## 3 Conventional and Proposed Methods
### Proposed Method  
#### 3.2.1 CSI-Based Nonlinear Allocation Method  
The objective of the CSI-based nonlinear allocation method is to efficiently distribute transmission power according to the CSI gain of each antenna. This method is specifically designed to maximize communication performance, particularly in environments with non uniform channel conditions. By allocating more power to antennas with higher channel gains and reducing power allocation to antennas with lower channel gains, the limited power resources can be effectively utilized. Based on the nonlinear allocation method, the transmission power of each antenna element \(P_{m,n}\) is expressed as follows:  
\[P_{m,n}=P_{\text{total}}\cdot\frac{g_{m,n}^{\beta}}{\sum\limits_{k=1}^{M}\sum \limits_{l=1}^{N}g_{k,l}^{\beta}}. \tag{24}\]  
In this context, \(P_{\text{total}}\) represents the total transmission power, which signifies the overall power constraint of the system and corresponds to the sum of the transmission power allocated to each antenna. Within this constraint, optimal power allocation is performed based on the channel state. The parameter \(g_{m,n}\) denotes the CSI gain of each antenna, which reflects the channel conditions between each antenna and the receiving end. A higher value of \(g_{m,n}\) indicates better channel quality. Based on the channel conditions, more power is allocated to antennas with higher channel gains, while power distribution to antennas with lower channel gains is suppressed, ensuring the efficient utilization of transmission power. The parameter \(\beta\) controls the concentration level of the power allocation. Specifically, as the value of \(\beta\) increases, power becomes more concentrated on antennas with higher channel gains. Conversely, when \(\beta\) is smaller, the power distribution approaches a more uniform allocation. However, an excessively high \(\beta\) may lead to power over-concentration on a few antennas, reducing the overall communication robustness, while a too-low \(\beta\) results in inefficient power utilization. Therefore, an appropriate range of \(\beta\) is crucial for maintaining stable and efficient communication performance. Through simulation analysis (see Figure 6), we identified that an optimal range for \(\beta\) lies between 1.4 and 2.2, with 1.8 yielding the lowest bit error rate (BER). When \(\beta\) is within this range, the system effectively balances power distribution and energy efficiency, achieving optimal performance under varying channel conditions. To further adapt to dynamic environments, our proposed method employs an adaptive adjustment mechanism based on CSI variation, ensuring \(\beta\) remains within this optimal range in real-time operation. By appropriately setting this parameter, it is possible to adapt to different channel environments and maximize communication performance. The selection of \(\beta\) is dynamically adjusted based on the variation in CSI. Based on the transmission power allocation using the nonlinear allocation method, the received signal power \(R_{\text{rec,nonlinear}}\) at the receiving end, where signals transmitted from each antenna are combined, is expressed as follows. \[R_{\text{rec,nonlinear}}=\left|\sum\limits_{m=1}^{M}\sum\limits_{n=1}^{N}\sqrt {P_{\text{total}}\cdot\frac{g_{m,n}^{\beta}}{\sum\limits_{k=1}^{M}\sum \limits_{l=1}^{N}g_{k,l}^{\beta}}\cdot h_{m,n}\cdot e^{i\theta_{m,n}}}\right|^ {2}. \tag{25}\]  
In this context, \(h_{m,n}\) represents the channel gain between each antenna and the receiving end, indicating the attenuation of the signal between the transmitter and receiver. The term \(e^{i\theta_{m,n}}\) denotes the phase shift component for beamforming. Phase adjustments are applied to ensure that the signals from each antenna constructively interfere in the desired direction. In beamforming with an \(M\times N\) planar array antenna, an appropriate phase shift is required based on the position of each antenna element.