As the Internet of Things (IoT) continues to expand and wireless data traffic grows exponentially, the demand for reliable, high-speed, and ubiquitous connectivity has never been greater. Traditional terrestrial base stations face inherent limitations in coverage, capacity, and resilience, particularly in remote areas, disaster-stricken regions, or during temporary events with concentrated user density. In this context, unmanned aerial vehicles (UAVs) have emerged as a transformative solution, offering flexibility, rapid deployment, and cost-effectiveness for enhancing wireless communication networks. This article provides a comprehensive exploration of research on beamforming techniques and optimized deployment strategies for UAV-assisted communication systems, with a specific focus on multi-antenna UAVs. The discussion is structured around two primary contributions: a robust Capon beamforming algorithm based on volume integration for interference suppression, and an optimized deployment method for multi-antenna UAVs to minimize transmit power while satisfying user communication rate requirements. These approaches are critical for addressing the practical challenges of UAV communications, including limited battery life, dynamic positions, and complex signal environments.
Introduction
The rapid development of fifth-generation (5G) mobile communication technology has brought about significant improvements in data rates, latency, network coverage, and connection stability. According to industry forecasts, global mobile data traffic is projected to reach hundreds of exabytes per month in the coming years, driven by the proliferation of smart devices, autonomous systems, and industrial IoT applications. While terrestrial networks form the backbone of modern communication, they face significant challenges in specific scenarios such as emergency response, temporary events, and rural or mountainous regions. In these contexts, unmanned aerial vehicles (UAVs) have demonstrated remarkable potential as aerial communication platforms.
The integration of UAVs into wireless communication networks represents a paradigm shift from conventional fixed infrastructure. UAVs can function as aerial base stations, relay nodes, or data collectors, providing line-of-sight (LoS) communication links that are often superior to those of terrestrial base stations. The key advantages of using UAVs for communication include:
| Application Type | Key Features | Challenges |
|---|---|---|
| Aerial Base Station | Rapid deployment, temporary network offloading, LoS links | Limited battery life, power constraints, optimal positioning |
| UAV Relay | Extending coverage range, connecting distant nodes, D2D support | Trajectory planning, deployment optimization, interference management |
| UAV Data Collection | Efficient data gathering from IoT devices, wide-area sensing | Energy-efficient path planning, data transmission reliability |
The research presented in this article addresses two fundamental challenges in UAV-assisted communication. First, in scenarios where UAVs act as relays or base stations, the received signals are often corrupted by co-channel interferences from various directions. Traditional beamforming methods assume perfect knowledge of the signal directions and stationary conditions, which rarely hold in practical UAV deployments due to their inherent mobility and environmental complexity. To address this, a novel Capon beamforming algorithm based on volume integration is proposed to enhance robustness against steering vector mismatches and covariance matrix uncertainties.
Second, the energy constraint remains a primary bottleneck limiting the operational duration of UAVs. For multi-antenna UAVs operating as temporary base stations, the transmit power directly affects both the communication quality and the battery lifetime. Therefore, sophisticated deployment strategies that consider the spatial distribution of users and their communication requirements are essential for minimizing power consumption while ensuring quality of service (QoS).
Fundamentals of Beamforming and UAV-Assisted Communication
Beamforming is a signal processing technique used in sensor arrays for directional signal transmission or reception. It achieves spatial selectivity by combining signals from multiple antenna elements with appropriate weighting factors. The primary objectives of beamforming include enhancing the signal gain in the desired direction while suppressing interference from other directions. In the context of UAV-assisted communication, beamforming becomes particularly valuable due to the following reasons:
- Interference suppression: UAVs operating in shared frequency bands are susceptible to interference from other wireless devices. Beamforming enables spatial filtering to nullify interference sources.
- Spectral efficiency: By directing energy precisely toward target users, beamforming improves the signal-to-interference-plus-noise ratio (SINR), thereby increasing spectral efficiency.
- Coverage extension: Multi-antenna UAVs can steer narrow beams over long distances, extending the effective coverage area.
