**4. Experimental design**

In this section, we first present the design of delta-sigma ADC and discuss the experimental design, then demonstrate the results of one-bit and two-bit digitization, respectively. Finally, the performance tolerance against the bit error ratio (BER) of the coherent fiber link is also evaluated.

### **4.1 Delta-sigma ADC design**

The design of a fourth-order delta-sigma ADC based on cascaded resonator feedback (CRFB) structure is shown in **Figure 5**. The Z-domain block diagram is shown in **Figure 5(a)**, which consists of an output quantizer, a feedback DAC, and the rest parts can be considered as a filter to the quantization noise. The transfer function of this noise filter is described by a noise transfer function (NTF), which determines the frequency distribution of quantization noise. In **Figure 5(a)**, there are four integrators, and every two of them, 1/(z − 1) and z/(z − 1), are cascaded together to form a resonator (purple and green). The number of integrators equals to the order number of the NTF. A fourth-order NTF also has two conjugate pairs (four in total) of zeroes and poles, shown in **Figure 5(b)**. The frequency response of the NTF is shown in **Figure 5(c)**.

Our design is a low-pass delta-sigma ADC where the signal is located at the low frequency end, and quantization noise is at the high frequency end. So in **Figure 5(c)**, the NTF is a high-pass filter, which pushes the quantization noise to

**79**

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

the high frequency end and separates it from the signal. In the inset of

*Implementation of 32 GSa/s delta-sigma ADC. (a) Z-domain block diagram of a fourth-order cascade resonator feedback (CRFB) structure. (b) Zeroes and poles of the noise transfer function (NTF). (c) Frequency* 

**Figure 5(c)**, there are two notches in the stopband of the NTF, each corresponding to one pair of zeroes in **Figure 5(b)**. At the zeroes of NTF, quantization noise is minimized and signals at these frequency points have a maximized CNR. It should be noted that the only difference of one-bit and two-bit digitization is the quantizer at the output and the feedback DAC. Their NTFs are identical. The number of output levels is determined by the number of quantization bits. A log2(N)-bit quantizer outputs N levels, so one-bit quantizer outputs an OOK signal, and two-bit quantizer outputs a PAM4 signals. More details of delta-sigma

To evaluate the performance of delta-sigma digitization, 10 experimental cases are designed, shown in **Table 4**. Five DOCSIS 3.1 channels are digitized by deltasigma ADCs with sampling rates of 16, 20, 24, 28, and 32 GSa/s. Both one-bit (Case I-V) and two-bit (Case VI-X) digitization are carried out, and the fiver DCOSIS channels are digitized to a 16–32 Gbaud OOK (one-bit) or PAM4 (two-bit) signal, respectively. The signal baud rate after digitization is equal to the sampling rate of ADC. In a dual-polarization coherent fiber link, each polarization has I and Q components, and each component carries one OOK/PAM4 signal, so there are four data streams in total carrying 20 digitized channels. Due to the symmetry, only 5

Unlike Nyquist ADC, whose quantization noise is evenly distributed in the Nyquist zone, delta-sigma ADC has uneven noise floor due to the noise shaping technique. In experiments, different modulations are assigned to different channels according to their CNRs, e.g., in Case V, only Ch. 2 has sufficient CNR to support 16384QAM, Ch. 4 can only support 4096QAM, and the rest three can carry 8192QAM. In general, higher sampling rate leads to wider Nyquist zone and smaller in-band quantization noise, so higher modulation can be supported. Two-bit digitization always has smaller quantization noise thanks to the additional bit. Therefore,

in Case IX and X, all five channels have sufficient CNR to carry 16384QAM.

Spectral efficiency is an important figure of merit for digitization interfaces, and it is insightful to make a comparison of two digitization interfaces in terms of spectral efficiencies. Since DOCSIS 3.1 channels can support various modulations from 16QAM up to 4096QAM, the net data capacity per channel may vary dramatically;

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

ADC design can be founded in Ref [28, 29].

out of 20 DOCSIS 3.1 channels are listed in **Table 4**.

**4.3 Comparison with Nyquist ADC**

**4.2 Experimental cases**

**Figure 5.**

*response of the NTF.*

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

#### **Figure 5.**

*Fiber Optics - From Fundamentals to Industrial Applications*

*+CNR values in parentheses with 0.5-dB increment are for channels above 1 GHz.*

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

*we use 44(44.5) and 48(48.5) dB as temporary criteria.*

**Table 3.**

out by a digital filter to retrieve their analog waveforms.

terms of modulation error ratio (MER).

