## Abstract

Digital coherent passive optical network (PON), especially the coherent orthogonal frequency division multiplexing PON (OFDM-PON), is a strong candidate for the 2nd-stage-next-generation PON (NG-PON2). As is known, OFDM is very sensitive to the laser phase noise which severely limits the application of the cost-effective distributed feedback (DFB) lasers and more energy-efficient vertical cavity surface emitting lasers (VCSEL) in the coherent OFDM-PON. The current long-reach coherent OFDM-PON experiments always choose the expensive external cavity laser (ECL) as the optical source for its narrow linewidth (usually<100 KHz). To solve this problem, we introduce the orthogonal basis expansion based (OBE) phase noise suppression method to the coherent OFDM-PON and study the possibility of the application of the DFB lasers and VCSEL in coherent OFDM-PON. A typical long-reach coherent ultra dense wavelength division multiplexing (UDWDM) OFDM-PON has been set up. The numerical results prove that the OBE method can stand severe phase noise of the lasers in this architecture and the DFB lasers as well as VCSEL can be used in coherent OFDM-PON. In this paper, we have also analyzed the performance of the RF-pilot-aided (RFP) phase noise suppression method in coherent OFDM-PON.

© 2014 Optical Society of America

## 1. Introduction

PON is continuing to attract people’s attention because of the exponential growth in Internet traffic and bandwidth intensive applications. In recent years, a heated discussion on the technologies to be selected for the NG-PON2 is ongoing. Several new architectures of PON have been proposed to improve all aspects of performance, such as longer reach, more flexible bandwidth upgradeability and management, higher bandwidth/capacity and split ratio, lower cost and power consumption [1]. Among the proposed architectures, the digital coherent PON, which combines optical coherent detection and electronic digital signal processing (DSP), becomes a promising choice. More sensitive detection and impairments compensation in DSP can extend the system reach and support high user density. But a fatal flaw existing in coherent detection, especially for OFDM-PON, is the sensitivity to the laser phase noise which relates to the laser linewidth [2].

In order to suppress the laser phase noise, the current long-reach coherent OFDM-PON experiments have to choose the expensive ECL as the optical source for its narrow linewidth (usually<100 KHz) [3]. Obviously, this goes against the low cost and energy efficiency target of NG-PON2. So the potential candidate optical sources, i.e. DFB lasers and VCSEL come into our sight. The DFB lasers are widely available in the market and easy to setup and operate. Meanwhile, they have the flexibility in wavelength tuning by simply adjusting the applied bias current [4]. The possibility of the application of DFB lasers in coherent PON has been proved in a back-to-back coherent single carrier (SC) PON system in [5]. As mentioned in this work, the system performance will deteriorate drastically for longer reach or for transmission techniques using any form of OFDM. Besides DFB lasers, people pay more and more interest to VCSEL for its characteristics of low power and low cost [1, 6]. Furthermore, the VCSEL can be mass produced enabling on-the-wafer testing before dicing and packaging while the short-cavity VCSEL (SC-VCSEL) has a very short settling time. The advantages of the SC-VCSEL have been comprehensively analyzed and an experiment of direct detection PON using this optical source has been reported in [6]. Even so, the large linewidth of the DFB lasers and VCSEL, which are normally in the range of a few megahertz (MHz), severely limits their application in the long-reach digital coherent OFDM-PON.

