# A Novel OFDM Format and a Machine Learning Based Dimming Control for LiFi
## 5 Performance Evaluation of DPO  
The performance results of DPO and other OFDM schemes are obtained here with the help of simulations with the MATLAB (version 9.2) tool. The simulations were performed for an AWGN channel without considering any other sort of distortion. In order to keep consistency with the results described in the literature [12; 22], the target uncoded BER was considered to be \(10^{-3}\). This section discusses the power efficiency of the proposed LiFi system. The performance is evaluated using two terms. One is the electrical energy per bit to noise power spectral density, \(E_{b(elc)}/N_{O}\). In this case, the bit rate/normalized bandwidth (bit/s/Hz) is expressed as \(R\). The other one is the optical energy per bit to noise power spectral density, \(E_{b(opt)}/N_{0}\). Figure 4 shows the BER versus \(E_{b(elc)}/N_{O}\) when \(R\) is 2. It can be seen that both ADO and DPO have excellent efficiency in terms of \(E_{b(elc)}/N_{O}\). Figure 5 presents \(E_{b(elc)}/N_{O}\) versus \(R\) for the proposed DPO system. For comparison, plots are also provided for HDAP (50% DCO and 50% ACO-PAM), AHO, ADO, and DCO. Here we can see that for \(R\) of 2, 3, and 4, DPO requires a lower \(E_{b(elc)}/N_{O}\) than HDAP and AHO. For example, at an R of 3 for a BER \(10^{-3}\), DPO requires exactly 2 dB and 7 dB less \(E_{b(elc)}/N_{O}\) than HDAP (50% DCO and 50% ACO-PAM) and AHO, respectively. Compared to DCO, DPO has 2 dB and 3 dB more electrical power efficiency at \(R\) of 2 and 4, respectively. However, DPO has the same electrical power efficiency as DCO at an \(R\) of 3, and DPO is less efficient than ADO in terms of \(E_{b(elc)}/N_{O}\). Note that in DPO, an \(R\) of 2 is achieved using 4-QAM DCO and 4-PAM-DMT, R of 3 is achieved using 8-QAM DCO and 8-PAM-DMT, and \(R\) of 4 is obtained with 16-QAM DCO and 16-PAM-DMT. Figure 5 also indicates that the required \(E_{b(elc)}/N_{O}\) increases for an increase in the value of \(R\). For example, for a given BER of \(10^{-3}\), DPO requires \(E_{b(elc)}/N_{O}\) of 16 dB, 24 dB, and 25 dB when \(R\) has values of 2, 3, and 4, respectively. Figure 4: Bit error rate (BER) versus electrical energy per bit to noise power spectral density (\(E_{b(elc)}/N_{O}\)) for different orthogonal frequency division multiplexing (OFDM) forms. Figure 6 shows the BER versus \(E_{b(opt)}/N_{0}\) when \(R\) is 2. It can be seen that ADO has the best \(E_{b(opt)}/N_{0}\) efficiency followed by DCO and DPO. Figure 7 demonstrates \(E_{b(opt)}/N_{0}\) versus \(R\) for DPO, HDAP (50% DCO and 50% ACO-PAM), AHO, ADO, and DCO. Here we can see that for \(R\) of 2, 3, and 4, DPO requires a lower \(E_{b(opt)}/N_{0}\) than AHO, but higher than ADO. For \(R\) of 2, DPO requires approximately 4 dB lower \(E_{b(opt)}/N_{0}\) than HDAP, but for \(R\) of 3 and 4, DPO requires slightly less \(E_{b(opt)}/N_{0}\) than HDAP. DPO is more optically power-efficient than DCO at an \(R\) of 4. Next, simulations were performed to investigate the effect of the number of OFDM subcarriers on the BER performance for different OFDM forms in an AWGN channel. The total number of OFDM subcarriers, \(N\), was varied from 64 to 1024 as these are the numbers reported for OFDM-based LiFi [12; 19; 26]. In the simulations, the total transmitted optical power was kept fixed for different values of \(N\). Figure 8 shows the BER versus \(E_{b(dec)}/N_{O}\) for an \(R\) of 2 in an AWGN channel. For clarity of the illustration, the plots are shown only for DPO and HDAP, with \(N\) having only three values: 128, 512, and 1024. Figure 8 presents that for a given transmitted optical power and for AWGN, the BER performance does not change with the change in \(N\). Figure 5: Electrical energy per bit to noise power spectral density (\(E_{b(dec)}/N_{0}\)) versus bit rate/normalized bandwidth (\(R\)) for hybrid orthogonal frequency division multiplexing (OFDM) considering a bit error rate (BER) of \(10^{-3}\).