## Abstract

Driven by continuously growing mobile traffic, line rate of digital mobile fronthaul (MFH) network keeps surging. 4-level pulse amplitude modulation (PAM4) is a promising format to provide such high data capacity, due to its bandwidth and cost efficiency. In this paper, we propose an improved method to reduce mobile signal distortion caused by bit error of optical transmission. The concept comes from the characteristic that high order sample bit error induces far severer performance degradation to radio signal than low order one. In the solution, high order sample bits and low order sample bits are interleaved, so that they are respectively mapped to first bit (1stb) and second bit (2ndb) of PAM4 symbol. On the other hand, amplitude levels of PAM4 are set unequal to broaden the “middle eye”, levering accuracy of 1stb. Hence, the total fidelity of mobile signal is enhanced. The feasibility is confirmed both theoretically and experimentally. The investigation is based on two typical digital systems, i.e., 16-bit uniform quantizing and 8-bit nonuniform quantizing. Experimental results indicate that, EVM of LTE-A like radio signal decreases by up to 13dB in uniform quantizing system, and by up to 5dB in nonuniform quantizing system, compared with conventional equally-spaced PAM4.

© 2017 Optical Society of America

## 1. Introduction

In order to support exponentially increasing mobile traffic, base stations need to be densely deployed. To handle various problems (cost, energy consumption, control and operation, etc) brought by dense cell deployment, a cloud radio access network (C-RAN) has been proposed and considered as a promising candidate for future mobile communication framework [1]. The baseband processing units (BBU) are separated from base station and consolidated to perform centralized control. And radio units (RU) are distributed in respective cells to provide access points (AP) for terminals. Plentiful benefits can be easily got, including reduction of capital and operation expenses, easier implementation of coordinated multiple point (CoMP), flexible allocation of resource “slice”, and so on. One critical technical issue is the data transport between remote radio units (RRUs) and baseband units (BBU) pool. Both analog and digital radio over fiber (RoF) schemes have been widely studied [2–6]. Analog scheme transports radio signals in continuous waveforms. And digital scheme converts radio signals into discrete levels which are represented by sample bit streams. Digitized radio over fiber offers a distinct advantage due to its immunity to distortion of fiber link and transparency to mobile signal format. As well, it is easy to come into commercial use, because only minor modification needs to perform based on current mature industry standard, eg: common public radio interface (CPRI) [7].

However, considering diverse application of 5G, deployment of massive MIMO and application of multiple spectrum, data rate of digital MFH link will explosively increase [8,9]. Currently popular line rate of 10Gbps/λ (speculated in NG-PON2) can no longer provide a long-term sufficient transmission capacity. For example, 24Gbps per link is specified in CPRI 7.0. For transmission of beyond 10Gbps per link, multi-level pulse amplitude modulation (PAM) is gaining more and more research enthusiasm, because 1) it has higher bandwidth efficiency than NRZ format and lessens bandwidth requirement on optoelectronic devices, 2) it has simple DSP processing in transmitter and receiver side, compared with other short reach techniques, including DMT and CAP [10–14].

We focus on PAM4-based digital MFH link and make enhancement. It is well known that high order sample bit errors induce far severe performance degradation on radio signal than low order ones. Thus, we propose an improved method by levering accuracy of high order sample bits. In the scheme, high order sample bits and low order ones are interleaved, respectively mapped to first bit (1stb) and second bit (2ndb) of PAM4 symbol. Meanwhile, by enlarging the Euclidean distance of middle two constellations in PAM4, bit error ratio (BER) of 1stb is reduced, leading to accuracy improvement of high order sample bits. The total performance of radio signal will be improved even though low order sample bits are less accurate. In our previous report [15], the validity of proposed method has been confirmed by experimentally transmitting 16-bit uniformly quantized LTE-A like signals. In this paper, detailed theoretical studies are conducted from the perspective of general digital systems. Besides above-mentioned uniform quantizing, we further evaluate the proposed scheme based on nonuniform quantizing, which is widely regarded as an effective solution to compress data of mobile fronthaul [16]. Simulations are conducted to study this two typical digital systems, and results indicate that prominent EVM reduction can be achieved in ideal AWGN link. Finally, digitized radio signal transmission is demonstrated based on 25Gbps fiber link by experiments. According to the results, error vector magnitude (EVM) can decrease by 10~13dB in 16-bit uniform quantizing system, and by 4~5dB in 8-bit nonuniform quantizing system, compared with conventional equally-spaced PAM4.

