## Abstract

We report experimental validations of an adaptive 2^{nd} order Volterra equalization scheme for cost effective IMDD OFDM systems. This equalization scheme was applied to both uplink and downlink transmission. Downlink settings were optimized for maximum bitrate where we achieved 34Gb/s over 10km of SSMF using an EML with 10GHz bandwidth. For the uplink, maximum reach was optimized achieving 14Gb/s using a low-cost DML with 2.5GHz bandwidth.

© 2013 OSA

## 1. OFDM for optical access systems

Orthogonal Frequency Division Multiplexing (OFDM) offers several advantages for optical access systems compared to classical binary on-off keying at baseband [1]: increased spectral efficiency, enhanced equalization capabilities and flexible bandwidth allocation through sub-carrier granularity [2]. Unlike single carrier baseband modulation, the OFDM signal can be adapted to the transmission channel by means of bit and power loading [3]. However, contrary to baseband transmission, OFDM presents stringent requirements with regards to the linearity of the transmission channel. This will depend on the linearity of the Electro-Optical (EO) modulator power vs. injection current curve. Another cause for nonlinear transmission channel in Intensity Modulation Direct Detection (IMDD) systems is the interaction between laser chirp and Group Velocity Dispersion (GVD) which leads to Sub-carrier to Sub-carrier Intermixing Interferences (SSII) [4].

SSII reduction can be achieved through transmission over a Dispersion Shifted Fibre (DSF) or by operating near the fibre zero dispersion wavelength of the Standard Single Mode Fibre (SSMF). This approach might not be possible when this wavelength range is already occupied by existing systems. Another possibility of achieving SSII reduction is to reduce chirp. This is easily achievable by using low chirp EO conversion in the form of a standalone Electro Absorption Modulator (EAM) or an EAM with integrated laser (EML) or by using low modulation index (**m**) on a Directly Modulated Laser (DML).

For instance, transmission of 11.25Gb/s real valued OFDM (DMT) using a 1550nm DML over 25km of SSMF has been experimentally demonstrated using **m**≈10% [5]. However, this approach drastically limits the system power budget, which is a critical issue in Passive Optical Networks (PON). Another approach is to compensate SSII at the receiver using nonlinear filtering. This approach has been shown to be beneficial with regards to both power budget and capacity [6, 7]. Nonlinear equalization using Volterra filters has been first applied in baseband binary direct-detection systems to mitigate the impact of chromatic dispersion and intrachannel nonlinearity [8] and more recently in IMDD OFDM systems to reduce SSII for 100Gb/s transmission using a 10G-class DML [9].

In the present work we propose an adaptive nonlinear Volterra equalizer. Through the use of a training sequence, the Volterra equalizer is able to adapt its coefficients for different levels of SSII. We investigate the value of this equalization approach to meet NG-PON2 targets using EML and DML.

## 2. Nonlinear distortions in OFDM IMDD transmission

In optical access systems, cost effectiveness dictates the use of low cost EO conversion. Available options in this category: DML, EAM and EML will cause moderate to high amounts of chirp in the optical signal. Chirp will interact with GVD causing the chirped signal to suffer frequency to amplitude modulation (FM-AM) conversion, finally leading to amplitude distortion after the photodiode. At the receiver, cost effective direct detection is mandatory. These interferences constitute the previously defined SSII. As these arise from chirp-GVD interaction, they are not only dependent on the amount of chirp, but also on the accumulated GVD which causes different phase shifts for each spectral component. By removing either chirp or accumulated GVD, SSII will be drastically reduced. In DMT systems, part of the SSII lands in the same band as the signal band therefore reducing SNR while the remaining SSII land outside the signal band providing a rough estimate of the amount of in-band SSII. This can be seen in Fig. 1(left) where the chirp of the EML causes visible out-of-band SSII. The same can be seen on Fig. 1(right) for the DML where there is a perceivable increase of out-of-band SSII with increasing fibre lengths. The combination of high chirp and longer fibre length makes SSII especially high after 38km SSMF.

In our experiments, the value of nonlinear Volterra equalization will be investigated for low and high SSII scenarios.

## 3. Nonlinear Volterra equalizer

As Composite Second Order (CSO) products dominate the nonlinearities in DMT systems [6, 7], the considered Volterra equalizer is limited to the 2^{nd} order. The signal vector *y⃗* at the output of the filter is calculated as:

*u⃗*=

*x⃗*[

*n*−

*N*/2 + 1;

*n*+

*N*/2] and $\overrightarrow{{u}_{T}}=\overrightarrow{x}\left[n-M/2+1;n+M/2\right]$,

*x⃗*being a vector representing the downsampled received signal,

*L⃗*is the linear FIR filter with size

*N*and $\overrightarrow{NL}$ is the nonlinear FIR filter with size

*M*(

*M*+ 1)/2. The schematic of the Volterra equalizer can be seen in Fig. 2. Filter coefficients can be optimized using the Least Mean Squares (LMS) or Recursive Least Squares (RLS) algorithms [8]. In order to provide results that can be used for real-time Volterra implementation, signal downsampling is performed before the filter at a rate defined as

**r**samples per symbol. Although less samples per symbol are available, filter memory for a given number of considered symbols is now smaller improving convergence.

