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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 20376–20386
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Error vector magnitude based parameter estimation for digital filter back-propagation mitigating SOA distortions in 16-QAM

Siamak Amiralizadeh, An T. Nguyen, and Leslie A. Rusch  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 20376-20386 (2013)
http://dx.doi.org/10.1364/OE.21.020376


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Abstract

We investigate the performance of digital filter back-propagation (DFBP) using coarse parameter estimation for mitigating SOA nonlinearity in coherent communication systems. We introduce a simple, low overhead method for parameter estimation for DFBP based on error vector magnitude (EVM) as a figure of merit. The bit error rate (BER) penalty achieved with this method has negligible penalty as compared to DFBP with fine parameter estimation. We examine different bias currents for two commercial SOAs used as booster amplifiers in our experiments to find optimum operating points and experimentally validate our method. The coarse parameter DFBP efficiently compensates SOA-induced nonlinearity for both SOA types in 80 km propagation of 16-QAM signal at 22 Gbaud.

© 2013 OSA

1. Introduction

Various post- and pre-compensation schemes have been proposed to overcome the nonlinear effect of SOAs [13

13. A. Ghazisaeidi and L. A. Rusch, “On the efficiency of digital back-propagation for mitigating SOA-induced nonlinear impairments,” J. Lightwave Technol. 29(21), 3331–3339 (2011). [CrossRef]

18

18. S. Lange, Y. Yoshida, and K. Kitayama, “ A low-complexity digital pre-compensation of SOA induced phase distortion in coherent QAM transmissions,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2013), paper OTh3C.7. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2013-OTh3C.7

]. Both approaches rely on creating an inverse SOA to compensate for the SOA nonlinearity. In pre-compensation, the inverse SOA is applied at the transmitter before the signal is distorted by the SOA, whereas in post-compensation the inverse SOA is implemented at the receiver to deal with SOA distortion. While pre-compensation can be attractive when SOA parameters are known, post-compensation has the ability to blindly adapt itself to unknown SOA parameters.

We propose a simple, low overhead method to optimize DFBP parameters. We used the error vector magnitude (EVM) as a figure of merit for the optimization (as opposed to bit error rate) to reduce complexity. We further propose a strategy to reduce the search space for optimal parameters, and show that coarse resolution can achieve compensation on a par with a computationally expensive search over a space with fine resolution. We demonstrate the efficiency of this technique in DFBP adaptation via both experiment and simulations. We examine SOAs designed for both linear and nonlinear performance. We determine the operating point of each SOA to obtain high gain while staying in a regime where post-compensation is effective. We target bit error rate (BER) below forward error correction (FEC) threshold with ~7% overhead. We investigate the propagation performance by including up to 80 km of fiber to the system.

The paper is structured as follows. In section 2, we discuss the relationship between parameters of the DFBP and parameters of the transmitting SOA. We also discuss our strategy for reducing the computational burden of DFBP parameter optimization. In section 3, the experimental setup is explained. Section 4 is devoted to experimental and numerical results. Finally, conclusions are drawn in section 5.

2. EVM based parameter estimation of DFBP

The efficiency of DFBP for post-compensating SOA nonlinearities in coherent communication systems has been investigated via both simulations and experiments [13

13. A. Ghazisaeidi and L. A. Rusch, “On the efficiency of digital back-propagation for mitigating SOA-induced nonlinear impairments,” J. Lightwave Technol. 29(21), 3331–3339 (2011). [CrossRef]

, 14

14. S. Amiralizadeh, A. T. Nguyen, C.-S. Park, A. Ghazisaeidi, and L. A. Rusch, “Experimental validation of digital filter back-propagation to suppress SOA-induced nonlinearities in 16-QAM,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2013), paper OM2B.2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2013-OM2B.2 [CrossRef]

]. DFBP parameters were shown to play an important role in post-compensation performance. These parameters can be determined in one of two ways. In the first case the SOA can be characterized experimentally, e.g., the parameters can be inferred for the SOA gain and conversion efficiency (CE) curve [13

