# Maximal Ratio Combining Detection in OFDM Systems with Virtual Carriers Over V2V Channels
## 7 Discussion  
The incorporation of virtual carriers (VC) into the proposed OFDM system results in a reduction in at least half of the spectral efficiency when factor \(\
u=2\). This reduction occurs because half of the subcarriers must be deactivated. However, the VC subcarriers serve as protective guards for the data-carrying subcarriers, mitigating intercarrier interference (ICI) during detection. The inclusion of VC introduces diversity to the transmitted data, leading to significant advantages. In particular, the MRC detection with VC surpasses other detection methods at certain SNR levels. This enhanced performance is a direct result of the improved diversity and robustness achieved through the inclusion of virtual carriers. The LS and MMSE estimators exhibit poor performance due to their inadequate counteraction of ICI. In contrast, the OSIC detector effectively utilizes signal diversity during successive interference cancellation, showing better results. Although it sacrifices spectral efficiency, higher code rates in FEC and increased modulation orders help compensate for this loss by enabling the transmission of more bits per active carrier. For instance, in the case of \(\
u=2\), half of the subcarriers are turned off. To compensate for these subcarrier losses, we can increase the data modulation order to 16 QAM, allowing the transmission of 4 bits per active subcarrier. This results in the same spectral efficiency as a conventional OFDM system without VC, which uses a data modulation order of 4 QAM, transmitting 2 bits per active subcarrier. The obtained results are depicted in Figure 4. It is evident that, as the SNR decreases, the MRC detector's performance becomes similar to that of the MMSE detector. However, when the SNR exceeds 20 dB, the proposed system achieves an improvement of approximately 2.5 dB compared to the MMSE detector while still maintaining a performance level close to the OSIC detector. Notably, both MMSE and OSIC  
Figure 5: Comparison in BER vs SNR performance of the proposed system with \(\
u=\{2,4,8\}\) for a decreasing exponential delay power profile with an RMS delay of 0.4 μs and a Doppler spread frequency of 1 kHz modeling a non-line-of-sight scenario with Rayleigh fading. The channel model utilizes a Jakes Doppler profile for each channel tap. detectors exhibit higher computational complexity compared to the MRC detector. As a result, the proposed system not only achieves better performance at high SNRs but also offers the advantage of lower computational burden, which can be crucial in real-time applications or systems with limited resources. The application of virtual carriers could have potential benefits for both linear and nonlinear detectors by mitigating ICI. The inclusion of VC helps to improve the performance of linear and nonlinear detectors, as depicted in Figure 4. The study of how virtual carriers interact with different detection algorithms provided valuable insights into their overall impact on system performance and identified possible enhancements in various scenarios. Based on the results obtained, the maximum ratio combining (MRC) detector demonstrated performance comparable to nonlinear detectors at low SNR. However, beyond 15 dB, nonlinear detectors outperformed MRC but at the expense of increased complexity. Increasing the diversity factor \(\
u\) significantly enhances the performance of the proposed system, effectively making it behave like an equivalent single-input multiple-output (SIMO) system with \(\
u-1\) replicas of the transmitted data vector (see Figure 3), that is, an SIMO system of \(1\times\
u\). This behavior is due to the conjugate symmetry property of the Fourier transform (see Appendix A). This indicates that MRC detection efficiently utilizes the data diversity introduced by the inclusion of virtual carriers while maintaining a linear complexity of \(\mathcal{O}(N)\). Furthermore, this finding suggests that the MRC detector could be a valuable choice in situations where balancing performance and computational complexity is essential.