In recent years, the application of unmanned aerial vehicle (UAV) formations has expanded significantly, particularly in areas such as surveillance, delivery, and entertainment. One of the most captivating uses is the formation drone light show, where hundreds or thousands of drones coordinate to create intricate aerial displays. These formation drone light shows rely heavily on robust and efficient communication networks to ensure synchronized movements and real-time data exchange. However, as the scale of these formation drone light shows increases, challenges in maintaining reliable communication links become more pronounced. Drones in a formation drone light show must operate in dense environments, often leading to interference, signal degradation, and increased latency. To address these issues, this article proposes a cooperative communication relay selection strategy based on Device-to-Device (D2D) technology, which optimizes relay member selection to enhance throughput and overall network performance in UAV formation support networks. By considering both the adjacent domains of formation members and their social interdependence relationships, this strategy aims to ensure basic communication capabilities while maximizing system efficiency, crucial for large-scale formation drone light shows.
The core of a successful formation drone light show lies in the seamless coordination among drones, which is facilitated by a support network that enables information sharing and situational awareness. Traditional cellular networks may not suffice due to high latency and infrastructure dependence, making D2D communication an attractive alternative. In D2D-based UAV formations, drones can communicate directly with each other, reducing reliance on base stations and improving spectral efficiency. However, in dynamic and dense formation drone light show scenarios, direct communication may fail due to distance or interference, necessitating the use of relay drones. Selecting optimal relay members is critical to maintain link quality and throughput. This article delves into a novel relay selection method that integrates physical proximity and social interdependence metrics, specifically tailored for formation drone light show applications where drones exhibit collaborative behaviors.
The system model for a UAV formation network in a formation drone light show typically includes a primary member (e.g., a lead drone or ground station), multiple idle members (potential relays), cellular members (using licensed spectrum), and D2D members (including source and target drones). Let the formation consist of one primary member \( m \), \( I \) idle members denoted as \( \mathcal{I} = \{i_1, i_2, \dots, i_I\} \), \( C \) cellular members as \( \mathcal{C} = \{c_1, c_2, \dots, c_C\} \), and \( D \) D2D members as \( \mathcal{D} = \{d_1, d_2, \dots, d_D\} \). In a formation drone light show, drones are arranged in stable patterns, but their relative positions can vary over time due to choreography. The communication occurs in a three-dimensional Euclidean space, with drones operating within a defined region, such as a sphere of radius 500 meters for typical formation drone light show setups. Cellular members communicate with the primary member via orthogonal channels, avoiding interference, while D2D members reuse these cellular uplink resources for transmission, as uplink traffic is often less congested. This reuse can lead to interference, which must be managed to ensure quality of service (QoS).
The signal-to-interference-plus-noise ratio (SINR) for cellular and D2D links is crucial for evaluating communication quality. For a cellular link between a cellular member \( c \) and the primary member \( m \), the SINR is given by:
$$ \gamma_c = \frac{p_c^T g_{cm} |h_{cm}|^2}{p_t^T g_{tm} |h_{tm}|^2 + N_0} $$
where \( p_c^T \) and \( p_t^T \) are the transmission powers of the cellular member and D2D source member, respectively; \( g_{cm} \) and \( g_{tm} \) represent path losses; \( h_{cm} \) and \( h_{tm} \) are channel gains; and \( N_0 \) is the noise power. Similarly, for a D2D link between a source member \( t \) and a target member \( a \), the SINR is:
$$ \gamma_d = \frac{p_t^T g_{ta} |h_{ta}|^2}{p_c^T g_{ca} |h_{ca}|^2 + N_0} $$
In a formation drone light show, maintaining these SINR levels above thresholds is essential for reliable communication. The conditions for direct D2D communication are:
$$ \gamma_c \geq \gamma_{c\_th} \quad \text{and} \quad \gamma_d \geq \gamma_{d\_th} $$
where \( \gamma_{c\_th} \) and \( \gamma_{d\_th} \) are the minimum SINR thresholds for cellular and D2D links, respectively. If these conditions are not met, even with maximum transmission powers \( p_{c\_max} \) and \( p_{d\_max} \), relay-assisted communication becomes necessary. This is common in large formation drone light shows where drones are spaced widely or experience high interference.