Antenna Array Theory
The foundation of beamforming lies in the antenna array configuration. The uniform linear array (ULA) is the most commonly used configuration in beamforming research. Consider an array of $M$ isotropic antenna elements equally spaced along the x-axis with inter-element spacing $d$. The array steering vector for a signal arriving at an angle $\theta$ relative to the array boresight is expressed as:
$$
\mathbf{a}(\theta) = \left[ 1, e^{-j\frac{2\pi}{\lambda} d \sin\theta}, e^{-j\frac{2\pi}{\lambda} 2d \sin\theta}, \ldots, e^{-j\frac{2\pi}{\lambda} (M-1)d \sin\theta} \right]^T
$$
where $\lambda$ represents the wavelength of the carrier signal. This steering vector encapsulates the phase differences of the received signal across the antenna elements due to the propagation path difference. The output of a beamformer is given by:
$$
y(k) = \mathbf{w}^H \mathbf{x}(k)
$$
where $\mathbf{w} \in \mathbb{C}^{M \times 1}$ is the complex weight vector, and $\mathbf{x}(k)$ is the received signal vector at snapshot $k$. The choice of $\mathbf{w}$ determines the beam pattern, including the main lobe direction, null placements, and side lobe levels.
Types of Beamforming
Beamforming techniques can be categorized based on various criteria: implementation structure (analog vs. digital) and adaptation strategy (fixed vs. adaptive). Digital beamforming (DBF) offers superior flexibility and precision by processing signals at the baseband level with high-resolution algorithms. Adaptive beamforming algorithms, such as the Capon beamformer and its variants, adjust the weight vector in real time based on received data to optimize performance under changing conditions.
| Beamforming Type | Characteristics | Advantages | Disadvantages |
|---|---|---|---|
| Analog Beamforming | Phase shifters at RF front-end | Low hardware complexity, power-efficient | Limited precision, single-beam operation |
| Digital Beamforming | Baseband weighted processing per antenna | High accuracy, multi-beam capability, flexible algorithm deployment | Higher hardware cost, increased complexity |
| Fixed Beamforming | Pre-computed weights | Simple, predictable | No adaptation to environment changes |
| Adaptive Beamforming | Weights updated via algorithms | Real-time optimization, interference suppression | Computational overhead, stability concerns |
UAV-to-Ground Channel Models
Accurate channel modeling is essential for the design and evaluation of UAV communications. The UAV-to-ground channel is typically characterized by both large-scale fading (path loss and shadowing) and small-scale fading (multipath and Doppler effects). The Rician fading channel model is commonly adopted for UAV communication scenarios where a LoS component exists along with scattered multipath components. The channel coefficient between a single-antenna UAV and a ground user $k$ can be expressed as:
$$
h_k = \sqrt{\beta_k} \tilde{h}_k
$$
where $\beta_k$ is the large-scale fading coefficient accounting for path loss and shadowing, and $\tilde{h}_k$ represents the small-scale fading coefficient. The large-scale fading term is given by:
$$
\beta_k = \beta_0 d_k^{-\varphi} = \beta_0 \left( \|\mathbf{u}_k – \mathbf{u}_u\|_2^2 + h_u^2 \right)^{-\varphi/2}
$$
where $\beta_0$ is the reference channel gain, $d_k$ is the distance between the UAV and user $k$, $\varphi$ is the path loss exponent, $\mathbf{u}_u$ and $\mathbf{u}_k$ are the two-dimensional horizontal coordinates of the UAV and user $k$, respectively, and $h_u$ is the UAV flight altitude.
For multi-antenna UAVs with $M$ antenna elements, the channel model incorporates the array geometry. Assuming a ULA with half-wavelength spacing, the LoS component of the channel vector between the multi-antenna UAV and ground user $k$ is:
$$
\mathbf{h}_{k,\text{LoS}} = \sqrt{M} \mathbf{a}(\theta_k)
$$
where $\theta_k$ is the angle of departure from the UAV to user $k$. The full channel vector is then:
$$
\mathbf{h}_k = \sqrt{\beta_k} \mathbf{h}_{k,\text{LoS}} = \sqrt{\beta_k} \sqrt{M} \mathbf{a}(\theta_k)
$$
Given that the Rician factor in UAV communications is often high (indicating a strong LoS dominance), the LoS component serves as the primary channel characteristic, which is the principal modeling approach used in subsequent analyses.
