}} \mathbf{a}(\theta_k),
\]
where \(d_k\) is the distance between the unmanned aerial vehicle and user \(k\), and \(\mathbf{a}(\theta_k)\) is the steering vector. The distance is:
\[
d_k = \sqrt{\|\mathbf{u} – \mathbf{u}_k\|^2 + (h_u – h_k)^2}.
\]
The unmanned aerial vehicle employs zero-forcing (ZF) beamforming to eliminate inter-user interference. The ZF beamforming matrix is:
\[
\mathbf{Z} = \mathbf{H}^H (\mathbf{H} \mathbf{H}^H)^{-1},
\]
where \(\mathbf{H} = [\mathbf{h}_1, \ldots, \mathbf{h}_K]\). The normalized weight vector for user \(k\) is \(\mathbf{w}_k = \mathbf{z}_k / \|\mathbf{z}_k\|\). With ZF beamforming, the effective channel satisfies \(\mathbf{h}_m^H \mathbf{w}_n = 0\) for \(m \neq n\) and \(\mathbf{h}_m^H \mathbf{w}_m = \sqrt{\beta_0} M d_m^{-\varphi/2}\). Thus, the received SINR at user \(k\) simplifies to the signal-to-noise ratio:
\[
\mathrm{SINR}_k = \frac{p_k \beta_0 M^2 d_k^{-\varphi}}{\sigma_n^2}.
\]
The data rate of user \(k\) is:
\[
C_k = B \log_2 \left(1 + \mathrm{SINR}_k \right),
\]
where \(B\) is the channel bandwidth. By rearranging the equation, the transmit power for user \(k\) is:
\[
p_k = \frac{\sigma_n^2 (2^{C_k/B} – 1)}{\beta_0 M^2} d_k^{\varphi}.
\]
The total transmit power of the unmanned aerial vehicle is:
\[
P_{\mathrm{total}} = \sum_{k=1}^{K} p_k = \frac{\sigma_n^2}{\beta_0 M^2} \sum_{k=1}^{K} (2^{C_k/B} – 1) d_k^{\varphi}.
\]
I aim to minimize the total transmit power by optimizing the horizontal position of the unmanned aerial vehicle, subject to the constraint that each user’s rate meets a minimum threshold. The optimization problem is:
\[
\min_{\mathbf{u}} \; P_{\mathrm{total}}(\mathbf{u}) \quad \text{subject to} \quad C_k \ge C_k^{\min}, \; x_{\min} \le x_u \le x_{\max}, \; y_{\min} \le y_u \le y_{\max}.
\]
The objective function is highly nonlinear and non-convex because the distances \(d_k\) depend on the unmanned aerial vehicle position. Therefore, I employ a metaheuristic algorithm to find the optimal deployment.
4.2 Improved Firefly Algorithm for Deployment
The standard firefly algorithm is inspired by the flashing behavior of fireflies. In the algorithm, each firefly represents a candidate solution. The brightness of a firefly is proportional to the objective function value, and the attractiveness decreases with distance. The movement of firefly \(i\) toward a brighter firefly \(j\) is given by:
\[
\mathbf{x}_i(t+1) = \mathbf{x}_i(t) + \beta_{ij} (\mathbf{x}_j(t) – \mathbf{x}_i(t)) + \alpha (\mathrm{rand} – 0.5),
\]
where \(\beta_{ij} = \beta_0 e^{-\gamma r_{ij}^2}\), \(r_{ij} = \|\mathbf{x}_i – \mathbf{x}_j\|\), \(\gamma\) is the light absorption coefficient, and \(\alpha\) is the step length factor. However, the standard firefly algorithm suffers from slow convergence and may get stuck in local optima. To overcome these issues, I propose an improved firefly algorithm with inertia weight and dynamic step size, named FABD.
First, I introduce a self-adaptive inertia weight that controls the influence of the global best firefly on the population:
\[
\omega_i(t) = e^{- \left| f_{\mathrm{best}}(t) – \frac{1}{N_{\mathrm{pop}}} \sum_{i=1}^{N_{\mathrm{pop}}} f_i(t) \right|},
\]
where \(f_i(t)\) is the objective function value of firefly \(i\) at iteration \(t\), and \(f_{\mathrm{best}}(t)\) is the best value in the current population. The position update equation becomes:
\[
\mathbf{x}_i(t+1) = \mathbf{x}_i(t) + \beta_{ij} (\mathbf{x}_j(t) – \mathbf{x}_i(t)) + \alpha(t) (\mathrm{rand} – 0.5) + \omega_i(t) (\mathbf{x}_{\mathrm{best}}(t) – \mathbf{x}_i(t)).
\]
Second, I use a nonlinear decreasing step size:
\[
\alpha(t) = \alpha_0 \delta^t,
\]
where \(\alpha_0\) is the initial step size and \(\delta\) is a scaling factor between 0.9 and 0.98. This dynamic step size provides good global search capability in the early iterations and fine local tuning in the later iterations.
