# 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)
Now, the size of a 3D cluster of nodes can be expressed as follows:

\[\Delta_{\text{3D cluster}}=\varepsilon_{\text{linear}}\times\Delta_{\text{ planer}} \tag{14}\]Interested readers are encouraged to refer to [25] for a more detailed description of modeling 3D clusters. Assume that \(S_{\text{F}}\) and \(S_{\text{C}}\) denote respectively the maximum number of small cells, (i.e., femtocells) and CGC stations per building so that \(s\in\{1,2,\dots,S_{\text{F}}\}\) and \(c\in\{1,2,\dots,S_{\text{C}}\}\) for \(S_{\text{F}}\
eq S_{\text{C}}\). Let \(\xi_{\text{reuse}}\) denote the spectrum reuse factor per building of small cells so that using (A6), it can be expressed as follows. \[\xi_{\text{reuse}}=S_{\text{F}}/\Delta_{\text{3D cluster}}\] (A7)

The above expression implies the fact that the same satellite spectrum can be shared with small cells per building with the nOSS technique \(\xi_{\text{reuse}}\) times than that performed by the OSS technique. ## References

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