# Low Complexity DSP for High Speed Optical Access Networking +
## 5 DSP Analysis and Experimental Transmission-Reach Limitations  
The simplification of the NLE filter taps is illustrated in Figure 5. Note that for the simplified DSP case, the equalization runs again after the taps below the threshold are disabled from the complete DSP. On convergence, the survived taps show different values compared to their complete DSP counterparts since the interaction between taps changed. Taking the nonlinear FFE term as an example, Figure 5 shows that the most significant nonlinear terms are the square terms and the product terms between most adjacent symbols, which corresponds to the nonlinear FFE coefficient \(\text{a}_{ij}\) for \(\mid i-j\mid\leq 1\). The product terms between symbols further away from each other are negligible and can be eliminated to reduce computational complexity. It is observed that the penalty of the simplified nonlinear FFE/DFE, relative to the full nonlinear FFE/DFE, increases slightly with increasing the fiber length beyond 20 km. This is because of the increased fiber dispersion and stronger distortion (as shown in Figure 2), and the fact that a small part of the eliminated nonlinear product terms shown above are no longer negligible. It is noticeable that both the FFE and DFE terms show that more weighted taps survived via simplification. While for the NS filter, the tap significance was changed slightly via simplification. This is because the change of the FFE/DFE taps has an influence on the noise correlation. Overall, the total tap count is reduced by 75% (from 44/10/10 to 10/4/3 taps). The simplified DSP makes the receiver comparable to a commercial simply equalized clock and the data recovery (CDR) of PAM-4 as regards the complexity and power dissipation.  
Figure 6a summarizes the optical power sensitivity at the threshold BERs of both of the proposed FECs for various fiber lengths under two receiver DSP configurations: 8/4 tap FFE/DFE without 2 nd-order terms, and a simplified 10/4/3 tap FFE/DFE/NS filter with both linear and 2 nd-order terms as well as the NS filter. It clearly shows that when compared with a linear FFE/DFE, 2 nd-order Volterra nonlinear equalizations with an NS filter considerably enhance the receiver sensitivity and that the gain is more significant at longer fiber distances. The linear equalization fails to support 30 km SMF transmission for both FECs.  
Considering a launch power of 12 dBm, Figure 6b presents the achievable link power budget, subject to the DSP configurations in Figure 6a. As references, three different high value power budget specifications from 10 G EPON standard are illustrated. It indicates that the proposed 40 Gb/s PAM-4 PON can achieve a link power budget of 39 dB (33 dB) and 37 dB (27 dB) for 20 km (30 km) SMF transmissions by using the 10 G EPON FEC and KP-4 FEC, respectively. The system can support PR30 and PR40 power budget specification with 20 km and 25 km distances, respectively, under all DSP configurations. Only the FFE/DFE/NS configuration together with 10 G EPON FEC can support PR50 by considering a 25 km reach. It is worth mentioning that the pre-amplified receiver may  
Figure 5: Feedforward and decision feedback equalizer (FFE/DFE) and noise suppression (NS) filter tap coefficients for full DSP and simplified DSP cases with 20 km SMF at an optical power of \(-\)21 dBm.  
be replaced by an APD in the downlink system for cost reasons and the corresponding achievable power budgets will be ~7.5 dB less [7, 8, 12]. In this case, the PR30 power budget (20 km reach) can still be achieved. When dynamic biasing APD is used, it is expected that the power budget can be reasonably improved [28]. In the case of using an APD without a receiver EDFA, simulations in Figure 4 have revealed that 20 km reach can be achieved and so it can cover the PR30 power budget as depicted in Figure 6b.