In the last few years, we have put much effort into phase noise compensation. A family of orthogonal basis expansion based (OBE) phase noise suppression methods for multi-carrier systems which can mitigate both laser phase noise induced common phase error (CPE) and inter carrier interference (ICI) has been proposed in [7–9]. In this paper, we introduce the OBE method to digital coherent OFDM-PON and analyze its performance in a typical long-reach coherent UDWDM-OFDM-PON. The numerical results show that the OBE method can greatly improve the bit error rate (BER) performance and help the system run well even though the laser linewidth is large to 12MHz. In other words, the DFB lasers and VCSEL can be used in the long-reach digital coherent PON with the help of the OBE phase noise suppression method. Simultaneously, we study the performance of the RFP phase noise suppression method in [10], which is also for OFDM techniques to mitigate both laser phase noise induced CPE and ICI, in the same architecture. The simulation results also support the above conclusion that the application of the DFB lasers and VCSEL in long-reach coherent OFDM-PON is feasible. In [11], the authors discussed the application of the cost-effective distributed Bragg reflector (DS-DBR) lasers in UDWDM-PON. But they focused on mitigating the impact of local oscillator laser (LO) relative intensity noise (RIN) on receiver sensitivity, and proposed an algorithm which could compensate for this impairment. In our paper, we also study the application of cost-effective lasers in UDWDM-PON, but we focus on the large laser linewidth tolerance instead of RIN tolerance. The rest parts of this paper are organized as follows: In section 2, the principles of OBE and RFP phase noise compensation are presented. Next, we make theoretical analysis about the laser linewidth tolerance enhancement by the OBE method in section 3. Then we illustrate the architecture of a typical long-reach coherent UDWDM-OFDM-PON and shows the simulation results and discussions in section 4. Finally, we draw a conclusion in section 5.

## 2. The principles of OBE and RFP phase noise suppressions

Figure 1 shows the schematic of coherent optical OFDM systems utilizing the OBE or RFP phase noise suppression method. At the transmitter, the data is first mapped to M-quadrature amplitude modulation (QAM) symbols and pilots are inserted if the OBE method is used. After inverse fast Fourier transform (IFFT), cyclic prefix (CP) and preambles are added in the OFDM modulation module. For RFP, the RF-pilot will be inserted before the OFDM signal is modulated by an optical wave. At the receiver, after coherent optical demodulation, FFT as well as channel equalization and phase noise suppression are operated in the OFDM demodulation module. Different phase noise compensation schemes execute different processing flows, which will be elaborated in the following. Finally, we can get the detected data after the M-QAM demapping.

#### 2.1 The OBE phase noise suppression

Assuming that the FFT size is *N*, the pilots ${a}_{i}^{p}={[{a}_{i}({k}_{0})\text{\hspace{0.17em}}{a}_{i}({k}_{1})\text{\hspace{0.17em}}\cdot \cdot \cdot \text{\hspace{0.17em}}{a}_{i}({k}_{M-1})]}^{T}$are uniformly inserted in the *i*th OFDM
transmitted data block${a}_{i}={[{a}_{i}(0)\text{\hspace{0.17em}}{a}_{i}(1)\text{\hspace{0.17em}}\cdot \cdot \cdot \text{\hspace{0.17em}}{a}_{i}(N-1)]}^{T}$, where ${k}_{q}={k}_{0}+qD$$(q=0,1,\cdot \cdot \cdot ,M-1)$denotes the index of the *M* pilots and
*D* is the density. The superscript *T* denotes transpose. In
the time domain, laser phase noise induces a phase distortion ${\phi}_{i}(j)$on the *j*th sampling point of the
*i*th received OFDM symbol. Define the phase noise vector
${\Psi}_{i}$as ${\Psi}_{i}={[{e}^{j{\phi}_{i}(0)}\text{\hspace{0.17em}}{e}^{j{\phi}_{i}(1)}\text{\hspace{0.17em}}\cdot \cdot \cdot \text{\hspace{0.17em}}\text{\hspace{0.17em}}{e}^{j{\phi}_{i}(N-1)}]}^{T}$for the *i*th received OFDM symbol. Then it can be
expanded by orthogonal basis as

*L*-dimensional space. ${\Gamma}_{i}={[{\gamma}_{i}(0)\text{\hspace{0.17em}}{\gamma}_{i}(1)\text{\hspace{0.17em}}\cdot \cdot \cdot {\gamma}_{i}(L-1)]}^{T}$is the coefficient vector. At the receiver, the processing flow of the

*i*th received OFDM symbol ${r}_{i}={[r(0)\text{\hspace{0.17em}}r(1)\text{\hspace{0.17em}}\cdot \cdot \cdot \text{\hspace{0.17em}}r(N-1)]}^{T}$is shown in Fig. 2. First, employing the channel estimation methods such as the time-domain maximum-likehood (TDML) method [12], the intra-symbol frequency-domain average (ISFA) method [13] and so on, the channel frequency response matrix ${H}_{i}$can be estimated by the preamble and the channel equalization can be performed aswhere $F={[{f}_{0}\text{\hspace{0.17em}}{f}_{1}\text{\hspace{0.17em}}\cdot \cdot \cdot \text{\hspace{0.17em}}{f}_{N-1}]}^{H}$denotes FFT transformation whose element ${f}_{m}$is described as

