Delta-Sigma Digitization and Optical Coherent Transmission of DOCSIS 3.1 Signals in Hybrid Fiber Coax Networks

We first demonstrate delta-sigma digitization and coherent transmission of data over cable system interface specification (DOCSIS) 3.1 signals in a hybrid fiber coax (HFC) network. Twenty 192-MHz DOCSIS 3.1 channels with modulation up to 16384QAM are digitized by a low-pass cascade resonator feedback (CRFB) delta-sigma analog-to-digital converter (ADC) and transmitted over 80-km fiber using coherent single-λ 128-Gb/s dual-polarization (DP) quadrature phase-shift keying (QPSK) and 256-Gb/s DP-16QAM optical links. Both one-bit and two-bit delta-sigma digitization are implemented and supported by the QPSK and 16QAM coherent transmission systems, respectively. To facilitate its practical application in access networks, the coherent system is built using a low-cost narrow-band optical modulator and RF amplifiers. Modulation error ratio (MER) larger than 50 dB is successfully demonstrated for all 20 DOCSIS 3.1 channels, and high-order modulation up to 16384QAM is delivered over fiber for the first time in HFC networks. The raw DOCSIS data capacity is 54 Gb/s with net user information ∼45 Gb/s. Moreover, the bit error ratio (BER) tolerance is evaluated by measuring the MER performance as BER increases. Negligible MER degradation is observed for BER up to 1.5 × 10−6 and 1.7 × 10−4 for one-bit and two-bit digitization, respectively.


Introduction
Video-intensive services, such as virtual reality and immersive applications are driving the growth of data traffic at user premises in an explosive way, making access networks become a bottleneck of user quality of experience. Various optical and wireless access technologies have been investigated, including passive optical networks (PON) [1][2][3], cloud-radio access networks (C-RAN) [4][5][6][7], and hybrid fiber coax (HFC) networks [8,9]. In the United States, there are more than 50 million subscribers using cable services for broadband access, which is 40% more than digital subscriber line (DSL) and fiber-to-the-home (FTTH) users [10]. Given the emergence of data over cable service interface specification (DOCSIS) 3.1, it is expected that HFC networks will continue to dominate the broadband access market in the United States, delivering fastest access speed to the broadest population.
As a fifth-generation broadband access technology, DOCSIS 3.1 specifications are being commercialized at a historically rapid pace to support ultra-high-resolution videos (4 K/8 K), mobile backhaul/fronthaul (MBH/MFH), and other emerging applications enabled by virtual reality and internet of things [10][11][12][13][14]. DOCSIS 3.1 specifications involve enhancement in both physical and MAC layers, which transform the physical layer signal from single-carrier QAM (SC-QAM) to orthogonal frequency division multiplexing (OFDM), for increased data rate, improved spectral efficiency, and flexible resource allocation. It provides up to 10 Gb/s downstream and 1.8 Gb/s upstream capacities to each subscriber [15,16]. With subcarrier spacing of 25 or 50 kHz, DOCSIS 3.1 specifications support downstream channel bandwidths  MHz, and upstream channel bandwidths 6.4-96 MHz [17][18][19]. Moreover, higher order modulations up to 4096QAM were adopted with optional support of 8192 and 16384QAM [10,15]. Similar to the LTE carrier aggregation in MFH networks [20,21], DOCSIS 3.1 specifications support channel bonding to designate more than one DOCSIS channels to a single user.
The continuous envelope and high peak-to-average power ratio (PAPR) of OFDM signals, on the other hand, make them vulnerable to noise and nonlinear impairments in analog HFC networks [22][23][24]. Combined with demanding carrierto-noise ratio (CNR) requirements of high order modulations (>4096QAM), it is difficult to support DOCSIS 3.1 signals by legacy analog fiber links [15]. In this paper, we for the first time demonstrate the digitization of DOCSIS 3.1 signals to enable the upgrade of fiber distribution networks from analog to digital, so mature digital fiber technologies, e.g., intensity modulation/direct detection (IM/DD) and coherent optical transmission, can be exploited.
To enable digital transmission of DOCSIS 3.1 signals, a digitization interface, i.e., analog-to-digital converter (ADC), is needed in the hub to digitize the analog signals into bits, and a digital-to-analog converter (DAC) is needed in the fiber node to retrieve the analog waveforms from digital bits for the following transmission over coaxial cable plant. Different from conventional Nyquist AD/DA that uses Nyquist sampling rates, such as common public radio interface (CPRI) in MFH networks [25], which has quantization noise evenly distributed in the frequency domain and needs many quantization bits, delta-sigma ADC features high sampling rate but only a few (one or two) quantization bits, and most importantly, it utilizes a noise shaping technique to push the quantization noise out of the signal band, so that signal and noise are separated in the frequency domain, and the in-band CNR of digitized signals can be optimized [26][27][28][29]. Moreover, a simplified DAC design based on low-cost passive filters can be used in the fiber node, which filters out the desired signals, eliminates the out-of-band noise, and at the same time, retrieves the analog waveforms. In the hub, a high-speed delta-sigma ADC is shared by multiple fiber nodes; whereas in each fiber node, only a low-cost passive filter is needed to filter out the desired signal and convert it to the analog waveform. Since there are more fiber nodes than hubs, especially given the fact that fiber node number is continuing to grow due to node segmentation and fiber deep migration, replacing Nyquist DAC with a low-cost passive filter can significantly reduce the cost and complexity of fiber nodes.
In this paper, we for the first time demonstrate the delta-sigma digitization of twenty 192-MHz DOCSIS 3.1 channels with 16384QAM modulation, based on a low-pass cascade resonator feedback (CRFB) delta-sigma ADC. We transmit the digitized bits over 80 km fiber by a low-cost single-λ 128-Gb/s dual-polarization (DP)-QPSK or 256-Gb/s DP-16QAM coherent fiber link. Both one-bit and two-bit delta-sigma digitization are realized and supported by the coherent QPSK/16QAM links, respectively. To facilitate its application in access networks, the coherent fiber link is built using low-cost narrowband RF amplifiers and optical modulator. More than 50 dB modulation error ratio (MER) is achieved for all 20 DOCSIS 3.1 channels, and high order modulation up to 16384QAM is demonstrated and delivered over fiber for the first time in HFC networks. The raw DOCSIS data rate is 54 Gb/s with net user information ~45 Gb/s. The bit error ratio (BER) tolerance of deltasigma digitization is also evaluated and negligible MER performance degradation is observed for BER values up to 1.5 × 10 −6 and 1.7 × 10 −4 , for one-bit and two-bit digitization, respectively.
This chapter is organized as follows. Section 2 discusses the operation principles of delta-sigma digitization. Section 3 presents the experimental setup. Section 4 shows the design of delta-sigma ADC. The experimental results are shown in Section 5. Section 5 concludes the paper.

