## 3 System Model and Problem Formulations
### Link Budget Analysis  
Link budget calculation is performed for both FR1 (3.5 GHz) and FR2 (28 GHz) separately. Maximum radius and MAPL for both frequencies are calculated based on (3 GPP TR-38.901) specifications [47]. The placement is based on the Cartesian plane coordinates RRU (\(x^{i},y^{i}\)). RRU\({}_{\text{m}}\) and RRU\({}_{\text{M}}\) are initially placed randomly, and the minimum number of RRU\({}_{\text{m}}\) and RRU\({}_{\text{M}}\) is calculated as per link budget analysis to satisfy the capacity and coverage constraints. The user equipment (UE) location is denoted as UE (\(x^{i},y^{i}\)). The population distribution is considered in two scenarios. Scenario I (Urban) : The population is distributed heavily in urban areas, 20,000 per square kilometer [48]. An area of 4 km\({}^{2}\) was taken for simulation. A case study of the area of Baneshwor and Gaushala in Kathmandu was chosen. Scenario II (Suburban) : The suburban area with a population density of about 7500 per square kilometer was chosen for study. An area of 16 km\({}^{2}\) of Nepaltaar and Tokha in Kathmandu was considered as a case study and simulation analysis [49; 50]. RRU\({}_{\text{m}}\) and RRU\({}_{\text{M}}\) have \(N_{sector}\) numbers of sector antenna. All the UEs have the same parameters, such as transmit power, cable loss, temperature, interference margin, bandwidth, and height. It is for clarity and uniformity, as different parameters can also be considered for different UE types. The Effective Isotropic Radiating Power (EIRP) for RRU\({}_{\text{M}}\), RRU\({}_{\text{m}}\), and UE is calculated using the formula listed in Equation (1). \[EIRP=TXP+AG-CL \tag{1}\]  
where \(TXP\) = Transmit Power, \(AG\) = Antenna Gain, and \(CL\) = Cable Loss. Figure 2: Proposed 5G network optimization framework. The Thermal Noise (TN) for RRU\({}_{\text{M}}\), RRU\({}_{\text{m}}\), and UE is calculated [51] using Equation (2). \[TN[\text{dBm}]=10\times log_{10}(T\times K\times BW) \tag{2}\]  
where \(T\) = Temperature in Kelvin, \(K\) = Boltzmann's constant, and \(BW\) = Bandwidth in Hz,  
Now, we calculate the radio link budget for each micro cell and macro cell in each downlink and uplink side. We calculate MAPL from RRU\({}_{\text{m}}\) to UEs and RRU\({}_{\text{M}}\) to UEs for downlink and vice versa for uplink. MAPL is the total energy loss of transmitted signal from the transmitter in both uplink and downlink transmission, maintaining adequate signal quality [52]. The _MAPL_ for uplink and downlink is calculated using Equation (3). \[MAPL=EIRP+Uleg-PL-FL-BL-IM-RIL-SFM-NF-DT-RBL \tag{3}\]  
where \(Uleg\) = UE Gain, \(PL\) = Penetration Loss, \(FL\) = Foliage Loss, \(BL\) = Body Block Loss, \(IM\) = Interference Margin, \(RIL\) = Rain/Ice Loss, \(SFM\) = Slow Fading Margin, \(NF\) = Noise Figure, \(DT\) = Demodulation Threshold SNR, and \(RBL\) = 10 \(log_{10}\)(SCQ). Subcarrier Quantity (SCQ) is formulated as the product of subcarrier per resource block and number of resource blocks as specified by 3 GPP TS-38.101-2 [53]. For the 100 MHz and 200 MHz bandwidths, SCQ is calculated as \(12\times 273=3276\) and \(12\times 264=3168\), respectively [54]. Table 2 shows the specification of RRU\({}_{\text{m}}\), RRU\({}_{\text{M}}\), and UE, and Table 3 lists the values for calculation of MAPL. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **RRU\({}_{\text{M}}\)** & **RRU\({}_{\text{m}}\)** & **UE** \\ \hline Frequency Band & n78 & n257 & – \\ \hline Frequency & 3.5 GHz & 28 GHz & – \\ \hline Frequency Range & FR1 & FR2 (mmWave) & – \\ \hline Duplex Mode & TDD & TDD & – \\ \hline Channel BW (MHz) & 5, 10, 20, 40, 80, 100 & 50, 100, 200, 400 & – \\ \hline UL-DL Range (MHz) & 3300–3800 & 26,500–29,500 & – \\ \hline Height (m) & 23 & 8 & \(1.5\) \\ \hline Bandwidth (MHz) & 100 & 200 & \(10\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RRU\({}_{\text{M}}\), RRU\({}_{\text{m}}\), and UE specifications [55; 56].