13. A. Ghazisaeidi and L. A. Rusch, “On the efficiency of digital back-propagation for mitigating SOA-induced nonlinear impairments,” J. Lightwave Technol. 29(21), 3331–3339 (2011). [CrossRef]

,19

19. B. Filion, A. Ghazisaeidi, L. A. Rusch, and S. Larochelle, “Extraction of semiconductor optical amplifier parameters for wavelength conversion modeling,” in Proceedings of IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, Arlington, 2011), pp. 367–368. [CrossRef]

]. The second method is to sweep the parameters, choosing those resulting in the best BER [14

14. S. Amiralizadeh, A. T. Nguyen, C.-S. Park, A. Ghazisaeidi, and L. A. Rusch, “Experimental validation of digital filter back-propagation to suppress SOA-induced nonlinearities in 16-QAM,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2013), paper OM2B.2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2013-OM2B.2 [CrossRef]

]. From a mathematical standpoint, and assuming only linear impairments and AWGN, performance should be similar.

The nature of post-compensation is, however, that the source of the nonlinearity is remote from the digital signal processing. The optical and electrical systems in the link will introduce various impairments, as will the digital signal processing algorithms used for filtering, dispersion compensation and retiming before post-compensation can be applied. The accumulation of these effects will change the nature of the SOA-induced distortion, making the use of parameters gleaned from the SOA characterization less likely to be effective. Sweeping the parameter set to minimize BER yields better results. The parameter set essentially characterizes the overall channel, including but not limited to the SOA.

2.1 DFBP parameters

The DFBP method is predicated on inversing the transmitter SOA behavior. The SOA model and the parameters capturing SOA behavior in forward propagation are critical for DFBP. The relationship between SOA input and output fields is given by [20

20. A. Saleh, “Nonlinear models of travelling-wave optical amplifiers,” Electron. Lett. 24(14), 835–837 (1988). [CrossRef]

]
Eout(t)=Ein(t)e12(1jα)h(t),
(1)
where Ein(t) and Eout(t) are respectively the SOA input and output fields, α is the linewidth enhancement factor and h(t) represents the gain exponent or integrated material gain. The following SOA dynamic gain equation can be solved to find h(t):
τcdh(t)dt=h0h(t)(eh(t)1)|Ein(t)|2Psat,
(2)
where h0, Psat and τc are the unsaturated gain exponent, the saturation power and the carrier lifetime, respectively. Therefore, knowledge of h0, α, Psat and τc enables us to model the relationship between the SOA input and output fields. These four values are the parameter set describing SOA behavior and those needed to implement the DFBP. The input power |Ein|2 can be easily measured.

The DFBP is developed from a linearized version of the gain Eq. (2) to reduce complexity [13

13. A. Ghazisaeidi and L. A. Rusch, “On the efficiency of digital back-propagation for mitigating SOA-induced nonlinear impairments,” J. Lightwave Technol. 29(21), 3331–3339 (2011). [CrossRef]

,15

15. F. Vacondio, A. Ghazisaeidi, A. Bononi, and L. A. Rusch, “Low-complexity compensation of SOA nonlinearity for single-channel PSK and OOK,” J. Lightwave Technol. 28(3), 277–288 (2010). [CrossRef]

]. In this approach, h(t) is assumed to be equal to the sum of the average gain exponent and zero-average fluctuations, i.e., h(t)=h¯+δh(t). Using the following static gain equation, h¯ can be found
h0h¯=(eh¯1)|Ein(t)|2Psat,
(3)
where the negative sign of h0 is introduced to implement an “inverse SOA”. Let Δt be the sampling period, which is equal to symbol time since the DFBP input signal is one sample per symbol in our implementation (oversampling factor = 1). As shown in the DFBP block diagram in Fig. 1
Fig. 1 Block diagram of coarse estimation method for DFBP.
, we find the zero-average fluctuations, δh(t), using a digital filter which is derived from the linearized SOA model by taking z-transform [13

13. A. Ghazisaeidi and L. A. Rusch, “On the efficiency of digital back-propagation for mitigating SOA-induced nonlinear impairments,” J. Lightwave Technol. 29(21), 3331–3339 (2011). [CrossRef]

]. For convenience we define two parameters, c1 and c2, from the SOA parameter set and the easily measured input power |Ein|2 via
c1=1eh¯1+|Ein|2eh¯PsatΔtΔt+τeff,
(4)
c2=Δt2τeffΔt+2τeff,
(5)
where
τeff=τc1+|Ein|2eh¯Psat.
(6)
Having found h(t), the compensated output is found by multiplying the input by e(1jα)2h(t).

