**3. Experimental setup**

**Figure 4** shows the experimental setup. OFDM parameters of DOCSIS 3.1 specifications are listed in **Table 2**. There are two sets of FFT sizes and subcarrier spacing. In this experiment, we use the FFT size of 4096 and subcarrier spacing of 50 kHz.

In a 1.2 GHz DOCSIS 3.1 implementation, the downstream signal contains five channels, each with 192-MHz bandwidth and occupying 960-MHz (258–1218 MHz) frequency band in total. In this experiment, these five downstream channels are digitized by delta-sigma ADCs with sampling rates of 16, 20, 24, 28, and 32 GSa/s. Both one-bit and two-bit digitization are carried out, and the five channels are digitized to an OOK (one-bit) or PAM4 (two-bit) signal with baud rate of 16–32 Gbaud. In a dual-polarization (DP) coherent fiber link, each polarization has in-phase (I) and quadrature (Q ) components, and each component can carry one OOK/PAM4 signal, so there are four data streams in total carrying 20 digitized DOCSIS 3.1 channels, i.e., a DP-QPSK/16QAM link can carry 20 digitized DOCSIS 3.1 channels with one-bit or two-bit digitization, respectively. Delivering 20 DOCSIS channels over a single wavelength quadruples the capacity of current HFC networks and enables a 4x1 fiber node split. In the following sections, only the results of 32 Gbaud are discussed in detail due to the limited space.

In **Figure 4**, the two arms of IQ Mach-Zehnder modulator (MZM) are driven by two independent OOK/PAM4 signals to synthesize a QPSK/16QAM signal, and

#### **Figure 4.**

*(a) Experimental setup; (b) waveforms for one-bit delta-sigma digitization; (c) waveforms for two-bit delta-sigma digitization; (d) eye diagram of 32 Gbaud PAM4 signal after delta-sigma ADC (point ii); (e) PAM4 eye diagram after scrambling (point iii); (f) PAM4 eye diagram after pre-equalization (point iv).*

**77**

intact.

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

**Active BW**

MHz

**Data subcarriers**

3800 190

**Data BW**

MHz

**Guard band**

1 MHz

**Active subcarriers**

8192 25 kHz 7680 7600

4096 50 kHz 3840 192

after the polarization multiplexer, a DP-QPSK/16QAM signal carries four streams

It is worth noting that although there are several reports of high speed deltasigma ADC with sampling rate up to 8.6 GSa/s [35–37], there is no commercially available delta-sigma ADC that runs faster than 10 GSa/s. For a proof-of-concept experiment in this paper, the delta-sigma digitization is realized offline using MATLAB, and the digitized bits are loaded into a Keysight arbitrary waveform generator (AWG) M8196A, and then transmitted over a 80-km coherent fiber link. In real implementations, to alleviate the speed limit, several low speed delta-sigma ADCs can be used in parallel, each digitizing only one DOCSIS channel, rather than using a high-speed ADC to digitize all five channels together. The output bits from parallel low speed ADCs can be interleaved in the time domain by TDM technology, so the sampling rate of each ADC is reduced, while keeping the overall capacity

In **Figure 4(b)** and **(c)**, analog DOCSIS 3.1 signal at point i is plotted in red; after delta-sigma digitization, OOK/PAM4 signals at point ii are plot in green; retrieved analog signals after filters at point v are plotted in dashed blue lines. The initial (red) and retrieved (dashed blue) analog signals are fairly close to each other, indicating that the digitization introduces almost no impairment. In the green curve of **Figure 4(c)**, there are more ±1 symbols than ±3 symbols. This is because DOCSIS 3.1 is an OFDM signal with Gaussian distribution, and there are much more small samples than large ones. Therefore, the PAM4 signal after digitization also has unequal distribution. More than 80% symbols are ±1 s, and only less than 20% are ±3 s. This also makes the 16QAM signal has unequal distribution on the constellation. Most symbols are at (±1 ± j), and only a few at (±3 ± 3j). Unequally distributed constellation introduces challenges to the digital signal processing (DSP) of the coherent receiver, especially for constant multiple modulus algorithm (CMMA). To equalize the symbol distribution, a scrambler is inserted in the transmitter (only for two-bit digitization). Eye diagrams before and after the scrambler are shown in **Figure 4(d)** and **(e)**. In **Figure 4(d)**, there are much more

±1 s than ±3 s; in **Figure 4(e)**, the amount of ±1 s and ± 3 s are equalized.

to the boosted high frequency components.

