## 6 Power Budget Analysis  
The cost performance of the IM/DD Fast-OFDM-CDMA system is calculated as the optical power budget using an APD and a CW laser at OLT and ONU, respectively, as shown in Figure 9.  
Table 3 presents the power budget calculation related to the proposed hybrid system configuration with 4 dBm and 15 dBm emitted average powers, corresponding to the local and long reach access network [27], respectively.  
For the connector attenuation, four connectors are required in total to relay each component in the link, as shown in Figure 8 (i.e., a connector is needed to connect ONU, SSMF, splitter 1 \(\times\) 16, SSMF and OLT), and if we consider that each connector has a loss of 0.4 dB [28], we get a total connector attenuation in the link in the order of 4 \(\times\) 0.4 = 1.6 dB. In addition, each splitter 1 \(\times\) 16 introduces a loss equal to 12 dB. On the one hand, it is shown that the maximum reachable distance between the ONU and OLT for the Fast-OFDM-CDMA system is equal to 112 km and 167 km for the lower case and the upper case, respectively. Likewise, we show that the proposed hybrid system can reach a long-reach PON distance of 167 km using an emitted average power of 15 dBm.  
Figure 8: Eye diagrams: (**a**) for the first user; (**b**) for the second user; (**c**) for the third user; (**d**) for the fourth user.  
Table 4 presents the power budget comparison related to the proposed hybrid system configuration compared to the OCDMA-WDM and AO-OFDM-CDMA systems.  
Moreover, with a 10 dBm average launched optical power, our hybrid system increases the maximum achievable transmission reach to 142 km, compared to 108 km for AO-OFDM-CDMA. As a result, our hybrid Fast-OFDM-CDMA system can improve the total power budget with an increment equal to 6.8 dB (i.e., the power budget passed from 21.6 to 28.4 dB), as compared to the AO-OFDM-OCDMA PON configuration.  
Table 5 summarizes the relevant 2D-OCDMA-PON systems. To make a fair comparison among our IM/DD Fast-OFDM-CDMA and the other proposed systems in the literature, we consider various features, such as the coding scheme, cardinality (i.e., number of users), performance measured metrics (i.e., BER and Q-factor), system components and reachability distance.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **OCDMA-WDM** & **AO-OFDM-CDMA** & **Fast-OFDM-CDMA** \\ \hline Emitted average power (dBm) & 15 & 10 & 10 \\ \hline Connectors attenuation (dB) & \(-\)3.6 & \(-\)2.4 & \(-\)1.6 \\ \hline Splitter attenuation (dB) & \(-\)27 & \(-\)18 & \(-\)12 \\ \hline System margin (dB) & \(-\)3 & \(-\)3 & \(-\)3 \\ \hline Received average power (dBm) & \(-\)(\(-\)35) & \(-\)(\(-\)35) & \(-\)(\(-\)35) \\ \hline a = Available attenuation & 16.4 & 21.6 & 28.4 \\ \hline Maximal distance between ONU and OLT(\(\frac{a}{a}\)) & 82 km & 108 km & 142 km \\ \hline \hline \end{tabular}
\end{table}
Table 4: Budget power comparison.  
Figure 9: PON configuration used to perform power budget calculation.  
As shown in Table 5, various 2D-OCDMA codes are proposed for PON applications, such as hybrid codes (2D-HC), prime hop system (2D-PHS) and 2D permutation vectors (2D-PV) codes. We can also see that when the bit rate is less than 40 Gb/s, the system authorizes a high cardinality, for instance in the 2D-OCDMA-WDM, 2D-OCDMA, 2D-PV and Fast-OFDM-CDMA PON configurations. Nonetheless, for a bit rate equal to 100 Gb/s, the number of simultaneous users is reduced to 5 and 15 for the IMDD OOFDM-CDMA and CO-OFDM-CDMA systems, respectively. As a conclusion, the IM/DD Fast-OFDM-CDMA system outperforms the AO-OFDM-CDMA, CO-OFDM-CDMA, IMDD OOFDM-CDMA and 2D-PV systems in terms of cardinality and reachability as well.