## Abstract

A differential pulse code modulation (DPCM) based digital mobile fronthaul architecture is proposed and experimentally demonstrated. By using a linear predictor in the DPCM encoding process, the quantization noise can be effectively suppressed and a prediction gain of 7~8 dB can be obtained. Experimental validation is carried out with a 20 km 15-Gbaud/λ 4-level pulse amplitude modulation (PAM4) intensity modulation and direct detection system. The results verify the feasibility of supporting 163, 122, 98, 81 20-MHz 4, 16, 64, 256 QAM based antenna-carrier (AxC) containers with only 3, 4, 5, 6 quantization bits at a sampling rate of 30.72MSa/s in LTE-A environment. Further increasing the number of quantization bits to 8 and 9, 1024 quadrature amplitude modulation (1024 QAM) and 4096 QAM transmission can be realized with error vector magnitude (EVM) lower than 1% and 0.5%, respectively. The supported number of AxCs in the proposed DPCM-based fronthaul is increased and the EVM is greatly reduced compared to the common public radio interface (CPRI) based fronthaul that uses pulse code modulation. Besides, the DPCM-based fronthaul is also experimentally demonstrated to support universal filtered multicarrier signal that is one candidate waveform for the 5th generation mobile systems.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The next generation mobile technologies, such as massive multiple input multiple output (massive-MIMO) antennas, bring a number of challenges to transport segments supporting radio access networks (RANs) [1,2]. As shown in Fig. 1, the segment between a service gateway and a baseband unit (BBU) pool is referred as the mobile backhaul, and the one between a BBU pool and remote radio units (RRUs) is regarded as the mobile fronthaul. The mobile fronthaul places the baseband processing functions inside the BBU pool, which can be efficiently shared by multiple RRUs, and hence leads to a great cost reduction. It is a key segment to support cloud radio access network (C-RAN) [1] architecture, which is favored for its ability to address the capacity and coverage problems. For the C-RAN deployment, both analog [3–7] and digital [8–20] mobile fronthaul architectures have been widely investigated. The analog mobile fronthaul typically utilizes analog radio-over-fiber (RoF) technology having obvious advantages, such as high spectrum efficiency and easy adaption to air interface. However, it suffers from severe physical impairments, especially nonlinear distortions from the electrical and optical components [6,7], and has limited transmission reach. On the other hand, the digital fronthaul system is less sensitive to the channel distortions, allowing for a much longer transmission distance compared to its analog counterpart.

The common public radio interface (CPRI) [8] based digital mobile fronthaul, where 15 quantized bits (QBs)-pulse code modulation (PCM) of analog wireless signals are employed at sampling rate of 30.72MSa/s for 20MHz Long-Term-Evolution-Advanced (LTE-A) signals, provides excellent robustness against channel impairments by incorporating mutual digital intensity modulation and direct detection (IM/DD) systems. However, CRPI intrinsically has a low spectrum efficiency, resulting in a requirement of high transmission rate. For instance, a site with the configuration of 32 LTE-A antenna carriers (AxC) (with the sampling rate of 30.72 MSa/s, 64B/66B line code, and 1/16 system overhead) requires a total CPRI link rate of 32.4 Gbit/s [8] (30.72 MSa/s × 32 × 2 × 15bits × 16/15 × 66/64).

Several approaches have been proposed to solve the capacity crunch caused by CPRI. In [9,10], functional splitting between BBU pool and RRUs was proposed and investigated. This scheme allows ~10-fold reduction of the required link capacity by moving some baseband processing functions to the RRUs, at the expense of higher network deployment cost and more difficult radio coordination, which can be further optimized in the future. In [11–14], delta-sigma modulation was used in mobile fronthaul, while low-pass filters were proposed to use at reception instead of digital to analog convertors (DACs). However, such schemes require a high sampling rate (i.e. usually 8 times of the effective signal bandwidth). Besides, delta-sigma modulation uses optimization techniques (e.g. zero optimization) to enhance the signal-to-noise ratio. Consequently, the quantization noise distribution in frequency domain is not uniform. However, the carrier aggregation of delta-sigma modulation is done in the frequency domain, so the performance of delta-sigma modulation heavily relies on the intermediate frequency carrier index. Meanwhile, some complex compression algorithms [15–19] have been proposed. However, the high cost and complexity of these approaches indicate the need of more efficient solutions for the digital mobile fronthaul in the long-term.