Volumetric Capon Beamforming for Multi-Antenna UAV Communications
Motivation and Problem Statement
In UAV relay networks or UAV-mounted base station scenarios, the UAV’s receiver is subject to interference from multiple directions, which degrades communication performance. The Capon beamformer is a widely recognized adaptive beamforming technique that minimizes the output power while maintaining distortionless response in the desired signal direction. The optimal weight vector is obtained by solving the following constrained 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, and $\mathbf{a}(\theta_0)$ is the steering vector corresponding to the desired signal direction. The closed-form solution is:
$$
\mathbf{w}_{\text{opt}} = \frac{\mathbf{R}_{i+n}^{-1} \mathbf{a}(\theta_0)}{\mathbf{a}^H(\theta_0) \mathbf{R}_{i+n}^{-1} \mathbf{a}(\theta_0)}
$$
In practical systems, the ideal interference-plus-noise covariance matrix is unavailable and must be estimated. The sample covariance matrix is computed from received snapshots:
$$
\hat{\mathbf{R}} = \frac{1}{L} \sum_{k=1}^{L} \mathbf{x}(k)\mathbf{x}^H(k)
$$
where $L$ is the number of snapshots. However, when the received signal contains the desired signal component (as is typical), the sample covariance matrix is contaminated, causing degradation in beamformer performance, especially at high SNRs. Moreover, in UAV scenarios, the exact steering vector is often unknown due to position estimation errors, UAV mobility, and multipath propagation.
Proposed Volumetric Capon Beamforming Algorithm
The proposed algorithm addresses the aforementioned challenges through a multi-step process. First, the ROOT-MUSIC algorithm is employed to obtain accurate estimates of the desired signal and interference directions. Second, a novel covariance matrix reconstruction method based on volume integration is developed. Third, the steering vector is refined by maximizing the beamformer output power.
ROOT-MUSIC-Based Angle Estimation
The MUSIC (Multiple Signal Classification) algorithm and its polynomial-root variant ROOT-MUSIC exploit the orthogonality between the signal and noise subspaces. The eigendecomposition of the sample covariance matrix is:
$$
\hat{\mathbf{R}} = \mathbf{U}_s \boldsymbol{\Sigma}_s \mathbf{U}_s^H + \mathbf{U}_n \boldsymbol{\Sigma}_n \mathbf{U}_n^H
$$
where $\mathbf{U}_s$ and $\mathbf{U}_n$ are the signal and noise subspace eigenvectors, respectively. The spatial spectrum function is:
$$
P_{\text{MUSIC}}(\theta) = \frac{1}{\mathbf{a}^H(\theta) \mathbf{U}_n \mathbf{U}_n^H \mathbf{a}(\theta)}
$$
ROOT-MUSIC simplifies spectral scanning by reformulating the problem as polynomial rooting. By constructing the polynomial:
$$
f(z) = \mathbf{a}^T(1/z) \mathbf{U}_n \mathbf{U}_n^H \mathbf{a}(z)
$$
where $z = e^{j\omega}$, the angles of arrival are obtained from the roots of $f(z)$ that lie on or near the unit circle:
$$
\theta_i = \arcsin\left( \frac{\lambda}{2\pi d} \arg\{z_i\} \right)
$$
After identifying the angles, the desired signal angle $\hat{\theta}_s$ and interference angles $\hat{\theta}_i$ (for $i = 1, \ldots, P-1$) are determined. These estimates are used to define the integral intervals for covariance matrix reconstruction.
| Signal Type | True DOA | Estimated DOA via ROOT-MUSIC |
|---|---|---|
| Desired Signal | 60.0° | 59.96° |
| Interference Signal 1 | 10.0° | 9.81° |
| Interference Signal 2 | 20.0° | 20.14° |
Volumetric Integration-Based Covariance Matrix Reconstruction
The core novelty of the proposed method lies in the interference covariance matrix reconstruction via volume integration over a spherical uncertainty set. Conventional reconstruction methods typically perform linear integration over the spatial power spectrum. However, these methods are sensitive to steering vector errors. The proposed volume integration approach adds an extra dimension of robustness by integrating over a hypersphere centered at the nominal steering vector.