Since delta-sigma digitization is designed to be utilized in access networks, such as HFC and C-RAN, a low-cost coherent system was built based on narrowband devices, e.g., 10 GHz RF drivers (Picosecond Pulse Labs 5822B) and 14 GHz IQ-MZM (Covega LN86S-FC). For 32 Gbaud QPSK/16QAM, these narrowband devices significantly impair the transmission performance, and frequency domain pre-equalization was used to compensate the bandwidth limitation. **Figure 4(f )** shows the 32 Gbaud PAM4 eye diagram after pre-equalization. The eye is closed due

After 80-km single mode fiber, the DP-QPSK/16QAM signal is received at the fiber node. In experiments, a Keysight N4391A optical modulation analyzer is used as a polarization diversity receiver. Four received signals (two polarizations, each polarization has in-phase and quadrature components) are captured by a real-time

of OOK/PAM4 with totally 20 digitized DOCSIS channels.

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

**Subcarrier spacing**

*In experiments, we use FFT size of 4096 and subcarrier spacing of 50 kHz.*

**FFT size**

*OFDM parameters of DOCSIS 3.1 signals.*

**Sampling rate**

204.8 MSa/s

**Table 2.**

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


#### **Table 2.**

*Fiber Optics - From Fundamentals to Industrial Applications*

node is only designed for one specific service.

discussed in detail due to the limited space.

**3. Experimental setup**

50 kHz.

**Table 1** compares different analog/digital fiber technologies in HFC networks. As a waveform-agnostic interface, delta-sigma ADC works with not only OFDM signals but also 5G multicarrier waveforms, such as filter-band multicarrier signals, as we reported in [50]. Since analog fiber, BDF/BDR, and delta-sigma digitization do not modify the bit information, they are service-agnostic and can carry various and a combination of services, even though these services evolve in the future. Remote PHY, on the other hand, is not service-transparent. Its RPD in the fiber

**Figure 4** shows the experimental setup. OFDM parameters of DOCSIS 3.1 specifications are listed in **Table 2**. There are two sets of FFT sizes and subcarrier spacing. In this experiment, we use the FFT size of 4096 and subcarrier spacing of

In a 1.2 GHz DOCSIS 3.1 implementation, the downstream signal contains five channels, each with 192-MHz bandwidth and occupying 960-MHz (258–1218 MHz) frequency band in total. In this experiment, these five downstream channels are digitized by delta-sigma ADCs with sampling rates of 16, 20, 24, 28, and 32 GSa/s. Both one-bit and two-bit digitization are carried out, and the five channels are digitized to an OOK (one-bit) or PAM4 (two-bit) signal with baud rate of 16–32 Gbaud. In a dual-polarization (DP) coherent fiber link, each polarization has in-phase (I) and quadrature (Q ) components, and each component can carry one OOK/PAM4 signal, so there are four data streams in total carrying 20 digitized DOCSIS 3.1 channels, i.e., a DP-QPSK/16QAM link can carry 20 digitized DOCSIS 3.1 channels with one-bit or two-bit digitization, respectively. Delivering 20 DOCSIS channels over a single wavelength quadruples the capacity of current HFC networks and enables a 4x1 fiber node split. In the following sections, only the results of 32 Gbaud are

In **Figure 4**, the two arms of IQ Mach-Zehnder modulator (MZM) are driven by two independent OOK/PAM4 signals to synthesize a QPSK/16QAM signal, and

*(a) Experimental setup; (b) waveforms for one-bit delta-sigma digitization; (c) waveforms for two-bit delta-sigma digitization; (d) eye diagram of 32 Gbaud PAM4 signal after delta-sigma ADC (point ii); (e) PAM4* 

*eye diagram after scrambling (point iii); (f) PAM4 eye diagram after pre-equalization (point iv).*

**76**

**Figure 4.**

*OFDM parameters of DOCSIS 3.1 signals.*

after the polarization multiplexer, a DP-QPSK/16QAM signal carries four streams of OOK/PAM4 with totally 20 digitized DOCSIS channels.

It is worth noting that although there are several reports of high speed deltasigma ADC with sampling rate up to 8.6 GSa/s [35–37], there is no commercially available delta-sigma ADC that runs faster than 10 GSa/s. For a proof-of-concept experiment in this paper, the delta-sigma digitization is realized offline using MATLAB, and the digitized bits are loaded into a Keysight arbitrary waveform generator (AWG) M8196A, and then transmitted over a 80-km coherent fiber link. In real implementations, to alleviate the speed limit, several low speed delta-sigma ADCs can be used in parallel, each digitizing only one DOCSIS channel, rather than using a high-speed ADC to digitize all five channels together. The output bits from parallel low speed ADCs can be interleaved in the time domain by TDM technology, so the sampling rate of each ADC is reduced, while keeping the overall capacity intact.