2.2 DFBP parameter estimation

Our objective is to select the remaining two parameters to minimize the BER. Simulation of BER can be computationally costly and require use of training sequence (i.e., knowledge of bits transmitted). The EVM is known to correlate well with BER at reasonable SNR levels and is given by [21

21. R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photon. Technol. Lett. 24(1), 61–63 (2012). [CrossRef]

]
EVM=1Ni=1N|EiE0,i|2,
(7)
where Ei, E0,i and N are received symbol, ideal constellation point for received symbol and number of randomly transmitted data. The EVM figure of merit does not require knowledge of transmitted bits thus enabling blind adaptation. We propose the use of EVM for optimization of Psat and τc in a computationally simple manner and show via simulation and experiment that such an optimization leads to significant BER improvement.

2.3 SOA characterization

We use the simulator presented in [22

22. D. Cassioli, S. Scotti, and A. Mecozzi, “A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(9), 1072–1080 (2000). [CrossRef]

] and consider a SOA waveguide as cascade of K small sections for greater accuracy. The SOA distributed loss and amplified spontaneous emission (ASE) is included in this model. The propagation equations are solved using Runge-Kutta fourth order algorithm when K = 80 as “ground truth”. For back-propagation, we set K = 1 (one inverse gain block) to reduce complexity, as it has been shown this causes minimal penalty [14

14. S. Amiralizadeh, A. T. Nguyen, C.-S. Park, A. Ghazisaeidi, and L. A. Rusch, “Experimental validation of digital filter back-propagation to suppress SOA-induced nonlinearities in 16-QAM,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2013), paper OM2B.2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2013-OM2B.2 [CrossRef]

].

Table 1

Table 1. SOA Parameters used for simulation of SOA (K = 80) and in DFBP (K = 1)

table-icon
View This Table
indicates the parameters extracted by characterization of the two SOAs used in our experiments. We examined two commercial SOAs with differing design objectives; the first stresses gain and linearity (linear Covega BOA-2679 or L-SOA with noise figure of 7.3 dB), while the second enhances the nonlinear response for optical signal processing applications (nonlinear CIP-NL-OEC-1550 or NL-SOA with noise figure of 8.4 dB). We varied the three parameters h0, Psat and L (SOA loss) and fitted them to the average gain versus SOA input power curve. To extract the remaining two parameters, α and τc, we measured CE for four-wave mixing in SOAs as a function of frequency detuning. We compared the theoretical curve of CE versus frequency detuning with experimental results, and varied α and τc to find a good fit between the two curves [19

19. B. Filion, A. Ghazisaeidi, L. A. Rusch, and S. Larochelle, “Extraction of semiconductor optical amplifier parameters for wavelength conversion modeling,” in Proceedings of IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, Arlington, 2011), pp. 367–368. [CrossRef]

].

3. Experimental setup

In this section we take the techniques laid out in section 2 and validate them experimentally. Our investigation includes back-to-back (B2B) measurements as well as propagation for up to 80 km. Please note that while our transmitter is constructed from discrete components for experimental convenience, DFBP for post-compensation targets integrated transmitter sources with a SOA booster stage, or other subsystems (e.g., wavelength converters) where SOAs may be operated in saturation.

