## 4 Simulations and Results
Because this beam width is represented when the BER is optimized, Figure 6a does not clearly indicate the scintillation effect. In Figure 6b, the BER according to the pointing errors shows the scintillation effect more clearly. In Figure 6b, the BER plot shows a significant difference under the same assumption. The BER that satisfies \(10^{-5}\) becomes less than \(10^{-3}\) with the consideration of scintillation. Thus, the scintillation causes a considerable reduction in BER. Figure 7 shows the scintillation index according to the pointing error in both fixed and adaptive beams. As previously mentioned, the fixed beam was optimized with a beam width with a minimum BER, and the adaptive beam was widened according to the pointing error. In the case of the optimal fixed beam, the scintillation index increased  
Figure 6: Difference between cases with and without scintillation in terms of (**a**) divergence angle according to the pointing error; (**b**) BER according to the pointing error of each divergence angle. rapidly with a slight increase in pointing error. However, the scintillation effect was constant for the pointing error when the beam was controlled adaptively. The adaptive beam control is based on calculated pointing errors. A larger number of pointing errors cause a greater scintillation effect, which can be reduced by expanding the beam divergence angle. Compared to Figure 3, we proved that the proposed adaptive beam reduced the scintillation effect caused by pointing error. Figure 8 presents the BER relative to SNR in both fixed and adaptive beams based on the strength of ground turbulence from top to bottom in order. The relative SNR is as a function of the variation in noise power. Although Figure 8 is not a graph that directly reflects the pointing error result, the improvement in adaptive performance is still apparent. In weak turbulence (\(1.7\times 10^{-15}\)), the relative SNR performance of the adaptive beam improved by 6 dB compared to the fixed beam. In moderate turbulence (\(1.7\times 10^{-14}\)), it improved by 5 dB, and in strong turbulence (\(1.7\times 10^{-13}\)), it improved by 4 dB. Thus, as ground turbulence strengthens, adaptive beam performance is enhanced compared to a fixed beam. This phenomenon is due to two main reasons. First, the fixed beam was optimized to a broad beam in strong turbulence and a narrow beam in weak turbulence. Because the narrow fixed beam could not sufficiently compensate for pointing errors in weak turbulence, the BER was degraded. In addition, the BER performance of a narrow beam for weak turbulence was further impaired owing to the increase in scintillation caused by the pointing error. The second reason is the flexibility of an adaptive beam. The fixed beam is a narrow beam, whereas the adaptive beam is broadened according to the pointing error. Consequently, the adaptive wide beam in weak turbulence is less affected by scintillation. As mentioned above, the scintillation affects the wide beam more than the narrow beam. Because the fixed beam is optimized to a minimum BER, the beam is fixed to the broad beamwidth to compensate for the pointing error. Therefore, in a comparison based on SNR, the difference is less significant. However, the use of additional power allocation schemes can increase SNR performance in adaptive beam control systems. Figure 9 shows the SNR-BER relationship in fixed and adaptive beamwidth using power allocation. The received power decreases because of broadening to compensate for the pointing error. To enhance the SNR, the power secured in the narrow beam was allocated to the broad  
Figure 7: Scintillation index according to the pointing error: comparison of fixed and adaptive beams. beam. Thus, the result showed significant differences in SNR performance in fixed and adaptive beams. In addition, the data rate can be enhanced in an adaptive modulation method by adjusting the beam adaptively.