Operation principles
The architecture of a HFC network is shown in Figure 1. Due to their similarity, a C-RAN architecture is also presented for comparison. In Figure 1(b), the network segment from service gateway (S-GW) or mobile management entity (MME) to Fiber Optics -From Fundamentals to Industrial Applications baseband unit (BBU) is defined as mobile backhaul (MBH), which transmits the control and payload bits of LTE signals in digital baseband. The digital bits are received by BBUs, which synthesizes OFDM modulation and generates analog waveform of LTE signals. The network segment from BBU to remote radio heads (RRH) is defined as mobile fronthaul (MFH), where the LTE signals are transmitted over fiber in either analog waveform using RoF technology or digital waveform using CPRI digitization interface. The last segment of C-RAN involves the wireless transmission from the RRHs to mobile users, where LTE signals are transmitted in their analog waveforms via air interface.
Similarly, HFC networks in Figure 1(a) can also be divided into three segments, i.e., the core network segment from headend to hub, the fiber distribution network from hub to fiber nodes, and the coaxial cable plant from fiber nodes to cable modems (CMs). Similar to MBH, the segment from headend to hub transmits net bit information; similar to MFH, the fiber distribution segment from hub to fiber node is supported by either analog or digital fiber technologies, e.g., C-RAN uses RoF technology to deliver analog mobile signals; HFC uses analog fiber links to deliver analog DOCSIS/video signals; C-RAN uses CPRI as a Nyquist digitization interface; HFC has a similar interface called baseband digital forward or return (BDF/BDR). The last segment from fiber node to CMs is also similar to the wireless segment of C-RAN, where both DOCSIS and LTE signals are transmitted in their analog waveform over coaxial cable or air interface, respectively. Different analog or digital implementations of the fiber distribution segment are shown in Figure 2.