Figure 2
Fig. 2 Experimental setup for 22-Gbaud 16-QAM single-channel coherent detection system. SOA is used at transmitter to obtain higher launched power. Post-compensation block is added in the DSP part to mitigate nonlinearity induced by SOA. In configuration (B), 80 (or 60) km of SSMF is added and ASE noise loading is employed to adjust OSNR comparing to (A). The inset illustrates efficiency of coarse parameter DFBP for compensating nonlinearity induced by each of the two SOAs utilized in our experiment. BPG: bit pattern generator
shows the experimental setup. An external cavity laser (ECL) source with less than 100 kHz 3-dB linewidth is used at 1550 nm. Each of two 22-Gb/s 4-level electrical signals is obtained by combining two 220-1 pseudo-binary random sequences (PRBSs). These signals form the 16-QAM signal set that drives the I/Q (in-phase/quadrature) Mach-Zehnder external modulator (SHF 46213D). The SOA is used in a booster configuration at the transmitter to increase launched power. The 1-nm optical band-pass filter after the SOA has 3.8-dB loss, and limits ASE.

We performed our experiment in two different configurations. In configuration (A) we examine back-to-back performance with the SOA present. In configuration (B) the signal is launched through 80 (or 60) km of standard single mode fiber (SSMF) with 0.19 dB/km loss. The received optical signal-to-noise ratio (OSNR) is adjusted using a variable optical attenuator (VOA) and an EDFA. After a polarization controller (PC), a VOA adjusts the received power to −7 dBm for configuration (A) and −10 dBm for configuration (B). The local oscillator (LO) was a narrow linewidth ECL with 14 dBm output power. We used these values for LO and receiver input power to operate the coherent receiver at its optimum working regime.

After coherent detection with a 22-GHz 3-dB bandwidth integrated receiver, the signal is digitized using two channels of a commercial 80-GS/s real-time oscilloscope with 30 GHz bandwidth. Signal processing is performed offline on 2 million captured samples. In the digital signal processing (DSP), we apply a Gaussian low-pass filter and do dispersion compensation, if needed. We then perform resampling and timing recovery. Afterwards, we numerically boost the signal power to its inferred value at the SOA output and utilize the DFBP method to post-compensate the SOA-induced nonlinearity. We remove the frequency offset between the LO and the received signal using the estimator suggested in [23

23. M. Selmi, Y. Jaouen, and P. Cibalt, “Accurate digital frequency estimator for coherent PolMux QAM transmission systems,” in European Conference and Exhibition on Optical Communication, Vienna, Austria, P3.08 (2009).

]. We apply a MMSE filter to mitigate the effect of limited receiver bandwidth. We then employ a decision-aided maximum likelihood algorithm to estimate the carrier phase [24

24. S. Zhang, C. Yu, P. Y. Kam, and J. Chen, “Parallel implementation of decision-aided maximum likelihood phase estimation in coherent M-ary phase-shifted keying systems,” IEEE Photon. Technol. Lett. 21(19), 1471–1473 (2009). [CrossRef]

]. Finally, we choose the closest symbol to the received I/Q coordinates from 16-QAM constellation and carry out symbol to bit mapping. We synchronize to the transmitted PRBS, count errors and estimate bit error rate (BER). The signal constellations for two SOAs are shown as an inset in Fig. 2. The amplitude and phase distortions deteriorate signal performance, nevertheless, application of coarse parameter DFBP leads to recovery of the 16-QAM signal.

4. Experimental and numerical results

In our first set of results, we show the effect of the induced nonlinearity on BER when varying SOA input power and applying different bias currents to specify a suitable working point for each SOA. We devote the second subsection to comparing the performance of the proposed DFBP with parameters optimized over the discrete parameter set (Fig. 1) to a DFBP whose parameters were optimized over the same range of values, but with much greater granularity. Having the appropriate working conditions, we concentrate on the results from configuration (B) to find the OSNR penalty due to application of SOA as compared to the B2B case for which we have no SOA and fiber. By transmitting the distorted signal from SOA over a certain length of fiber, it is expected to experience degradation of performance comparing to results from first subsection due to interaction between SOA nonlinearity and effects originated from transmission, e.g., dispersion. Therefore, in choosing suitable operating points for the SOAs, sufficient distance of BER from the FEC limit was targeted.