## 2. Principles of digital MFH based on unequally-spaced PAM4

Figure 1 gives the schematic of proposed digital MFH system, which is based on unequally-spaced PAM4. Original radio signal ($x(t)$) is injected into the analog-to-digital converter (ADC) for sampling, quantization, and coding operations. Two typical ADC schemes are discussed in this paper. The first one is uniform quantizing as speculated in CPRI [7]. Each analog sample is directly converted to a folded 16-bit codeword, containing one sign bit representing the polarity, and 15 bits representing the amplitude. The second one is nonuniform quantizing as described in [16]. Nonlinear mapping is firstly implemented for each analog sample, enlarging small signal and compressing large signal. Then the mapping result is converted to an 8-bit codeword containing one sign bit and 7 amplitude bits.

After ADC, the bits of every codeword are divided into high order half and low order half. And the two parts are interleaved for the sake that high order bits are mapped to 1stb of PAM4 symbol and low order bits are mapped to 2ndb of PAM4 symbol. After that, the rearranged sample bits are converted to PAM4 pulse. According to the relationship between PAM4 symbols and binary codes (illustrated in the dotted box of Fig. 1), error of 1stb is only induced by the confusion between symbol2 and symbol3. And error of 2ndb is caused by confusion between symbol1 and symbol2 or between symbol3 and symbol4. Hence, enlarging the middle constellation distance can reduce BER of 1stb, and increase BER of 2ndb. Assume that the distance of the middle two constellations is 2*w*_{1}, and the other two distances are both 2*w*_{2}. Constellation distance ratio is defined as$\gamma ={w}_{1}/{w}_{2}$, and set greater than or equal to 1. Specially, *γ* equals 1 when equally-spaced PAM4 is adopted. Then PAM4 pulses are converted into optical field and transmitted through the fiber link. After PD detection, the electrical PAM4 signal processing is employed to make decision and recover the binary sample bits. Finally, the interleaved sample bits are recovered to normal order and injected to the digital analog convertor (DAC) to reconstruct the radio signal (z(t)).

The distinction from conventional PAM4 based method lies in two aspects (the blocks with yellow background). Firstly, high/low order bit interleaving is added after coding of ADC. Secondly, amplitude of PAM4 pulse is not proportional to 0, 1, 2 and 3. The distance of the middle two constellation is enlarged and other two constellation distances are reduced. Accordingly, reverse procedures are operated at the receiver side. On the whole, there is no complicated signal processing added in both transmitter and receiver side, which caters to the low cost requirement of access networks. On other hand, for practical application, control words transmission and channel coding need to be taken into consideration:

- (a) Since control bit does not have priorities and prominent performance should be guaranteed for each one, procedures of PAM4 symbol modulation is a little different from sample bits. Each control bit is firstly repeated once, and then control bit stream is sent into the above mentioned interleaving and unequally-spaced PAM4 generating modules. In this way, ‘0’ bit of control bit is replaced by ‘00’, and mapped into symbol0, ‘1’ bit is replaced by ‘11’, and mapped into symbol3. Only symbol0 and symbol3 are selected to transmit control bits. Due to the large constellation distance, the bit error can be guaranteed within a low proportion. In the receiver side, the 1stb of PAM4 symbol is extracted to make decision.
- (b) Channel coding can be respectively performed upon high order bit part and low order bit part rather than directly aiming at the whole bit stream. After that, encoded two branches of bits are combined and converted into unequally-spaced PAM4 pulses. At receiver side, the process is reverse.

