## 3 System Model and Problem Formulations
### Capacity and Coverage Dimensioning
#### 3.2.2 Capacity Dimensioning  
For capacity planning, first of all, the total number of population (UEs), \(NU_{total}\) of the total serving area \(A_{total}\), is estimated. It is based on the population density of the serving area. We assume that total throughput is equally shared between the UEs of particular cells, ensuring the required data rate. Let \(T_{mmax}\), \(N_{sec}\) and \(DR_{UE}\) be the total throughput of an \(\text{RRU}_{\text{m}}\), number of sector antenna of \(\text{RRU}_{\text{m}}\) and data rate required per UE then, the number of UEs to be served by an \(\text{RRU}_{\text{m}}\), \(N_{RRU_{m}}\) is expressed as,  
\[N_{RRU_{m}}=\frac{T_{mmax}\times N_{sec}}{DR_{UE}} \tag{15}\] \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{\(\text{RRU}_{\text{M}}\) **(3.5 GHz)**} & \multicolumn{2}{c}{\(\text{RRU}_{\text{m}}\) **(28 GHz)**} \\ \hline
**Parameters** & **Uplink** & **Downlink** & **Uplink** & **Downlink** \\ \hline MAPL (dB) & 101.052 & 98.052 & 109.947 & 106.947 \\ \hline \(d^{\prime}_{BP}\) (m) & 513.333 & 513.333 & 1306.666 & 1306.666 \\ \hline \(d_{3D}\) (m) & 669.829 & 489.326 & 206.304 & 148.467 \\ \hline \(d_{2D}\) (m) & 669.828 & 488.853 & 206.299 & 146.902 \\ \hline Total urban area (km\({}^{2}\)) & 4 & 4 & 4 & 4 \\ \hline Total Suburban area (km\({}^{2}\)) & 16 & 16 & 16 & 16 \\ \hline Coverage dimensioning & & & & \\ \hline Minimum RRU (Urban) & 2.83 (\(\approx\)3) & 5.32 (\(\approx\)6) & 29.91 (\(\approx\)30) & 59.00 (=59) \\ \hline Minimum RRU (Suburban) & 11.35 (\(\approx\)12) & 21.31 (\(\approx\)22) & 119.66 (\(\approx\)120) & 236.00 (=236) \\ \hline Capacity dimensioning & & & & \\ \hline Minimum RRU (Urban) & 69.44 (\(\approx\)70) & 138.88 (\(\approx\)139) & 34.72 (\(\approx\)35) & 69.44 (\(\approx\)70) \\ \hline Minimum RRU (Suburban) & 17.36 (\(\approx\)18) & 34.72 (\(\approx\)35) & 8.68 (\(\approx\)9) & 17.36 (\(\approx\)18) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: \(\text{RRU}_{\text{M}}\) and \(\text{RRU}_{\text{m}}\) requirements calculations. The throughput of RRUs is calculated using Equation (16), The throughput calculation for RRU\({}_{\text{m}}\) and RRU\({}_{\text{M}}\) are based on the 3 Gpp 38.306 specification [58] is expressed as,  
\[T_{max}(Mbps)=10^{-6}\sum\
olimits_{j=1}^{J}(v_{Layers}^{(j)}\times Q_{m}^{(j)} \times f^{(j)}\times R_{(max)}\times\frac{N_{PRB}^{BW(j),\mu}}{T_{s}^{\mu}} \times(1-OH^{j})) \tag{16}\]  
where \(J\) is the number of aggregated component carriers, \(v_{Layers}^{(j)}\) is the maximum number of supported layers; \(Q_{m}^{(j)}\) is the maximum supported modulation order; \(f^{(j)}\) is the scaling factor; \(\mu\) is the numerology as defined in TS 38.211; \(T_{s}^{\mu}\) is the average OFDM symbol duration in a subframe for numerology, i.e., \(T_{s}^{\mu}=\frac{10^{-3}}{14\times 2^{\text{P}}}\); \(\frac{N_{PRB}^{BW(j),\mu}}{T_{s}^{\mu}}\) is the maximum RB allocation, where BW(j) is the UE supported maximum bandwidth and \(OH^{j}\) is the overhead; and \(R_{max}\) is the target coding rate. The number of users to be served by an RRU\({}_{\text{M}}\) to ensure the required data rate (required data rate per UE for RRU\({}_{\text{M}}\) is the same as that of RRU\({}_{\text{m}}\) is also calculated using the same formula with relevant parameters,  
\[N_{RRU_{M}}=\frac{T_{Mmax}\times N_{sec}}{DR_{UE}} \tag{17}\]  
The total throughput of an RRU\({}_{\text{m}}\) or RRU\({}_{\text{M}}\) in one sector antenna in terms of bandwidth and spectral efficiency is expressed as \(T_{max}\) = Bandwidth \(\times\) Spectral Efficiency. The values of \(N_{Mcap}\) and \(N_{mcap}\) are calculated by dividing the total number of population in the case study area by \(N_{RRU_{M}}\) and \(N_{RRU_{m}}\), respectively.