## 4 Adaptive OFDM-IM Method
### Fuzzy Logic Optimization  
In this section, we employ the concept of fuzzy logic to optimize the performance of the OFDM-IM system. Fuzzy logic expresses information through linguistic variables rather than numerical ones, facilitating the handling of systems with inherent ambiguities in their descriptions and decision-making processes [32; 33; 34]. Based on this, we propose a method to adaptively adjust the key parameters of OFDM-IM, such as the number of subcarriers, the number of active subcarriers, and the modulation order, according to different scenarios and user requirements. The core of this method lies in appropriately weighting the three performance indicators--the spectral efficiency, bit error rate, and energy consumption--based on scenario-specific requirements to maximize the overall performance.  
Fuzzy logic is a reasoning method based on fuzzy set theory, aiming to simulate human reasoning by processing fuzzy information. Its core framework consists of three main steps:  
Figure 8: Trend of the BER versus SNR in the urban traffic scenario.  
Figure 9: Trend of the BER versus SNR in the highway scenario.  
fuzzification, fuzzy inference, and defuzzification. The fuzzification process converts the precise values of input variables into membership degrees, mapping the variables to corresponding fuzzy sets using membership functions. Membership functions are typically represented in forms such as triangular, trapezoidal, or Gaussian curves to quantify the fuzziness of the input values. For example, for the fuzzy set \"low BER\", a specific triangular membership function can be defined to map the BER values to membership degrees ranging from 0 to 1. During the fuzzy inference phase, the system performs logical deduction on the input variables based on predefined fuzzy rules (commonly in the form of IF/THEN rules). For instance, the rule \"IF energy consumption is low AND BER is low THEN performance is excellent\" combines membership degrees to derive the fuzzy set of output variables. Finally, defuzzification converts the output fuzzy set into a specific numerical value, with commonly used methods including the maximum membership method, weighted average method, or centroid method, providing clear decision support for system optimization. By designing appropriate membership functions and fuzzy rules, fuzzy logic effectively handles complex nonlinear relationships among multidimensional input variables, making it particularly suitable for optimizing the OFDM-IM communication parameters in this study. The selection of membership functions and fuzzy rules should be adjusted based on the user requirements in specific scenarios (such as urban traffic or highway scenarios) to ensure the applicability and reliability of the optimization results.  
The reason for the use of fuzzy logic in parameter adjustment is that different application scenarios prioritize performance indicators differently, and these priorities often cannot be precisely expressed with fixed numerical values. Instead, they require adjustment within a fuzzy range. This weight distribution based on fuzzy ranges allows the system to adapt more flexibly and efficiently to various complex communication environments, thereby improving the application effectiveness and reliability of multicarrier modulation techniques in the Internet of Vehicles.