*H*denotes Hermitian transpose. Subsequently, the pilots can be picked up to estimate the conjugation of the phase noise coefficient vector aswhereHere $S={[{e}_{{k}_{0}}\text{\hspace{0.17em}}{e}_{{k}_{1}}\text{\hspace{0.17em}}\cdot \cdot \cdot \text{\hspace{0.17em}}{e}_{{k}_{M-1}}]}^{T}$and ${e}_{{k}_{i}}$is an

*N*× 1 vector with ${k}_{i}$th entry equal to 1 and the other equal to 0. The superscript * denotes conjugation and $diag(x)$is a diagonal matrix with the vector

**x**as the diagonal. The final output ${z}_{i}$after phase noise correction can be obtained as

According to Eq. (4) and (5), the number of the pilots *M* and the dimension of the orthogonal basis *L* play crucial roles for the accuracy of phase noise estimation. Generally, large *M* can bring about more efficient phase noise suppression, but leads to lower spectral efficiency. For the dimension of the orthogonal basis, it couldn’t exceed the pilot number *M*. Although a large *L* should be used for serious phase noise, increasing *L* may degrade the accuracy of the least square (LS) estimation in Eq. (5) when *M* is fixed.

If the phase noise is very serious and Eq. (4) can’t make an accurate estimation, an extra data-enhanced (DE) phase noise suppression can be used to further improve the performance of the OBE method as shown in Fig. 2. Before this, we need to derive ${\widehat{a}}_{i}$as

where $Q(\cdot )$is a quantization operation performed in the threshold detector. Then ${\widehat{a}}_{i}$could be fed back to replace the pilots to update ${\widehat{\Gamma}}^{*}{}_{i}$as#### 2.2 The RFP phase noise suppression

For the RFP method, an RF-pilot is inserted in the middle of the OFDM spectrum and several
subcarriers around it are left unmodulated so that the RF-pilot and the modulated subcarriers
do not spectrally overlap [14]. At the receiver, as
shown in Fig. 3, ${s}_{i}$, the time-domain information of the RF-pilot in the
*i*th received OFDM symbol, will be filtered out by a digitallow pass filter
(LPF). The RF-pilot is supposed to get the same phase distortions induced by laser phase noise
as the OFDM signal and can be used to remove the phase distortions from the OFDM signal. The
phase noise suppression can be operated as

*2.1*. So the final output ${z}_{i}$can be calculated as

In this scheme, the pilot-to-signal ratio (PSR) and the bandwidth of the LPF have a major influence on the receiver performance, which both depend on the laser linewidth. The PSR is defined as

where ${\text{P}}_{\text{RF}}$and ${\text{P}}_{\text{OFDM}}$represent the electrical power of the RF-pilot and the OFDM baseband signal.#### 2.3 Complexity analysis

For the OBE method, the computational complexity is mainly induced by the calculation of ${C}_{i}$(Eq. (5)), ${\widehat{\Gamma}}^{*}{}_{i}$(Eq. (4)) and ${z}_{i}$(Eq. (6)) which include both matrix multiplication and inversion. For diagonal matrix exists and FFT can be used, the actual multiplications needed to calculate them are respectively $O(NL\mathrm{log}(N)),O(N{L}^{2})+O({L}^{3})$and$O(N\mathrm{log}(N))$. If the phase noise is serious and the DE suppression is used, the extra multiplications needed are $O(N\tilde{L}\mathrm{log}(N)),O(N{\tilde{L}}^{2})+O({\tilde{L}}^{3})$and$O(N\mathrm{log}(N))$. For the RFP method, assuming that the order of the LPF is $\kappa $ and the length of cyclic prefix is *N _{cp}*, the multiplications needed are

*O*(

*N*log(

*N*)) +

*O*($\kappa $(

*N*+

*N*). Generally speaking, The OBE method needs more computation complexity than the RF-pilot method. Note that phase noise is usually narrow band, in other words,

_{cp}*L*or $\tilde{L}$are usually sufficiently small, thus the increase of computation complexity brought by the OBE method is limited.

