I. Introduction

The explosive growth of mobile data caused by millimeter wave small cells, carrier aggregation (CA), and massive multiple-input multiple-output (MIMO) has led to significant challenges to the existing optical and wireless access networks. To enhance the capacity and coverage of mobile networks, a new cloud-radio access network (C-RAN) architecture [1–3] has been proposed to consolidate signal processing and management functions into the baseband processing units (BBUs), thus dividing radio access networks (RANs) into two segments, i.e., mobile backhaul (MBH) from core network to BBUs and mobile fronthaul (MFH) from BBUs to remote radio heads (RRHs) [4–6].

In 5G mobile data networks, to accommodate broadband wireless services from various radio access technologies (RATs), both analog and digital MFH architectures have been investigated. Analog MFH based on radio-over-fiber (RoF) technologies features simple, low-cost implementations, high spectral efficiency, and RAT/waveform transparency, and has been experimentally demonstrated by exploiting digital signal processing (DSP)-enabled carrier aggregation [7,8], analog carrier aggregation [9], and intermediate frequency over fiber [10] technologies. Since most air interfaces utilize multicarrier waveforms, which have continuous envelope and high peak-to-average power ratio (PAPR), analog MFH is susceptible to noise and transmission impairments. Nonlinear distortions of analog MFHs have been investigated extensively for both single-carrier [11] and multicarrier signals [12,13], and linearization techniques based on polynomial-memory predistortion have been demonstrated [14]. For 5G heterogeneous mobile data networks, however, it would be challenging to dynamically track and compensate the nonlinear channel response, especially given the fact of broadband time-varying data traffic from multiple RATs.

Digital MFHs, on the other hand, sample and quantize the continuous waveforms of mobile signals using a digitization interface, and transport the digitized bit/symbol streams by leveraging existing optical intensity modulation-direct detection (IM-DD) links. Thanks to the digitization interface, digital MFH offers excellent tolerance against transmission impairments with the penalty of relatively low spectral efficiency. For example, common public radio interface (CPRI) digitizes each LTE signal using a Nyquist analog-to-digital converter (ADC) with sampling rate of 30.72 MSa/s and 15 quantization bits. According to the CPRI data rate options [15], each LTE component carrier (CC) consumes 1.23-Gb/s fronthaul capacity (option 2), and to support eight LTE CCs (option 7) it can take up to 9.83-Gb/s fronthaul capacity. On the other hand, the rapidly growing LTE carrier aggregation (CA) makes CPRI become the data rate bottleneck of digital MFH. LTE CA was initially standardized by 3GPP release 10, allowing 5 CCs [16], and then quickly expanded to 32 CCs by 3GPP release 13 [17], consuming up to 40-Gb/s fronthaul capacity if digitized by CPRI, which cannot be supported by any existing optical/wireless access network. I/Q compression of CPRI with $\sim 50\%$ compression ratio has been demonstrated [18,19]. Compressed CPRI over time-division-multiplexed passive optical network (TDM-PON) [20], uncompressed CPRI over wavelength-division-multiplexed passive optical network (WDM-PON) [21], and split physical layer (split-PHY) functions [22] have also been investigated.

To circumvent the data-rate bottleneck of CPRI and increase the fronthaul capacity, one promising solution is to replace the Nyquist ADC of CPRI by a delta–sigma modulator, where an oversampling ADC samples a carrier-aggregated LTE signal with a sampling rate much higher than its Nyquist rate [23] and utilizes a noise-shaping technique to push the quantization noise out of the signal band to optimize the in-band signal-to-noise ratio (SNR) of the digitized signal [24–26]. The quantization noise of a Nyquist ADC is evenly distributed in the Nyquist zone [27], whereas delta–sigma modulators have an uneven noise floor due to noise shaping. Delta–sigma modulation has been employed by RF transmitters [28–36], power amplifiers [37–39], wireless receivers [40–45], fiber-wireless transmissions [46–48], and visible light communications [49,50]. There have been quite a few works reported about high-speed delta–sigma modulators with sampling rate up to several GSa/s [31–36].