(BER) of the coherent fiber link is also evaluated.

**4. Experimental design**

**4.1 Delta-sigma ADC design**

the NTF is shown in **Figure 5(c)**.

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

**QAM 16 64 128 256 512 1024 2048 4096 8192\* 16384\*** CNR (dB) 15 21 24 27 30.5 34 37 (37.5)+ 41 (41.5)+ 44 (44.5)+ 48 (48.5)+ *\*For DOCSIS 3.1 downstream, 8192QAM and 16384QAM are optional, and their CNRs are not specified yet. Here* 

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

In this section, we first present the design of delta-sigma ADC and discuss the experimental design, then demonstrate the results of one-bit and two-bit digitization, respectively. Finally, the performance tolerance against the bit error ratio

The design of a fourth-order delta-sigma ADC based on cascaded resonator feedback (CRFB) structure is shown in **Figure 5**. The Z-domain block diagram is shown in **Figure 5(a)**, which consists of an output quantizer, a feedback DAC, and the rest parts can be considered as a filter to the quantization noise. The transfer function of this noise filter is described by a noise transfer function (NTF), which determines the frequency distribution of quantization noise. In **Figure 5(a)**, there are four integrators, and every two of them, 1/(z − 1) and z/(z − 1), are cascaded together to form a resonator (purple and green). The number of integrators equals to the order number of the NTF. A fourth-order NTF also has two conjugate pairs (four in total) of zeroes and poles, shown in **Figure 5(b)**. The frequency response of

Our design is a low-pass delta-sigma ADC where the signal is located at the low frequency end, and quantization noise is at the high frequency end. So in **Figure 5(c)**, the NTF is a high-pass filter, which pushes the quantization noise to

**78**

*Implementation of 32 GSa/s delta-sigma ADC. (a) Z-domain block diagram of a fourth-order cascade resonator feedback (CRFB) structure. (b) Zeroes and poles of the noise transfer function (NTF). (c) Frequency response of the NTF.*

the high frequency end and separates it from the signal. In the inset of **Figure 5(c)**, there are two notches in the stopband of the NTF, each corresponding to one pair of zeroes in **Figure 5(b)**. At the zeroes of NTF, quantization noise is minimized and signals at these frequency points have a maximized CNR. It should be noted that the only difference of one-bit and two-bit digitization is the quantizer at the output and the feedback DAC. Their NTFs are identical. The number of output levels is determined by the number of quantization bits. A log2(N)-bit quantizer outputs N levels, so one-bit quantizer outputs an OOK signal, and two-bit quantizer outputs a PAM4 signals. More details of delta-sigma ADC design can be founded in Ref [28, 29].

### **4.2 Experimental cases**

To evaluate the performance of delta-sigma digitization, 10 experimental cases are designed, shown in **Table 4**. Five DOCSIS 3.1 channels are digitized by deltasigma ADCs with sampling rates of 16, 20, 24, 28, and 32 GSa/s. Both one-bit (Case I-V) and two-bit (Case VI-X) digitization are carried out, and the fiver DCOSIS channels are digitized to a 16–32 Gbaud OOK (one-bit) or PAM4 (two-bit) signal, respectively. The signal baud rate after digitization is equal to the sampling rate of ADC. In a dual-polarization coherent fiber link, each polarization has I and Q components, and each component carries one OOK/PAM4 signal, so there are four data streams in total carrying 20 digitized channels. Due to the symmetry, only 5 out of 20 DOCSIS 3.1 channels are listed in **Table 4**.

Unlike Nyquist ADC, whose quantization noise is evenly distributed in the Nyquist zone, delta-sigma ADC has uneven noise floor due to the noise shaping technique. In experiments, different modulations are assigned to different channels according to their CNRs, e.g., in Case V, only Ch. 2 has sufficient CNR to support 16384QAM, Ch. 4 can only support 4096QAM, and the rest three can carry 8192QAM. In general, higher sampling rate leads to wider Nyquist zone and smaller in-band quantization noise, so higher modulation can be supported. Two-bit digitization always has smaller quantization noise thanks to the additional bit. Therefore, in Case IX and X, all five channels have sufficient CNR to carry 16384QAM.

