**5.4 BER tolerance**

*Fiber Optics - From Fundamentals to Industrial Applications*

worst case, channel 3 with lowest MER of 44.5 dB, is shown.

**Figure 7** shows the experimental results of 32 GSa/s one-bit digitization (Case V). 20 DOCSIS 3.1 channels are digitized into four 32 Gb/s OOK signals, and then transmitted by a 32 Gbaud DP-QPSK link. The RF spectra before (blue) and after (red) delta-sigma digitization are shown in **Figure 7(a)**. Five 192-MHz DOCSIS 3.1 channels occupy a frequency range from 258 to 1218 MHz. It can be seen that after delta-sigma digitization, the signal spectrum is kept intact, and the quantization noise is pushed out of the signal band with in-band CNR larger than 40 dB. **Figure 7(b)** shows the MER performance of five channels, and each of them satisfies the requirements (dashed lines) of DOCSIS 3.1 specifications. Channel 2 has MER > 50 dB carrying 16384QAM; channel 4 has MER > 41 dB carrying 4096QAM; the remaining three have MER > 44 (44.5) dB carrying 8192QAM. This is the first time that modulation orders higher than 4096QAM have been demonstrated over fiber in HFC networks. Constellations of each modulation are shown in **Figure 7(c, d, e)**. For 8192QAM, the

**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

*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.*

**5.2 One-bit digitization**

**5.3 Two-bit digitization**

**82**

**Figure 7.**

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

**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 is 1 × 10<sup>−</sup><sup>6</sup> , and error free transmission is achieved for received optical power larger 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

#### **Figure 8.**

*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).*


### **Table 5.**

*Experimental design of BER tolerance evaluation.*

**Figure 9.**

*BER tolerance of 32 GSa/s one-bit delta-sigma digitization: (a) BER and EVM versus received optical power; (b) MER degradation as BER increases; (c) 4096QAM constellation at BER threshold.*

**Figure 10.**

*BER tolerance of 32 GSa/s two-bit delta-sigma digitization: (a) BER and EVM versus received optical power; (b) MER degradation as BER increases; (c) 4096QAM constellation at the BER threshold.*

of BER, 0, 1.5 × 10<sup>−</sup><sup>6</sup> , and 1.1 × 10<sup>−</sup><sup>5</sup> were tested, and good consistency is achieved between simulation and experimental results. As BER increases to 2.5 × 10<sup>−</sup><sup>6</sup> , MER of Channel 4 (worst case) drops to 41 dB, i.e., the minimum CNR requirement of 4096QAM. Therefore, the BER threshold of 32 GSa/s one-bit digitization is 2.5 × 10<sup>−</sup><sup>6</sup> . For BER < 2.5 × 10<sup>−</sup><sup>6</sup> , all 20 channels have sufficient CNR to support 4096QAM, but for BERs beyond this threshold, some channels' performance will drop below the DOCSIS 3.1 criteria. **Figure 9(c)** shows the 4096QAM constellation at the BER threshold.

Similar results for two-bit delta-sigma digitization (Case XII) are shown in **Figure 10**. The experimentally measured EVM and BER of 32 Gbaud DP-16QAM are shown in **Figure 10(a)**, and the minimum achievable BER is 3 × 10<sup>−</sup><sup>5</sup> . **Figure 10(b)** shows the MER performance degradation as a function of increasing BER. Simulation results (solid lines) are obtained by flipping a certain number of bits after digitization to emulate various BER values; experimental results (dots) at BER = 3 × 10<sup>−</sup><sup>5</sup> , 5.6 × 10<sup>−</sup><sup>5</sup> , 9.5 × 10<sup>−</sup><sup>5</sup> , 3 × 10<sup>−</sup><sup>4</sup> , 5.2 × 10<sup>−</sup><sup>4</sup> are obtained by adjusting the received optical power. Thanks to the additional quantization bits, two-bit digitization has larger tolerance against BER. Its MER performance becomes more resilient against the increasing BER, and the BER threshold is increased to 1.7 × 10<sup>−</sup><sup>4</sup> . The 4096QAM constellation at the threshold BER is shown in **Figure 10(c)**.