In Ref. [51], we first demonstrated delta–sigma modulation as a new digitization interface for digital MFH networks to replace the conventional CPRI, and realized 32 LTE CA for 3GPP release 13. Compared with CPRI-based MFH, the fronthaul capacity was increased by four times at the penalty of error vector magnitude (EVM) performance. Moreover, due to the pre-emphasis technique used in [51], 32 LTE CCs have unequal power for wireless emission, and high-frequency CCs cannot support high-order modulations due to the large quantization noise. In this paper, we extend our previous work with improved noise transfer function and demonstrate both one-bit and two-bit delta–sigma modulations. The digitized signals were transmitted using optical single-$\lambda$ 10-Gb/s on–off keying (OOK) or 10-Gbaud 4-level pulse-amplitude-modulation (PAM4) IM-DD links, respectively. Carrier aggregation of 32 LTE CCs was realized to support 3GPP release 13, and EVMs less than 5% and 2.1% were obtained for one-bit and two-bit delta–sigma modulators, respectively, so that high-order modulation formats (256QAM/1024QAM) can be supported. Compared with CPRI, the fronthaul capacity is increased by four times without significant sacrifice of EVM performance. As a waveform-agnostic digitization interface, delta–sigma modulators can work with not only 4G-LTE but also 5G multicarrier waveforms, and their 5G compatibility was verified by filter-bank-multicarrier (FBMC) signals.

II. Operation Principles

A C-RAN architecture is shown in Fig. 1(a), with three different MFH implementations illustrated in Figs. 1(b)–1(d). Figure 1(b) shows an analog MFH architecture based on RoF technologies, where mobile signals are aggregated in BBUs and delivered to RRHs in their analog waveforms without digitization. It features simple, low-cost implementation and high spectral efficiency but imposes high linearity requirements on the channel response of MFH links. Digital MFH architectures based on two digitization interfaces, CPRI and delta–sigma modulation, are presented in Figs. 1(c) and 1(d), respectively, where the analog mobile signals are first digitized into a bit/symbol stream and then delivered to RRHs via an optical digital IM-DD link.

 

Fig. 1. (a) Typical architecture of a cloud-radio access network (C-RAN), including the mobile backhaul (MBH) network from the service-gateway (S-GW) or the mobile management entity (MME) of the core network to baseband processing units (BBUs), and the mobile fronthaul (MFH) network from BBUs to remote radio heads (RRHs). (b) Analog MFH based on radio-over-fiber (RoF) technologies. (c) Digital MFH based on common public radio interface (CPRI). (d) Digital MFH based on delta–sigma modulation.

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A. Common Public Radio Interface (CPRI)

The operation principles of two digitization interfaces are illustrated in Fig. 2. In Fig. 2(a), CPRI exploits a Nyquist ADC with a sampling rate of 30.72 MSa/s, and uses 15 quantization bits and one control bit per sample. The quantization noise of a Nyquist ADC is evenly distributed in the Nyquist zone in the frequency domain, which can be approximated by Gaussian white noise [27]. To reduce the quantization noise and increase the SNR of the digitized signal, a large number of quantization bits are needed, leading to low spectral efficiency and tremendous data bandwidth after digitization, making CPRI become the data rate bottleneck of digital MFH networks. Table I lists the standard data rate options of CPRI. Line coding of 8b/10b or 64b/66b is used for DC balance, disparity check, and to ensure sufficient 0/1 transitions for clock recovery. In option 1, each I or Q component of a 20 MHz LTE CC consumes fronthaul capacity of $30.72\mathrm{MSa}/\mathrm{s}\times 16\mathrm{bit}/\mathrm{Sa}\times 10/8=614.4\mathrm{Mb}/\mathrm{s}$; in option 2, each 20-MHz LTE CC consumes 1.23 Gb/s (including both I and Q); for 10-Gb/s PON, only 8 LTE CCs can be accommodated (option 7). In order to support 32 CA of 3GPP release 13, up to 40-Gb/s fronthaul capacity is required, which cannot be supported by existing optical/wireless access networks. It is worth noting that CPRI digitizes each LTE carrier individually, and it works in a symmetric way for downstream and upstream. Both BBUs and RRHs are equipped with a Nyquist ADC as the CPRI interface. It works at a fixed chip rate (integer multiples of 3.84 MHz), and can accommodate LTE, WiMAX, and GSM signals.