The deployment procedure is summarized as follows:
- Initialize the coverage area, user positions, user rate requirements, and firefly parameters.
- Randomly place \(N_{\mathrm{pop}}\) fireflies in the coverage area.
- Evaluate the objective function \(P_{\mathrm{total}}\) for each firefly and determine the brightest one.
- Update each firefly’s position using the modified update equation.
- Re-evaluate the objective function and update the global best.
- Repeat steps 3–5 until the maximum number of iterations is reached.
- Output the optimal unmanned aerial vehicle position and the minimum total transmit power.
4.3 Simulation Results
I simulate an unmanned aerial vehicle coverage area of 500 m × 500 m. The unmanned aerial vehicle flies at a fixed altitude of 100 m. Four ground users are randomly distributed in the area, and the system parameters are listed in the table below.
| Parameter | Value |
|---|---|
| Area size | 500 m × 500 m |
| Unmanned aerial vehicle altitude | 100 m |
| Number of antennas \(M\) | 10 |
| Bandwidth \(B\) | 1 MHz |
| Channel gain \(\beta_0\) | 1.42 × 10\(^{-4}\) |
| Path loss exponent \(\varphi\) | 3.8 |
| Noise power \(\sigma_n^2\) | 10\(^{-9}\) W |
| Users’ coordinates | See figure |
| Users’ rate requirements | 1.44, 2.23, 1.33, 3.83 Mbit/s |
Figure 4.3 shows the total transmit power distribution over the coverage area. The optimal position is not at the geometric center, which confirms the need for deployment optimization. Figure 4.4 and Figure 4.5 show the convergence curves for different population sizes \(N_{\mathrm{pop}}\). The proposed FABD algorithm converges faster than the standard firefly algorithm, ant colony optimization, and particle swarm optimization. When \(N_{\mathrm{pop}}\) increases from 10 to 20, all algorithms converge faster, but the proposed algorithm still achieves the lowest number of iterations. Figure 4.6 compares the number of iterations for different population sizes. The FABD algorithm consistently outperforms the other methods.
The final deployment positions are compared in Figure 4.8. The FABD algorithm places the unmanned aerial vehicle at a position closer to the optimum, resulting in lower total transmit power. Figure 4.9 shows the total transmit power versus the number of antennas. Increasing the number of antennas reduces the required power, but the improvement saturates beyond \(M=30\). The proposed algorithm always yields the lowest total power. Figure 4.10 shows the total transmit power versus the path loss exponent. As the path loss increases, the required power grows exponentially, and the FABD algorithm maintains a lower power than the other methods. Finally, Figure 4.11 shows the total transmit power versus the user data rate requirement. The proposed algorithm achieves the minimum power for all rate values.
5. Conclusion and Future Work
In this thesis, I have studied beamforming and optimized deployment for unmanned aerial vehicle-assisted communication systems. The main contributions are summarized as follows:
First, I proposed a robust Capon beamforming algorithm based on volume integration for a multi-antenna unmanned aerial vehicle operating in an interference environment. The algorithm uses ROOT-MUSIC for accurate angle estimation, reconstructs the interference-plus-noise covariance matrix through a volume integration over a ring uncertainty set, and refines the steering vector by maximizing the output power. Simulation results show that the proposed algorithm achieves higher output SINR than conventional methods, especially at high signal-to-noise ratios and with limited snapshots. The algorithm also maintains good performance when the number of interference signals increases. This demonstrates that the volume integration approach effectively mitigates the impact of steering vector mismatch and environmental uncertainties.
Second, I proposed an optimized deployment method for a multi-antenna unmanned aerial vehicle serving multiple ground users. By using zero-forcing beamforming, the problem is simplified to minimize the total transmit power as a function of the unmanned aerial vehicle position. I developed an improved firefly algorithm with a self-adaptive inertia weight and a dynamic step size to solve this non-convex optimization problem efficiently. The simulation results show that the proposed algorithm converges faster and finds a deployment position that requires less transmit power than the standard firefly algorithm, ant colony optimization, and particle swarm optimization. The method is robust to variations in the number of antennas, path loss, and user data rate requirements.
There are several directions for future work. First, the channel model in this thesis assumes Rician fading with a dominant line-of-sight component. In practice, the unmanned aerial vehicle’s high mobility may introduce Doppler shift, which should be incorporated to make the model more realistic. Second, the ground users are assumed to be single-antenna devices. Extending the system to include multi-antenna ground users would provide diversity gain and may further improve the performance. Third, the current optimization only considers the transmit power from the unmanned aerial vehicle to ground users, but the backhaul link between the unmanned aerial vehicle and the core network is equally important. Including the backhaul power in the optimization would yield a more comprehensive solution. These topics are promising for future research in unmanned aerial vehicle-assisted wireless communications.