## 4 Adaptive OFDM-IM Method
### Fuzzy Logic Optimization
#### 4.4.1 Calculation of Fuzzy Factors  
* Calculation of the Spectral Efficiency Factor \[\eta=\eta_{OFDM-IM}=\left(\log_{2}C_{N}^{K}+K\log_{2}M\right)/(N+N_{CP}/G).\] (23)  
The spectral efficiency here is represented by the spectral efficiency of the OFDM-IM system. When \(N=K\), the system degrades to the classical OFDM system. As \(\eta\) increases, the OFDM-IM system achieves better spectral efficiency, and, when \(\eta\) reaches its maximum, the OFDM-IM system also reaches its maximum spectral efficiency. When the total number of U subcarriers increases, the number of subblocks G = U/N also increases, reducing the CP overhead per subblock and thus improving the spectral efficiency. However, increasing the number of subcarriers per subblock N enriches the subcarrier activation modes but also increases the symbol duration and CP overhead, requiring a trade-off among the system parameters. Furthermore, increasing the length of the cyclic prefix \(N_{CP}\) reduces the spectral efficiency, which is the cost of improving the robustness against interference by multiple paths. Since the cyclic prefix is not considered and \(N_{CP}\) is set to 0, (23) simplifies to  
\[\eta=\eta_{OFDM-IM}=\frac{\log_{2}C_{N}^{K}+K\log_{2}M}{N}. \tag{24}\]  
In the IoV, adjusting the spectral efficiency is crucial in meeting various real-time and reliability requirements. While higher spectral efficiency typically improves resource utilization by achieving better bandwidth usage, it may lead to increased interference or energy consumption under certain conditions, such as dense IoV scenarios or energy-constrained devices. Conversely, lower spectral efficiency often results in reduced capacity,potentially affecting the system's ability to support real-time and critical applications. Therefore, finding the optimal balance of spectral efficiency tailored to specific IoV scenarios is essential. In most cases, traditional OFDM achieves higher spectral efficiency than OFDM-IM because all subcarriers in OFDM are utilized for data transmission, whereas OFDM-IM employs index modulation by activating only a subset of the subcarriers for transmission. This difference gives traditional OFDM an advantage in terms of spectral efficiency but results in significantly higher energy consumption. Moreover, OFDM-IM achieves a significantly lower BER over a wider range of SNRs compared to traditional OFDM. This indicates that high spectral efficiency is not inherently \"bad\"; rather, it needs to be weighed against the specific application demands. By sacrificing a small amount of spectral efficiency, OFDM-IM demonstrates substantial advantages in terms of energy consumption and the BER. These improvements will be detailed in the subsequent section. * Calculation of the Energy Consumption Factor \[NH=NH_{OFDM-IM}=\frac{K}{N}.\] (25)  
Energy consumption here is defined as the energy consumption ratio of the OFDM-IM system, represented by the ratio of the number of active subcarriers K to the total number of subcarriers N. Multicarrier index modulation transmits index information by activating only a subset of the subcarriers, thereby reducing the energy consumption. A smaller K/N value indicates lower energy consumption and better system performance. In the IoV context, proper energy management is crucial. Excessive energy consumption increases power use, drives up the maintenance costs, and may hinder the widespread adoption of IoV technology, complicating the pursuit of low-carbon, eco-friendly travel. Conversely, insufficient energy consumption could limit the performance of IoV devices, affecting the communication quality and stability. For electric vehicles, which rely heavily on batteries, this could impact the driving range and usage time. Therefore, when designing and implementing IoV systems, it is important to strike a balance between energy consumption and performance to promote the healthy development of IoV technology.