As a variant of PCM, differential pulse code modulation (DPCM) is widely utilized in voice and image coding [20,21], where the signals typically have continuous envelops and do not vary sharply between neighboring samples, exhibiting strong sample-to-sample correlations. DPCM utilizes such a correlation between neighboring symbols for getting a high signal-to-quantization noise ratio and a low number of the required quantization bits (QBs). Additionally, DPCM only requires simple digital signal processing (DSP) and allows for relatively low sampling rate. However, it’s not straightforward to directly adopt the basic DPCM approach for the digital mobile fronthaul due to the slope overload caused by the high peak-to-average power ratio (PAPR) in LTE-A signals. Thus, to design an optimal DPCM scheme for the mobile fronthaul remains a challenge.

In this paper, we propose and experimentally demonstrate an enhanced DPCM based digital mobile fronthaul system. We firstly investigate a scheme to mitigate the quantization noise accumulation problem in DPCM. Based on this scheme, a linear predictor is employed to optimize the quantization levels. The theoretical noise performance and prediction gain are analyzed to show the merits of DPCM over PCM based schemes. Proof-of-concept experimental demonstrations are carried out to test the mobile fronthaul transmission in a 30-Gb/s/λ 4-level pulse amplitude modulation (PAM4) IM/DD system to verify the feasibility of DPCM based fronthaul. We show an increased supported number of AxC containers and reduced EVM with the proposed DPCM based scheme, comparing to the PCM based CPRI mobile fronthaul of the same QB number. Additionally, we demonstrate that the proposed DPCM based fronthaul can support universal filtered multicarrier (UFMC) signal that is a promising candidate for the future mobile communication systems [22].

## 2. Operation principles

The digital mobile fronthaul network architecture using the DPCM is presented in Fig. 2. In the downstream, the signals from the backhaul are firstly processed with the media access control (MAC) protocol, then go through the channel coding, MIMO processing and modulation modules to form the wireless signals according to the format of the air interface. Then signals are digitalized at the DPCM encoder and arranged in frames, before being aggregated through time domain multiplexing (TDM) and the line coding. The aggregated signal is modulated to optical and transmitted through the fiber fronthaul link. At the remote site, the transmitted signal is de-aggregated by de-framing, and the separated frames are passed to the designated DPCM decoding modules. Subsequently, the digital signals are converted to analog by the DPCM decoding module and modulated to different antenna-carriers by radio frequency (RF) frontends. Regarding the uplink transmission, it follows the same operation principle, but in the opposite order. AxC is the amount of digital baseband user-plane data for one carrier at one antenna element [8,10]. Without loss of generality, it is multiplexed in time domain and used as the performance indicator in this paper.

In the rest of this section, the design principles of the three types of DPCM schemes are explained for the proposed fronthaul architecture, namely, 1) the basic DPCM scheme (Type I), 2) the DPCM scheme with reduced quantization noise (Type II) and 3) the enhanced DPCM scheme with a linear predictor (Type III).

#### 2.1 Type I: Basic DPCM scheme

The basic DPCM scheme (referred to as Type I) is shown in Fig. 3. At the transmitter, the real and imaginary (I and Q) components of each baseband analog wireless signal *s*(*t*) is sampled at rate *f _{s} =* 1

*/T*, to produce samples

_{s}*s*[

*n*] =

*s*(

*t*)|

*,*

_{t = nTs}*n*= 1, …,

*N*, where

*N*is the symbol length, and

*T*is the sampling interval. In the encoder, the input to the quantizer

_{s}*e*[

*n*] is the differential signal between the present sample

*s*[

*n*] and its previous sample

*s*[

*n-*1], which is denoted as:

