# Binary PSO with Classification Trees Algorithm for Enhancing Power Efficiency in 5G Networks
## 4 Proposed Algorithms
### SC Sub-Band Allotment Using Classification Trees (CTs)  
After the on/off switching decisions for all SCs are taken, the second phase is initialized, which is the sub-band allocation for the active SCs based on the SFR, which is illustrated in Figure 2, over three cells without loss of generality. In the shown example, if we have three hexagonal-shaped cells, each split into center and edge regions, the frequency band is divided to three (\(N_{sub}=3\)) sub-bands: X, Y, and Z. The edge region of cells 1, 2, and 3 are allocated sub-bands X, Y, and Z, respectively. Consequently, cell 1 is allocated sub-bands Y and Z in the center region. Similarly, cell 2 is allocated X and Z, and cell 3 is allocated X and Y. In this technique, every SC is divided into center and edge regions. One of the \(N_{sub}\) sub-bands can be used in the edge region of every SC, on condition that it is not used by the edge regions of the adjoin SCs. The center region of every SC can use the remaining sub-bands with reduced transmission power. This alleviates not only the interference to the adjoin SCs but also the power consumption of the whole network. To determine the vertices of the center region, the distance between the center of the SC and every vertex of the SC is computed. Then the distance between the center of the SC and the nearest SC vertex (the smallest distance) is determined and is regarded as the SC radius. The radius of the center zone is chosen as 50% of the SC radius as it maximizes the throughput of the system [13]. A real example is demonstrated in Figure 3a, displaying an SC (the purple SC) and its adjoining SCs. Figure 3b displays the seven sub-bands. Every SC uses one of the seven sub-bands in its edge region. While the center region of this SC (the grey region) can use the remaining six sub-bands. First, the SC senses the signals of the edge region of the adjoin SCs upon switching to obviate utilizing them. A binary indicator, \(\tau_{m}=1\), indicates the presence of unused sub-bands by the edge region of the adjoin SCs; otherwise, \(\tau_{m}=0\). If there are unused sub-bands by the edge region of the adjoined SCs (\(\tau_{m}=1\)), then for every unused sub-band \(f\), the distance between the SC and the closest nonadjacent SC using sub-band \(f\) in its edge region (\(D_{Non-aff}\)) is measured, and this is repeated for the rest of the remaining unused sub-bands. If all the sub-bands are used (\(\tau_{m}=0\)), then for every sub-band \(q\), the distance between the SC and the adjoin SC using sub-band \(q\) in its edge region (\(D_{Adq}\)) is measured. Then, the edge region of the SC is allocated the sub-band used in the farthest adjoined SC. Figure 2: SFR example for hexagonal shaped cells with \(N_{sub}=3\). According to \(\tau_{m}\) and \(D_{Non-adf}\) or \(D_{Adq}\), the CT takes the decision to assign which sub-band to the edge region of the SC. A CT example of 3 sub-bands is shown in Figure 4. In case of the presence of unused sub-bands in the edge region of the adjoin SCs (\(\tau_{m}=1\)), then if the distance between the SC and the closest SC using the sub-band \(1\) in its edge region (\(D_{Non-adf}=D_{Non-ad1}\)) is larger than \(D_{Non-ad2}\); \(D_{Non-ad1}\) and \(D_{Non-ad3}\) are checked. If \(D_{Non-ad1}\) is larger than \(D_{Non-ad3}\), then sub-band \(1\) is selected. In case all the sub-bands are utilized (\(\tau_{m}=0\)), then if the distance between the SC and the adjacent SC using sub-band \(2\) (\(D_{Adq}=D_{Ad2}\)) is larger than \(D_{Ad1}\), then \(D_{Ad2}\) and \(D_{Ad3}\) are checked. If \(D_{Ad3}\) is larger than \(D_{Ad2}\), then sub-band \(3\) is selected. Afterward, the center region can utilize the remaining sub-bands with lower transmission power. Unlike the computational complexity of the conventional SFR algorithm \(O(5^{2}\). \(N_{sub}{}^{2})\), which depends on the network size (\(S\)) and the number of sub-bands (\(N_{sub}\)) [60], the computational complexity of the proposed CTs algorithm is much lower.