Usually the reference signal required for tap adaptation is an estimate provided by the decision circuit. In the present case such an estimate is not available at the output of the filter as OFDM decoding has not been performed at this stage. Instead we propose to use a training sequence, i.e. a known OFDM waveform: the receiver has a stored copy of this waveform $\overrightarrow{{t}_{\mathit{ref}}}$ to be used as a reference for error signal estimation ( $\epsilon =\overrightarrow{y}-\overrightarrow{{t}_{\mathit{ref}}}$). Filter coefficients remain fixed until the next training sequence is transmitted. By using this approach the filter has self adapting coefficients that can cope with system changes and modulation changes, as adaptation is independent of the receiver. The training sequence can also be used for other purposes such as synchronization.

The effect of equalization can be seen on the received signal spectra [Fig. 1] where SSII is mitigated, indicated by out-of-band SSII mitigation.

## 4. Experimental set-up

Since we consider a complete transmission system, uplink and downlink experimental tests are performed. As in the downlink of a PON system, there is one Optical Line Terminal (OLT) for many Optical Network Units (ONUs), the choice of the EO converter is less sensitive to cost effectiveness as this is diluted by the number of users. For this reason we chose a lower chirp, higher bandwidth alternative in the form of an EML. For the ONU, cost effectiveness is paramount. Therefore a more cost effective EO conversion, albeit with more chirp and less bandwidth was selected in the form of a DML. We have then two set-ups for different transmitters as seen in Fig. 3.

The transmitted DMT signal is generated offline with an FFT size of 64 (31 sub-carriers, first sub-carrier is discarded) 9Gbaud(downlink)/4Gbaud(uplink) 12.5% cyclic prefix. It is passed to the DAC, a 6bit@28GS/s HHI AWG.

The CyOptics LIM10 is a 1550nm EML with an S21 3dB bandwidth of 10GHz and with 9dBm peak output power. The Optilab LDM5S515 is a 1550nm DFB laser with an analogue bandwidth of 2.5GHz@30mA and 3dBm maximum output power. This laser is intended for CWDM analogue communication schemes and for cable television transmission systems return-paths.

Two fibre lengths are investigated: 10km and 10km+28km SSMF. The system is set up so that NG-PON2 targets are met in both transmission directions for 10km SSMF. After initial tests, uplink transmission still showed a large power budget, therefore we chose to use extra 28km SSMF to further investigate Volterra equalization merits in a lower power budget, higher accumulated GVD system.

At the receiver side a Discovery Semiconductor R409 PIN+TIA is used. The LeCroy SDA830Zi sampling oscilloscope serves as an 8bit@40GS/s ADC with digital filtering at 6GHz. Signal equalization, OFDM decoding and BER estimation are performed offline.

For the EML, bias was set to −0.6V, driving signal was 1Vpp (**m**≈60%) and laser bias was set to 16mA, optimizing bitrate for 10km SSMF transmission. The DML biasing was set at 1.1V (41mA), with **m**≈60% allowing large power budget optimizing reach for a 38km SSMF transmission.

For the EML, optimization of filter size has shown that memory of nonlinear effects is longer than the one of linear effects. The optimum filter settings were 2 symbols for the linear part and 4.5 symbols for the nonlinear part. Using a sampling rate of **r**=4 this led to N=8 and M=18.

DML tests showed the opposite case, where memory of nonlinear effects has been shown to be shorter than the one of linear effects. This is due to dominant nonlinear effects being different for both considered devices. Memory length of 3 symbols for the linear part and 2 symbols for the nonlinear part were used. Two different filter sampling rates were tested **r**=3 and **r**=4, leading to: N=9, M=6 and N=12, M=8, respectively. The latter has shown to lead to 1dB improvement in terms of Received Optical Power (ROP). The results reported in the following were obtained using **r**=4.

Simulations and experiments have shown that less than 200 OFDM frames are needed for convergence of the LMS algorithm. Figure 1 shows Volterra equalization effects on the received electrical signal spectrum for both, EML and DML transmission. Out-of-band SSII reduced when compared to non-equalized transmission.

Offline processing was performed using *VPItransmissionMaker Optical Systems*.

## 5. Experimental results

With EML downlink transmission we are testing Volterra equalization for a system with less EO converter chirp and fibre length, both leading to lower chirp-GVD interactions. Nevertheless, downlink bandwidth is higher than uplink, which will lead to greater phase shifts between highest and lowest frequency components due to GVD. Figure 4(squares) shows the transmission after bit-and-power loading. By considering the FEC limit to be BER=10^{−3} we successfully transmitted a bitrate of 34Gb/s (net 30.5Gb/s). After performing Volterra equalization, the system shows improvement when compared to the unequalized system. Although limited, there is improvement for mostly all sub-carriers as seen in Fig. 4(diamonds). This small improvement is expected as the dominating impairment is not SSII but noise.