Analog fiber
Figure 2(a) shows the architecture of an analog fiber link. DOCSIS and video signals are aggregated in the hub and delivered to the fiber node in analog waveforms. Then at the fiber node, the received analog signals are delivered to CMs via cable distribution networks. An analog fiber link features simple, low-cost implementation, and high spectral efficiency, but imposes high linearity requirements on channel response. Since it does not perform any data reformation, an analog fiber link is a waveform/service agnostic pipe, and can be used for various services, e.g., DOCSIS, MPEG, and analog TV. On the other hand, it suffers from noise and nonlinear impairments, limited signal-to-noise ratio (SNR), short fiber distance, and small number of WDM wavelengths. It also requires complex RF amplifiers and bi-annual calibration of fiber nodes.

BDF/BDR
Upgrading fiber distribution networks from analog to digital offers the opportunity to leverage the existing mature digital access technologies. Due to the wide  deployment of Ethernet, digital fiber link features low cost, high capacity, long fiber distance, and easy setup/maintenance, as compared with its analog counterpart. Moreover, the contribution of optical noise and nonlinear impairments can be isolated from the received signal quality, so large SNR and high order modulation can be achieved. Since it can support many (>80) WDM wavelengths, digital fiber link facilitates the migration to node split and fiber deep. Figure 2(b-d) shows three different digital fiber technologies. Figure 2(b) shows a digital fiber link based on BDF/BDR architecture, where a Nyquist ADC is inserted in the hub with 2.5 oversampling ratio and 12 quantization bits. At fiber node, a Nyquist DAC retrieves the analog signals, and feeds them to the coaxial cable plant. Same as CPRI, BDF/BDR provides a simple, low-cost, and servicetransparent digitization interface, but with low spectral efficiency. Similar to CPRI, the digitized bits of BDF/BDR are not encapsulated into Ethernet packets but framed by time-division-multiplexing (TDM), so it always runs at full data rate even without any real payload. This makes traffic engineering based on statistical multiplexing impossible. In today's HFC networks, there is only upstream BDR deployed, but no downstream BDF, and the BDR specifications are vendor proprietary and not interoperable.

Remote PHY
Digital fiber link based on remote PHY architecture is shown in Figure 2(c), where the PHY chips for OFDM/QAM modulation and demodulation are moved to fiber node, and an integrated converged cable access platform (CCAP) is separated into the CCAP core in hub and the remote PHY device (RPD) in fiber node [52][53][54][55][56]. In the downstream, payload and control bits are packetized into Ethernet packets and transmitted from hub to fiber node, where the OFDM/QAM modulators synthesize analog DOCSIS/MPEG signals for cable distribution. In the upstream, OFDM/QAM demodulators interpret the received analog signals into baseband bits and transmit back to hub in Ethernet packets. Compared with analog fiber link in Figure 2(a), the RF interface in hub is replaced by an Ethernet interface, and in fiber node, there is an Ethernet interface connecting to the digital fiber and a RF interface connecting to the coaxial cable plant. With the help of Ethernet packetization, remote PHY architecture can exploit Ethernet access technologies, such as Ethernet PON (EPON), gigabit PON (GPON), and Metro Ethernet [52][53][54], and enable statistical multiplexing for traffic engineering. Compared with other digital solutions, remote PHY features smaller traffic load in the fiber, but with the penalty of increased complexity and cost of fiber nodes. Due to the modulation/demodulation at RPD, the fiber link in remote PHY architecture is no longer a service-transparent pipe, although it maintains the least amount of hardware exported to RPD, and preserves the compatibility with existing hubs in analog fiber links. It should be noted that the concepts of remote PHY/MAC are very similar to the function split of MFH networks [57][58][59], by moving partial physical and/or MAC layer functions from the centralized entity (hub/BBU) to a remote node (fiber node/RRH).