## 3. Theoretical analysis about the laser linewidth tolerance enhancement by the OBE method

Since laser phase noise is narrow-band, the pilot-aided OBE method can estimate laser phase noise with minimized mean square error based on its orthogonal basis expansion. For the orthogonal bases of *L-*dimensional space, *L* discrete Fourier transform (DFT) coefficients of the phase noise can be estimated by the OBE method and the phase noise on the relevant frequency can be compensated accordingly.

In [15], signal to interference ratio (SIR) has been proposed to measure the signal quality in the presence of phase noise. In the deduction below, we assume the back-to-back OFDM system to focus on the research of laser phase noise, where the channel is ideal and signal to noise ratio (SNR) is high. In the effect of phase noise, the observation at the *k*th subcarrier can be written as

*i*th OFDM symbol and the

*k*th subcarrier. The frequency-domain phase-noise complex exponential is given bywhere ${\phi}_{i}(n)$denotes the actual phase noise value at the

*n*th sample within the studied

*i*th OFDM symbol. In particular, ${J}_{i}(0)$is commonly referred to as the CPE and all the other terms of ${J}_{i}(k)$summed up denote the effect of ICI. The power of the first term of the right hand side in Eq. (13) is thought to be useful power and the second term to be interference caused by phase noise. Thus, the SIR of the

*k*th subcarrier is defined as

As described in section *2.1*, $\Gamma ={[\gamma (0)\text{\hspace{0.17em}}\gamma (1)\text{\hspace{0.17em}}\cdot \cdot \cdot \gamma (L-1)]}^{T}$ composed of the *L* DFT coefficients of the phase-noise complex exponential vector $\Psi ={[{e}^{j\phi (0)}\text{\hspace{0.17em}}{e}^{j\phi (1)}\text{\hspace{0.17em}}\cdot \cdot \cdot \text{\hspace{0.17em}}\text{\hspace{0.17em}}{e}^{j\phi (N-1)}]}^{T}$, can be estimated by the OBE method. If we assume that the laser linewidth is very narrow, i.e. the values of the phase noise$\phi (n)$ are relatively small, we can make an approximation ${e}^{j\phi (n)}\approx 1+j\phi (n)$. Then the *L* DFT coefficients of the phase noise vector $\phi $ can also be calculated by $\Gamma $. So the SIR after the OBE phase noise suppression can be derived as

*L*DFT coefficients of $\phi $calculated by$\Gamma $. If $\phi (n)$is small enough and the estimation is accurate, i.e. ${\widehat{\psi}}_{k}\approx {\psi}_{k}$, Eq. (17) can be further simplified as

Based on Eq. (16) and (18), the improvement of SIR brought by the OBE method can be calculated as

For the laser phase noise is narrow-band and its energies aggregate at low frequency, we can get the result

Based on the theoretical analysis above, we add more simulation results as shown in Fig. 4 below to further prove the laser linewidth tolerance enhancement by OBE.

Here the signal of the back-to-back OFDM system is only affected by the generated Lorentzian linewidth phase noise samples and the OBE method without the help of DE suppression is used to suppress it. The DFT size is 256 and 20 pilots are inserted. The SIR is calculated by Eq. (16). From Fig. 4, we can see that the SIR improves with the increase of *L* when the OBE method is used. But if *L* is too large, the SIR becomes worse instead of better. Large *L* will decrease the accuracy of the least squares (LS) estimation in calculating the DFT coefficients of the phase noise. The red curve in Fig. 4 stands for the SIR improvement when the OBE method (without DE suppression, *L =* 7) is used. Although Eq. (20) is derived under the approximation that the laser linewidth is relatively narrow, the results show the OBE method is still effective when the laser linewidth is large. The SIR can be improved 5.5dB when the linewidth is 200KHz and 3.5dB for 2MHz linewidth.