## 3. Theoretical analysis

The radio signal distortion is related to sample bit error, and the sample bit error is further related to constellation distances of PAM4. In this section, we will make theoretical analysis of the two relationships. Subsection 3.1 illustrates the analysis of radio signal distortion caused by different sample bit error. Subsection 3.2 gives BER of 1stb and 2ndb of unequally-spaced PAM4. Finally, in subsection 3.3, we derive the total radio signal distortion of the proposed system.

#### 3.1 Analysis on radio signal distortion caused by sample bit error

In the digital MFH system, each sample is represented by a binary codeword, and bit errors after optical link will make the received sample codeword incorrect, inducing additive noise on radio signal. We first derive the expression of the additive noise, and then calculate corresponding power.

The signal in different phases are shown in Fig. 2. Assume the sampling period is *T*, the *m*th sample of radio signal is expressed as$x(mT)$. Then it is transformed to$y(m)=f(x(mT))$, where $f$($\cdot $) is the mapping function. (The mapping is linear if employing uniform quantizing, and$f$($\cdot $) is μ law compression function if employing nonuniform quantizing [16].) After mapping, $y(m)$is uniformly quantized and coded as the *m*th binary codeword (The resolution equals 16 when uniform quantizing is used, and the resolution equals 8 when nonuniform quantizing is used). In the receiving side, DAC reconstructs signal based on the received sample codewords.${y}_{q}(m)$will be got when sample codeword is correct, and ${y}_{qe}(m)$will be obtained if bit error occurs in the codeword. Lastly, inverse transformation ${f}^{-1}$($\cdot $) is done to recover the radio signal, that is to say, $z(mT)={f}^{-1}({y}_{q}(m))$ or${z}_{e}(mT)={f}^{-1}({y}_{qe}(m))$. Due to sufficient signal to quantizing noise ratio (SQNR), $z(mT)$almost has no deviation from$x(mT)$, and can be regarded as the ideally recovered signal. ${z}_{e}(mT)$ is the noisy signal, and the deviation between ${z}_{e}(mT)$and$z(mT)$(or $x(mT)$)is regarded as the additive noise induced by sample bit error.

Herein, only case that one bit error exists in a sample codeword is considered, and more than two bit error cases are ignored due to low possibility. That is, the noise $\Delta (mT)$has *n* different types, which are respectively written as${\Delta}_{i}(mT),i=1,2,\mathrm{3...},n$. For a given error position, the deviation ${\Delta}_{i}\text{(}mT\text{)}$ is related to$x(mT)$. And the relation is defined as function *ε _{i}*($\cdot $), noted as:

*i*denotes the error position in a codeword. The expectation of corresponding noise power can be expressed as:

*E*($\cdot $) is the expectation function, $p(x)$refers to the amplitude distribution function of input radio signal, and ${P}_{ei}$ is the error probability of

*i*th sample bit. The total noise power (

*N*) induced by bit error is the sum of noise power of every type:where

*n*is the quantizing resolution.

#### 3.2 Error probability of 1stb and 2ndb in unequally-spaced PAM4

Performance of unequally-spaced PAM4 in addictive white Gaussian noise (AWGN) channel is discussed in this subsection. The symbol decision in receiver side is in the light of maximum likelihood (ML) rules. From the appendix, corresponding bit error probability can be derived as:

where ${P}_{Fe}$and${P}_{Se}$denote bit error probability of 1stb and 2ndb, and σ is power density of Gaussian noise power. Note that fiber link is power limited, so*w*

_{1}+ 2

*w*

_{2}is a constant which equals half used range of modulation curve.(Usually, to guarantee same constellation distance ratio between transmitter and receiver side, it is desirable to make amplitude range of driving signal fall into the linear range of modulator.) In this study, we define channel quality metric as peak signal to noise ratio (peak SNR)$=\frac{{({w}_{1}+2{w}_{2})}^{2}}{{\sigma}^{2}}$, where ${w}_{1}+2{w}_{2}$ indicates the half linear range. Figure 3 shows the bit error ratio of 1stb and 2ndb versus peak SNR. Different

*γ*is adopted and the results are shown in different colored lines. Obviously, when

*γ*>1, error probability of 1stb reduces and error probability of 2ndb increases. As

*γ*goes larger, the effect is more apparent.

