# An Energy-Efficient Coverage Algorithm for Macrocell--Small Cell Network Systems
## 4 Proposed Algorithm
* The relay process has SBSs providing support overlay, and the starting and end points can be covered after adjusting the power levels of SBSs in the relay process closest to the two points to \(P_{\mathrm{s}}^{\mathrm{(high)}}\), respectively. In this case (NYN), the power levels of both SBSs are each adjusted to \(P_{\mathrm{s}}^{\mathrm{(high)}}\), and service is provided using the corresponding SBSs in the path process. An example is shown in Figure 8a. * The relay process has SBSs providing support overlay, but the starting and end points cannot be covered after adjusting the power levels of SBSs closest to the two points to \(P_{\mathrm{s}}^{\mathrm{(high)}}\), respectively. In this case (NXN), service is provided by using the MBS in the path process. An example is shown in Figure 8b. * The relay process does not have SBSs providing support overlay. In this case (NNN), service is provided by using the MBS in the path process. An example is shown in Figure 8c. Figure 5: Conceptual illustrations of (**a**) SSS, (**b**) YNY, and (**c**) XNX. Case 2. The end point of user \(i\) will fall within a coverage hole, and the starting point is in the SBS service state. 1. The relay process has SBSs providing support overlay. 1. There is at least one available SBS next to the coverage hole center (i.e., the coverage hole can be fully covered after adjusting the power level of any available SBS to \(P_{\mathrm{s}}^{\mathrm{(high)}}\)). In this case (SSD), the cell of the SBS closest to the coverage hole center is enlarged (note that such an SBS is denoted as SBStag to facilitate description later), and service is provided using the corresponding SBSs in the path process. An example is shown in Figure 9a. 2. There is no available SBS next to the coverage hole center. In this case (SSO), the power level of the SBS deployed in the coverage hole center is set to \(P_{\mathrm{s}}^{\mathrm{(low)}}\) (note that such an SBS is denoted as SBShtag to facilitate description later), and service is provided using the corresponding SBSs in the path process. An example is shown in Figure 9b. 3. The relay process has no SBSs providing support overlay. Figure 8: Conceptual illustrations of (**a**) NYN, (**b**) NXN, and (**c**) NNN. Figure 6: Conceptual illustrations of (**a**) SYN, (**b**) SXN, and (**c**) SNN. Figure 7: Conceptual illustrations of (**a**) NYS, (**b**) NXS, and (**c**) NNS. * There is at least one available SBS next to the coverage hole center. In this case, the cell of the SBS closest to the coverage hole center, which is denoted as SBStag, is enlarged. * Together with SBStag, the coverage insufficiency in the relay process can be compensated after adjusting the starting point SBS power level to \(P_{\text{s}}^{\text{(high)}}\). In this case (YND), service is provided using these two cell-enlarged SBSs in the path process. An example is shown in Figure 10a. * However, for the above power adjustment, the relay process cannot be compensated. In this case (XND), service is provided by transferring the connection to the MBS for the starting point and the relay process and by using SBStag for the end point. An example is shown in Figure 10b. * There is no available SBS next to the coverage hole center. In this case, the power level of the SBS deployed in the coverage hole, which is denoted as SBSh_tag, is set to \(P_{\text{s}}^{\text{(low)}}\). * Together with SBSh_tag, the coverage insufficiency in the relay process can be compensated after adjusting the starting point SBS power level to \(P_{\text{s}}^{\text{(high)}}\). In this case (YNO), service is provided using these two SBSs adjusted in the path process. An example is shown in Figure 11a. * However, for the above power adjustment, the relay process cannot be compensated. In this case (XNO), the processing method is almost identical to that used in Case 2.B.a.ii; the only difference is that we use SBSh_tag for covering the end point. An example is shown in Figure 11b. Figure 10: Conceptual illustrations of (**a**) YND and (**b**) XND.