# Maximal Ratio Combining Detection in OFDM Systems with Virtual Carriers Over V2V Channels
## 6 Simulation and Results  
In this section, the performance in terms of BER and computational complexity of an OFDM system is analyzed when VC are included during transmission to generate diversity in the received data. Table 2 presents the system configuration parameters employed in our simulations. The performance of the proposed receiver (see Figure 3) is compared with that of an OFDM system with VC with the same spectral efficiency using linear/nonlinear data detection. The simulations are conducted following the specifications outlined in the 802.11 p standard [28]. The V2V channel was modeled with selective Rayleigh fading in frequency, incorporating a maximum delay spread (\(\tau_{rms}\)) of 0.4 us and a Doppler frequency (\(f_{D}\)) of 1 kHz to emulate a V2V scenario with a vehicle speed of \(v=100\) km/h [5]. Each OFDM symbol block consisted of \(N=64\) subcarriers, complemented by a cyclic prefix of size \(CP=16\). These parameters are selected considering an urban scenario with typical values of speed [5; 9]. Figure 4 shows the BER performance obtained by the proposed OFDM system with VC in transmission and MRC detection (\(\
u=2\)). For the specific case of signal-to-noise ratio (SNR) of 15 dB, the MRC detector outperforms the OSIC and MMSE detectors by 5 and 7 dB, respectively. Analyzing the graphs, the poor performance of the LS and MMSE estimators can be clearly highlighted, mainly due to their inability to counteract the ICI produced by the V2V channel adequately. On the other hand, it is observed that the OSIC detector is suitable for mitigating ICI. However, during the interference cancellation process, it does not adequately utilize the diversity in the signals. Due to the use of VC during transmission, at least half of the spectral efficiency of an OFDM system must be sacrificed. However, higher code rates in the forward error correction (FEC) stages can \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Detection** & **Complexity** \\ \hline \multirow{3}{*}{Linear} & MRC & \(\mathcal{O}(N)\) \\  & LS & \(\mathcal{O}(N^{3})\) \\  & LMMSE & \(\mathcal{O}(N^{3})\) \\ \hline \multirow{3}{*}{Nonlinear} & OSIC & \(\mathcal{O}(N^{3})\) \\  & QR-MLD & \(\mathcal{O}(N\Omega^{N})\) \\ \cline{1-1}  & Full MLD & \(\mathcal{O}(N\Omega^{N})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computational complexity in terms of complex products per OFDM symbol. Figure 3: Proposed OFDM receiver with MRC detection. compensate for this spectral efficiency loss. To compensate for the spectral efficiency loss, the modulation order was increased to 16 QAM in the data. It is evident that, at lower SNR levels, the MRC detection demonstrates performance comparable to the MMSE detector. However, as the SNR surpasses 20 dB, the proposed system exhibits an approximate gain of 2.5 dB compared to the MMSE detector while maintaining a performance similar to that of the OSIC detector. It is important to note that both the MMSE and OSIC detectors have significantly higher computational complexity. The proposed system does not exhibit an error floor at low SNR levels, as shown for the LS and the MMSE detectors. This is because the proposed system utilizes the diversity of the received OFDM signal during MRC detection. Furthermore, it is essential to mention that the computational complexity required by the MRC detector of \(\mathcal{O}(N)\) is much lower than that reported by the linear MMSE detector of \(\mathcal{O}(N^{3})\). The MRC detection of the proposed system demonstrates near performance to nonlinear detectors, such as QR-MLD and MLD, at low SNR levels. However, beyond 15 dB of SNR, the nonlinear detectors exhibit a notable advantage. It is important to consider that there is a significant disparity in the number of operations required for nonlinear detection compared to MRC detection. While MRC detection has linear complexity, nonlinear detection exhibits exponential complexity relative to the size of \(N\).