 

Fig. 2. Operation principles of two digitization interfaces of digital MFH networks. (a) CPRI is based on a Nyquist ADC with a 30.72-MSa/s sampling rate and 15 quantization bits per sample. (b) Delta–sigma modulation only uses one or two quantization bits, which leads to significant quantization noise if sampled at the Nyquist rate. (c) Oversampling extends the Nyquist zone, so that quantization noise can be spread over a wider frequency range. (d) The noise transfer function acts as a low-pass filter to the signal and a high-pass filter to the noise, so that quantization noise is pushed out of the signal band, and the signal and noise are separated in the frequency domain. (e) Low-pass filtering eliminates the out-of-band quantization noise and retrieves the original analog signal.

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TABLE I. CPRI Data Rate Options [15]

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B. Delta–Sigma Modulation

Delta–sigma modulation, on the other hand, exploits an oversampling ADC and only a few (one or two) quantization bits. Due to the limited number of quantization bits, Nyquist sampling would lead to significant quantization noise, as shown in Fig. 2(b). Therefore, in a delta–sigma modulator, oversampling is used to extend the Nyquist zone, as shown in Fig. 2(c), so that the quantization noise is spread over a wide frequency range to reduce the in-band noise.

Moreover, a noise-shaping technique is exploited to push the quantization noise out of the signal band. For low-pass delta–sigma modulation in Fig. 2(d), signals are located at the low-frequency end, whereas noise is located at the high-frequency end. The noise transfer function acts as a low-pass filter to signal and a high-pass filter to noise, so that the signal and noise are separated in the frequency domain. After digitization, the output of a delta–sigma modulator is an oversampled bit/symbol stream whose low-frequency components follow the analog input and high-frequency components are contributed by the quantization noise, as shown in Fig. 2(d). For a sinusoidal analog input, one-bit quantization generates an OOK (0/1) output with the density of “1”s proportional to the amplitude of analog input. When the input is close to its maximum, the output contains almost all “1”s; when the input is close to its minimum, the output contains all “0”s. For intermediate inputs, the output has equal density of “0”s and “1”s.

This is a key difference from Nyquist ADC, where analog signals are sampled at their Nyquist frequencies, with each sample quantized individually. Oversampling ADC, on the other hand, samples an analog signal at a much higher rate than its Nyquist frequency and digitizes these samples consecutively. Its output is a high-data-rate bit stream whose amplitude follows the input amplitude after a weighted moving average. Since averaging is essentially a low-pass filtering, a low-pass filter (LPF) can smooth out the high-frequency oscillation of the bit stream and retrieve the original analog signal. This can also be explained more intuitively in the frequency domain, as shown in Fig. 2(e). In RRH, a LPF filters out the original signal. Since the out-of-band quantization noise is eliminated, the original analog waveform can be retrieved. Note that the retrieved signal has an uneven noise floor due to the noise shaping.

In our experiments, we use a 10-GSa/s delta–sigma modulator to digitize 32 LTE CCs into a 10-Gb/s OOK or 10-Gbaud PAM4 signal transmitted over a single-$\lambda$ optical IM-DD link. Compared with CPRI option 7 (8 LTE CCs requiring 10-Gb/s fronthaul capacity), the fronthaul capacity is increased by four times. As a waveform-agnostic digitization interface, the delta–sigma modulator works with not only orthogonal-frequency-division-multiplexing (OFDM) signals such as 4G-LTE, Wi-Fi, and WiMAX but also 5G multicarrier waveforms. In Section III, its 5G compatibility was verified by FBMC signals. A detailed comparison of three MFH technologies is summarized in Table II.

TABLE II. Comparison of Three MFH Technologies: ROF-Based Analog MFH, CPRI-Based Digital MFH, and Delta–Sigma Modulation-Based Digital MFH

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It is worth noting that CPRI digitizes each LTE carrier individually, and it works in a symmetric way for downstream and upstream. Both BBUs and RRHs need to be equipped with a Nyquist ADC as the CPRI interface. Delta–sigma modulation, on the other hand, digitizes the LTE signal after carrier aggregation, and is able to work in an asymmetric way by leveraging the asymmetric signal bandwidth of downstream and upstream. Due to the tree architecture of MFH networks and large number of RRHs, many RRHs share a common BBU, and the downstream signal bandwidth from a BBU to multiple RRHs is much wider than the upstream bandwidth from each RRH to the common BBU. Therefore, for downstream, a high-speed oversampling ADC is centralized in the BBU and shared by multiple RRHs, and each RRH only needs a low-cost LPF to retrieve the original LTE signal, which can reduce the cost significantly considering the large number of RRHs in the network. For upstream, each RRH is equipped with a delta–sigma modulator with a sampling rate much lower than the downstream modulator in the BBU due to the small bandwidth of upstream signals. By leveraging the asymmetric downstream/upstream bandwidths and simplified DAC design based on a LPF, delta–sigma modulation can lower the overall system cost of MFH networks.