#### 3.3 Total radio signal distortion in proposed system

Firstly, uniform quantizing is discussed. For the sign bit error, which causes the signal reverse, and corresponding average noise power is derived:

For other bits, voltage deviation depends the weight of bit. If the error occurs at the*i*th bit,

Secondly, nonuniform quantizing is discussed. According to previous studies, the OFDM amplitude has Gaussian distribution, so μ law compression is a suitable scheme, described as$y=f(x)=\frac{\mathrm{ln}(1+\mu x)}{\mathrm{ln}(1+\mu )}$. The *x* is a normalized version of original signal, ranging from 0 to 1. After nonlinearly mapped, *y* also has the range of 0 to 1, but distributes more evenly than *x*. Then, the *y* is uniformly quantized with resolution of 8. Reduced resolution is counteracted by “pre-amplifying” operation upon small signals. Besides, the value of μ is optimized to minimize the nonlinear noise. Total EVM degradation caused by nonuniform quantizing is −41dB (0.7%). The distortion can be neglected, compared with other link factors [16]. Similar as uniform quantizing, the average noise power caused by sign bit error is

## 4. Simulation and results

Simulations are conducted to testify the feasibility of the proposed system, which is based on orthogonal frequency division multiplexing (OFDM) signal specified as 4G + LTE protocol. 64 quadrature amplitude modulation (QAM) format is taken. The bandwidth of OFDM signal is 20MHz, and spacing between two subcarriers is 15kHz. Datacarrier number is 1200, and FFT point number is 2048. The sample frequency for baseband signal generator is 30.72MHz to favor IFFT/FFT operation. At the same time, to remove frequency redundancy and reduce data rate of I/Q sample. 3/4 downsampling and 4/3 upsampling are respectively employed before ADC and after DAC [16]. The sample frequency of ADC and DAC can be regarded as 30.72*3/4 = 23.04MHz.

The expectation of noise power introduced by different sample bit error can be calculated from Eq. (6), (7), (9) and (10), and concluded in Tables 1 and 2. Since *p(x)* does not have an analytical solution, a statistic of amplitude distribution based on 10^{6} OFDM symbols is used as an alternative. Note that the signal voltage is normalized, that is to say, the maximum instantaneous power is 0dBm. The results of table indicate that high order sample bit error causes far severer noise than low order ones. Since we fix the peak power as 0dBm, other simulation may show different results due to the random peak to average ratio (PAPR). In this simulation, PAPR of our generated OFDM signal is 13.81dB, which is higher than most OFDM signal, especially signal with PAPR reducing. If PAPR is reduced, signal power can be relatively increased, and the noise power induced by sign bit error will increase accordingly. The noise weight of high order bit error increases, so high order bits become more important. That means, better performance can be obtained in ordinary cases than the results reported.