First, a spherical uncertainty set is constructed around the interference steering vector:
$$
\mathcal{G}_a'(\hat{\theta}_i) = \left\{ \mathbf{a} \; \middle| \; \|\mathbf{a} – \mathbf{a}(\hat{\theta}_i)\|_2 \leq \varepsilon \right\}
$$
where $\varepsilon$ is the uncertainty radius. The union of these spherical sets across all interference angles forms a ring-shaped uncertainty set. The interference covariance matrix is then reconstructed as:
$$
\hat{\mathbf{R}}_i = \int_{\mathcal{G}_a”} p(\mathbf{a}) \frac{\mathbf{a}\mathbf{a}^H}{\mathbf{a}^H \hat{\mathbf{R}}^{-1} \mathbf{a}} \, d\sigma
$$
where $p(\mathbf{a})$ represents the power distribution over the uncertainty surface, and the integration is performed over the surface of the ring uncertainty set. This volumetric (surface) integration collects potential estimation errors into the reconstruction, thereby enhancing the robustness of the beamformer.
The continuous integral is approximated through discretization for computational tractability:
$$
\hat{\mathbf{R}}_i \approx \sum_{m=1}^{M} \sum_{n=1}^{N} \frac{\mathbf{a}_{mn}\mathbf{a}_{mn}^H}{\mathbf{a}_{mn}^H \hat{\mathbf{R}}^{-1} \mathbf{a}_{mn}}
$$
where $M$ is the number of discrete angles in the estimated interference direction interval, and $N$ is the number of discrete points on the uncertainty surface per angle. The reconstructed interference-plus-noise covariance matrix is:
$$
\hat{\mathbf{R}}_{i+n} = \hat{\mathbf{R}}_i + \lambda_M \mathbf{I}
$$
where $\lambda_M$ is the smallest eigenvalue of the sample covariance matrix, serving as an estimate of the noise power.
Steering Vector Refinement
To further improve accuracy, the steering vector is refined by solving the following optimization problem:
$$
\min_{\mathbf{a}_s} \; \mathbf{a}_s^H \hat{\mathbf{R}}_{i+n}^{-1} \mathbf{a}_s \quad \text{subject to} \quad \|\mathbf{a}_s – \mathbf{a}(\hat{\theta}_s)\|_2 \leq \varepsilon_s
$$
This refinement maximizes the beamformer output power while keeping the corrected steering vector within a feasible region defined by the nominal angle estimate. The final beamforming weight vector is computed as:
$$
\mathbf{w} = \frac{\hat{\mathbf{R}}_{i+n}^{-1} \hat{\mathbf{a}}_s}{\hat{\mathbf{a}}_s^H \hat{\mathbf{R}}_{i+n}^{-1} \hat{\mathbf{a}}_s}
$$
The complete algorithm is summarized below:
| Step | Operation | Description |
|---|---|---|
| 1 | Compute sample covariance matrix | $\hat{\mathbf{R}} = \frac{1}{L}\sum_{k=1}^{L} \mathbf{x}(k)\mathbf{x}^H(k)$ |
| 2 | ROOT-MUSIC angle estimation | Estimate $\hat{\theta}_s$ and $\hat{\theta}_i$ via polynomial rooting |
| 3 | Volumetric matrix reconstruction | Construct $\hat{\mathbf{R}}_i$ via volume integration of spatial power spectrum |
| 4 | Noise covariance estimation | Use smallest eigenvalue $\lambda_M$ of $\hat{\mathbf{R}}$ as noise power |
| 5 | Steering vector correction | Refine $\hat{\mathbf{a}}_s$ via output power maximization |
| 6 | Weight vector computation | $\mathbf{w} = \frac{\hat{\mathbf{R}}_{i+n}^{-1}\hat{\mathbf{a}}_s}{\hat{\mathbf{a}}_s^H\hat{\mathbf{R}}_{i+n}^{-1}\hat{\mathbf{a}}_s}$ |
Simulation Results and Analysis
The proposed algorithm was evaluated through extensive simulations using a ULA with $M=10$ elements and half-wavelength spacing. The desired signal arrives at $0^\circ$, while two interference signals arrive at $-30^\circ$ and $40^\circ$ with an interference-to-noise ratio (INR) of 30 dB. The performance is compared against diagonal loading, the algorithm from literature [74], and the algorithm from literature [75].
The beampattern comparison at SNR = 20 dB demonstrates the superiority of the proposed method. The resulting beam pattern exhibits these key characteristics:
- Main lobe precisely directed toward the desired signal at $0^\circ$
- Deep nulls exceeding -40 dB at both interference angles of $-30^\circ$ and $40^\circ$
- Uniformly lower sidelobe levels across the entire angular domain
The output SINR versus input SNR results reveal that the proposed algorithm maintains near-optimal performance across a wide SNR range from -20 dB to 20 dB. Notably, at high SNRs (greater than 15 dB), competing algorithms experience performance degradation due to signal self-cancellation, whereas the proposed volumetric reconstruction effectively eliminates this effect.