### **4.3 Comparison with Nyquist ADC**

Spectral efficiency is an important figure of merit for digitization interfaces, and it is insightful to make a comparison of two digitization interfaces in terms of spectral efficiencies. Since DOCSIS 3.1 channels can support various modulations from 16QAM up to 4096QAM, the net data capacity per channel may vary dramatically;



**81**

**Figure 6.**

*16QAM at each baud rate.*

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

but the frequency band of five downstream DOCSIS 3.1 channels are always the same, from 258 to 1218 MHz. Therefore, to make a fair comparison, we can use the

In **Table 4**, for one-bit delta-sigma ADC, depending on the sampling rate, 16–32 Gb/s fiber link capacity is needed to support five digitized channels. For Case V (32 GSa/s), all five channels can support at least 4096QAM, within which at least three of them can support 8192QAM and one can carry up to 16384QAM. For twobit ADC, the required bit number doubles. On the other hand, consider the Nyquist ADC defined in BDR/BDF with 2.5 oversampling ratio and 12 quantization bits, it requires 1218 × 2.5 MSa/s × 12 b/Sa = 36.54 Gb/s to digitize five DOCSIS channels. Compared with Nyquist ADC, one-bit delta-sigma ADC can save at least 12.4% (Case V) fiber link capacity. If CNR requirements can be relaxed, and lower sampling rate are allowed, it can save up to 56.2% (Case I) fiber link capacity. For twobit delta-sigma ADC, although it provides much higher CNR, it generates more bits after digitization and consumes more fiber link capacity than Nyquist ADC. The main advantage of applying delta-sigma digitization in HFC networks is to simplify fiber node design by replacing the conventional DAC by a low-cost passive filter.

In this section, we first demonstrate the experimental results of DP-QPSK and DP-16QAM coherent transmission, and then discuss the results of one-bit and two-bit digitization supported by QPSK/16QAM, respectively. Finally, we will

**Figure 6** shows the results of coherent transmission of DP-QPSK/16QAM, where error vector magnitude (EVM) is plotted as a function of baud rate. Due to the limited bandwidth of low-cost RF amplifiers and the optical IQ MZM, EVM increases with baud rate. **Figure 6(b)** shows the constellations at each baud rate. For DP-QPSK, error free transmission can be achieved for all baud rates. For DP-16QAM, error free transmission is only achievable for 16 and 20 Gbaud. BER values for 24, 28 and 32 Gbaud are labeled in **Figure 6(a)**. In the following discussion, we only present the results of 32 GSa/s delta-sigma digitization. Results of

*Coherent transmission results of low-cost DP-QPSK and DP-16QAM systems, for one-bit and two-bit digitization, respectively. (a) Error vector magnitude (EVM) vs. baud rate. (b) Constellations of QPSK and* 

number of bits needed to digitize five DOCSIS channels as a reference.

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

Improvement of spectral efficiency is a side effect.

investigate the BER tolerance of delta-sigma digitization.

other sampling rates are similar and omitted here for brevity.

**5. Experimental results**

**5.1 Coherent transmission**

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

but the frequency band of five downstream DOCSIS 3.1 channels are always the same, from 258 to 1218 MHz. Therefore, to make a fair comparison, we can use the number of bits needed to digitize five DOCSIS channels as a reference.

In **Table 4**, for one-bit delta-sigma ADC, depending on the sampling rate, 16–32 Gb/s fiber link capacity is needed to support five digitized channels. For Case V (32 GSa/s), all five channels can support at least 4096QAM, within which at least three of them can support 8192QAM and one can carry up to 16384QAM. For twobit ADC, the required bit number doubles. On the other hand, consider the Nyquist ADC defined in BDR/BDF with 2.5 oversampling ratio and 12 quantization bits, it requires 1218 × 2.5 MSa/s × 12 b/Sa = 36.54 Gb/s to digitize five DOCSIS channels.

Compared with Nyquist ADC, one-bit delta-sigma ADC can save at least 12.4% (Case V) fiber link capacity. If CNR requirements can be relaxed, and lower sampling rate are allowed, it can save up to 56.2% (Case I) fiber link capacity. For twobit delta-sigma ADC, although it provides much higher CNR, it generates more bits after digitization and consumes more fiber link capacity than Nyquist ADC. The main advantage of applying delta-sigma digitization in HFC networks is to simplify fiber node design by replacing the conventional DAC by a low-cost passive filter. Improvement of spectral efficiency is a side effect.
