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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 Optical Fiber Technology 15 (2009) Contents lists available at ScienceDirect Optical Fiber Technology Sensitivity to signal quantization of 43 Gb/s and 107 Gb/s optical 16-QAM OFDM transmission with coherent detection Stephan Pachnicke a, *, Sinan Özdür b, Helmut Griesser c, Cornelius Fürst c, Peter M. Krummrich a a High Frequency Institute, TU Dortmund, Dortmund, Germany b EnBW AG, Karlsruhe, Germany c Ericsson GmbH, Stuttgarter Str. 139, Backnang, Germany article info abstract Article history: Received 13 February 2009 Revised 8 May 2009 Available online 24 July 2009 Keywords: Fiber optic transmission systems Long-haul transmission Optical fiber nonlinearity Orthogonal-frequency division multiplexing (OFDM) The sensitivity of optical orthogonal-frequency division multiplexing (OFDM) transmission to the finite resolutions of the digital-to-analog (DAC) and analog-to-digital converters (ADC) has been analyzed using numerical simulations. We show that for back-to-back configuration the requirements regarding the number of quantization bits for the DACs are similar to the ones of the ADCs. After transmission over metro and long-haul distances a higher resolution of the DAC/ADC is required compared to back-to-back configuration. We show that after transmission it is sufficient to enhance either the ADC resolution or the DAC resolution by 1 bit. Ó 2009 Elsevier Inc. All rights reserved. 1. Introduction Orthogonal-frequency division multiplexing (OFDM) is a multicarrier modulation technique where a single data stream is transmitted over a number of lower rate orthogonal subcarriers. OFDM is well known from wireless communications, and it has recently gained interest as an attractive modulation format for ultra high bit rate fiber-optic communications because of its tolerance towards linear effects. One of the major challenges for optical OFDM is its practical realization with ultra high data rate, which requires high-speed electronics and parallel processing for generating and recovering OFDM signals [1]. Scaling to higher bit rates also makes it extremely difficult to build digital-to-analog and analog-to-digital converters with the desired bandwidth and effective resolution requirements. We study 43 Gb/s and 107 Gb/s optical OFDM transmission with coherent detection in back-to-back configurations as well as in regio and long-haul transmission environments with focus on the finite digital-to-analog converter (DAC) and analog-todigital converter (ADC) resolutions. The motivation of these studies is to analyze the impact of different ADC and DAC resolutions on the receiver sensitivity, and to investigate by which amount the optimum resolution changes compared to the back-to-back configuration, if the transmission channel is distorted by dispersion and fiber nonlinearity. We show that transmission over several fiber spans has an impact on signal quantization, but it is sufficient to * Corresponding author. Fax: address: stephan.pachnicke@uni-dortmund.de (S. Pachnicke). increase the resolution by 1 bit only to tolerate the additional impairments. If one intends to increase the resolution of only one of the two converters, it is better to enhance the resolution of the ADCs. 2. Simulation setup The performance of 107 Gb/s and 43 Gb/s OFDM transmission is studied with a receiver based on coherent detection as an example for a possible realization of OFDM. For 107 Gb/s transmission a number of different modulation formats have been proposed in the past. In [2] a comparison of the different formats regarding the ADC/DAC requirements has been presented. As a summary the use of less complex modulation formats (such as OOK) lowers the requirements regarding the resolution, however, comes at the expense of a very high sampling rate. Multilevel formats such as 16-QAM require a higher resolution of 6 bits at a sampling rate of 53.5 GS/s [2]. In this paper the required DAC/ADC resolutions for 43 and 107 Gb/s OFDM transmission are investigated by simulations. Our simulation setup is structured as follows (compare Fig. 1). A binary data stream (pseudorandom bit sequence of length ) is mapped into complex 16-quadrature amplitude modulation (QAM) symbols and parallelized (serial-to-parallel conversion, S/P). The transmitter uses an inverse fast Fourier transform (IFFT) of size 1024 to generate a sampled waveform. Oversampling twice is implemented by using only half of the 1024 bits for data transmission and setting the other to zero at the input of the IFFT /$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi: /j.yofte