There have been quite a few works demonstrating high-speed delta–sigma modulators with sampling rates in the range of 3–8 GSa/s [31–36]; however, there is no 10-GSa/s delta–sigma modulator reported to our knowledge. For proof-of-concept experiments, we use a 10-GSa/s modulator which is realized by an arbitrary waveform generator (AWG). But for real implementations, to alleviate the ADC speed limit, a 10-GSa/s delta–sigma modulator can be replaced by four parallel 2.5-GSa/s modulators or eight 1.25-GSa/s modulators, and the output bit streams from multiple modulators are interleaved together in the time domain by TDM technology. In this way, the sampling rate of each modulator is reduced by four/eight times, while keeping the overall fronthaul capacity unchanged. A 10-GSa/s modulator with an oversampling ratio (OSR) of 8 can digitize 32 LTE CCs, with the signal band ranging from 0 to 625 MHz; a 2.5-GSa/s modulator with the same OSR is able to digitize 8 LTE CCs with a signal band of 0–156.25 MHz, so four modulators in total still support 32 LTE CCs.

III. Experimental Setup

The experimental setup is shown in Fig. 3(a). We use a 10G-PON compatible architecture with a BBU located in the optical line terminal (OLT) and RRHs in optical network units (ONUs). In the BBU, 32 LTE CCs are aggregated by DSP with a sampling rate at 1.25 GSa/s, then fed into a delta–sigma modulator with an OSR of 8, where the analog input is first oversampled to 10 GSa/s and then digitized into a 10-Gb/s OOK or 10-Gbaud PAM4 signal by one-bit or two-bit quantization, respectively. With $\mathrm{OSR}=8$, in order to keep the analog input signal real, the available bandwidth to accommodate LTE signals is 625 MHz. A 1554-nm DFB laser is used in the OLT, followed by a Mach–Zehnder modulator. After 25-km single-mode fiber, a 10-GHz photodetector in the ONU receives the OOK or PAM4 signal, captured by a real-time digital storage oscilloscope. In our experiments, delta–sigma modulation was realized by a Tektronix 7122C AWG.

 

Fig. 3. (a) Experimental setup. (b) Signal waveforms and eye-diagram of one-bit digitization: analog LTE signal (red) before delta–sigma modulation at point i; 10-Gb/s OOK (blue) after delta–sigma modulation at point ii; retrieved analog signal (green) after the LPF at point iii. (c) Signal waveforms and eye-diagram of two-bit digitization: analog signal (red) at point i; 10-Gbaud PAM4 (blue) at point ii; retrieved analog signal (green) at point iii.

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The measured waveform and eye diagrams of one-bit quantization are shown in Fig. 3(b). At point i, the input analog signal before the delta–sigma modulator is plotted in red; at point ii, the output OOK signal after the delta–sigma modulator is plotted in blue; at point iii, the retrieved LTE signal after the LPF in the RRH is plotted in green. The difference between the original (red) and retrieved (green) signals is caused by quantization noise. Results of two-bit quantization are shown in Fig. 3(c), where the difference between the original (red) and retrieved (green) waveforms are much smaller than Fig. 3(a) due to the reduced quantization noise contributed by the additional quantization bit. The eye diagrams of OOK and PAM4 are shown in the insets, where the central dots are caused by zero-padding of the AWG between successive data patterns. The PAM4 eye diagram has unequal intensities of $\pm 1$ and $\pm 3$ levels, which is because the OFDM-based signal has Gaussian distribution and so, after digitization, there are many more $\pm 1$ samples than $\pm 3$ samples.

IV. Experimental Results

As shown in Table III, five experimental cases are designed to evaluate the performance of delta–sigma modulation as a new digitization interface to replace CPRI for digital MFH networks. The order of a delta–sigma modulator, by definition, is the number of cascaded integrators, resonators, or feedback loops used in the modulator [25] and also equals the number of zeroes or poles of the noise transfer function. On the other hand, the quantization bit number determines the number of output levels of the quantizer used in a delta–sigma modulator, e.g., a ${\log }_2\mathrm{N}$-bit quantizer outputs N levels, so a one-bit quantizer outputs an OOK signal and a two-bit quantizer outputs a PAM4 signal.