In terms of snapshot requirements, the proposed algorithm converges rapidly, achieving output SINR close to the theoretical optimum with as few as 30 snapshots, while maintaining stability as the snapshot count increases. When evaluating performance against the number of interference signals, the proposed method demonstrates higher tolerance to 2 to 4 interfering sources compared to reference methods.
Optimal Deployment Strategy for Multi-Antenna UAVs
System Model and Problem Formulation
This section addresses an emergency communication scenario where a multi-antenna UAV serves as an aerial base station to provide communication services to $K$ ground users. The UAV is equipped with $M$ antennas in a ULA configuration, and each ground user has a single antenna. The coordinates of the UAV and user $k$ are given by:
$$
\boldsymbol{p}_u = (x_u, y_u, h_u), \quad \boldsymbol{p}_k = (x_k, y_k, h_k)
$$
The channel vector between the multi-antenna UAV and a ground user $k$ is modeled as:
$$
\mathbf{h}_k = \sqrt{\beta_k} \sqrt{M} \mathbf{a}(\theta_k)
$$
where the large-scale fading and array response function $\mathbf{a}(\theta_k)$ follow the definitions in the fundamental theory section. The distance between the UAV and user $k$ is:
$$
d_k = \sqrt{\|\mathbf{u}_k – \mathbf{u}_u\|_2^2 + (h_k – h_u)^2}
$$
Zero-Forcing Beamforming Design
To eliminate multi-user interference at the UAV base station, the zero-forcing (ZF) beamforming scheme is adopted. This approach ensures that the beam directed toward one user creates nulls in the directions of all other users. Let the channel matrix be:
$$
\mathbf{H} = [\mathbf{h}_1, \ldots, \mathbf{h}_K] \in \mathbb{C}^{M \times K}
$$
where $M \geq K$ is required for ZF feasibility. The ZF beamforming matrix is:
$$
\mathbf{Z} = \mathbf{H}(\mathbf{H}^H \mathbf{H})^{-1}
$$
The normalized beamforming vector for user $k$ is obtained by normalizing the corresponding column of $\mathbf{Z}$:
$$
\mathbf{w}_k = \frac{\mathbf{z}_k}{\|\mathbf{z}_k\|}
$$
where $\mathbf{z}_k$ is the $k$-th column of $\mathbf{Z}$. With ZF beamforming, the effective channel satisfies:
$$
\mathbf{h}_m^H \mathbf{w}_n = \begin{cases} 0, & m \neq n \\ C, & m = n \end{cases}
$$
Power Minimization Optimization
The communication rate for ground user $k$ based on Shannon’s formula is:
$$
C_k = B \log_2 \left( 1 + \frac{p_k |\mathbf{h}_k^H \mathbf{w}_k|^2}{\sum_{i \in I, i\neq k} p_i |\mathbf{h}_k^H \mathbf{w}_i|^2 + \sigma_n^2} \right)
$$
where $B$ is the channel bandwidth, $p_k$ is the transmit power for user $k$, and $\sigma_n^2$ is the noise power. Under ZF beamforming, the interference terms vanish, yielding the simplified rate expression:
$$
C_k = B \log_2 \left( 1 + \frac{p_k \beta_0 M d_k^{-\varphi}}{\sigma_n^2} \right)
$$
Solving for $p_k$ under the constraint that $C_k \geq c_k$ (where $c_k$ is the minimum required rate), the minimal power for each user is:
$$
p_k = \frac{\sigma_n^2}{\beta_0 M} d_k^{\varphi} \left( 2^{c_k/B} – 1 \right)
$$
Consequently, the total transmit power minimization problem is formulated as:
$$
\min_{x_u, y_u} \; P_{\text{total}} = \min_{x_u, y_u} \; \sum_{k=1}^{K} \frac{\sigma_n^2}{\beta_0 M} d_k^{\varphi} \left( 2^{c_k/B} – 1 \right)
$$
subject to the coverage range constraints:
$$
x_{\min} \leq x_u \leq x_{\max}, \quad y_{\min} \leq y_u \leq y_{\max}
$$
Firefly Algorithm with Inertia Weight and Dynamic Step (FABD)
The optimization problem formulated above is non-convex with respect to the UAV position, making it suitable for metaheuristic approaches. The standard firefly algorithm, inspired by the flashing behavior of fireflies, is a swarm-based method that balances exploration and exploitation through the following mechanisms:
The brightness of a firefly corresponds to the objective function value, and the relative brightness between firefly $j$ and firefly $i$ is:
$$
I_{ij}(r_{ij}) = I_j e^{-\gamma r_{ij}^2}
$$