4.1 Appropriate SOA operating condition

We change the input power to the SOA in configuration (A) of the experimental setup and examine system performance for different SOA saturation levels. The BER versus launched power, Plaunched, for NL-SOA and L-SOA are presented in Figs. 3(a)
Fig. 3 BER versus launched power to the fiber with and without coarse parameter DFBP. (a) NL-SOA; inset: gain versus bias current. (b) L-SOA. sim.: simulations, exp.: experiment.
and 3(b), respectively. We observe significant improvement (~6 dB) in launched power to the fiber when applying DFBP to mitigate nonlinearity for both SOAs. As expected, with higher bias currents, the SOA gives more gain which in turn leads to higher launched powers. The performance is, however, limited due to severe nonlinearity.

In Fig. 3(a), the launched power is 1 dB less for Ibias = 160 mA as compared to launched powers for Ibias = 250 mA and 300 mA. Although BER less than a FEC limit of 3.8e-3 is achievable for all three examined bias currents, we choose Ibias = 160 mA as a good working point for two reasons. First, the BER distance from the FEC limit is more reliable for this case and second, the SOA power consumption is less for lower bias currents. We show the gain versus bias current of the CIP nonlinear SOA as an inset to demonstrate that the obtained gain decreases quickly for currents below around 160 mA. Therefore, Ibias = 160 mA is a good compromise between gain and performance. As shown in Fig. 3(b), the difference between launched power for Ibias = 400 mA and 600 mA is 1 dB for the linear Covega SOA, as well. Therefore, we select Ibias = 400 mA as operating point for the Covega SOA considering above the previously mentioned reasons, and especially to lower power consumption. Simulation results for the selected bias currents are shown with diamond makers for both SOAs in Fig. 3 verifying the experimental results for coarse parameter DFBP. As mentioned in section 2.3, forward propagation parameters for SOA in simulations are adjusted using the information from SOA characterizations.

4.2 Coarse vs. fine parameter estimation

We captured over 1 million symbols per SOA input power level to compare the performance of EVM-optimized coarse parameter estimation vs. BER optimized, fine parameter estimation. In the first case, we examine only 4000 symbols and find Psat and τc (examining 45 pairs) that minimizes the EVM for those symbols. We then take the EVM optimized Psat and τc and find the BER over the entire captured data set. In the second case, we take all captured data and minimize the BER by examining in turn a total of ~300 pairs of values for Psat and τc. The same captured data is used in both cases. We repeated the procedure for each SOA type examined.

The BER versus input power of SOA is reported in Fig. 4
Fig. 4 BER versus SOA input power for fine parameter DFBP, coarse parameter DFBP and DFBP using the parameters obtained from characterization of NL-SOA and L-SOA.
. Results are given for the nonlinear NL-SOA (160 mA bias current) and for the L-SOA (400 mA bias current). BER for the DFBP found with EVM optimization using coarse resolution is given with circle markers, while results for the DFBP found with BER optimization using fine resolution are given with triangle markers. In addition, the results for parameters attained by SOA characterization are shown with square markers. For both SOA types, we see negligible BER degradation when using the simpler, less computationally expensive EVM based optimization. Our demonstration establishes that post-compensation can be applied without use of a training sequence, and with minimal delay and computation. However, when using the parameters obtained by SOA characterization, we observe significant performance degradation especially for L-SOA. These results suggest that, in contrast to our proposed method, parameters given by measurement do not guarantee efficient compensation. The degradation stems from two effects: first, the SOA operating point for characterization and for coherent detection are in most cases different and second, the accumulation of various effects during transmission, e.g. dispersion and filtering effect, are not captured during characterization of SOA parameters.