TABLE III. Experimental Designs of Delta–Sigma Modulation-Based Digital MFH and ROF-Based Analog MFH

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In our experiments, for Cases I and II, we designed a simple second-order one-bit delta–sigma modulator based on a cascade-of-resonators feedforward (CRFF) structure, whose noise transfer function is shown in Table III with both zeroes located at DC ($f=0$, $z=1$). By using this modulator, digitization of 32 carrier-aggregated LTE signals and 30 FBMC signals was demonstrated in [51]. Cases I and II suffer from uneven noise floor and EVM penalty at high-frequency CCs due to the large quantization noise at these frequencies. To improve the performance of high-frequency CCs, pre-emphasis is needed to boost up the signal power of these CCs. In this paper, we designed a new fourth-order CRFF delta–sigma modulator which exploits a zero-spreading technique to move the zeroes away from DC to reduce the in-band quantization noise. The fourth-order noise transfer function is shown in Section III, and both one-bit and two-bit digitizations are realized in Cases III and IV, respectively. Carrier aggregation of 32 LTE CCs within a 10G-PON optical IM-DD link was implemented, so that 3GPP release 13 can be supported. EVM performance of all 32 CCs are reduced to less than 5% or 2.1% in Cases III and IV, respectively, and high-order modulation formats, such as 256QAM and 1024QAM, can be supported. Compared with CPRI, which only supports 8 LTE CCs within a 10-Gb/s fronthaul link, delta–sigma modulation is able to aggregate 32 LTE CCs within the same fronthaul link and increase the fronthaul capacity by four times without significant EVM penalty. The EVM requirements of four LTE modulation formats (QPSK, 16QAM, 64QAM, and 256QAM) have been specified by 3GPP release 12 [52], which are listed in Table IV. The EVM requirement of 1024QAM has not been specified yet, and we use 1% as a temporary criterion. It should be noted that these EVM specifications are performance criteria of MFH links from the BBU up to the RRH, excluding the wireless air transmission of LTE signals [53].

TABLE IV. 3GPP Specifications of EVMs for Various Modulation Formats [52]

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Low-pass delta–sigma modulation is used in Cases I–IV, where signals are located in the low-frequency end and quantization noise at the high-frequency end. At the RRH, a LPF eliminates the out-of-band noise and retrieves the original analog signal, and an IF/RF conversion is needed to up-convert the mobile signals to their wireless transmission frequencies before feeding to the air interface. To make a fair comparison with analog MFH, we design Case V, where 24 LTE CCs, each carrying 64QAM, are aggregated together and transmitted in their analog waveform using RoF technology. The experimental setup of Case V is similar to Fig. 3 without digitization interface.

A. Case I

The experimental results of Case I are shown in Fig. 4. The $Z$-domain block diagram of a second-order delta–sigma modulator based on CRFF structure is presented in Fig. 4(a), with the zeroes and poles of its noise transfer function shown in Fig. 4(b). 32 LTE CCs are aggregated within a single-$\lambda$ 10-Gb/s OOK link, with 18 CCs carrying 64QAM, and 14 CCs carrying 16QAM. Electrical spectra of 32 CCs after delta–sigma modulation are shown in Fig. 4(c), where LTE CCs are aggregated in the low-frequency end and quantization noise is pushed to the high-frequency end. Figure 4(d) is a zoom-in of Fig. 4(c). Each LTE CC has 20-MHz bandwidth with 1200 data-carrying subcarriers. Subcarrier spacing of 15.26 kHz is used to accommodate the sampling rate of our AWG, and a 763-kHz guard band is inserted between neighboring CCs. Thanks to the digitization, 32 LTE CCs can be aggregated closely without severe inter-carrier interference. EVMs of all 32 CCs are shown in Fig. 4(e), where 18 CCs have $\mathrm{EVM}<8\%$ to support 64QAM and the remaining 16 CCs have $\mathrm{EVM}<12.5\%$ to support 16QAM. The EVMs of all the CCs comply with the 3GPP specifications listed in Table IV. Constellations of CC 1, 18, 19, and 32 are shown in Fig. 4(f), corresponding to the best and worst cases of 64QAM and 16QAM, respectively.

