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Performance Assessment of High Density Wavelength Division Multiplexing Systems with Dispersion Supported Transmission at 10 Gbit/s Mário M. Freire Department of Mathematics and Computer Science, University of Beira Interior Rua Marquês d'Ávila e Bolama, P-6200 Covilhã, Portugal Henrique J. A. da Silva Department of Electrical Engineering, Pole II of University of Coimbra Pinhal de Marrocos, P-3030 Coimbra, Portugal Abstract solution for high-capacity DST on long spans of SMF is This paper presents a simulation methodology for the optical transmission of wavelength division performance assessment of wavelength division multiplexed (WDM) 10 Gbit/s channels. We have multiplexing (WDM) systems using directly modulated discussed the impact of single- and double-cavity Fabry- quantum-well lasers and optically preamplified direct Perot (FP) demultiplexers on the performance of detection receivers. The methodology is based on a pure dispersion supported transmission of two [5] and three [6] semi-analytical method which combines noiseless WDM 10 Gbit/s WDM channels separated 1 nm. In a further transmission simulation with noise analysis in those study, we have assessed the system performance for three systems. Using this approach, we discuss performance 10 Gbit/s WDM channels separated 0.5 nm, assuming that implications of single-cavity, double-cavity and three- a three-mirror FP filter is used as demultiplexer [7]. mirror Fabry-Perot (FP) demultiplexers for dispersion In this paper, a modeling and simulation methodology supported transmission (DST) of three WDM channels is presented for performance assessment of multichannel separated 1 nm. Assuming that a three-mirror filter is optical communication systems. Using this methodology, used as demultiplexer, the performance of a 40 Gbit/s we compare the performance of three-channel WDM-DST capacity four-channel WDM-DST system is assessed for with 1 nm channel spacing for single-cavity, double-cavity 0.5 nm channel spacing. The robustness of the and three-mirror FP demultiplexers. The performance of a multichannel DST method against pattern dependencies is 40-Gbit/s capacity four-channel WDM-DST system is also investigated for this channel spacing. assessed for 0.5 nm channel spacing, assuming that a three-mirror Fabry-Perot filter is used as demultiplexer. 1. Introduction 2. Modeling and simulation methodology Single-channel lightwave systems operated at 10 The most appropriate performance measure for digital Gbit/s are being introduced commercially, but long term optical communication systems is the average error trends indicate that signaling rates double every two years probability or bit error rate (BER). In the methodology and it is predicted that there will be a need for 40 Gbit/s outlined here, the average error probability is estimated by the end of the decade [1]. As a consequence, the next using a pure semi-analytical method, which combines generation of commercial lightwave transmission systems noiseless transmission simulation of the signal and will have transmission capacities over 10 Gbit/s using interfering channels with noise analysis in wavelength- wavelength division multiplexing (WDM) and optical selective optically preamplified direct-detection receivers. amplifiers [2]. The method of dispersion supported In the following, a description of the model used for transmission (DST) has shown to be very powerful for simulation of the WDM-DST system is presented. This is optical transmission at 10 Gbit/s over long spans of followed by the BER estimation and the noise analysis. standard singlemode fiber (SMF) [3]. However, in a Fig. 1(a) shows the block diagram of a WDM-DST recent DST experiment at 20 Gbit/s, the link length was system with N channels. A brief description of the model reduced to 53 km SMF [4], as expected from the principle used for each system component follows. In this paper, we of dispersion supported transmission [3]. Thus, one assume the signal channel was represented by its lowpass equivalent, and each lowpass equivalent of the other dNb I N N N channels (interfering channels) was frequency juxtaposed = − b − b + b , (1) dt qVw τ cap τ n τ esc relatively to the lowpass equivalent of the signal channel, as shown in Fig. 1(b). dN w N N N N − N0 = b − w − w − g0 w S , (2) DRIVER MQW dt τ cap τ esc τn 1 + εS PPG dS N − N0 S N = Γg0 w S− + Γβ sp w , (3) λ1 dt 1 + εS τp τn DRIVER MQW WDM dφ α = Γg0 ( N w − N wr ) + (1 − Γ ) gb w ( Nb − Nbr ) , PPG MUX EDFA V λ2 dt 2 Vs (4) ... with Vs DRIVER MQW Nb = N s , (5) PPG Vw λN where Nb is a fictitious density, Ns is the carrier density in SMF the SCH, Nw is the carrier density in the quantum wells, S EDFA SMF EDFA SMF is the photon density in the laser cavity, φ is the phase of the optical field, I is the injection current, q is the electronic charge, Nwr is the carrier density in the FPF EDFA PIN PD AMP LPF quantum wells for the reference bias level, Nbr is the fictitious density corresponding to the carrier density in the SCH for the reference bias level, and the other (a) symbols are defined in table I, which was obtained from [8]-[9]. Some lasers exhibit a strongly non-linear light Interfering Signal Interfering versus current characteristic above threshold due to Channels Channel Channels thermal effects. As that was the case of the laser used by Wedding in DST experiments [3], such effects have been ch. 1 ch. nsc-1 ch. nsc ch. nsc+1 ch. N taken into account by expressing the bimolecular ... ... recombination lifetime, tn, as [9]: ... −∆ω 0 ∆ω ... Ω=ω−ω τ n = τ n0e − KT I 0 , (6) nsc (b) where where tn0 and, KT are given in table I, and I0 is the Fig. 1. WDM-DST system with N channels. laser mean input current. (a): Block diagram; At the WDM optical multiplexer output, the total (b): Lowpass equivalent spectrum. electric field is the sum of the input electric