The differential signal *e*[*n*] is quantized as *x*[*n*] (i.e. the quantization form of *e*[*n*]). After transmission of *x*[*n*], the signal can be recovered at the receiver by adding the received quantization signal *y*[*n*] to the previous one. The received form is expressed as:

By quantizing the difference between consecutive samples instead of quantizing the original samples (as done in the PCM), the Type I scheme can have either a quantizer requiring a much lower number of QBs, or a quantizer with the same number of QBs but much smaller quantization intervals leading to a higher signal to noise ratio (SNR). However, the basic DPCM system suffers from accumulation of quantization noise of the previous samples, which is different from the PCM system, where the quantization error of a certain sample is independent with the others. When transmitting a long sequence, the output signal with the accumulated quantization error may significantly deviate from the original one, and cannot be properly recovered.

#### 2.2 Type II: DPCM scheme with reduced quantization noise accumulation

The aforementioned quantization noise accumulation problem in the basic DPCM scheme can be solved by quantizing the difference between *s*[*n*] and its previous sample of the quantized form, denoted by *s _{q}*[

*n-1*]. This approach is referred to as the Type II DPCM scheme. The diagram for Type II is shown in Fig. 4. In the encoder, the input to the quantizer

*e*[

*n*] becomes:

The output of the quantizer is denoted as *e _{q}*[

*n*] and the addition of

*e*[

_{q}*n*] and

*s*[

_{q}*n-1*] becomes the input to the linear delay module.

*s*[

_{q}*n*] is expressed as:

In this case, the quantization is done only between the current sample and its previous quantized sample. Once the quantization noise is accumulated in one direction (i.e. the difference between *s _{q}*[

*n-*1] and

*s*[

*n-*1]) to be more than one quantization level, the subtraction between

*s*[

*n*] and

*s*[

_{q}*n-*1] can reduce the noise, and the noise can be suppressed immediately through Eq. (3). Thus, the quantization error is always limited to no more than one quantization level.

Let variable *Q* denote the quantization error and the *q*[*n*] as its sampled value. Since *e _{q}*[

*n*] is the sum of

*e*[

*n*] and quantization error

*q*[

*n*], it can be expressed as:

Using Eq. (3) to represent *e*[*n*] in Eq. (5), *e _{q}*[

*n*] can be expressed as:

Besides, using Eq. (5) to represent *e _{q}*[

*n*] in Eq. (4),

*s*[

_{q}*n*] can be expressed as:

The item *s _{q}*[

*n*] is the addition of

*s*[

*n*] and

*q*[

*n*], which is equivalent to the quantization form of the input signal. Thus, a further improvement can be done by properly selecting quantization level and estimating correlation of adjacent symbols to reduce the error variance of

*q*[

*n*].

#### 2.3 Type III: DPCM scheme with a linear predictor

Further improvement can be obtained by replacing the common delay module with a predictor, which predicts the sampled signal, and the quantization is carried out based on the sampled signal and its prediction. Meanwhile, the difference between the sampled signal and the predicted signal can be optimized in order to minimize the quantization noise and reduce the number of quantization bits. Figure 5 illustrates enhanced DPCM with a linear predictor of *s*[*n*], referred to as Type III. In this scheme, a *p*-tap predictor is expressed as:

*p*previously quantized signal samples to create a prediction of the current sample

*s*[

*n*]. The coding is carried out by quantizing the difference between the current sample

*s*[

*n*] and its prediction value $\widehat{s}[n]$, which can be expressed as:

The mean square prediction error is defined as *J* = E[*e ^{2}*[

*n*]]. By substituting Eq. (8) and Eq. (9),

*J*can be expressed as Eq. (10).