 

Fig. 4. Experimental results of Case I. (a) $Z$-domain block diagram of a second-order delta–sigma modulator based on CRFF structure. (b) Zeroes and poles of the noise transfer function. (c),(d) Electrical spectra of 32 carrier aggregated LTE signals after delta–sigma modulation. (d) is a zoom-in of (c). (e) EVMs of all 32 LTE CCs, including 18 CCs carrying 64QAM and 14 CCs carrying 16QAM. (f) Constellations of the best and worst cases for 64QAM and 16QAM, respectively.

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Due to the uneven noise floor, high-frequency CCs suffer from severe EVM penalties. The motivation of pre-emphasis is to improve the performance of high-frequency CCs by boosting up their signal power. However, since the second-order noise transfer function used in Cases I and II has two degenerated zeroes, both located at DC ($f=0$, $z=1$), low-frequency CCs, which are closer to the zeroes, have much smaller quantization noise than high-frequency CCs. The pre-emphasis technique can only increase the signal power but is not able to eliminate the residual quantization noise left in the signal band due to the imperfect noise shaping. The performance of high-frequency CCs is improved, but still not as good as that of low-frequency CCs.

Moreover, pre-emphasis makes the aggregated LTE CCs have unequal power, which needs to be re-equalized before feeding to the air interface for wireless transmission. In Cases III and IV, a fourth-order noise transfer function is used to realize a steeper high-pass filter for quantization noise and push more noise out of the signal band. A zero-spreading technique is exploited to separate the zeroes and move them away from DC, so that the quantization noise is more evenly distributed across all LTE CCs rather than concentrated in the high-frequency CCs.

B. Case II

As a waveform-agnostic digitization interface, delta–sigma modulation can digitize not only OFDM signals, but also 5G multicarrier waveforms. We verify its 5G compatibility by FBMC signals. In Figs. 5(a) and 5(b), 30 FBMC CCs are aggregated within a single-$\lambda$ 10-Gb/s OOK link. Each FBMC CC is filtered by a Nyquist filter with coefficients of $H=[0,0.972,0.707,0.235]$ and has an overlap factor of 4. The EVMs of all 30 CCs are shown in Fig. 5(c). According to the 3GPP specifications in Table IV, there are 10 CCs with $\mathrm{EVM}<3.5\%$, which can support 256QAM; 8 CCs with $\mathrm{EVM}<8\%$, which can support 64QAM; 6 CCs with $\mathrm{EVM}<12.5\%$ for 16QAM; and 6 CCs with $\mathrm{EVM}<17.5\%$ for QPSK. It should be noted that the carrier aggregation number is limited to 30 due to the imperfect noise transfer function and high PAPR of FBMC signals.

 

Fig. 5. Experimental results of Case II. (a, b) Electrical spectra of 30 carrier aggregated FBMC signals after delta–sigma modulation. (b) is a zoom-in of (a). (c) EVMs of all 30 FBMC CCs, including 10 CCs carrying 256QAM, 8 CCs carrying 64QAM, 6 CCs carrying 16QAM, and the remaining 6 CCs carrying QPSK. (d) Constellations of the best and worst cases for each modulation format.

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C. Case III

In Cases I and II, high-frequency CCs suffer from severe EVM penalty due to the uneven noise floor caused by imperfect noise shaping. In Cases III and IV, a new fourth-order noise transfer function is designed to form a steeper high-pass filter for quantization noise, so that more noise is pushed out of the signal band. A zero-spreading technique is also used to separate the zeroes and move them away from DC, so the quantization noise can be evenly distributed across all CCs rather than concentrated on high-frequency CCs. The experimental results of Case III are presented in Fig. 6, where the $Z$-domain block diagram of a fourth-order delta–sigma modulator based on CRFF structure is shown in Fig. 6(a) and the zeroes and poles of its noise transfer function are shown in Fig. 6(b). The electrical spectra of 32 LTE CCs are shown in Figs. 6(c) and 6(d). In Fig. 6(e), the EVMs of all CCs are reduced to less than 5%, with 16 CCs having $\mathrm{EVM}<3.5\%$, which can carry 256QAM, and the other 16 with $\mathrm{EVM}<5\%$ to support 64QAM. Constellations of CC 12, 17, 6, and 32 are shown in Fig. 6(f), corresponding to the best and worst cases of 256QAM and 64QAM, respectively.

