# On Developing Techniques for Sharing Satellite Spectrum with Indoor Small Cells in 5G +
## 3 Mathematical Analysis
### Estimation of an Optimal Number of Almost Blank Subframes (ABSs)
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters and Assumptions** & **Value** \\ \hline E-UTRA simulation case [1] & 3 GPP case 3 \\ \hline Satellite type and operating frequency band & GEO or LEO, S-band \\ \hline Effect of the mobility of satellite spot-beam cells on & \\ the satellite UE handover between the satellite and & None \\ a CGC station & \\ \hline Cellular layout [2] and Inter-site distance (ISD) [1, 2] & Hexagonal grid, dense urban, 3 sectors per macrocell site and \\  & 1732 m \\ \hline Carrier frequency [2] and transmit direction & 2 GHz (mobile system), 3.5 GHz (satellite system), and \\  & downlink \\ \hline System bandwidth & 40 MHz (for both mobile and satellite systems) \\ \hline Operating spectrum band (satellite) & CGC stations, in-building SBSs \\ \hline Operating spectrum band (aTMS) & Macrocell BS, picocell BSs \\ \hline Considered system for performance evaluation & TMSs only \\ \hline Number of cells per building & 1 macrocell, 2 picocells, 16 CGC stations (maximum), and 16 \\  & SBSs (maximum) \\ \hline External wall penetration loss [1] (\(L_{\text{ow}}\)) & 20 dB \\ \hline Total BS transmit power [1] (dBm) & 46 for microcell [1], 37 for picocell [1], 20 for CGC station or SBS[1] \\ \hline Co-channel fading model [1] & Frequency selective Rayleigh for macrocell and picocell and \\  & Rician for SBS and CGC station \\ \hline \multirow{4}{*}{Path loss} & Indoor macro UE & \(PL(\text{dB})=15.3+37.6\text{log}_{10}R\), \(R\) is in m \\ \cline{2-3}  & \multirow{2}{*}{Outdoor macro UE} & \(PL(\text{dB})=15.3+37.6\text{log}_{10}R+L_{\text{ow}}\), \(R\) is \\  & & in m \\ \hline Picocell BS and a UE [1] & \(PL(\text{dB})=140.7+36.7\text{log}_{10}R\), \(R\) is in km \\ \hline SBS/CGC and a UE [1, 2] & \(PL(\text{dB})=127+30\text{log}_{10}(R/1000)\), \(R\) is in m \\ \hline \multirow{2}{*}{Lognormal shadowing standard deviation (dB)} & 8 for Macrocell BS [2], 10 for Picocell BS [1], 10 for CGC station and \\  & 10 for SBS [2] \\ \hline Antenna configuration & Single-input single-output for all terrestrial mobile BSs and UEs \\ \hline Antenna pattern (horizontal) & Directional (120\({}^{0}\)) for macrocell [1] and omnidirectional for \\  & picocell [1], CGC stations and SBS[1] \\ \hline Antenna gain plus connector loss (dBi); UE antenna gain [2] & 14 for Macrocell BS [2], 5 for Picocell BS [1], 5 for CGC station and \\  & SBS [1]; 0 dBi \\ \hline UE noise Figure 2 and UE speed [1] & 9 dB, 3 km/h \\ \hline Total number of macro UEs; Maximum number of & \\ satellite UEs served simultaneously by a CGC & 30; 1 \\ station & \\ \hline Maximum number of small cell UEs served & 1 \\ simultaneously by a SBS & \\ \hline Picocell coverage and macro UEs offloaded to all & \\ picocells [1]; Indoor macro UEs [1] & 40 m (radius), 2/15; 35\% \\ \hline \multirow{4}{*}{3D multi-story building (regular square-grid)} & \multirow{2}{*}{Floors per building} & 4 \\ \cline{2-3}  & Apartments per floor & 8 \\ \cline{2-3}  & Number of the apartment per building & 32 \\ \cline{2-3}  & Apartment area & \((10\times 10)\) m\({}^{2}\) \\ \hline \multirow{4}{*}{Number of apartments with} & Collocated CGC stations and SBSs & 8 \\ \cline{2-3}  & Only SBSs & 8 \\ \cline{1-1} \cline{2-3}  & Only CGC stations & 8 \\ \cline{1-1} \cline{2-3}  & Neither CGC stations nor SBSs & 8 \\ \hline Scheduler and traffic model [2] & Proportional Fair and full buffer & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Default parameters and assumptions. Furthermore, we considered an ideal scenario for the mobility of satellite spot-beams so that there was no impact of the type of satellite spot-beam cells (e.g., geostationary for a GEO satellite or non-geostationary for an LEO satellite) on the capacity of aTMS. Furthermore, as given in Table 1, we considered two component carriers (i.e., channel bandwidths) each with 20 MHz, resulting in a 40 MHz system bandwidth for the performance evaluation of fourth-generation (4G) LTE systems.