To formalize the relay selection problem, we define the adjacent domain of a drone member \( \epsilon_i \) in the formation drone light show. The adjacent domain is a spherical region centered at the drone’s position \( \mathbf{l}_i(t) \) at time \( t \), with radius \( d_{i\_max} \), where \( d_{i\_max} = k_{i\_max} \cdot dis \). Here, \( k_{i\_max} \) is an adjacency coefficient, and \( dis \) is a safety distance to prevent collisions in the formation drone light show. The neighboring set \( \nu(\mathbf{l}) \) includes pairs of drones \( (i, j) \) such that the expected distance margin \( \mu_{ij} < d_{i\_max} \). For relay selection, we focus on the overlap of adjacent domains between source and target drones. As illustrated in the figure above, the ideal relay candidate should lie in Region I, which is the intersection of the hemispherical adjacent domains of the source and target drones along their connecting line. This positioning balances distances to both ends, optimizing relay performance in a formation drone light show.
The social interdependence relationship (SIR) among drones is another key factor in relay selection for formation drone light show networks. In a collaborative environment like a formation drone light show, drones exhibit social behaviors based on their capabilities and interactions. We define the social interdependence degree \( \rho_{ij} \) between drone \( \epsilon_i \) and drone \( \epsilon_j \) as:
$$ \rho_{ij} = \frac{C_{ij}}{C_i} = \frac{C_{ij}}{C_{ij} + C_{b_i}} $$
where \( C_{ij} \) represents the social ability, defined as the SINR of the communication link from \( \epsilon_i \) to \( \epsilon_j \):
$$ C_{ij} = \frac{p_i^T g_{ij} |h_{ij}|^2}{p_c^T g_{cj} |h_{cj}|^2 + N_0} $$
and \( C_{b_i} \) is the basic communication ability of drone \( \epsilon_i \), given by \( C_{b_i} = p_{max} / d_{i\_max} \), where \( p_{max} \) is the maximum transmission power. A higher \( \rho_{ij} \) indicates stronger social interdependence, implying better communication quality and reliability, which is vital for coordination in a formation drone light show.
The throughput of a communication link is a primary performance metric for formation drone light show networks. According to Shannon’s formula, the throughput for a direct link is:
$$ R_{ij} = B \log_2 \left(1 + \gamma_{ij}\right) = B \log_2 \left(1 + \frac{p_i |h_{ij}|^2}{p_c |h_{cj}|^2 + N_0}\right) $$
where \( B \) is the channel bandwidth, and \( p_i = p_i^T g_{ij} \) and \( p_c = p_c^T g_{cj} \) are the effective powers incorporating path loss \( \tau (d_{ij})^{-\alpha} \), with \( \tau \) as the path loss constant and \( \alpha \) as the path loss exponent. For relay-assisted communication using decode-and-forward (DF) protocol, the throughput becomes:
$$ R_r = \frac{1}{2} \min \left( R_{ir}, R_{rj} \right) $$
where \( R_{ir} \) and \( R_{rj} \) are the throughputs for the first hop (source to relay) and second hop (relay to target), respectively:
$$ R_{ir} = B \log_2 \left(1 + \frac{p_i |h_{ir}|^2}{p_c |h_{cr}|^2 + N_0}\right), \quad R_{rj} = B \log_2 \left(1 + \frac{p_r |h_{rj}|^2}{p_c |h_{cj}|^2 + N_0}\right) $$
Incorporating social interdependence, the overall throughput for relay-assisted communication in a formation drone light show can be expressed as:
$$ R_d = \frac{B}{2} \min \left( \log_2 \left(1 + \frac{p_i |h_{ir}|^2}{p_c |h_{cr}|^2 + N_0}\right), \log_2 \left(1 + \frac{\rho_{ij} p_i |h_{ij}|^2}{p_c |h_{cj}|^2 + N_0} + \frac{p_r |h_{rj}|^2}{p_c |h_{cj}|^2 + N_0}\right) \right) $$
The optimization problem for relay selection in a formation drone light show network aims to maximize the total throughput while satisfying constraints. Let \( \mathcal{C}_{R,i} \) be the set of candidate relay members for drone \( \epsilon_i \), and \( x_r \) be a binary variable indicating whether relay \( r \) is selected. The objective function and constraints are:
Maximize:
$$ \max \sum_{r \in \mathcal{C}_{R,i}} x_r R_d $$
Subject to:
$$ \gamma_{ir} \geq \gamma_{d\_th}, \quad \gamma_{rj} \geq \gamma_{d\_th} $$
$$ \gamma_c \geq \gamma_{c\_th} $$
$$ 0 < p_c^T \leq p_{c\_max}, \quad 0 < p_d^T \leq p_{d\_max} $$
$$ \sum_{r \in \mathcal{C}_{R,i}} x_r = 1, \quad x_r \in \{0, 1\} $$
These constraints ensure that each hop in relay communication meets SINR thresholds, cellular links remain viable, transmission powers are within limits, and exactly one relay is selected per communication pair. This formulation is critical for maintaining the artistic integrity of a formation drone light show, where any communication failure could disrupt the visual display.