 

Fig. 6. Experimental results of Case III. (a) $Z$-domain block diagram of a fourth-order delta–sigma modulator based on CRFF structure. (b) Zeroes and poles of the noise transfer function. (c, d) Electrical spectra of 32 LTE CCs after delta–sigma modulation. (d) is a zoom-in of (c). (e) EVMs of all 32 LTE CCs, including 16 CCs carrying 256QAM and 16 CCs carrying 64QAM. (f) Constellations of the best and worst cases of 256QAM and 64QAM, respectively.

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D. Case IV

In order to further reduce the EVM degradation contributed by the digitization interface and leave more EVM budget to the analog RF link (including amplifier chain and antenna), Case IV is designed using a fourth-order two-bit delta–sigma modulator. A total of 32 LTE CCs are aggregated within a single-$\lambda$ 10-Gbaud PAM4 (20 Gb/s) IM-DD link. In recent years, Gbaud multilevel, e.g., PAM4, PAM8, transmission over short fiber distance ($<100\mathrm{km}$) has attracted intensive research interest for data center interconnects, where the application scenarios are very similar to MFH networks. With the help of one additional bit, the quantization noise is reduced significantly compared with Case III. In Figs. 3(b) and 3(c), this improvement can be observed by comparing the input analog signal before delta–sigma modulation (red) with the retrieved signal after LPF (green). The experimental results of Case IV are shown in Fig. 7, with EVMs of all CCs reduced to less than 2.1%. A total of 10 CCs with $\mathrm{EVM}<1\%$ can support the modulation format of 1024QAM, and the other 22 CCs with $\mathrm{EVM}<2.1\%$ can support 256QAM. Constellations of CC 12, 28, 16, and 22 are shown in Fig. 7(d), corresponding to best and worst cases of 1024QAM and 256QAM, respectively.

 

Fig. 7. Experimental results of Case IV. (a, b) Electrical spectra of 32 LTE CCs after two-bit delta–sigma modulation. (b) is a zoom-in of (a). (c) EVMs of all 32 LTE CCs, including 10 CCs carrying 1024QAM and 22 CCs carrying 256QAM. (d) Constellations of the best and worst cases of 1024QAM and 256QAM, respectively.

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E. BER Tolerance

In experiments, error-free transmissions were achieved for both 10-Gbaud OOK and PAM4 over 25-km fiber. The tolerance to bit error ratio (BER) of EVM performance in a delta–sigma modulation-based digital MFH link is also investigated. In Cases I and III, EVMs of all 32 LTE CCs are evaluated under different BER conditions and the results are shown in Figs. 8(a) and 8(c), respectively.

 

Fig. 8. BER tolerance of the EVM performance of delta–sigma modulation-based digital MFH. (a) EVMs of 32 LTE CCs in Case I under different BER conditions of a 10-Gb/s OOK link. BER threshold is $1\times {10}^{-4}$, i.e., for BER below that value, EVMs of all CCs still satisfy the 3GPP specifications. (b) Constellations of CC 8, 18, 19, and 31 at $\mathrm{BER}=1\times {10}^{-4}$, corresponding to the best and worst cases of 64QAM and 16QAM, respectively. (c) EVMs of 32 LTE CCs in Case III under different BER conditions with threshold of $3\times {10}^{-5}$. (d) Constellations of CC 12, 17, 6, and 32 at $\mathrm{BER}=3\times {10}^{-5}$, corresponding to the best and worst cases of 256QAM and 64QAM, respectively.

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For Case I, the EVM performance as a function of BER of the 10-Gb/s OOK link is shown in Fig. 8(a), and EVM has weak dependence on BER for BER up to $1\times {10}^{-4}$. This BER insensitivity is due to the operation principle of delta–sigma modulation, where the digitized signal only follows the low-frequency components of analog input and random error bits will be smoothed out by the LPF in RRH and have weak impact on the received signal quality. In Fig. 8(a), the BER threshold is $1\times {10}^{-4}$, i.e., for BER below this value, the digital MFH can support 32 CCs without exceeding 3GPP specifications. The constellations at BER threshold are shown in Fig. 8(b), where CC8, 18, 19, and 31 correspond to the best and worst cases of 64QAM and 16QAM, respectively. Figure 8(c) shows the EVM performance in Case III as a function of BER with threshold at $3\times {10}^{-5}$. Constellations of 256QAM and 64QAM at the threshold are shown in Fig. 8(d).

