# DFT-Spread Spectrally Overlapped Hybrid OFDM-Digital Filter Multiple Access IMDD PONs
## 3 Upstream Optimum ONU Operating Conditions
### Simulation Models and Key Parameters  
In this paper, two ONUs are considered, each producing an optical sub-band signal sharing the same subwavelength with the other ONU. To conduct the simulations, MATLAB tools were used for signal generation and detection, while VPItransmissionMaker was used for optical fibre transmission. To implement the shaping filter in each individual ONU, a widely used digital filter construction approach called the Hilbert-pair approach was adopted to produce two orthogonal digital shaping filters sharing a subwavelength spectral region. These two orthogonal filters form a Hilbert pair, which have similar amplitude characteristics, but with a \(\pi/2\) phase difference in the frequency domain [26; 27; 28]. To support two independent ONUs, the up-sampling factor was set at \(M=2\)[26]. Since the DAC/ADC operates at 12.5 GS/s and the two ONUs occupy the same spectral region, the signal bandwidth for each ONU is equal to the Nyquist frequency, \(f\)s/\(M\), while the central frequency of the orthogonal digital filter pair is \(f\)s/\(2M\), where \(f\)s is the DAC/ADC sampling speed. For the \(M=2\) case, Figure 2a,b illustrate the spectral locations of digitally filtered sub-band signals (I-phase and Q-phase) and their spectra. To generate the real-value OFDM signal necessary for intensity modulation, a 32-point IFFT size was considered, in which 15 subcarriers in the positive frequency bins convey real data, one subcarrier contains no power, and the remaining 16 subcarriers in the negative frequency bins are the complex conjugates of data-bearing subcarriers. To reduce the power leakage caused by crosstalk between spectrally overlapped digital orthogonal sub-bands, and maximize the upstream signal transmission capacity, 14 data-bearing subcarriers out of 15 were employed to deliver the acceptable upstream performance for each sub-band. Thus, the DFT block size \(K\) was set to be 14. It is, however, expected that all 15 of the subcarriers can be supported if channel interference mitigation techniques are applied [29; 30]. In this demonstration, all of the subcarriers were encoded with a 64-QAM signal modulation format; however, any modulation formats are applicable. Detailed explorations of the impact of quantization and clipping noise on the upstream transmission performance of the digitally filtered spread-spectrum OFDM signals are  
Figure 2: (**a**) Spectral location of orthogonally digitally filtered sub-band signals (I-phase and Q-phase) and (**b**) their spectra. CCDFs of PAPR for (**c**) varying digital filter lengths and a fixed 64-QAM modulation format, and (**d**) varying modulation formats and a fixed digital filter length of 64.  
undertaken in Section 3.3, in which an optimal 7-bit resolution and optimal clipping ratios of 11 dB and 12 dB are identified for the cases of including and excluding the DFT-spread, respectively. These identified optimal parameters are adopted throughout this paper. Unless otherwise stated, all other system parameters are summarized in Table 1.  
In the OLT, an ideal positive-intrinsic-negative (PIN) photodetector for direct detection of the optical signal is employed, with a receiver sensitivity of \(-19\) dBm and a quantum efficiency of 0.8 A/W. Both shot noise and thermal noise are considered, and are simulated using procedures similar to those presented in [30]. In addition, the OLT-based receiver consists of a variable optical attenuator (VOA) to adjust the received optical power (ROP) level, while the ADC incorporates an ideal antialiasing electrical filter with a 6.25 GHz bandwidth to remove out-of-band receiver noise before signal sampling. Taking into account the transceiver parameters listed in Table 1 and the adopted signal modulation formats, the upstream signal transmission rate per ONU is \(-13.12\) Gb/s, while the aggregate upstream PON transmission rate is \(\sim\)26.25 Gb/s.