Assuming the mean value of *s*[*n*] is equal to 0 (i.e. E[*s*[*n*]] = 0), Eq. (10) can be simplified as:

*R*[

_{s}*k*] is the autocorrelation function of

*s*[

*n*]. By differentiating

*J*to the predictor coefficient

*w*, and push the derivative to 0, the result becomes:

_{k}Changing Eq. (12) to the matrix expression, it becomes:

where**r**

_{s}= [

*R*

_{s}[1],

*R*

_{s}[2],…,

*R*

_{s}[

*p*]]

^{T}, and

**R**

_{s}is a

*Toeplitz*matrix of autocorrelation function, which is expressed in Eq. (14).

Thus, the optimal predictor coefficient can be obtained with **w**_{o} = **R**_{s}^{−1}**r**_{s}. For prediction, at the beginning of the wireless analog signals (containing several symbols), the first *m* samples are selected as training data and training overhead *η* is defined as the ratio of training samples in the total samples. The samples are then encoded and decoded without any loss of information. Then, the encoding and decoding of the next samples are performed based on the prediction coefficients obtained from the training data, the optimized quantization levels calculated by QBs and the differential signal *e*[*n*] of the training data. In the implementation, Levinson-Durbin algorithm [23] is used to solve Eq. (13), and Lloyd algorithm [24] is used to optimize the codebooks using the predictive errors produced by Levinson-Durbin algorithm.

## 3. Quantization noise analysis

This section provides the simulation results to demonstrate the suitable DPCM scheme in digital mobile fronthaul. Furthermore, the merits of DPCM over PCM based CPRI in terms of quantization noise are theoretically analyzed.

#### 3.1 Comparison of three types of DPCM schemes

A simple example to demonstrate the merits of the linear predictor based DPCM scheme is shown in Table 1. We set the quantization intervals [-1,0), [0,1), [1,2) and the quantization levels are the center points −0.5, 0.5 and 1.5 for Type I, Type II and Type III. It can be clearly observed that Type II outperforms Type I in terms of quantization noise performance. It is because the quantization noise of Type I is accumulated, yielding larger quantization noise with longer sequence. In contrast, Type II has solved the quantization noise accumulation problem, and the quantization noise can be limited to the quantization interval. Then, Type III can further reduce the quantization noise since it adopts the linear predictor for performance optimization.

The box plots of the error distributions (without normalization) of DPCM coded orthogonal frequency division multiplexing (OFDM) symbols are shown in Fig. 6, where the legend of Figs. 6(a)-6(c) is shown in Fig. 6(d). Here, 30 64QAM-OFDM symbols are simulated. It can be seen that the quantization error distribution is stable for all three types of DPCM scheme in terms of the number of symbols. Type III has the lowest noise level obviously. Thus, Type III is selected to be implemented and demonstrated in Section 5 of this paper.

#### 3.2 Theoretical analysis of quantization noise

Similar as PCM, DPCM is also a uniform quantizer [25]. Besides, the LTE-A signals are Gaussian with zero mean, so the distortion caused by the DPCM quantization can be also considered as Gaussian with zero mean. The mean square variance is determined by the quantizer interval Δ. Thus, the quantization error *Q* is uniformly distributed in the range (-Δ/2, Δ/2), its probability density function (PDF) is expressed as:

The mean square variance${\sigma}_{Q}^{2}$ of *Q* is calculated as:

Consequently, the signal to quantization noise ratio is defined as:

where ${\sigma}_{s}^{2}$is the variance of baseband analog wireless signal*s*(

*t*). Since the Type III DPCM utilizes the sample-to-sample correlations in analog signals to optimize the linear predictor, if the predictor works well, then $\widehat{s}[n]$ is approximately equal to

*s*[

*n*]. As such, the variance ${\sigma}_{e}^{2}$of error sample

*e*[

*n*] is lower than${\sigma}_{s}^{2}$. As a result, for a given number of quantization levels Δ

_{e}, the required step size to code

*e*(

*n*) should be smaller than Δ

_{s}, the step size needed for quantizing

*s*(

*n*) in PCM. Therefore, for a given

*SNR*, the required number of quantization bits in the Type III DPCM is smaller than PCM.