where $\gamma$ is the light absorption coefficient and $r_{ij}$ is the Euclidean distance between fireflies $i$ and $j$. The attractiveness is:
$$
\beta_{ij}(r_{ij}) = \beta_0 e^{-\gamma r_{ij}^2}
$$
The position update equation for a firefly attracted to a brighter one is:
$$
\mathbf{x}_i(t+1) = \mathbf{x}_i(t) + \beta_{ij} \cdot (\mathbf{x}_j(t) – \mathbf{x}_i(t)) + \alpha \cdot (\text{rand} – 0.5)
$$
Despite its effectiveness, the standard FA suffers from slow convergence in later iterations and a tendency to get trapped in local optima. To overcome these limitations, the FABD algorithm introduces two key improvements:
Inertia Weight
The position is updated with an additional term influenced by the global best position, weighted by an adaptive inertia weight. The modified update formula is:
$$
\mathbf{x}_i(t+1) = \mathbf{x}_i(t) + \beta_{ij}(\mathbf{x}_j(t) – \mathbf{x}_i(t)) + \alpha(\text{rand} – 0.5) + \omega_i(t) \cdot (\mathbf{x}_{\text{best}}(t) – \mathbf{x}_i(t))
$$
The adaptive inertia weight is computed based on the objective function values at current and previous iterations, providing a larger weight during early iterations for fast convergence and a smaller weight later to preserve local search ability:
$$
\omega_i(t) = e^{-\frac{|f_{\text{best}}(t) – f_i(t-1) + f_i(t-2)|}{|M_f – f_{\text{best}}(t)|}}
$$
This formulation allows the inertia weight to adapt based on whether the firefly is close to the current best solution, promoting diversity and preventing premature convergence.
Dynamic Step Size
Instead of using a fixed step size $\alpha$, FABD adopts a nonlinearly decreasing dynamic step:
$$
a_t = a_0 \cdot \delta^t
$$
where $a_0$ is the initial step size and $\delta \in (0.90, 0.98)$ is a scaling factor. This dynamic schedule balances global exploration in early iterations with refined local exploitation in later stages.
| Parameter | Symbol | Value |
|---|---|---|
| Coverage area | $X \times Y$ | 500 m × 500 m |
| UAV altitude | $h_u$ | 100 m |
| Number of antennas | $M$ | 10 |
| Bandwidth | $B$ | 1 MHz |
| Reference channel gain | $\beta_0$ | 1.42 × 10⁻⁴ |
| Path loss exponent | $\varphi$ | 3.8 |
| Number of ground users | $K$ | 4 |
| User positions | $(x_k, y_k, h_k)$ | Given in simulation |
| Required rates | $c_k$ | [1.43, 2.23, 1.33, 3.83] Mbit/s |
Simulation Results of Deployment Optimization
The performance of the FABD algorithm was compared against the standard FA, ant colony optimization (ACO), and particle swarm optimization (PSO) algorithms under identical initial conditions with 1000 independent runs.
The convergence characteristics shown in the results indicate that FABD achieves faster convergence than all benchmark algorithms. With a population size of $npop=10$, FABD converges after approximately 17 iterations, while FA requires 20 iterations, ACO requires 24 iterations, and PSO requires 28 iterations. Increasing the population size to 20 further accelerates convergence for all methods, confirming the benefit of a larger population in exploring the solution space.
| Algorithm | npop = 10 | npop = 20 |
|---|---|---|
| FABD | 17 iterations | 13 iterations |
| FA | 20 iterations | 14 iterations |
| ACO | 24 iterations | 19 iterations |
| PSO | 28 iterations | 24 iterations |
The trajectory comparison reveals that FABD moves more swiftly toward the optimal region in early iterations due to the inertia weight acceleration, while maintaining adequate exploration through the dynamic step size and random perturbation term. The final UAV deployment positions obtained by each algorithm are:
- FABD: (350.17, 208.81, 100)
- FA: (357.53, 215.37, 100)
- ACO: (332.01, 205.13, 100)
- PSO: (317.57, 195.28, 100)
To demonstrate the superiority of the optimization-based deployment, additional comparative analyses considered fixed deployment positions: the center of the coverage area, two random positions, and the FA/FABD optimized positions. The total transmit power was evaluated under varying antenna counts, path loss exponents, and required data rates.
