# DFT-Spread Spectrally Overlapped Hybrid OFDM-Digital Filter Multiple Access IMDD PONs
## 3 Upstream Optimum ONU Operating Conditions
### PAPR Performance of DFT-Spread Hybrid OFDM-DFMA PON  
Having chosen the simulation parameters, identified the optimal conditions, and understood the operating principle of the proposed DFT-spread spectrally overlapped hybrid OFDM-DFMA IMDD PON, in this section, we numerically explore the PAPR reduction efficiency of the proposed PON consisting of two ONUs. Figure 2a,b show the spectral locations of two digitally filtered sub-band signals (I-phase and Q-phase) and their spectra. In addition, the comparative complementary cumulative distribution functions (CCDFs) of the PAPR, including and excluding DFT-spread, are presented in Figure 2c,d, respectively, for various digital filter lengths ranging from 16 to 256 and signal modulation formats varying from 16-QAM to 256-QAM. For the sake of simplicity, only ONU-2--referred to as channel-2--CCDF curve is plotted for both cases, as the curves of ONU-1--referred to here as channel-1--are similar to those of channel-2. It can be seen from Figure 2 that, compared to the case without DFT-spread, the case with DFT-spread can reduce the PAPR ratio by \(>\)2 dB at the CCDF value of \(1\times 10^{-3}\) when the optimal clipping ratio of 11 dB is adopted. The results are similar to those of our previous work, and those observed in WDM-PONs [19; 31; 32]. It is also very interesting to note in Figure 2c,d that the proposed PON's upstream transmissions have very similar PAPR performances when varying both digital filter lengths up to 256 and signal modulation formats up to 256-QAM. This indicates that the DFT-spread-induced PAPR reductions are independent of the digital filter length and the signal modulation. Moreover, the obtained \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \multirow{2}{*}{IFFT/FFT Size} & \multirow{2}{*}{32/64} & Clipping Ratio—Including & \multirow{2}{*}{11 dB/12 dB} \\  & & /Excluding DFT-spread & \\ \multirow{2}{*}{Number of Used Data} & \multirow{2}{*}{14} & Digital Filter Length/Excess & \\  & & Bandwidth & \\ \multirow{2}{*}{Subcarriers per ONU} & \multirow{2}{*}{64-QAM} & \multirow{2}{*}{PIN Detector Quantum} & \multirow{2}{*}{0.8 A/W} \\  & & Efficiency & \\ \multirow{2}{*}{Cyclic Prefix} & \multirow{2}{*}{25\%} & PIN Detector Sensitivity & \(-19\) dBm \\ \multirow{2}{*}{Channel Bitrate} & \multirow{2}{*}{13.12 Gb/s} & PIN Detector Bandwidth & Ideal \\ \multirow{2}{*}{Optical Launch Power} & \multirow{2}{*}{0 dBm} & Fibre-Dispersion & 17 ps/nnm/km \\ \multirow{2}{*}{DAC/ADC Sample Rate} & \multirow{2}{*}{12.5 GS/s} & Fibre-Dispersion Slope & 0.08 ps/nnm\({}^{2}\)/km \\ \multirow{2}{*}{Number of Bits} & \multirow{2}{*}{7-bits} & Fibre Loss & 0.2 dB/km \\ \multirow{2}{*}{Up-sampling Factor} & \multirow{2}{*}{M = 2} & Fibre Kerr Coefficient & \(2.6\times 10^{-20}\) m\({}^{2}\)/W \\ \multirow{2}{*}{FEC Limit 1  & \(1\times 10^{-3}\) & Transmission Distance & 25 km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. results also suggest that, under the same transmission power constraints, the DFT-spread case with a low PAPR can achieve a higher optical signal-to-noise ratio (OSNR); this is one of the factors leading to the increased upstream channel rate presented in Section 4.2. Nevertheless, it is worth noting that the performance of the PONs reported in [6] is largely limited by digital-filter-induced signal distortion. As such, in this paper, to highlight the unique features of the DFT-spread technique, a digital filter length of 64--as listed in Table 1--is utilized to minimize the digital filter impairments. From the above discussion, it is easy to understand that the proposed PON-induced PAPR reduction gives rise to an excellent improvement in system performance robustness to quantization noise induced by limited DAC/ADC bit resolutions.