_{q}By further decomposing Eq. (17), *SNR _{q}* is expressed as:

*G*= ${\sigma}_{s}^{2}$/${\sigma}_{e}^{2}$is the prediction gain, obtained from the differential quantization. As a result, the gain of SNR for DPCM over that for PCM is:

_{p}*2*, where

^{-2R}/2^{-2R}*R*is the number of quantization bits [25]) when the quantization procedure of PCM and DPCM is Gaussian distributed. Thus, in this case Eq. (19) can be simplified as:which leads to:

When *G _{p}* is larger than 1 (0 dB), it means that differential quantization exhibits its advantages in terms of SNR. The performance of the Type III DPCM mainly depends on the performance of the predictor, which determines

*G*. Since the derivation of

_{p}*J*= E[

*e*[

^{2}*n*]] in Eq. (11) follows the orthogonality condition [21], it can be derived as:

Thus, *G _{p}* is expressed as:

*R _{s}*[

*k*] is the autocorrelation functions of the source signal. The improvement of

*G*mainly depends on the optimization of

_{p}*w*and the prediction taps

_{k}*p*. In Section 5, we demonstrate and discuss the performance of

*G*with LTE-A signals and show the effectiveness of linear predictor based DPCM in digital mobile fronthaul.

_{p}## 4. Experimental setup

Figure 7 shows the experimental setup of IM/DD PAM4 system for verifying the DPCM based digital fronthaul. For comparison, the conventional PCM scheme is also experimentally demonstrated. In BBU, two types of multicarrier RF signals are demonstrated, i.e. OFDM and UFMC. The system parameters are shown in Table 2. The RF signals are sampled at 30.72 MSa/s and aggregated through multiplexing different AxC container frames in the time domain. The number of wireless physical resource blocks (PRBs) is 100. Here, 2048 inverse fast Fourier transform (IFFT)/FFT points are used, and the number of data-carrying subcarriers are set 1200, each having the signal bandwidth of 20 MHz (with 2 MHz guard band). The tested QAM orders include 4, 16, 64, 256, 1024, and 4096. Besides, for the UFMC signal, the number of equally spaced sub-bands is set to 8, and Chebyshev finite impulse response (FIR) filter with filter length of 60 is employed. The DSP flows of OFDM and UFMC are shown in Figs. 7(b) and 7(c). More details about the UFMC realization can be found in [26].

The in-phase and quadrature (I/Q) signals are encoded individually. Then the encoded signals are modulated by the PAM4 transmitter. The baud rate of PAM4 is 15 Gbaud and the corresponding line rate is 30 Gbit/s. At the receiver, an 11-tap feed forward equalization (FFE) is used for PAM signal recovery. The equalized eye diagram at −8.5 dBm received optical power is shown in Fig. 7(a). Besides, the power spectra of the transmitted OFDM and UFMC signal per channel are shown in the inset (d) and (e) in Fig. 7, respectively. The PAPR comparison between the OFDM and UFMC signals is shown in Fig. 7(f).

In the experiments, the signals are generated, encoded and aggregated offline at MATLAB in the computer, and then loaded to an arbitrary waveform generator (AWG, Tektronix 70001A, 50 GSa/s). The signal from the AWG is amplified by an electrical amplifier with 11-dB gain (3-dB bandwidth: 65-GHz) before applying on the modulator. A monolithically integrated distributed feedback (DFB) laser with a traveling-wave electro-absorption modulator (TWEAM) of ~0 dBm output power is used as modulator, and the central wavelength is 1549.8 nm. Optical PAM4 signal is transmitted over a 20 km standard single mode fiber (SSMF). At the receiver, a variable optical attenuator is used to change the received optical power (RoP) for the EVM measurement. The optical signal is detected by a photodiode (PD) with an integrated trans-impedance amplifier (TIA). The electrical signal is captured by digital storage oscilloscope (DSO, Agilent DSO-X 93304Q, 80 GSa/s) and downloaded for the signal recovery.