3 S. Pachnicke et al. / Optical Fiber Technology 15 (2009) Fig. 1. Block diagram of the transmitter and receiver setup. The first half of the complex IFFT array corresponds to the positive frequencies whereas the second half corresponds to the negative ones. As illustrated in Fig. 2 the virtual subcarriers are located in the middle of the array as these channels correspond to high frequency subcarriers after the IFFT operation (the zero frequency component is located at the beginning of the array as in typical hardware realizations of the IFFT). The required amount of oversampling is depending on the low pass filter characteristic of the DAC/ADC components. The sharper the edges the less oversampling will be required. After the IFFT, the symbol period is extended by adding a cyclic prefix. The cyclic prefix (cp) length is 25% of the FFT size. We believe that in practical system design the cp will have a fixed length and will not be tailored to the exact transmission distance leading to a larger overhead in many cases than actually required. Sixty-four pilot subcarriers are used for channel estimation and phase error correction. Thus 448 channels can be used for data transmission (14.29% overhead relative to the used subcarriers). If all overheads are included the raw data rate is Gb/s for the 107 Gb/s and Gb/s for the 43 Gb/s signal, respectively. Afterwards the OFDM time domain signal is parallel- Fig. 2. Position of the zero padding.

4 416 S. Pachnicke et al. / Optical Fiber Technology 15 (2009) to-serial (P/S) converted, clipped and sent into two separate digital-to-analog converters for the real and imaginary parts. For the above parameters minimum sampling rates of GS/s (for 107 Gb/s) and GS/s (for 43 Gb/s) are required in our setup for ADC/DACs (with two separate branches for the I and Q-parts). Current state-of-the-art ADCs operate at 24 GS/s with 6 bit resolution (4.2 bit effective at 12 GHz) built in 90 nm CMOS (compare e.g. [3]). DACs with 22 GS/s and 6 bit resolutions have been reported in e.g. [4]. Recently Fujitsu announced the availability of its Chargemode Interleaved Sampler (CHAIS) technology for use in its standard 65 nm CMOS process technology offering ADCs with 56 GSa/ s with 8 bit resolution [5]. In our setup the outputs of the DACs for the real and imaginary signal parts are combined and subsequently up-converted in the RF-domain using an electrical carrier with an intermediate frequency (IF) of 50 GHz for 107 Gb/s transmission and an IF of 35 GHz for 43 Gb/s OFDM transmission. We assumed that forward-error correction (FEC) with 7% overhead is used in the system. The resulting signal is fed into a Mach Zehnder Modulator (MZM). The MZM is biased at the null point for carrier suppression, and the modulation depth is set to 5%. Our simulations use the simulation platform PHOTOSS [6]. In the optical domain 16 samples/bit have been computed. In our setup we used a second order super Gaussian optical filter with a 3-dB bandwidth of 50 GHz for carrier and sideband suppression. The optical spectrum after SSB filtering is depicted in Fig. 3. The fiber link consists of 8 80 or km fiber spans with a dispersion parameter D = 17 ps/ nm/km, a dispersion slope S = 0.09 ps/nm 2 /km, a nonlinearity constant c SSMF = 1.37 (W km) 1 and an attenuation coefficient a = 0.2 db/km. No optical dispersion compensation is used. For the simulation of the signal propagation along the fiber a split-step Fourier method has been used. For an accurate simulation the choice of the split-step length is crucial. We allowed a maximum nonlinear phase shift of 1 mrad in our simulations. The noise figure (NF) of the erbium-doped fiber amplifiers (EDFAs) is set to 5.5 db. Amplified spontaneous emission noise has been added to the signal numerically (Monte-Carlo method), which also models nonlinear-phase noise impairments accurately. In the simulations we assumed that a BER of 10 3 (pre-fec) equivalent to a Q-factor of 10 db is sufficient to yield an error-free signal (BER < ) after the FEC. This boundary condition allows us to significantly lower the number of required bits for a statistically