To solve this optimization problem, we propose a relay selection strategy that integrates adjacent domain overlap and social interdependence. The steps are as follows:
- When a drone \( \epsilon_i \) in the formation drone light show requires communication, it sends a request to the primary member to identify a target drone \( \epsilon_j \) with the needed resources, minimizing the distance \( d_{ij} \).
- If the direct link SINR \( \gamma_{ij} \geq \gamma_{d\_th} \), use direct communication; otherwise, proceed to relay selection.
- Define the relay selection region based on adjacent domain overlap: prioritize Region I (intersection of hemispherical domains along the source-target line).
- If Region I contains idle drones, add them to candidate set \( \Omega \); if \( \Omega \) is empty, check Region II (remainder of adjacent domains).
- If multiple candidates exist, compute their social interdependence degrees \( \rho_{ij} \) with the source drone and select the one with the highest value.
- Establish the relay-assisted communication link using the selected drone.
This strategy ensures that relays are physically proximate and socially reliable, enhancing throughput for formation drone light show networks. To evaluate performance, we simulate a formation drone light show scenario with parameters typical for large-scale displays. The simulation settings are summarized in the table below:
| Parameter | Value | Description |
|---|---|---|
| Formation radius | 500 m | Maximum spread of drones in the formation drone light show |
| Minimum D2D distance | 25 m | Closest spacing between drones in the formation drone light show |
| Maximum D2D distance | 60 m | Farthest spacing for direct communication in the formation drone light show |
| Update period | 100 ms | Time interval for formation updates in the formation drone light show |
| Path loss exponent (\( \alpha \)) | 2 | Exponent for signal attenuation in the formation drone light show environment |
| Maximum transmission power | 23 dBm | Peak power for drones in the formation drone light show |
| Noise power (\( N_0 \)) | -120 dBm/Hz | Background interference in the formation drone light show |
| Channel bandwidth (\( B \)) | 180 kHz | Bandwidth allocated for communication in the formation drone light show |
The performance of the proposed relay selection strategy is compared with existing methods, such as distance-based and SNR-based strategies, in terms of throughput cumulative distribution function (CDF). The results show that the proposed strategy significantly improves throughput for most drones in the formation drone light show. For instance, at a CDF of 0.5, the proposed strategy achieves a throughput of approximately 12 Mbps, compared to 10 Mbps for the SNR-based strategy and 8 Mbps for the distance-based strategy. This improvement is attributed to the combined consideration of physical proximity and social interdependence, which better adapts to the dynamic conditions of a formation drone light show.
Another key aspect is the impact of social interdependence on relay selection. As shown in the formula for \( \rho_{ij} \), drones with higher social abilities contribute more to reliable links. In a formation drone light show, drones often have varying capabilities based on their roles (e.g., leaders vs. followers). By incorporating \( \rho_{ij} \), the strategy prioritizes drones that are not only close but also socially robust, reducing the risk of link failure during complex maneuvers in the formation drone light show.
To further illustrate the optimization, consider the throughput gain from relay-assisted communication. The overall system throughput \( R_{total} \) for the formation drone light show network can be expressed as the sum of throughputs for all active links, including direct and relay-assisted ones:
$$ R_{total} = \sum_{i \in \mathcal{D}} \left( \mathbb{I}_{\gamma_{ij} \geq \gamma_{d\_th}} R_{ij} + \mathbb{I}_{\gamma_{ij} < \gamma_{d\_th}} R_d \right) $$
where \( \mathbb{I} \) is an indicator function. Maximizing \( R_{total} \) involves careful relay selection, as demonstrated by the proposed strategy. In simulations, the proposed strategy achieves a 20% increase in median throughput compared to baseline methods, which is crucial for high-density formation drone light shows with hundreds of drones.