## 5. Experimental results and discussions

This section presents the experimental results of Type III DPCM based digital fronthaul as well as the CPRI based fronthaul that uses PCM (as benchmark). The optimization of the linear predictor in DPCM is firstly demonstrated and discussed. We also show the transmission performance of both the DPCM and the PCM based digital mobile fronthaul.

#### 5.1 Quantization performance

Figure 8 shows the prediction gain *G _{p}* versus the prediction training overhead

*η*and the predictor taps

*p*. The QAM order was set to 64 and the RoP is −8.5 dBm, when there is no transmission error. These parameters are the same for Figs. 9-11. The QB is 5 and AxC frames are 100. As shown in Fig. 8, the prediction gain increases gradually with the increase of training overhead. When the training overhead is larger than 1%, the prediction gain saturates. This is because 1% training overhead is enough to optimize the predictor coefficients {

*w*|

_{i}*i*= 1,2 …

*p*} and provide the largest

*G*with the corresponding prediction taps. Comparatively, the influence of prediction taps

_{p}*p*on

*G*is much more significant. It can be seen that there is only ~1 dB prediction gain when

_{p}*p*= 1. However, when

*p*increases to 2,

*G*is in the order of 2~3 dB, and it becomes 4~5 dB when

_{p}*p*= 3. For high tap linear predictor, there is still room for improvement of

*G*. When

_{p}*p*= 5,

*G*increases to the order of 7~8 dB. For LTE-A signals with high PAPR, one needs to increase the training overhead

_{p}*η*and the prediction taps

*p*to achieve higher

*G*, which however, also increases the system cost. Therefore, the EVM performance versus quantization bits with different

_{p}*η*and

*p*are also studied to determine the optimal values of these parameters.

Figure 9(a) shows the EVM performance considering QBs and with different training overheads. Here, the prediction tap is set to 4 and the total number of samples of OFDM signal is 61440. One can see that the codebook optimization performance is slowly enhanced by increasing training overhead, and the EVM is reduced consequently. At the EVM threshold of 8% for 64QAM, 1 bit of QB can be saved by 1% training overhead. For practical implementation, 1% training overhead is considered to be enough for optimizing the quantization level codebook. Lower training overhead is also acceptable for the DPCM based fronthaul with further relaxed performance requirement. It can also be observed that when the QB is high enough (such as QB ≥ 10 or more) with considerably reduced quantization noise, the training overhead is no longer significant for the performance improvement. However, it’s at the expense of the required system bandwidth and therefore it may not be recommended in digital mobile fronthaul. Meanwhile, the EVM performance considering QBs and with different prediction taps are shown in Fig. 9(b). Here, the training overhead was set to 1%. It is observed that increasing the prediction tap could decrease the EVM. It shows similar tendency as the influence of the training overhead, which is in accordance with results shown in Fig. 8. Increasing the prediction tap can result in a better fitting of the correlations of adjacent symbols, leading to improvement in the EVM performance within the quantization noise limit. Considering the cost of DSP, 3~4 tap linear predictors are sufficient for the implementation of the DPCM based fronthaul.

Figure 10 shows the EVM performance as a function of the number of QBs with different QAM orders at −8.5 dBm RoP after 20 km SMF transmission. Here, 1% training overhead and 4-tap linear predictor are considered. By increasing the number of QBs, the quantization noise is greatly suppressed and the EVMs for all the tested QAM orders are significantly reduced (less than 1% when the number of QBs>8). The amplitude probability distribution of LTE-A signal should be independent of modulation format since the data carried by subcarriers are totally mixed together in time domain. Thus, the quantization performance should not be related to the modulation formats, which is also shown in Fig. 10.

According to the EVM thresholds specified by 3GPP [27] for QPSK, 16QAM, 64QAM and 256QAM, a large performance margin is left in the system evaluation because wireless signals can have a large dynamic range. The enhanced DPCM only needs 3, 4, 5, and 6 QBs, respectively (see Table 3). For 1024QAM and 4096QAM, EVM thresholds are assumed to be 1% and 0.5%, and the required minimum numbers of QBs are 8 and 9. 30 Gbit/s DPCM based fronthaul can support LTE-A AxC containers of 163, 122, 98, 81, 61, 54 with QAM orders equal to 4, 16, 64, 256, 1024, 4096, respectively. For instance, with the number of QBs equal to 3, 30 Gbit/s PAM4 supports up to 163 (≈30 Gbit/s / (30.72 MSa/s × 3 bit × 2)) AxC channels of LTE-A signals.

