**5.3 Two-bit digitization**

**Figure 8** shows the experimental results of 32 GSa/s two-bit delta-sigma digitization (Case X). Five DOCSIS 3.1 channels are digitized into a 32 Gb/s PAM4 signal. The RF spectra before (blue) and after (red) digitization are shown in **Figure 8(a)**. Compared with **Figure 7(a)**, the in-band quantization noise is reduced thanks to the additional quantization bit, and CNR > 50 dB is achieved. In Case IX and X, with sampling rates of 28 and 32 GSa/s, all 20 DOCSIS 3.1 channels have enough CNR to support 16384QAM. The raw data rate of these 20 channels is 53.2 Gb/s, and the net user information is ~45 Gb/s. Since the minimum data capacity of a coherent fiber link to support 2016384QAM channels

### **Figure 7.**

*Experimental results of 32 GSa/s one-bit delta-sigma digitization (Case V): (a) RF spectra; (b) MER of five DOCSIS 3.1 channels; (c) Channel 2 16384QAM; (d) channel 3 8192QAM; (e) channel 4 4096QAM.*

**83**

**Table 5.**

**Figure 8.**

**Case Sampling rate (GSa/s)**

*Delta-Sigma Digitization and Optical Coherent Transmission of DOCSIS 3.1 Signals in Hybrid…*

In **Table 4** and **Figure 6**, error free transmission is achieved for all baud rate DP-QPSK (Case I–V); but for DP-16QAM, error free transmission is only achieved at 16 and 20 Gbaud (Case VI, VII). In this section, we design BER tolerance test to measure the MER performance degradation of delta-sigma digitization as a function of increasing BER, as shown by Case XI and XII in **Table 5**, where 4096QAM are assigned to all 20 channels since it is the highest modulation specified in

**Figure 9** shows the results of one-bit delta-sigma digitization (Case XI). The experimentally measured EVM and BER of 32 Gbaud DP-QPSK at different received optical power are presented in **Figure 9(a)**, with constellations plotted in the insets. Due to the limited memory of our AWG, the minimum measurable BER

than −10 dBm. **Figure 9(b)** shows the MER degradation as a function of increasing BER. Both simulation (solid lines) and experiments (dots) are carried out. In the simulation, various BER values are emulated by flipping a certain number of bits after delta-sigma digitization; whereas in the experiments, different BER values are obtained by reducing the received optical power. In experiments, it is impossible to achieve exact BERs by adjusting the optical power. In **Figure 9(b)**, only three values

*Experimental results of 32 GSa/s two-bit delta-sigma digitization (Case X): (a) RF spectra; (b) MER performance of five DOCSIS 3.1 channels; (c) channel 4 16384QAM (worst of the five channels).*

> **Coherent transmission**

XI 32 One-bit OOK QPSK 4096 4096 4096 4096 4096 XII 32 Two-bit PAM4 16QAM 4096 4096 4096 4096 4096

**Modulation formats of five DOCSIS channels**

**Quantization Waveform** 

*Experimental design of BER tolerance evaluation.*

**after ADC**

, and error free transmission is achieved for received optical power larger

DOCSIS 3.1 specifications (8192/16384QAM are optional).

is 28 × 4 × 2 = 224 Gb/s, the net information ratio of delta-sigma digitization is 45/224 = 20.1%, which is higher than BDF/BDR interface based on Nyquist digitization. **Figure 8(b)** shows the MER performance of 5 out of 20 DOCSIS channels, each with a MER larger than 52.5 dB, which is 4.5 dB higher than the required 48 dB for 16384QAM in DOCSIS 3.1 specifications. This indicates that two-bit digitization at 32 GSa/s has the potential to support an even higher modulation reaching up to 32768QAM. **Figure 8(c)** shows the worst-case constellation of 16384QAM, which corresponds to channel 4 with the lowest MER of

*DOI: http://dx.doi.org/10.5772/intechopen.82522*

52.5 dB.

is 1 × 10<sup>−</sup><sup>6</sup>

**5.4 BER tolerance**

*Delta-Sigma Digitization and Optical Coherent Transmission of DOCSIS 3.1 Signals in Hybrid… DOI: http://dx.doi.org/10.5772/intechopen.82522*

is 28 × 4 × 2 = 224 Gb/s, the net information ratio of delta-sigma digitization is 45/224 = 20.1%, which is higher than BDF/BDR interface based on Nyquist digitization. **Figure 8(b)** shows the MER performance of 5 out of 20 DOCSIS channels, each with a MER larger than 52.5 dB, which is 4.5 dB higher than the required 48 dB for 16384QAM in DOCSIS 3.1 specifications. This indicates that two-bit digitization at 32 GSa/s has the potential to support an even higher modulation reaching up to 32768QAM. **Figure 8(c)** shows the worst-case constellation of 16384QAM, which corresponds to channel 4 with the lowest MER of 52.5 dB.