Delta-sigma digitization
Figure 2(d) shows the architecture of delta-sigma digitization. Compared with Figure 2(b), Nyquist AD/DA in BDF/BDR are replaced by a delta-sigma ADC in hub and a passive filter in fiber node. Different from the Nyquist ADC with oversampling ratio of 2.5 and 12 quantization bits, delta-sigma ADC trades quantization bits for sampling rate, using high sampling rate but only a few (one or two) quantization bits. Its operation principle is shown in Figure 3. For reference, the operation principle of Nyquist ADC is also presented in Figure 3(a). In this Fiber Optics -From Fundamentals to Industrial Applications paper, we designed a delta-sigma ADC to digitize five DOCSIS 3.1 channels with channel bandwidth of 192 MHz and total frequency range from 258 to 1218 MHz (5 × 192 = 960 MHz). Due to the limited quantization bits, Nyquist sampling rate will lead to significant quantization noise (Figure 3b). Oversampling is utilized to extend Nyquist zone and spread the quantization noise over a wide frequency range, so the in-band noise is reduced (Figure 3c).
Furthermore, noise shaping technique is used to push the quantization noise out of the signal band, which acts as a high-pass filter (HPF) to the quantization noise and separates the signal and noise in the frequency domain, as shown in Figure 3(d). It should be noted that during the delta-sigma digitization, the signal spectrum is kept intact; it is the out-of-band quantization noise added by the deltasigma ADC that converts the signal waveform from analog to digital. Therefore, in Figure 3(e) at the receiver side, when the out-of-band quantization noise is eliminated, the signal waveform will automatically be converted back from digital to analog, i.e., a passive filter can not only filter out the desired signal channel, but also realize the digital-to-analog conversion. In HFC networks, a high-speed delta-sigma ADC is centralized in the hub and shared by many fiber nodes, and each fiber node only needs a low-cost passive filter to select the desired DOCSIS channels and at the same time convert them to the analog waveform. Given the fact that there are many more fiber nodes than hubs/headends, this design significantly reduces the cost and complexity of fiber nodes. It should be note that Nyquist ADC has evenly distributed quantization noise, whereas delta-sigma digitization has a shaped distribution of quantization noise, so the retrieved analog signal has an uneven noise floor.
In time domain, if we use an analog sinusoidal signal as an example, a Nyquist ADC samples the analog input with Nyquist rate and each sample is quantized individually (Figure 3a); whereas delta-sigma ADC samples the analog input at a much higher rate and the samples are digitized consecutively (Figure 3c and d), i.e., the current digitization bits not only depend on the current analog input, but also depend on previous input. One-bit delta-sigma digitization outputs a high data rate on-off keying (OOK) signal with the density of "1" bits being proportional to the amplitude of analog input. For maximum input, it outputs continuous "1"s; for minimum input, it outputs continuous "0"s. For intermediate inputs, the densities of "0"s and "1"s are almost equal. Two-bit digitization outputs a 4-level pulseamplitude-modulation (PAM4) signal. Both one-bit and two-bit digitization are implemented in our experiment.   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 node is only designed for one specific service. 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.

Experimental setup
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  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][36][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  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).

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.

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  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].

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.

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;  Table 4.
Experimental design of one-bit and two-bit delta-sigma digitization. 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.

Experimental results
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 investigate the BER tolerance of delta-sigma digitization. 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 other sampling rates are similar and omitted here for brevity.  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 worst case, channel 3 with lowest MER of 44.5 dB, is shown. 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 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.

BER tolerance
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 −6 , 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   Fiber Optics -From Fundamentals to Industrial Applications of BER, 0, 1.5 × 10 −6 , and 1.1 × 10 −5 were tested, and good consistency is achieved between simulation and experimental results. As BER increases to 2.5 × 10 −6 , 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 −6 . For BER < 2.5 × 10 −6 , 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 −5 . 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 −5 , 5.6 × 10 −5 , 9.5 × 10 −5 , 3 × 10 −4 , 5.2 × 10 −4 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 −4 . The 4096QAM constellation at the threshold BER is shown in Figure 10(c).

Conclusions
In this paper, we proposed and demonstrated delta-sigma digitization and coherent transmission of DOCSIS 3.1 signals for the first time. A low-pass CRFB delta-sigma ADC was designed to digitize 20 × 192-MHz DOCSIS 3.1 channels   with 16384QAM and transmit the digitized RF spectrum over 80 km of fiber via a single-λ 128-Gb/s DP-QPSK or 256-Gb/s DP-16QAM coherent fiber link. Both one-bit and two-bit digitization were realized and supported by QPSK and 16QAM coherent links, respectively. To facilitate its application in HFC networks, a low-cost coherent fiber system was built based on narrowband optical modulator and RF amplifiers. Frequency pre-equalization was exploited to compensate the bandwidth limitation. MER larger than 50 dB was achieved for all 20 DOCSIS 3.1 channels, and high order modulation up to 16384QAM was supported. To date, this is the highest order of modulation transmitted over fiber in HFC networks. BER tolerance of delta-sigma digitization was also evaluated and negligible degradation of MER performance was observed for BER values up to 1.5 × 10 −6 and 1.7 × 10 −4 , for one-bit and two-bit digitization, respectively.