## 3 Problem Formulation
### Unlicensed Shared Access  
Let \(M_{\text{ULS}}\) denote the number of RBs in the 60 GHz unlicensed spectrum (ULS) bandwidth. Since MNO 1 operates at a different frequency from that of the ULS, the transceiver 2 of SBSs in LAA enabled with the ULS can operate in all TTIs \(t_{\text{ULS}}\in\mathbf{T}\). The capacity served by the ULS enabled transceiver of an SBS is given by:  
\[\sigma_{s}^{\text{ULS}}=\sum_{t=t_{\text{ULS}}\in\mathbf{T}}\sum\
olimits_{i=1}^{M _{\text{ULS}}}\sigma_{t,i}(\rho_{t,i}) \tag{45}\]  
Hence, for \(S_{\text{F}}\) SBSs, the aggregate capacity per 3D building is given by:  
\[\sigma_{\text{LSA,Tans\,2}}^{\text{SC}}=\sum\
olimits_{s=1}^{S_{\text{F}}} \sigma_{s}^{\text{ULS}} \tag{46}\]  
However, the transceiver 1 of each SBS operates at the MNO 1 spectrum, the capacity which is given by:  
\[\sigma_{\text{LAA,Tans\,1}}^{\text{SC}}=\sigma_{\text{MNO,1}}^{\text{SC,DedA}}= \sum\
olimits_{s=1}^{S_{\text{F}}}\sigma_{s,\text{DedA}} \tag{47}\]  
Now with LAA, the total capacity served by all the SBSs enabled with both the MNO 1 spectrum and the ULS in a 3D building is given by:  
\[\sigma_{\text{LAA,MB}}^{\text{SC}}=\sigma_{\text{LAA,Tans\,1}}^{\text{SC}}+ \sigma_{\text{LAA,Tans\,2}}^{\text{SC}} \tag{48}\]Now, using (4), the system level capacity of MNO 1 for the multiband enabled SBSs with LAA per building is given by:  
\[\sigma^{\text{SYS}}_{\text{LAA,MB}}=\sigma^{\text{MC,WIM}}_{\text{MNO,1}}+\sigma^{ \text{SC}}_{\text{LAA,MB}} \tag{49}\]  
Note that, since ULS is license free, then following the consideration mentioned in Remark 2, the average system-level spectral efficiency of MNO 1 for LAA per building is given by:  
\[\sigma^{\text{SE}}_{\text{LAA,MB}}=\sigma^{\text{SYS}}_{\text{LAA,MB}}/(M_{ \text{MNO,1}}\times Q) \tag{50}\]  
The average system-level energy efficiency of MNO 1 for LAA per building in Joules/bit (J/b) is given by:  
\[\sigma^{\text{EE}}_{\text{LAA,MB}}=\Bigg{(}\begin{array}{l}\big{(}S_{\text{F} }\times\big{(}\big{|}T^{\text{MNO,1}}_{\text{non-ABS}}\big{|}/\big{|}T\big{|} \big{)}\times P_{\text{SC,1}}\big{)}+\\ \big{(}S_{\text{F}}\times P_{\text{SC,2}}\big{)}+\big{(}S_{\text{P}}\times P_{ \text{PC}}\big{)}+\big{(}S_{\text{M}}\times P_{\text{MC}}\big{)}\end{array} \Bigg{)}/\big{(}\sigma^{\text{SYS}}_{\text{LAA,MB}}/Q\Big{)} \tag{51}\]  
Now, following the assumptions for \(L>1\), the average aggregate capacity of MNO 1 with LAA is roughly given by:  
\[\sigma^{\text{SYS}}_{\text{LAA,MB,}L}=\sigma^{\text{MC,WIM}}_{\text{MNO,1}}+ \Big{(}L\times\sigma^{\text{SC}}_{\text{LAA,MB,}L}\Big{)} \tag{52}\]  
Hence, the spectral efficiency for \(L\) buildings is then given by:  
\[\sigma^{\text{SE}}_{\text{LAA,MB,}L}=\sigma^{\text{SYS}}_{\text{LAA,MB,}L}/(M_ {\text{MNO,1}}\times Q) \tag{53}\]  
Similarly, the energy efficiency for \(L\) buildings is given by:  
\[\sigma^{\text{EE}}_{\text{LAA,MB,}L}=\Bigg{(}\begin{array}{l}\big{(}L\times S _{\text{F}}\times\big{(}\big{|}T^{\text{MNO,1}}_{\text{non-ABS}}\big{|}/\big{|} T\big{|}\big{)}\times P_{\text{SC,1}}\big{)}+\\ \big{(}L\times S_{\text{F}}\times P_{\text{SC,2}}\big{)}+\big{(}S_{\text{P}} \times P_{\text{PC}}\big{)}\end{array}\Bigg{)}/\big{(}\sigma^{\text{SYS}}_{ \text{LAA,MB,}L}/Q\Big{)} \tag{54}\]