When the number of antennas varied from 10 to 50, the optimized deployment positions consistently achieved lower total transmit power. The transmit power decreases with more antennas due to increased array gain, but the deployment position has a more significant impact. FABD outperforms FA at lower antenna counts, with the gap narrowing as antenna count increases, though FABD maintains a measurable advantage throughout.
Under varying path loss exponents from 3.2 to 4.2, the transmit power increases exponentially for all deployment positions, but the optimized positions exhibit significantly lower power consumption. At $\varphi=3.8$, FABD achieves approximately 17.6% power reduction compared to the center deployment and substantial improvements relative to random positions. When the path loss exponent exceeds 3.8, FABD shows an even more pronounced advantage over the standard FA algorithm.
Analysis of the effect of user data rate requirements from 1 to 5 Mbit/s confirms that higher data rates necessitate higher transmit power. The FABD-optimized UAV position consistently requires the least power among all evaluated configurations, verifying that the optimized deployment strategy effectively reduces energy consumption while satisfying QoS constraints.
Conclusion and Future Directions
This article has comprehensively presented a study on beamforming and optimized deployment techniques for unmanned aerial vehicles (UAVs) in wireless communication systems. The research makes meaningful contributions to the field of UAV-assisted communications, specifically focusing on enhancing system robustness and energy efficiency through multi-antenna technology.
The first major contribution is the development of a volumetric Capon beamforming algorithm that effectively addresses the challenges of interference suppression in UAV relay networks, particularly under conditions of steering vector mismatch and environmental uncertainty. This algorithm integrates ROOT-MUSIC-based angle estimation with a novel volume integral approach for covariance matrix reconstruction, thereby achieving superior performance in terms of output SINR across a wide range of SNR conditions. The results demonstrate excellent nulling capability of -30 dB at interference directions, nearly 2-3 dB improvement in output SINR at low SNR conditions compared with existing methods, and strong convergence and stability with fewer snapshots.
The second contribution is the FABD algorithm, a modified firefly algorithm incorporating adaptive inertia weight and dynamic step size for efficient UAV deployment optimization. This algorithm effectively solves the non-convex optimization problem of minimizing total transmit power for multi-antenna UAV base stations while satisfying per-user data rate constraints. Comparative analysis confirms that FABD achieves faster convergence (approximately 15% fewer iterations than FA), better optimization accuracy with 5-8% lower total transmit power than standard FA, and greater robustness across various antenna configurations and propagation conditions.
Collectively, the proposed beamforming and deployment methods provide an integrated framework for enhancing the reliability and sustainability of UAV-assisted communication systems. These techniques are particularly valuable in emergency response scenarios, temporary network expansion, and remote area coverage.
Future research directions in this domain include several promising extensions. The incorporation of Doppler effect modeling is essential to account for the inherent mobility of unmanned aerial vehicles, which was assumed negligible in the current research. The extension to multi-antenna ground users would introduce diversity gains and further enhance system performance. Additionally, modeling the backhaul link between the UAV and the data exchange center would yield a more realistic power consumption estimation and potentially lead to joint optimization problems with even greater practical impact. Exploring UAV trajectory optimization in conjunction with dynamic beamforming and deployment would enable real-time adaptive coverage in time-varying environments. Furthermore, the integration of machine learning techniques for channel prediction and adaptive parameter tuning in dynamic UAV communication scenarios represents a compelling direction for future exploration.
As unmanned aerial vehicles continue to play an increasingly vital role in wireless networks, the combination of advanced beamforming algorithms and intelligent deployment strategies will be instrumental in realizing the full potential of UAV-assisted communication systems, paving the way for more resilient, flexible, and energy-efficient next-generation networks.