## 4 Numerical Results
### Angular Protection with Distance Protection: Restriction Zone  
Similar to the case of the exclusion zone with angular protection, more antenna array elements lead to more effective angular protection. Without angular protection, the restriction zone of the 8 \(\times\) 8 and 16 \(\times\) 16 arrays is larger than that of the 4 \(\times\) 4 array. However, when the beam shut-off range is set to 45\({}^{\circ}\) or higher, the restriction zones of the 8 \(\times\) 8 and 16 \(\times\) 16 arrays become smaller than that of the 4 \(\times\) 4 array. Figure 12 illustrates the reduction in the restriction zone when using the proposed angular protection for various antenna array sizes in RMa, UMa, and UMi. A higher beam shut-off range results in lower BS interference, leading to a smaller restriction zone. In contrast to the exclusion zone, the size of the restriction zone keeps significantly decreasing as the beam shut-off range increases to 90\({}^{\circ}\), 180\({}^{\circ}\) and 270\({}^{\circ}\). The advantage of increasing the number of elements of an antenna array in terms of angular protection efficiency is more significant in UMi than RMa. Without angular protection, the zone of the 8 \(\times\) 8 and 16 \(\times\) 16 arrays are larger than that of the 4 \(\times\) 4 array, as illustrated in Figure 12c. However, when the beam shut-off range is set to 45\({}^{\circ}\) or higher, the zone of the 8 \(\times\) 8 and 16 \(\times\) 16 arrays become smaller than that of the 4 \(\times\) 4 array. Figure 11: Reduction in the exclusion zone using the proposed angular protection for various antenna types. **(a)** Rural macrocell (RMa); **(b)** urban macrocell (UMa); **(c)** urban microcell (UMi). For easier understanding of the results, we combined the exclusion zone figure, restriction zone figure and the data, as shown in Tables 3-5. Tables list the mean transmission (Tx) power reduction in the restriction zone for RMa, UMa, and UMi using 4 \(\times\) 4, 8 \(\times\) 8 and 16 \(\times\) 16 antenna arrays, respectively. The number of deployable base stations was calculated by simulation based on [8], and there will be some base stations in restriction zone, this is the number of restriction zone base stations. Using a higher beam shut-off range (sacrificing more beam angles) can bring following 3 kinds of affect, case 1 is a smaller exclusion zone that can increase the total number of BSs which can be deployed; case 2 is a smaller exclusion zone that can increase number of BSs in restriction zone; and case 3 is a smaller restriction zone that can decrease the number of BSs in the restriction zone. Therefore, the higher beam shut-off range can cause case 2 and case 3, which affect is the dominant will decide the increase or decrease in number of BSs in restriction zone. The percentage of deployed BS requiring Tx power control depends on the ratio of the number of BSs in the restricted area to the total number of deployable BSs. The size change in Exclusion Zone and Restriction Zone will make BSs move into or move out  
Figure 12: Restriction zone reduction using the proposed angular protection for antenna sizes in (**a**) RMa, (**b**) UMa, and (**c**) UMi. (**a**) Rural macrocell (RMa); (**b**) urban macrocell (UMa); (**c**) urban microcell (Umi). of the Restriction Zone. Some BSs provide relatively higher interference (BSs are closer to ES) and some of these BSs provide relatively low interference (BSs are farther from to ES). BSs that provide higher interference are required to decrease more Tx power in the proposed iterative power control scheme. This makes the mean Tx power reduction in restriction zone increase. Therefore, the percentages of BSs which provide different level of interference in number of BSs in Restriction Zone decide the change in mean Tx power reduction in restriction zone.