reliable simulation result (compared to a simulation without FEC). After transmission through the fiber link the optical signal is filtered with a second order super Gaussian filter with FWHM bandwidth of 50 GHz for both 107 Gb/s OFDM regio and 43 Gb/s long-haul OFDM transmission. At the receiver the optical signal is transformed back into the electrical domain with subsequent downconversion to the baseband. Heterodyne detection is realized with a local oscillator, a coupler and a balanced detector comprising of two single photodiodes. It is assumed that the polarization is adjusted ideally by an optical polarization controller. Laser phase noise is modeled as white Gaussian noise [7]. The linewidths of the transmitter and local-oscillator lasers are assumed as 2.5 MHz. The electrical signals are analog-to-digital converted, and after serial-to-parallel conversion the OFDM signal is transformed back to the frequency domain by applying the FFT. After pilot-aided phase recovery and symbol demapping the binary data is recovered, and the bit error ratio (BER) is evaluated numerically [8]. 3. Sensitivity to clipping and signal quantization In practical applications, the finite resolutions of the analog-todigital and digital-to-analog converters have to be considered [9,10]. Before digital-to-analog conversion the digital OFDM baseband signal is clipped to reduce the peak-to-average power ratio (PAPR). Signal clipping is modeled by a memory-less limiter [11]. The degree of clipping is measured with the logarithmic clipping ratio which is given as c log ¼ 10 log A2 max r 2 rms ð1þ Fig. 3. Optical OFDM spectrum of the 107 Gb/s signal after SSB filtering.

5 S. Pachnicke et al. / Optical Fiber Technology 15 (2009) where A max denotes the maximum desired amplitude and r rms is the root mean square value of the digital signal. The optimum clipping ratio has been determined in a back-to-back configuration and kept constant for transmission over fiber spans. The PAPR has been computed after the oversampling (with a resolution of 16 samples/bit). Fig. 4 shows the simulation results for 43 Gb/s and 107 Gb/s OFDM transmission in the back-to-back configuration. The required OSNR for a BER = 10 3 is depicted as a function of the clipping ratio for different (effective) DAC/ADC resolutions. Both the digital-to-analog and analog-to-digital converters operate at this point with the same resolutions. Because signal clipping causes nonlinear signal distortions, the clipping ratio should be rather low. The optimum clipping ratio is found around 11 db for both 43 Gb/s and 107 Gb/s back-to-back transmission. In the following 11 db signal clipping is assumed, and the simulations are repeated with different resolutions for the digital-to-analog and analog-todigital converters. Furthermore in the rest of this paper we will use the Q-factor instead of the required OSNR as a figure of merit. Because noise is added numerically to the signal in our simulations and nonlinear-phase noise interactions may occur along the fiber it is not possible to do noise-loading at the receiver. Thus the calculation of the required OSNR instead of the Q-factor increases the computational time significantly as it is necessary to perform a large number of simulations to estimate the required OSNR for the given BER = The use of the Q-factor on the other hand allows us to perform only a single calculation for each combination of ADC/DAC resolutions. As can be observed in Fig. 5 the Q-factor increases with the ADC resolution for a constant DAC resolution. The same behavior is found, if the DAC resolution is varied and the ADC resolution is kept constant. Our simulations show that for 43 Gb/s transmission a Q-factor of >10 db can be achieved with 5-bit DACs and 5-bit ADCs (Fig. 5, top), which is above FEC threshold. Further increase of the ADC resolution does not offer significant benefits. For 107 Gb/s transmission also 5 bit ADC/DAC resolutions satisfy the Q-factor requirements (Q > 9.7 db before FEC) in the back-to-back Fig. 4. Required OSNR for a BER = 10 3 for 43 Gb/s back-to-back transmission (top) and for 107 Gb/s back-to-back transmission (bottom) as a function of the clipping ratio and DAC/ADC resolutions from 4- to 8-bit. Fig. 5. Q-factor as a function of different DAC/ADC resolutions for 43 Gb/s back-toback transmission (top) and for 107 Gb/s back-to-back transmission (bottom).