Then, EVM performance of constructed OFDM signal after the emulated digital MFH system is calculated as the distortion measure, shown in Fig. 4. Uniform quantizing scheme and nonuniform quantizing scheme are respectively shown in Figs. 4(a) and (b). Different γ are adopted, shown with different colored lines. When γ equals 1, the system works as traditional equally-spaced PAM4 system. When γ is above 1, performance of 1stb is levered while sacrificing quality of 2ndb to some extent. The radio signal quality is greatly improved, confirming with the theory. However, larger γ value doesn’t always mean more significant improvement. When γ is too large, the performance gets worse. (γ = 2 is worse than γ = 1.5 when peak SNR is above 22dB in uniform quantizing system and above 20dB in nonuniform quantizing system.) It is because when the accuracy of low order bits is severely destroyed, it is equivalent that resolution of digitizing process is reduced, resulting in quantizing noise. The optimal γ value is related to the peak SNR of link. At a fixed peak SNR, as the γ increases from 1, the performance of radio signal expresses “first up and then down” trend. Hence, the optimal point must exist. Since the objective function is one-dimensional, simple advance and retreat method is adopted for searching the optimal γ [17]. For every peak SNR, we adopt the optimal γ (shown in Fig. 5), and corresponding radio signal quality is shown with the black dash line. Compared with the conventional method (blue line), EVM of radio signal decreases by up to 13dB in uniform quantizing system, and 5dB in nonuniform quantizing system.

Figure 5 shows optimal γ @ different peak SNR. The optimal γ shows a decreasing trend, when SNR of link gets better. And when peak SNR is very high, the optimal γ is close to 1. It is due to that at a high SNR condition, only small “broadening” of the middle eye can cause significant BER decline of 1stb. In addition, optimal value of γ is larger in uniform quantizing system than in nonuniform quantizing system. Because in uniform quantizing system, the total weight of high order sample bits is 10^{4}~10^{5} times higher than low order sample bits. And in nonuniform quantizing system, the total weight of high order sample bits is 10^{2}~10^{3} times higher than low order sample bits. More energy needs to be allocated to 1stb in uniform quantizing system.

## 5. Experimental setup and results

Experiments are conducted as illustrated in Fig. 6. The radio signal is set same as simulations of section 4. OFDM baseband signal generator, ADC sampling, sample bits interleaving are performed offline. Two branches of bit stream (high order sample bits and low sample bits) are obtained and respectively loaded into on off key (OOK) pulse pattern generator1 (PPG1) and pulse pattern generator 2 (PPG2). The data rate of two OOK signals is 12.5Gbps, and the amplitude of electrical signal is set to satisfy the value of γ, namely V_{pp1} = 2(w_{1} + w_{2}) and V_{pp2} = 2w_{2}. The offset of PPG1 equals to the bias voltage of EML and the offset of PPG2 is zero. The two electrical signals are then synchronized and combined with a power divider to generate unequally-spaced PAM4 pulse, which is at a rate of 25Gbps and could support 33 channels of 20MHz LTE streams with 16bit uniform quantizing or 67 streams with 8bit nonuniform quantizing. Then PAM4 signal drives electro absorption modulator laser (EML) and the output signal is launched into standard single mode fiber (SSMF). At the receiver side, a variable optical attenuator (VOA) is used to match the received optical power. Then the optical signal is retrieved by photodiode (PD) and sent to a digital sampling oscilloscope (DSO) at 80GSa/s for offline processing. Offline processing procedures include PAM4 symbol decision, binary bit recovery, sample bit de-interleaving, DAC converter and EVM calculation. In all cases (uniform quantizing@BtB and 20km, nonuniform quantizing @BtB and 20km), γ = 1, γ = 1.5 and γ = 2 are respectively adopted by adjusting V_{pp1} and V_{pp2}. Unequally-spaced PAM4 eye diagrams are shown in right top corner.