In **Figure 4(b)** and **(c)**, analog DOCSIS 3.1 signal at point i is plotted in red; after delta-sigma digitization, OOK/PAM4 signals at point ii are plot in green; retrieved analog signals after filters at point v are plotted in dashed blue lines. The initial (red) and retrieved (dashed blue) analog signals are fairly close to each other, indicating that the digitization introduces almost no impairment. In the green curve of **Figure 4(c)**, there are more ±1 symbols than ±3 symbols. This is because DOCSIS 3.1 is an OFDM signal with Gaussian distribution, and there are much more small samples than large ones. Therefore, the PAM4 signal after digitization also has unequal distribution. More than 80% symbols are ±1 s, and only less than 20% are ±3 s. This also makes the 16QAM signal has unequal distribution on the constellation. Most symbols are at (±1 ± j), and only a few at (±3 ± 3j). Unequally distributed constellation introduces challenges to the digital signal processing (DSP) of the coherent receiver, especially for constant multiple modulus algorithm (CMMA). To equalize the symbol distribution, a scrambler is inserted in the transmitter (only for two-bit digitization). Eye diagrams before and after the scrambler are shown in **Figure 4(d)** and **(e)**. In **Figure 4(d)**, there are much more ±1 s than ±3 s; in **Figure 4(e)**, the amount of ±1 s and ± 3 s are equalized.

Since delta-sigma digitization is designed to be utilized in access networks, such as HFC and C-RAN, a low-cost coherent system was built based on narrowband devices, e.g., 10 GHz RF drivers (Picosecond Pulse Labs 5822B) and 14 GHz IQ-MZM (Covega LN86S-FC). For 32 Gbaud QPSK/16QAM, these narrowband devices significantly impair the transmission performance, and frequency domain pre-equalization was used to compensate the bandwidth limitation. **Figure 4(f )** shows the 32 Gbaud PAM4 eye diagram after pre-equalization. The eye is closed due to the boosted high frequency components.

After 80-km single mode fiber, the DP-QPSK/16QAM signal is received at the fiber node. In experiments, a Keysight N4391A optical modulation analyzer is used as a polarization diversity receiver. Four received signals (two polarizations, each polarization has in-phase and quadrature components) are captured by a real-time


*\*For DOCSIS 3.1 downstream, 8192QAM and 16384QAM are optional, and their CNRs are not specified yet. Here we use 44(44.5) and 48(48.5) dB as temporary criteria. +CNR values in parentheses with 0.5-dB increment are for channels above 1 GHz.*

#### **Table 3.**

*Carrier-to-noise ratio (CNR) requirement of DOCSIS 3.1 specifications.*

digital storage oscilloscope Keysight DSAX92004A for offline DSP. We use standard coherent DSP algorithms, including Gram-Schmidt orthogonalization [60], chromatic dispersion (CD) compensation [61, 62], polarization de-multiplexing [63, 64], carrier frequency offset (CFO) recovery [65, 66], and carrier phase recovery (CPR) [67, 68]. For polarization de-multiplexing, QPSK uses constant modulus algorithm (CMA), 16QAM uses constant multiple modulus algorithm (CMMA). For CPR, QPSK uses Viterbi-Viterbi algorithm, 16QAM uses the maximum likelihood (ML) phase recovery algorithm. After coherent DSP, a de-scrambler is applied to the PAM4 signal to restore its initial symbol distribution, and five DOCSIS channels are filtered out by a digital filter to retrieve their analog waveforms.

To evaluate the performance of delta-sigma digitization and coherent transmission, we use carrier-to-noise ratio (CNR) of received DOCSIS channels as a measurement. Required CNR for different modulations in DOCSIS 3.1 specifications are listed in **Table 3** [15]. Higher order modulations need higher CNR, and there is 0.5 dB increment for the fifth channel above 1 GHz (1026–1218 MHz). The maximum mandatory modulation in DOCSIS 3.1 specification is 4096QAM. 8192 and 16384QAM are optional, and their CNR requirements are not specified yet. Here we use 44 and 48 dB based on extrapolation. In experiments, CNR is evaluated in terms of modulation error ratio (MER).
