## 4 Adaptive OFDM-IM Method
### Determination of Minimum SNR  
In vehicle-to-vehicle communication scenarios within the Internet of Vehicles (IoV), the complexity and dynamic nature of the environment usually restrict the range of the SNR, significantly impacting the design and performance of communication systems. Particularly in urban traffic or congested highway environments, the SNR may be limited due to multipath fading, reflections, and other interference. Thus, to optimize the communication performance in the IoV, particularly under these limited SNR conditions, it is crucial to determine the minimum SNR at which the BER of OFDM-IM can surpass that of traditional OFDM technology. This analysis will not only provide insights into the potential of OFDM-IM in the IoV but also offer valuable guidelines for the design and parameter optimization of OFDM-IM methods based on user needs and scenario adaptation.  
Before determining the minimum SNR, it is crucial to observe the trend of the BER as the SNR changes by controlling other variables. In Figure 6, we fix the number of subcarriers per subblock N = 8 and analyze the BER performance of OFDM-IM under different modulation orders M and numbers of active subcarriers K. As M increases from 2 to 16, the minimum SNR required for the BER of OFDM-IM to surpass that of traditional OFDM gradually increases. Specifically, the intersection point shifts from approximately 12 dB in Figure 6a to around 20 dB in Figure 6d. Within each subplot, when K = 8 (the number of active subcarriers equals the number of subcarriers in a subblock), the curve represents traditional OFDM. All other curves correspond to OFDM-IM. This comparison clearly demonstrates that, as M increases, achieving better BER performance with OFDM-IM relative to traditional OFDM requires higher SNR levels.  
Next, we fix the modulation order M at 4 and vary the number of subcarriers N and the number of active subcarriers K in each subblock to conduct further analysis. As illustrated in Figure 7, with M remaining constant, the minimum SNR required for OFDM-IM to surpass that of traditional OFDM increases as N increases. Based on these findings, we select N = 16 and M = 16 to pinpoint the SNR more precisely. This parameter configuration will encompass all possible combinations of (N, K, M) in this scenario.  
In the urban traffic scenario, where the reflection coefficient \(\mu=0.5\) and the Rice factor R is 10 dB, the trend of the BER as a function of the SNR is as illustrated in Figure 8, with N = 16 and M = 16. The minimum SNR required for the BER of OFDM-IM to surpass that of traditional OFDM is 16 dB. To enhance the robustness of the simulation, an SNR of 20 dB is chosen.  
In the highway scenario, with the reflection coefficient \(\mu=0.2\) and the Rice factor R at 20 dB, the trend of the BER as a function of the SNR is as illustrated in Figure 9, with N = 16 and M = 16. Similarly, the minimum SNR required for the BER of OFDM-IM to surpass that of traditional OFDM is determined to be 15 dB.  
To further clarify the results, it should be emphasized that the selection of 20 dB as a reference SNR level in this study does not imply that such a level can be easily attained in practical vehicular communication environments. Instead, this value is chosen as a theoretical benchmark to illustrate the upper bound of the system performance under ideal channel conditions. In real-world scenarios, achieving a stable 20 dB SNR is challenging due to factors such as multipath fading, reflections, interference, and high mobility. Nevertheless, modern communication techniques such as intelligent beamforming, multi-antenna cooperation, and adaptive modulation and coding are gradually enabling the temporary realization of higher SNR levels under controlled conditions or specific scenarios. Conse