The uplink transmission with the DML is shown in Fig. 5(squares). To ensure a high power budget, the laser has to be driven with a large modulation index, in this case **m**≈60%, which drives the laser out of the linear regime, thus increasing chirp. Nevertheless 11.63Gb/s (net 10.17Gb/s) transmission was achieved. After Volterra equalization Fig. 5(diamonds), there is an improvement for higher frequency sub-carriers. Lower frequency sub-carriers are affected by receiver noise alone, whereas sub-carriers in the upper half of the frequency range are mostly affected by SSII [6]. At this point, power loading was performed to maintain a flat BER Fig. 5(crosses), where approximately three decades of improvement in terms of average BER are seen when compared to the non-equalized system Fig. 5(squares vs. crosses).

As the equalized signal presents an additional power margin, this can be used to increase the system capacity. For the target BER (10^{−5}) we achieve an increase of ≈22.6% from a bitrate of 11.63Gb/s (net 10.17Gb/s) to a bitrate of 14.25Gb/s (net 12.4Gb/s).

Both curves in Fig. 6(squares, stars) show the same behaviour for ROP below −5dBm. However the curve for higher bitrate Fig. 6(stars) is more sensitive to noise due to the use of higher constellation density.

For the unequalized signal Fig. 6(squares) an error floor can be observed, with Volterra equalization Fig. 6(crosses, stars) none is observable, showing that the deterministic effect can be efficiently mitigated. The system becomes limited by noise only.

## 6. Conclusion

We investigated and experimentally demonstrated the value of a nonlinear equalization scheme based on Volterra filter for the mitigation of sub-carrier to sub-carrier intermixing interferences generated by chirp-GVD interaction in intensity modulation direct detection OFDM systems. Through the use of a training sequence, the Volterra equalizer was able to adapt coefficients for mitigation of different amounts of SSII arising from different devices and transmission distances.

We were able to show the value of this scheme even for low chirp systems where we achieved a transmission of 34Gb/s DMT signal at 1550nm over 10km SSMF using a medium cost EML (downlink). Using the same scheme we were able to achieve higher improvements for the high chirp system with DML (uplink). These improvements can be translated in increased system power budget or alternatively increased system capacity by more than 20%, thus we achieved transmission of 14Gb/s DMT signal at 1550nm over 38km SSMF using a low-cost DFB with 2.5GHz 3dB bandwidth.

The improvement has been shown to be moderate for the downlink (EML). However for the uplink (DML) Volterra equalization proved to be of value in enabling lower cost transmitters at the ONU. They can be driven out of the linear regime increasing the power budget in the process as SSII are digitally mitigated.

## Acknowledgments

This work was supported in part by the German Ministry of Education and Research (Grant #16 BP 1136) in Framework of the Piano+ Project “OCEAN”.

## References and links

**1. **W. Shieh and I. Djordjevic, *OFDM for Optical Communications* (Academic Press, 2009).

**2. **X. Q. Jin, E. Hugues-Salas, R. P. Giddings, J. L. Wei, J. Groenewald, and J. M. Tang, “First real-time experimental demonstrations of 11.25Gb/s optical OFDMA PONs with adaptive dynamic bandwidth allocation,” Opt. Express **19**(21), 20557–20570 (2011). [CrossRef] [PubMed]

**3. **P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Communications **43**(2), 773–775 (1995). [CrossRef]

**4. **C. Wei, “Small-signal analysis of OOFDM signal transmission with directly modulated laser and direct detection,” Opt. Lett. **36**(2), 151–153 (2011). [CrossRef] [PubMed]

**5. **J. L. Wei, C. Sánchez, R. P. Giddings, E. Hugues-Salas, and J. M. Tang, “Significant improvements in optical power budgets of real-time optical OFDM PON systems,” Opt. Express **18**(20), 20732–207459 (2010). [CrossRef] [PubMed]

**6. **W. Yan, B. Liu, L. Li, Z. Tao, T. Takahara, and J. C. Rasmussen, “Nonlinear Distortion and DSP-based Compensation in Metro and Access Networks using Discrete Multi-tone,” in Proceedings of ECOC’2012 (Mo1B2).

**7. **D. Hsu, C. Wei, H. Chen, C. Song, I. Lu, and J. Chen, “74.4% SSII Cancellation in an EAM-based OFDM-IMDD Transmission System,” in Proceedings of OFC/NFOEC’2013 (OM2C7).

**8. **C. Xia and W. Rosenkranz, “Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering,” J. Lightwave Technol. **25**(4), 996–1001 (2007). [CrossRef]

**9. **W. Yan, T. Tanaka, B. Liu, M. Nishihara, L. Li, T. Takahara, Z. Tao, J. C. Rasmussen, and T. Drenski, “100 Gb/s Optical IM-DD Transmission with 10G-Class Devices Enabled by 65 GSamples/s CMOS DAC Core,” in Proceedings of OFC/NFOEC’2013 (OM3H1).