# A Baseband Wireless Spectrum Hypervisor for Multiplexing Concurrent OFDM Signals
## 7 Simulation Results
The MSE estimation values shown in the table were calculated averaging the error between PHY and vPHY OFDM symbols over \(1\times 10^{5}\) iterations. The MER averaging was also executed over the same number of iterations. For each iteration, the same set of randomly picked data bits modulates both the single PHY and the 12 vPHYs. The table shows that the MSE is quite low and almost the same for all modulation schemes and that the MER is high and the same for all schemes, which means that both MSE and MER are independent of the employed modulation scheme. Additionally, it is worth mentioning that as all vPHYs are fed with the same set of bits, their resulting MSE and MER are the same, and due to the fact that we only present one value per modulation scheme in Figure 11.  
In Table 4 we show the comparison of MSE and MER for several different filter order values. As we noticed with the results in Table 3, the MSE and MER values are almost the same for all modulation schemes, and therefore, in this simulation, we use the same modulation scheme, QPSK, for all trials. As mentioned before, the filter order is important to guarantee a good signal fidelity. This is due to the fact that the higher the filter order, the closer it is to the perfect window filter frequency response, which does not impose any distortion to the filtered signal [57]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Filter Order**} \\ \hline  & **16** & **64** & **128** & **256** & **512** & **1024** \\ \hline
**MSE** & \(1.3317\times 10^{-3}\) & \(1.9853\times 10^{-8}\) & \(3.6452\times 10^{-9}\) & \(3.2091\times 10^{-9}\) & \(3.8513\times 10^{-10}\) & \(2.3038\times 10^{-10}\) \\ \hline
**MER [dB]** & \(5.1897\) & \(53.4555\) & \(60.8164\) & \(61.3699\) & \(70.5720\) & \(72.8092\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MSE and MER for several different filter orders. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Modulation Order**} \\ \cline{2-7}  & **BPSK** & **QPSK** & **16 QAM** & **64 QAM** & **128 QAM** & **256 QAM** \\ \hline
**MSE** & \(3.8517\times 10^{-10}\) & \(3.8521\times 10^{-10}\) & \(3.8533\times 10^{-10}\) & \(3.8526\times 10^{-10}\) & \(3.8514\times 10^{-10}\) & \(3.8526\times 10^{-10}\) \\ \hline
**MER [dB]** & \(70.572\) & \(70.572\) & \(70.572\) & \(70.572\) & \(70.572\) & \(70.572\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MSE and MER for several different modulation schemes. In Figure 11, depicts the comparison between OFDM symbols generated by a plain (i.e., single) PHY and 2 vPHYs having their output signals multiplexed by the hypervisor. Here, for the sake of comparison, the single PHY and the 2 vPHYs are fed with the same set of data bits. As can be seen, the vPHY OFDM symbols are quite similar to the OFDM symbol generated by the single PHY. In Figure 12, we show the frequency-domain representation of the wide baseband signal generated by the proposed wireless hypervisor. Here, in this figure, the hypervisor multiplexes, in the frequency domain, the signals of 12 vPHYs, \(M\), where each vPHY uses 128 subcarriers, \(N_{\rm vPHY}\), totaling 1536 subcarriers, which is the number of points used by the IFFT block in the hypervisor, N. Each vPHY only modulates 72 subcarriers and leaves the remaining subcarriers along its edges as guard bands. The subcarrier at the center of each vPHY channel is set to 0, which is used to allow receivers to employ simpler/cheap direct-conversion (i.e., zero intermediate-frequency) RF front-end receivers. In the example, shown in the figure, 64 QAM modulation is used to modulate the data signal. As can be seen, there are (i) a guard-band between consecutive vPHY signals, (ii) a null-subcarrier exactly at the center of each one of the vPHY transmissions, (iii) and different transmission levels for the vPHYs.