4.3 Propagation performance – two SOA types

In this section we examine the efficiency of DFPB in the presence of fiber propagation for two types of SOA. Figure 6
Fig. 6 BER versus OSNR in 0.1 nm resolution bandwidth. With application of SOA at transmitter and using DFBP with coarse parameter estimation, signal can be transmitted over 80 km of fiber which is accompanied with 3.8 dB OSNR penalty at FEC threshold of 3.8e-3 comparing to B2B case without SOA and fiber.
shows BER versus received OSNR measured in 0.1 nm resolution bandwidth; the BER curve with square markers corresponds to B2B without SOA (and hence no nonlinearity or DFBP), i.e., no SOA and no fiber. Two types of SOA, linear and nonlinear, are examined using a DFBP with parameters found per the method described in section 2. The SOA currents were fixed at the values determined in section 4.1. The SOA input power was set to Pin = −21 and −17 dBm (or equivalently, Plaunched ≈1 dBm) for NL-SOA and L-SOA, respectively. We launched the 16-QAM signal into 80 and 60 km of SSMF fiber for each SOA. The OSNR penalty is less than 4 dB for all cases when we apply the DFBP algorithm. While not shown in Fig. 6, we also observed that with 100 km of fiber, the BER is above the FEC limit within the achievable OSNR range.

5. Conclusion

We presented a simple method based on EVM to coarsely estimate parameters of DFBP. The proposed scheme determines DFBP parameters by processing a small portion of data (~4000 symbols). We demonstrated, via experiment and simulations, the efficiency of a DFBP using an EVM optimized, coarse parameter estimation for mitigating SOA-induced phase and amplitude distortions in 16-QAM with coherent detection at 22 Gbaud. The penalty due to coarse estimation of DFBP parameters is negligible compared to DFBP with very fine parameter estimation. We examined the OSNR penalty induced by application of SOA as booster at transmitter in transmission of signal over 80 km of SSMF. The experimental results show less than 4 dB OSNR penalty at FEC threshold (BER = 3.8e-3) for both nonlinear and linear SOAs employed in our experiment.

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S. Amiralizadeh, A. T. Nguyen, C.-S. Park, A. Ghazisaeidi, and L. A. Rusch, “Experimental validation of digital filter back-propagation to suppress SOA-induced nonlinearities in 16-QAM,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2013), paper OM2B.2. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2013-OM2B.2 [CrossRef]

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F. Vacondio, A. Ghazisaeidi, A. Bononi, and L. A. Rusch, “Low-complexity compensation of SOA nonlinearity for single-channel PSK and OOK,” J. Lightwave Technol. 28(3), 277–288 (2010). [CrossRef]

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B. Filion, A. Ghazisaeidi, L. A. Rusch, and S. Larochelle, “Extraction of semiconductor optical amplifier parameters for wavelength conversion modeling,” in Proceedings of IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, Arlington, 2011), pp. 367–368. [CrossRef]

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A. Saleh, “Nonlinear models of travelling-wave optical amplifiers,” Electron. Lett. 24(14), 835–837 (1988). [CrossRef]

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R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photon. Technol. Lett. 24(1), 61–63 (2012). [CrossRef]

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D. Cassioli, S. Scotti, and A. Mecozzi, “A time-domain computer simulator of the nonlinear response of semiconductor optical amplifiers,” IEEE J. Quantum Electron. 36(9), 1072–1080 (2000). [CrossRef]

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M. Selmi, Y. Jaouen, and P. Cibalt, “Accurate digital frequency estimator for coherent PolMux QAM transmission systems,” in European Conference and Exhibition on Optical Communication, Vienna, Austria, P3.08 (2009).

24.

S. Zhang, C. Yu, P. Y. Kam, and J. Chen, “Parallel implementation of decision-aided maximum likelihood phase estimation in coherent M-ary phase-shifted keying systems,” IEEE Photon. Technol. Lett. 21(19), 1471–1473 (2009). [CrossRef]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4510) Fiber optics and optical communications : Optical communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: June 18, 2013
Revised Manuscript: July 26, 2013
Manuscript Accepted: August 15, 2013
Published: August 22, 2013

Citation
Siamak Amiralizadeh, An T. Nguyen, and Leslie A. Rusch, "Error vector magnitude based parameter estimation for digital filter back-propagation mitigating SOA distortions in 16-QAM," Opt. Express 21, 20376-20386 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-20376


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