6 418 S. Pachnicke et al. / Optical Fiber Technology 15 (2009) configuration. The Q-factor varies about 2 db, if the ADC resolution is increased from 4- to 8-bit (using 5-bit DAC resolution). A similar behavior is found, if the DAC resolution is varied and the ADC resolution is kept constant. Using 5-bit ADCs, the Q-factor increases about 2 db with an increase of the DAC resolution from 4- to 8- bit. Simulations show that 4-bit DAC/ADC resolutions are insufficient to realize a Q-factor above 9.7 db, which corresponds to the FEC limit (see Fig. 5, bottom). Hence, 4 bit resolutions yield insufficient performance for practical systems. In the back-to-back configuration the ADC resolution should be at least as high as the DAC resolution. Nevertheless, the requirements for the DACs are very similar to that of the ADCs. In the following our investigations are extended to links with transmission over 8 (regio) and 12 (long-haul) fiber spans. Our simulations show that the optimum fiber launch power for a transmission over km fiber spans with a net data rate of 43 Gb/s is around 3 dbm, and for a transmission over 8 80 km fiber spans with a net data rate of 107 Gb/s it is around 1 dbm. For a higher signal power the BER does not fall below 10 3 due to strong (intrachannel) nonlinear distortions between different subcarriers. If the transmission channel is distorted by dispersion and fiber nonlinearity, the quantization requirements are expected to change. For the 43 Gb/s transmission it is observed that the FEC limit of Q > 10 db cannot be achieved with 5 effective bit ADC/ DAC resolutions (Fig. 6, top). However, the curves have not been merely shifted (compared to Fig. 5) as one might expect when the signal is degraded linearly, but the density of the contour lines has increased significantly for ADC/DAC resolutions below approximately This behavior most probably results from the fiber nonlinearity. The converter resolution must be increased (compared to the back-to-back case) to compensate for the transmission penalty and achieve the minimum Q-factor requirements. It is sufficient to increase the resolution of either the DAC or the ADC by 1 bit (to 6 bits), where increasing the ADC resolution provides slightly better performance. However, as it is easier to build a DAC with a higher resolution at very high sampling rates, the option to increase the number of DAC quantization bits may be preferred. In practical realizations the margin to the FEC threshold should be increased further to guarantee error free transmission in all system operating conditions. This may be achieved by a FEC with a higher coding gain or a decreased transmission distance. Similar results are also obtained for 107 Gb/s OFDM transmission (Fig. 6, bottom). Again the resolutions of the ADC/DACs should be increased by 1 bit compared to back-to-back configuration, and enhancing the resolution of the ADC shows better results. 4. Conclusions We have presented a study of 107 Gb/s metro and 43 Gb/s longhaul optical OFDM transmission using coherent detection with focus on finite resolutions of the digital-to-analog and analogto-digital converters. For both cases we have shown that in a back-to-back configuration the requirements for the digital-toanalog converters are similar to the ones of the analog-to-digital converters. An ADC resolution of more than 5 bits does not offer a significant performance improvement. For metro and long-haul transmission we have found that this behavior has changed due to the impairments introduced by the transmission over fiber spans. The ADC or DAC resolutions must be increased compared to the back-to-back configuration. This time no significant increase in the signal quality after transmission is found for more than 6 bits ADC resolution. The transmission performance dependents slightly more on the ADC resolutions than on the DAC resolutions. However, to achieve the desired Q-factor it is sufficient to increase Fig. 6. Q-factor as a function of different DAC and ADC resolutions after 43 Gb/s transmission over km fiber spans with a fiber launch power of 3 dbm (top) and after 107 Gb/s transmission over 8 80 km fiber spans with a fiber launch power of 1 dbm (bottom). either the DAC resolution or the ADC resolution by only 1 bit compared to the back-to-back case. References [1] W. Shieh et al., 107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing, Opt. Express 16 (9) (2008) [2] H. Sun et al., Modulation formats for 100 Gb/s coherent optical systems, in: OFC 09, OTuN1, March [3] P. Schvan, et al., A 24 GS/s 6b ADC in 90 nm CMOS, in: IEEE ISSCC 08, February [4] P. Schvan, et al., A 22 GS/s 6b DAC with integrated digital ramp generator, in: IEEE ISSCC 05, February [5] < FACTSHEET 56 GSa/s 8-bit ADC DEVELOPMENT KIT. [6] M. Windmann et al., PHOTOSS: the simulation tool for optical transmission systems, Proc. SPIE 5247 (September) (2003) Orlando. [7] X. Yi et al., Phase estimation for coherent optical OFDM, IEEE Photon. Technol. Lett. 19 (12) (2007) [8] S. Jansen et al., Coherent optical 25.8 Gb/s OFDM transmission over 4160-km SSMF, IEEE J. Lightwave Technol. 26 (1) (2008) 6 15.

