## 3 Conventional and Proposed Methods
### Proposed Method  
#### 4.2.1 CSI-Based Nonlinear Allocation Method  
From the results in Section 4.1, it was confirmed that power allocation according to the gain ratio between channels is effective in improving system performance under non-uniform channel environments. However, there are limitations to the CSI-based proportional allocation method. Specifically, in the proportional allocation method, power is simply distributed proportionally based on the gain ratio of each channel. When channel conditions fluctuate significantly or when excessive power is allocated to a particular channel, it may disrupt the overall SNR balance. In such environments, relying solely on proportional allocation may not yield optimal performance. Therefore, a more flexible and sophisticated power allocation method is required. In this section, simulations using the CSI-based nonlinear allocation method proposed in Section 3.2 are performed, and the results are compared with those from the equal power allocation method and CSI proportional allocation method. This nonlinear allocation method aims to achieve higher performance by nonlinearly adjusting the power based on the channel state, as shown in Equations (24) and (28). By optimizing the allocation according to the channel characteristics, the method seeks to provide better performance. The simulation results suggest that the nonlinear allocation method can significantly reduce  
Figure 4: Distance-BER characteristics for CSI-based proportional allocation method (non-uniform CSI). Figure 3: Distance-BER characteristics for CSI-based proportional allocation method (uniform CSI). BER, especially in non-uniform channel environments compared to the conventional equal power allocation and proportional allocation methods. Figure 5 shows the relationship between distance and BER for the equal power allocation method, CSI-based proportional allocation method, and the proposed CSI-based nonlinear allocation method. The results indicate that with the equal power allocation method, BER deteriorates sharply as the distance increases, with a significant degradation in communication quality, particularly for long-distance communication. On the other hand, the CSI-based proportional allocation method provides some BER improvement as the distance increases, but variability in BER due to channel non-uniformity is still observed. The proposed CSI-based nonlinear allocation method, compared to the conventional methods, achieves a generally lower BER, with particularly notable improvements for long-distance communication. This is due to the optimal power allocation achieved by the nonlinear distribution, where power is appropriately allocated to antennas with higher channel gains. Even within the same proposed method, increasing the distribution concentration factor \(\beta\) from 1.4 to 1.8 improved the concentration of power and resulted in a noticeable improvement in BER. However, when \(\beta\) was further increased from 1.8 to 2.2, power became excessively concentrated on specific channels, leading to insufficient power distribution to other channels. As a result, the BER performance worsened again, returning to a level similar to that of \(\beta=1.4\). This demonstrates that the distribution concentration factor \(\beta\) has a significant impact on the performance of the proposed method. This trend is further detailed in the following Figure 6.  
Figure 6 shows the relationship between the distribution concentration factor \(\beta\) and BER at a propagation distance of 2 km. The simulation results indicate that when the distribution concentration factor is small (\(\beta=1\)), power is almost evenly allocated, which causes power to be spread to antennas with lower channel gains, resulting in a higher BER. On the other hand, increasing the distribution concentration factor to \(\beta=1.8\) strengthens the power concentration on high-gain antennas, resulting in the minimum BER.