Table 1 Main variables and their meaning
Variable | Meaning | Variable | Meaning |
|---|---|---|---|
\(\mathcal{K}\) | Set of ground users | \(K\) | Number of ground users |
\(\mathcal{U}\) | Set of UAVs | \(U\) | Number of UAVs |
\(\mathcal{G}\) | Set of GBSs | \(G\) | Number of GBSs |
\(\mathcal{L}\) | Set of all transmission nodes | \(L\) | Number of all transmission nodes |
\({\mathcal{L}}_{m}[n]\) | Set of transmission nodes in cluster \(m\) at slot \(n\) | \({L}_{m}[n]\) | Number of transmission nodes in cluster \(m\) at slot \(n\) |
\(\mathcal{N}\) | Set of time slots | \(N\) | Number of time slots |
\(\mathcal{M}\left[n\right]\) | Set of clusters at slot \(n\) | \(M[n]\) | Number of clusters at slot \(n\) |
\({\mathcal{K}}_{m}[n]\) | Set of users in cluster \(m\) at slot \(n\) | \({K}_{m}[n]\) | Number of users in cluster \(m\) at slot \(n\) |
\({g}_{lk,m}^{\mathrm{L}}\left[n\right]\) | Large-scale channel gain from the transmission node \(l\) to user \(k\) in cluster \(m\) at slot \(n\) | \({g}_{lk,m}^{\mathrm{S}}\left[n\right]\) | Small-scale channel coefficient from the transmission node \(l\) to user \(k\) in cluster \(m\) at slot \(n\) |
\({P}_{lk,m}\left[n\right]\) | Transmit power from the transmission node \(l\) to user \(k\) in cluster \(m\) at slot \(n\) | \({R}_{k,m}[n]\) | Downlink achievable data rate of user \(k\) in cluster \(m\) at slot \(n\) |
\({{\varvec{p}}}_{g}\) | Horizontal position of each GBS \(g\) | \({{\varvec{p}}}_{u}[n]\) | Horizontal coordinate of each UAV \(u\) in slot \(n\) |
\({{\varvec{p}}}_{k,m}\) | Horizontal location of user \(k\) in cluster \(m\) | \({\varvec{P}}\left[n\right]\) | UAVs’ location matrix in slot \(n\) |
\({{\varvec{p}}}_{u}^{\mathrm{in}}\) | Initial and final locations of each UAV \(u\) | \(W\) | Wireless channel bandwidth |
\({\varvec{\beta}}\) | Rician factor | \(T\) | Flight cycle of each UAV |
\({L}_{m}^{\mathrm{max}}\) | Maximum number of the transmission nodes in each cluster \(m\) | \({C}_{l}^{\mathrm{BH}}\) | Maximum capacity of the backhaul link at the transmission node \(l\) |
\({d}^{\mathrm{max}}\) | Maximum distance that each UAV \(u\) can move between any two successive slots | \({d}^{\mathrm{min}}\) | Minimum distance between any two UAVs |