The adjacent domain model also plays a vital role. By defining Region I and Region II, the strategy limits the search space for relays, reducing computational overhead in real-time formation drone light show operations. The mathematical formulation for the adjacent domain overlap is based on drone positions and velocities. For drones \( \epsilon_i \) and \( \epsilon_j \) with initial positions \( \mathbf{l}_i(t_0) \) and \( \mathbf{l}_j(t_0) \) and velocities \( \mathbf{v}_i \) and \( \mathbf{v}_j \), the distance after time \( \Delta t \) is:
$$ d_{ij}^{t_0 + \Delta t} = \left[ \left( x_i^{t_0} + v_{ix} \Delta t – x_j^{t_0} – v_{jx} \Delta t \right)^2 + \left( y_i^{t_0} + v_{iy} \Delta t – y_j^{t_0} – v_{jy} \Delta t \right)^2 + \left( z_i^{t_0} + v_{iz} \Delta t – z_j^{t_0} – v_{jz} \Delta t \right)^2 \right]^{1/2} $$
This dynamic distance calculation ensures that relay selection adapts to drone movements in a formation drone light show, maintaining optimal links even during transitions.
In terms of implementation, the proposed strategy can be integrated into the control software of drones used in formation drone light shows. Each drone would periodically compute its adjacent domain and social interdependence degrees with neighbors, using lightweight algorithms to minimize processing delay. For large-scale formation drone light shows involving thousands of drones, distributed computation can be employed, where drones exchange information via D2D links to update their relay candidate sets.
The benefits of this approach extend beyond throughput. By improving communication reliability, the strategy reduces the probability of synchronization errors in formation drone light shows, which are often visible as glitches in the aerial display. Moreover, the use of D2D communication saves energy compared to traditional cellular modes, extending the flight time of drones in prolonged formation drone light shows.
To quantify the social interdependence effect, we can analyze the relationship between \( \rho_{ij} \) and throughput. A higher \( \rho_{ij} \) typically correlates with better channel conditions, as it reflects both SINR and basic capabilities. In simulations, drones with \( \rho_{ij} > 0.7 \) achieve throughput gains of up to 30% when selected as relays, underscoring the importance of social metrics in formation drone light show networks.
Challenges remain, however. In formation drone light shows, drones at the periphery of the formation may have fewer candidate relays due to sparser adjacent domain overlaps. To address this, future work could explore hybrid strategies that incorporate predictive mobility models or leverage centralized coordination for edge drones. Additionally, the social interdependence model could be enhanced by including historical interaction data, such as past collaboration success rates in formation drone light shows.
In conclusion, this article presents a cooperative communication relay selection method for UAV formation networks, with a focus on application in formation drone light shows. By combining adjacent domain analysis and social interdependence relationships, the strategy optimizes relay selection to maximize throughput and ensure reliable communication. The formulation using mathematical models and simulations demonstrates significant performance improvements over existing methods. As formation drone light shows continue to grow in scale and complexity, such advanced communication strategies will be essential for achieving seamless and captivating aerial displays. Future research could investigate machine learning techniques to dynamically adapt relay selection based on real-time conditions in formation drone light shows, further enhancing robustness and efficiency.
The integration of D2D technology with social-aware relay selection opens new avenues for scalable UAV networks. For formation drone light shows, this means more intricate patterns, longer durations, and higher resilience to interference. The proposed strategy not only addresses technical challenges but also aligns with the artistic goals of formation drone light shows, where precision and synchronization are paramount. By continuously refining these methods, we can push the boundaries of what is possible in aerial entertainment and collaborative robotics.
Finally, it is worth noting that the principles discussed here apply beyond formation drone light shows to other UAV applications, such as search and rescue or environmental monitoring. The core idea of leveraging social interdependence for network optimization can be adapted to various scenarios where drones operate in formations. However, the unique demands of formation drone light shows, with their emphasis on visual perfection and real-time coordination, make them an ideal testbed for these innovations. As technology advances, we anticipate even more sophisticated approaches to emerge, further revolutionizing the field of formation drone light shows and UAV networks at large.