7 S. Pachnicke et al. / Optical Fiber Technology 15 (2009) [9] Y. Tang et al., Coherent optical OFDM transmitter design employing predistortion, IEEE Photon. Technol. Lett. 20 (11) (2008) [10] C. Lee et al., Impacts of non-ideal analog interfacing factors on OFDM baseband signals, in: IEEE IMTC 05, May 2005, vol. 1, pp [11] R. You et al., Average power reduction techniques for multiple-subcarrier intensity-modulated optical signals, IEEE Trans. Commun. 49 (12) (2001) Stephan Pachnicke received the M.Sc. degree in Information Engineering from City University, London, United Kingdom in In 2002 and 2005 he received the Dipl.-Ing. and Dr.-Ing. degrees in Electrical Engineering from the TU Dortmund, Germany. In 2005 he received the Dipl.-Wirt. Ing. degree in Business Administration from Fern Universität, Hagen, Germany. Currently he is working at the High Frequency Institute, TU Dortmund, in the field of analytical modeling and simulation of optical communication systems and the assessment of physical-layer impairment aware routing algorithms. Helmut Griesser received the diploma and the Ph.D. in Electrical Engineering in 1996 and 2003, respectively, both from the University of Ulm. Since 2002 he is with Marconi Communications, Germany, (now Ericsson GmbH) working on optical fiber communication systems. His special interests are optical modulation formats, digital signal processing, and forward-error correction for optical transmission systems. He has been involved in the national and EC research programs MultiTeraNet and IST FP6 (NOBEL), and is currently coordinating the Ericsson subproject of the multinational Celtic Project 100GET. Cornelius Fuerst received the diploma and the Ph.D degrees both in physics from the Technical University of Munich, Germany, in 1995 and 1998, respectively. In 1998, he joined the Advanced Technology Department of Siemens Information and Communication Networks Optical Networks, where he was engaged in the development of optical transmission technologies. In 2002 he joined Marconi (now Ericsson GmbH), where he worked on Product and Technology Strategy for optical networks. Since 2007 he is head of the Advanced Technology group in Backnang, Germany. Cornelius Fuerst has 10 patents and more than 40 publications in the area of optical network technology. Peter M. Krummrich received his Dipl.-Ing. and Dr.- Ing. degrees in Electrical Engineering from the Technical University of Braunschweig, Germany, in 1992 and 1995, respectively, where he worked on wavelength tuning of laser diodes using external cavities and Praseodymium-doped fiber amplifiers. In 1995 he joined Siemens AG where his research interest focused on distributed Erbium-doped fiber amplifiers. The field of activity in the following years comprised technologies for the next generation of ultra high capacity DWDM transmission systems with an emphasis on technologies enabling more robust systems or enhanced reach such as Raman amplification, advanced modulation formats, adaptive equalizers, and PMD compensation. Since May 2007, he is working in his new position as a professor at the TU Dortmund, holding the chair for high frequency technology.

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