## 4. Simulation setup and results

Figure 5 illustrates the typical long-reach coherent
UDWDM-OFDM-PON architecture with an optical line terminal (OLT) comprising of
*ζ* transceivers, an optical distribution network (ODN) and multiple
optical network units (ONU). The OLT serves *ζ* long-reach high-split ratio PONs and is capable
of transmitting and receiving any one of the *ζ* wavelengths. Each of the
*ζ* PONs can only deal with one wavelength, so the local exchange exists
in the ODN for wavelength multiplexing/de-multiplexing. Each PONs may target a different
transmission reach, i.e.${u}_{1},{u}_{2},\cdot \cdot \cdot ,{u}_{\zeta}$, as well as different passive split ratio, i.e.
${\Lambda}_{1},{\Lambda}_{2},\cdot \cdot \cdot ,{\Lambda}_{\zeta}$ [16]. Unlike legacy PONs,
optical amplifiers (OA) can be deployed at the OLT and local exchange to optically amplify both
the downstream and upstream signals to compensate for high losses from long-reach and high split
ratios. For the downstream, after wavelength multiplexed and amplified at the OLT, the signal is
transmitted over *U* km of straight SSMF to the local exchange for wavelength
de-multiplexing. Then the data on ${\lambda}_{i}$will be transmitted over other ${u}_{i}$$(i=1,2,\cdot \cdot \cdot ,\zeta )$km and split to ${\Lambda}_{i}$ONUs for coherent receiving. The upstream from the entire ONUs has
the opposite processing procedure.

We use VPItransmissionMaker^{TM} V8.6 to simulate the long-reach coherent UDWDM-OFDM-PON described above and analyze the system performance when DFB lasers or VCSEL are used as optical sources in this architecture. The sample rate is 10GS/s. For simplicity but without loss of generality, the OLT sends data on 8 different wavelengths simultaneously whose frequency interval is 10GHz. The total transmission distance is 130km with *U* of 80km and ${u}_{i}(i=1,2,\cdot \cdot \cdot ,8)$of 50km. The OA in the OLT is used to adjust the launch power, while the OA in the local exchange is used to compensate the power loss in the optical link. The gain of the latter OA is set to be 16dB and the noise figure is 4dB. 1:128 splitters are used in ODN, each of which produces 21dB attenuation. The OBE or RFP method is applied in the transmitters and receivers for laser phase noise compensation. The frame structure of the OFDM signal is designed as follows. The IFFT/FFT size is 256. In an OFDM symbol, 220 subcarriers are used to transmit data with quadrature phase shift keying (QPSK) modulation and 16 subcarriers without modulation at both sides of band are used as guard band. For OBE, the left 20 subcarriers are used to add pilots which are uniformly inserted in the 220 subcarriers with transmitted data. For RFP, to guarantee equal spectral efficiency and a good performance, the left 20 subcarriers unmodulated are located in the center of the band around the RF-pilot. After IFFT, 32 cyclic prefix (CP) are added. For RFP, the RF-pilot is inserted by adding a DC offset to the in-phase and quadrature signal and the 3dB bandwidth of the digital LPF at the receiver is 625MHz. The net rate of the OFDM signal is 15.28Gbps. The preamble comprises of one OFDM symbol and the TDML method [12] is applied for channel estimation. The lasers at the transmitters and receivers are assumed to have the same linewidth.

Figure 6 shows the BER performance as a function of the
launched power for the long-reach coherent UDWDM-OFDM-PON when the sum of the laser linewidth at
the transmitter and receiver is 5MHz. As analyzed in Section 2, the dimension of the orthogonal basis *L* has an
important influence on the performance of the OBE method, just as the influence of PSR to RFP.
So we choose different *L* (*L* = 5, 7, 9) and PSR (PSR =
−12dB, −10dB, −8dB, −2dB) for the OBE and RFP methods when the
performances of the corresponding systems are evaluated. As a comparison, the performance of the
system utilizing the CPE correction for phase noise suppression proposed in [2] is also provided.