Figure 7 shows the EVM performance after being transmitted via fronthual link, when uniform quantizing is taken. For BtB case, EVM performance presents a similar changing law as simulation results. It is due to that BtB optical link can be considered as an AWGN channel. Among three γ values, when received optical power (ROP) is small (−24dBm), γ = 2 shows best signal quality, and when ROP is large (−16dBm), γ = 1.5 shows best signal quality. For 20km case, γ = 2 is the best one when ROP changes from −16dBm to −24dBm. Τhis distinction from BtB case is due to that inter symbol interference (ISI) caused by chromatic dispersion also induces bit error. Signal to noise ratio (SNR) is insufficient even at a large ROP, so larger γ is needed. At each ROP we obtain an optimal γ (shown in Fig. 7(c)), and corresponding EVM results are illustrated with cyan lines in Figs. 7(a) and (b). Several constellations in both equally-spaced PAM4 (γ = 1) and optimal unequally-spaced PAM4 (optimal γ) cases are gathered. BtB@-20dBm and BtB@-16dBm are shown in Table1 inserted, and 20km@-20dBm and 20km@-16dBm are shown in Table2 inserted. In BtB and 20km cases, EVM is reduced by 10dB and 13dB respectively, compared with conventional equally-spaced PAM4 (γ = 1).

The optimal γ is gathered in Fig. 7(c), showing a decrease trend. This phenomenon is similar as in simulation. The total noise contains high order bit error induced noise and low order bit error induced noise. Increasing γ can reduce the first part and increase the second part. When balance is achieved between the two variations, optimal γ is reached. At high optical power, the bit error ratio is quite low and varies more obviously with change of γ. Hence, the optimal γ is relatively small. That is the reason why the optimal ratio decreases as optical power increases.

Similarly, experimental results when adopting nonuniform quantizing is shown in Fig. 8. In BtB and 20km cases, EVM is reduced by 4dB and 5dB respectively, compared with conventional equally-spaced PAM4 (γ = 1).

## 6. Conclusion

In this paper, we have proposed a digital mobile fronthaul system based on unequally-spaced PAM4 format. The high order sample bits and low order sample bits are interleaved, mapped on 1stb and 2ndb of PAM4 symbols. By enlarging the middle eye of PAM4 symbol, the accuracy of high order bits is improved, leading to enhancement of radio signal fidelity. Two typical quantizing schemes are discussed, namely 16-bit uniform quantizing and 8-bit nonuniform quantizing. Digitized LTE-A like signal transmission is both emulated in AWGN channel, and demonstrated based on 25Gbps fiber link. Simulation and experimental results confirm with the theoretical analysis. Furthermore, results indicate that optimal constellation distance ratio is related to link quality (peak SNR of ideal AWGN channel, fiber length and ROP in experiments). The EVM improvements with optimal *γ* are gathered in the Table 3:

## Appendix

#### Bit error ratio of unequally-spaced PAM4

In AWGN channel, amplitude of unequally-spaced PAM4 signal are distributed as illustrated in Fig. (9). The symbol decision in receiver side is in the light of maximum likelihood (ML) rules. So the three threshold levels are adjusted to minimize the symbol error ratio.

Usually, only confusion between adjacent two symbols is taken into consideration, due to relatively good channel quality, as shown in Fig. (9). According to the mapping relationship, bit error probability can be derived as:

*k*= 1,2,3,4. ${P}_{e}({S}_{l}|{S}_{k})$is the probability that original symbol is ${S}_{k}$ and it is decided as ${S}_{l}$ by mistake.${P}_{e}({S}_{2}|{S}_{3})\text{=}{P}_{e}({S}_{3}|{S}_{2})\text{=}\frac{1}{2}erfc(\frac{{w}_{1}}{\sqrt{2}\sigma})$and${P}_{e}({S}_{1}|{S}_{2})\text{=}{P}_{e}({S}_{2}|{S}_{1})\text{=}{P}_{e}({S}_{3}|{S}_{4})\text{=}{P}_{e}({S}_{4}|{S}_{3})\text{=}\frac{1}{2}erfc(\frac{{w}_{2}}{\sqrt{2}\sigma})$, according to the theory of bipolar symbol [18]. Corresponding bit error ratio can be derived as: where σ is power density of Gaussian noise power.

## Funding

National Science and Technology Major Project of the Ministry of Science and Technology of China (2015ZX03001021), National Natural Science Foundation of China (NSFC) (61431009, 61371082 and 61521062).

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