# 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)
## 7 Conclusions

In this paper, we presented two spectrum sharing techniques, namely orthogonal spectrum sharing (OSS) and non-orthogonal spectrum sharing (nOSS), for a multisystem consisting of an integrated satellite-mobile system and an autonomous terrestrial-mobile system (iSMS/aTMS). OSS shares the whole satellite spectrum of iSMS/aTMS with all small cells per building of aTMS, whereas nOSS shares the whole satellite spectrum with only small cells per 3D cluster per building where a 3D cluster consists of a set of small cells within a building located in both intra-floor and inter-floor levels subject to satisfying co-channel interference constraints in both intra-and inter-floor levels. A realistic dynamic deployment of CGC stations and SBSs per apartment in each building has been considered so that the existence of a SBS and a CGC station in any time in an apartment of a building follows two independent and random processes with an equally likely occurrence of each deployment option for SBSs and CGC stations. Additionally, we developed an interference management strategy to avoid co-channel interference and deduced an optimal number of ABSs per APP to ensure a fair allocation of time resources in apartments with collocated CGC stations and small cells. Furthermore, we derived system-level capacity, spectral efficiency, and energy efficiency performance metrics as well as developed an algorithm for both OSS and nOSS techniques. With extensive system-level simulation and numerical results and analysis, it has been shown that, in general, aggregate capacity and spectral efficiency improve proportionally as the number of buildings of small cells \(L\) increases, whereas energy efficiency improves negative exponentially for low values of \(L\) and becomes almost steady for high values of \(L\) for both OSS and nOSS techniques. Since the same satellite spectrum can be reused more than once to SBSs per building using nOSS, compared to when using OSS, nOSS outperformed OSS in terms of capacity, spectral efficiency, and energy efficiency. Furthermore, by increasing the value of the aggregate co-channel interference threshold in the intra-floor and inter-floor levels, the required minimum distance between co-channel small cells can be reduced. This results in increasing the number of 3D clusters of small cells, which correspondingly increases the number of times the same satellite spectrum can be reused to the same number of small cells in a multistory building, and vice versa. Finally, it has been shown that, with a lower density of small cells by nOSS than that required by OSS, both OSS and nOSS can meet the expected spectral efficiency and energy efficiency requirements for 5G mobile networks. This research received no external funding. This paper was presented partly at the 2019 Joint Conference on Satellite Communications (JC SAT 2019), JR Hakata City, Fukuoka, Japan, 10-11 October 2019 [22]. This paper is a technical report without peer review, published by IEICE in the IEICE Technical Report SAT2019-61(2019-10), pp. 103-108, and hence, its polished and/or extended version may be published elsewhere [22]. The author declares no conflict of interest. ## Appendix A Link Throughput

Let \(\mathbf{T}\) denote the simulation run time with the maximum time of \(Q\), each lasting 1 ms, so that \(\mathbf{T}=\{1,\)\(2,\)\(3,\)\(\ldots,\)\(Q\}\) and hence \(|\mathbf{T}|=Q\). Let \(\mathbf{T_{\text{ABS}}}\) denote the number of ABSs in every APP of eight subframes so that \(\mathbf{T_{\text{ABS}}}=\{t\): \(t=8v+z\); \(v=0,\)\(1,\)\(2,\)\(\ldots,\)\(Q\)/\(8\); \(z=1,\)\(\ldots,\)\(T_{\text{ABS}}\}\) where \(T_{\text{ABS}}=1,\)\(2,\)\(\ldots,\)\(8\) corresponds to ABS patterns \(\varphi=1/8,\)\(2/8,\)\(\ldots,\)\(8/8\), respectively.