The cyan curve which denotes the case that the CPE correction is used states that the PON cannot work without effective phase noise compensation. And we can see that under the influence of the fiber nonlinearity, the optimum launched power is 4dBm. For the RFP method, the performances with different PSRs vary obviously. The best performance can be achieved when PSR equals to −8dB. For the OBE method, $L=7$ brings the best performance. If the DE phase noise suppression is used, the performance of the OBE method can be improved evidently, as the magenta curve shows where $\tilde{L}=21$. Overall, at the optimum launched power, the BERs of OBE and RFP are below the forward error correction (FEC) threshold of 3.8x10-3 for 7% hard-decision FEC [17], which is the green dashed line on Fig. 6 and 7.

Figure 7 presents the BER performance versus different linewidth at the optimum launched power of 4dBm. The linewidth here also denotes the sum of the laser linewidth at the transmitter and receiver.

For the OBE method, 7 is also the optimal value of *L* in this situation. Although *L* can be continuously increased and more DFT coefficients of the laser phase noise can be estimated, the limited pilots and other channel noise will decrease the estimation accuracy. So the performance will not improve when *L* increases beyond 7. More pilots may be needed to guarantee the estimation accuracy at this time. Besides increasing the pilots, we can also use the DE phase noise suppression to improve the performance of the OBE method. At this time, error-free transmission can be achieved even when the laser linewidth is large to 7MHz. As a result, more computational complexity is induced.

For the RFP method, bigger PSRs mean bigger energy of the RF-pilot and more accurate phase noise recovery. Meanwhile, the SNR of the data subcarriers will degrade. When the PSR increases to −2dB, the performance is worse than that of −10dB with linewidth larger than 6MHz. However, its performance is better when linewidth is smaller than 5MHz. It can be explained as follows. For Lorentzian linewidth, when the laser phase noise is mild, the energies of phase noise on RF-pilot aggregate at the low frequency and it will not affect the useful subcarrier data out of the LPF bandwidth. Improving the PSRs can reduce the relative effects from the outside-band data as well as inside-band noise and achieves better performance in this case. When the laser linewidth increases, the band of the phase noise will broaden. Part of the phase noise energies in high frequency out of the LPF band will affect the data subcarriers and decreasing the PSRs can reduce this part of energies and improve the SNR of the data subcarriers. Therefore, smaller PSRs in a certain limitation can acquire better performance.

We can also find that the OBE method without the help of the extra DE suppression is more effective for narrower linewidth compared with the RFP method. When the laser linewidth becomes larger, a small *L* for OBE can’t estimate the phase noise accurately. And, limited by the pilot number, enlarging *L* is meaningless. By contrast, the LPF has large bandwidth (625MHz here) and can realize better phase noise recovery especially for high frequency phase noise. So the RFP method shows better performance when the linewidth is large. To improve the performance of RFP, we can optimize the PSR and LPF according to the linewidth and channel information. In addition to them, more unmodulated subcarriers around the RF-pilot can guarantee better recovery of the phase distortion by LPF. Of course, if all parameters are optimized to the real-time channel information, higher complexity and lower spectral efficiency are following.

On the whole, both of the OBE and RFP phase noise suppression methods can help to maintain the BER of the long-reach coherent UDWDM-OFDM PON below the threshold of 3.8x10-3 for 7% hard-decision FEC, when the linewidth increases from 2MHz to12MHz. Therefore, the application of the DFB lasers and VCSEL whose linewidth are both of several megahertz in the long-reach coherent UDWDM-OFDM-PON is completely possible with the help of the two effective phase noise suppression methods.

## 5. Conclusion

In this paper, we study the possibility of the application of the DFB lasers and VCSEL in the long-reach coherent UDWDM-OFDM-PON with the help of the phase noise suppression methods. We introduce the OBE and RFP schemes to a typical long-reach coherent UDWDM-OFDM-PON and the numerical results demonstrate the system can run well even when the linewidth of the lasers is as large as 12MHz. So, with the aid of the OBE and RFP method in DSP, the DFB lasers and VCSEL with low cost and power consumption can be ideal choices of optical sources in coherent OFDM PONs, which match the development tendency of NG-PON2.

## Acknowledgments

This work was supported by National Natural Science Foundation of China (No. 61275005) and National Hi-tech Research and Development Program of China (2011AA01A106).

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