Due to the limited memory depth of our real-time oscilloscope, there are only ${10}^6$ bits transmitted, and the minimum achievable BER granularity is ${10}^{-6}$. We experimentally tested BER around 1e-6, 1e-5, and 1e-4, and found that the simulation results have very good consistency with experiments. Since it is difficult to control BER precisely in experiments, the results we show in Fig. 8 are based on simulations by flipping a desired number of bits.

F. Case V

To make a comparison with analog MFH, Case V was designed to evaluate the performance of analog MFH with 24 aggregated LTE CCs, all carrying 64QAM. The experimental setup is almost the same as Fig. 3 except for the digitization interface. In Case V, 24 LTE CCs are transmitted in their analog waveform without digitization. As discussed in [12,13], the performance of an analog MFH is limited by both noise and nonlinear impairments. The dynamic range of input signals is constrained by noise in the small signal end, and by nonlinear distortions in the large signal end. Figure 9 shows the average EVM of 24 CCs as a function of the peak-to-peak amplitude ($V_{\mathrm{pp}}$) of the input signal before the power amplifier in Fig. 3. The best achievable EVM is limited by the trade-off between noise and nonlinear impairments. Two power amplifiers (PAs) with different noise figures (NFs) of 5.8 and 11 dB are tried, respectively. In Fig. 9, square and circle dots represent experimental results; red and green curves are from simulations. The minimum achievable EVMs are 4% and 5.6% for both PAs, satisfying the 3GPP specification of 64QAM (8%). The PA with smaller NF provides smaller EVM and wider dynamic range due to the improved SNR. The best constellations at points i and ii are shown in the insets. Since the best EVM is limited to 4%, it would be challenging to support higher-order modulation formats such as 256QAM or 1024QAM using this analog MFH without nonlinear compensation. In contrast, the proposed digital MFH based on delta–sigma modulation can easily support 16 LTE CCs of 256QAM in Case III, and up to 22 CCs of 256QAM and 10 CCs of 1024QAM in Case IV.

 

Fig. 9. Experimental results of Case V RoF-based analog MFH. Average EVM of 24 LTE CCs as a function of the input $V_{\mathrm{pp}}$ before the power amplifier in Fig. 3. Two power amplifiers with noise figure (NF) of 5.8 and 11 dB were used, and the best achievable constellations are shown in insets.

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V. Conclusions

In this paper, we first demonstrated delta–sigma modulation as a new digitization interface for digital MFH networks to replace the conventional CPRI. Both one-bit and two-bit digitization are realized to support carrier aggregation of LTE or FBMC signals in a single-$\lambda$ 10-Gbaud OOK/PAM4 IM-DD link. Carrier aggregation of 32 LTE CCs is realized to support 3GPP release 13 with EVMs less than 5% or 2.1% achieved by using one-bit or two-bit digitization, respectively. High-order modulation formats up to 256QAM and 1024QAM can be supported. Compared with CPRI, which consumes 10 Gb/s for 8 LTE CCs, the fronthaul capacity is increased by four times by using delta–sigma modulation as the new digitization interface. As a waveform-agnostic interface, delta–sigma modulation can work with not only 4G-LTE but also 5G multicarrier waveforms, and its 5G compatibility was verified by FBMC signals. Besides FBMC, digitization of other 5G multicarrier waveforms, such as generalized frequency division multiplexing and universal filtered multicarrier, will be the next step of research.

It should be noted that this paper only focused on low-pass delta–sigma modulation, where mobile signals are located at the low-frequency end and quantization noise at the high-frequency end. In BBUs, analog mobile signals need to be down-converted to intermediate frequencies (IFs) before digitization, and in RRHs, the retrieved mobile signals need to be up-converted to radio frequencies (RFs) before feeding to the air interface. One interesting topic of future research will be bandpass delta–sigma modulation, especially concurrent multiband delta–sigma modulation, where multiband mobile signals can be digitized and recovered without frequency conversion. In RRH, after a bandpass filter, the retrieved signals can be directly fed to the air interface without IF/RF up-conversion.