# Tethered Balloon Cluster Deployments and Optimization for Emergency Communication Networks
## 3 System Model and Problem Formulation  
### Geometrical Model  
In this section, a high-altitude tethered balloon communication system model is constructed in which balloons are used as temporary airborne base stations to provide communication services to end-users. In this system, the air-to-air communication link between balloon base stations uses LTE backhaul link technology to achieve self-organized networking [17]. The communication between balloon base stations and ground users or ground base stations adopts the air-to-ground access link, using LTE technology, to provide wireless access service for ground equipment. A multi-hop, multi-link network architecture can be deployed between two distant ground stations. The network is formed by deploying multiple balloon base stations in the intermediate area, with each balloon base station acting as a relay node, supporting multi-path transmission to improve reliability and using the AODV routing protocol [18; 19] to achieve long-distance multi-hop communication. As shown in Figure 1, there are \(n\) balloons in this system providing data transmission to \(m\) users. The users are randomly distributed in a two-dimensional plane \(\mathcal{D}=\left\{(x,y)\left|x_{min}\leq x\leq x_{max},y_{min}\leq y\leq y_{ max}\right\}\right\), while balloons are deployed in a 3D area \(\mathcal{P}=\left\{(x,y,h)\left|x_{min}\leq x\leq x_{max},y_{min}\leq y\leq y_{ max},h_{min}\leq h\leq h_{max}\right\}\). Let \(\mathcal{N}=\left\{1,2,\cdots,N\right\}\) represent the set of balloon base stations. Let \(\mathcal{M}=\left\{1,2,\cdots,M\right\}\) represent the set of users; the set of users covered by balloon \(n\) can be expressed as \(\mathcal{M}_{n}=\left\{M_{1},M_{2},\cdots,M_{n}\right\}\). In addition, to decrease co-channel interference between neighboring balloon base stations, let \(\mathcal{B}=\left\{1,2,\cdots B\right\}\) denote the set of available frequency bands. Each base station can only use at most one band to provide communication for multiple users. The frequency band of base station \(n\) is denoted by \(b_{n}\). The set of base stations using band \(b\) is \(\mathcal{N}_{b}\)[20]. \begin{table}
\begin{tabular}{c l l l} \hline \hline
**Reference** & **Model** & **Objective Function** & **Methodology** \\ \hline
[1] & Not specified. & Throughput, delay. & Not specified. \\ \hline
[4] & Not specified. & Quality of service (QoS). & Not specified. \\ \hline
[9] & Okumura-Hata model. & Coverage. & Not specified. \\ \hline
[10] & Rician channel model. & Maximization of sum rate. & Interference alignment technique. \\ \hline
[11] & Multi-layer placement model. & Minimize the number of balloons and maximize user connections. & Greedy algorithm and \\ \hline
[12] & Hata model. & Path loss, coverage area, and & Not specified. \\  & received signal strength. & & \\ \hline
[13] & Markov decision problem (MDP). & Maximization of total rate. & Resource allocation and placement \\  & & control joint optimization scheme. \\ \hline
[14] & Ricean fading, free-space path loss (FSPL), and air-to-ground (ATG) & Maximize end-to-end throughput. & Joint layout and resource \\  & channel model. & & allocation algorithm. \\ \hline
[15] & Longley–Rice model. & Coverage. & Triangulation method. \\ \hline
[16] & Rayleigh fading, Nakagami-m fading, FSPL, and ATG model. & Maximize coverage probability. & Stochastic geometry tools and user \\  & & & association policy. \\ \hline Our contribution & Gauss–Markov mobility model, & Maximize target coverage and & MOPSO (Swarm intelligence \\  & FSPL, and ATG channel model. & system energy efficiency. & optimizing multiple objectives). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with existing research.