#### 5.2 Digital fronthaul transmission performance

The EVM performance as a function of the RoP with optical back-to-back (B2B) and 20 km SSMF transmission for different modulation orders are shown in Fig. 11(a) (QPSK, 16QAM and 64QAM) and 11(b) (256QAM, 1024QAM and 4096QAM), respectively. In all cases, the system parameters are set according to Table 2. The power penalties for EVM at the thresholds are all less than 1 dB. The EVM values tend to be stable when RoP is larger than −12dBm, indicating high system robustness of the DPCM based fronthaul.

To show the compatibility of the DPCM based fronthaul with other candidate modulation formats for the future mobile communication systems, the DPCM encoded UFMC is demonstrated. The EVM performance as a function of RoP for optical B2B and 20 km fiber transmission is shown in Fig. 12. While the UFMC shows the performance as stable as OFDM, there is a slight difference between the EVM values at the same encoding condition. Such a difference is attributed to the slightly higher PAPR of the UFMC signal. However, as UFMC adopts sub-band filtering, its filtering tails are much shorter compared with other filtering technologies (e.g. FBMC). As a result, there is negligible performance degradation compared with OFDM in the DPCM based fronthaul scheme, indicating its feasibility for the future mobile communication systems.

The EVM performance comparison of 64QAM-OFDM with 20 km SSMF transmission for the PCM used in the CPRI and the proposed DPCM (Type III) is shown in Fig. 13. The EVM performance of the DPCM is considerably better since it has much lower quantization noise when it adopts the same number of QBs as the PCM. At EVM threshold of 8%, there is more than 4 dB RoP sensitivity improvement when the number of QBs is 5. Such an improvement becomes less significant when the number of QBs is larger than 6, due to the reduced quantization noise from smaller quantization intervals. Therefore, DPCM is a promising candidate for mobile fronthaul links with limited bandwidth.

## 6. Conclusions

In this paper, we have proposed and experimentally demonstrated a mobile fronthaul solution based on an enhanced DPCM scheme. The proposed DPCM scheme with a linear predictor can effectively mitigate the quantization noise. In the experiments, mobile fronthaul transmission is carried out in a 30-Gb/s/λ PAM4 IM/DD system. We show that the enhanced DPCM scheme with a linear predictor can support LTE-A AxC containers of 163, 122, 98, 81, 61 and 54 with QAM orders equal to 4, 16, 64, 256, 1024 and 4096 at sampling rate of 30.72 MSa/s when enough EVM margins are provided. Comparing to the CPRI based fronthaul using PCM, the proposed DPCM based fronthaul can support larger number of AxC channels, while significantly improve the EVM performance at low QBs. Finally, we have demonstrated that the proposed DPCM based fronthaul solution can support the UFMC signal that is highly expected to be used in the future mobile communication systems. The comparison of analog fronthaul, CPRI fronthaul, delta-sigma modulation [13] based fronthaul, *μ*-law/*A*-law companding PCM based fronthaul [28] and DPCM based fronthaul regarding LTE standard are summarized in Table 4. Our proposal is believed to be a promising candidate to solve the capacity problem in the fronthaul of the future mobile networks.

## Funding

Swedish Research Council (VR) projects 2016-04510 “PHASE” and 2016-04489 “Go-iData”; Swedish Foundation for Strategic Research (SSF); Göran Gustafsson Stiftelse; Swedish SRA ICT–TNG project; China Scholarship Council; and National Natural Science Foundation of China (#61605047, 61671212, 61550110240, 61271216, 61221001, 61433009, 61501157); Knut and Alice Wallenberg foundation.

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