fields. Erbium doped fiber optical amplifiers (EDFAs) are assumed to be The pseudopattern generator (PPG) provides a used in the configurations of booster, in-line, and maximal-length pseudorandom binary sequence (PRBS) preamplifier, as in reported DST experiments [3]. It is with 27-1 bits at 10 Gbit/s. Each one of the N optical assumed that these optical amplifiers act as wideband transmitters consists of a laser driver and a MQW-DFB linear repeaters with the same optical gain of the booster, laser. Assuming the laser driver behaves as a non ideal in-line and preamplifier EDFAs used in the DST current source, the NRZ drive current applied to the laser experiments. An equivalent noise bandwidth of 1.25 THz is generated with exponential rising and falling edges. For and a spontaneous emission factor of 0.3 dB have been modeling and simulation of the dynamic response of considered for the optical preamplifier, as in [7]. The quantum-well lasers, a new rate equation model [8]-[9] standard singlemode fiber (SMF) was modeled using the has been used, which takes into account carrier transport lowpass transfer function with first order dispersion of effects. This model describes the carrier dynamics in the 16.2 ps/(nm.km) at 1532 nm. The transfer functions of quantum wells and in the separate confinement single- and double-cavity FPF have been modeled as in heterostructure (SCH) layers, and the photon dynamics in [5]. The finesse of the single-cavity FPF was considered the laser cavity, yielding the following set of equations to be 150, and for the double-cavity filter with equal written in terms of volumetric densities: cavities, the finesse of each one was also considered to be 150. The three-mirror Fabry-Perot filter (TMF) has been noise voltage, σ2sh is the variance of the shot noise modeled as in [7]. The reflectivities of the outer mirrors of voltage, and σ2th is the variance of the thermal noise the TMF were considered to be 0.8 and the reflectivity of voltage. The optical amplifier noise model we use here is the center mirror was chosen so that the frequency based on the model originally derived for single-channel response of the filter is of the second-order Butterworth systems using semiconductor optical amplifiers [11], and type. A PIN photodiode, with a 3-dB cutoff frequency of further extended to fiber amplifiers [12]. The model is 9.35 GHz, is assumed to be used. The receiver main used for multichannel systems, and signal dependent noise amplifier (AMP) and the lowpass filter (LPF) have been terms are evaluated for each bit of the PRBS. The signal jointly modeled as a lowpass RC filter with the 3-dB photocurrent, Ik, is obtained by simulation, which, for bandwidth required by the DST method. multichannel systems, is contaminated by crosstalk due to the imperfect response of the optical filter used as TABLE I. MQW-DFB laser parameters demultiplexer. Thus, for multichannel systems, the Description Parameter Value variance of the signal-ASE beat noise voltage includes the Volume of the quantum wells Vw 18 µm3 contribution of the signal-ASE (signal channel) plus the Volume of the SCH Vs 72 µm3 crosstalk-ASE beat noises. Being Isp the spontaneous Optical confinement factor Γ 0.093 emission noise photocurrent given by [12]: βsp 10-4 ηq n sp ( G − 1)hνBo La , Spontaneous emission factor I sp = 2 (9) Differential gain in the wells g0 4⋅10-12 m3/s hν Parameter of the SCH gb 4.17⋅10-13 m3/s the variance of the noise voltage terms are given by: Carrier density at transparency N0 1⋅1024 m-3 Bimolecular recombination τn0 0.718 ns Be lifetime 2 σ 2− sp = 2 Z R I k I sp s , (10) Bo Transport time across the SCH τcap 56.8 ps Thermionic emission time out τesc 225 ps 2 2 B B σ 2 − sp = Z R I sp e 1 − e , (11) sp of the quantum wells Bo 2 Bo Photon lifetime τp 3.95 ps Differential quantum efficiency per facet η 0.0442 W/A 2 σ 2 = 2 Be qZ R I k + I sp , sh [ ] (12) Gain compression factor ε 2.33⋅10-23 m3 2 2 σ 2 = Z R I th Be , (13) Linewidth enhancement factor α 3.22 th Thermal Constant KT 15.9 where Be is the electrical bandwidth, Bo is the optical Emission wavelength λnsc 1532 nm (signal channel) bandwidth, η is the quantum efficiency of the PIN photodiode, q is the electronic charge, h is Planck's For performance evaluation, a pure semi-analytical constant, ν is the optical frequency, G is the optical method has been used, which combines noiseless preamplifier gain, La is the loss between the optical transmission simulation of the signal and interfering preamplifier output and the photodetector input, nsp is the channels with receiver noise analysis. Using the Gaussian spontaneous emission factor of the EDFA, ZR is the approximation, the average error probability may be receiver transimpedance, and Ith is the spectral current estimated by [10]: density of the thermal noise, which is assumed to be 25 pA/ Hz . L v( τ k ) − Vth ∑ Q 1 Pe = , (7) 3. Simulation results and discussion L σ( τ k ) i =1 In this section, we assess the performance of WDM where L is the length of the used PRBS, Q is the well systems with dispersion supported transmission at 10 known Q-function, v(τk) is the value of the signal voltage Gbit/s. The performance assessment was focused on at the sampling instants tk, Vth is the decision threshold channel 2 (signal channel). Synchronous data patterns are level, and σk is the standard deviation of the noise voltage assumed to be transmitted in all channels, as in [5]-[7], for the k-th bit of the PRBS, which is given by: since this is the worst case for crosstalk. For each fiber length, the system parameters, namely the bias current, the σ 2 = σ 2− sp + σ 2 − sp + σ 2 + σ 2 , k s sp sh th (8) modulation current, the bandwidth of the FPF, and the receiver cutoff frequency, have been adjusted in order to where σ2s-sp is the variance of the signal-ASE beat noise minimize the EDFA preamplifier input mean optical voltage, σ2sp-sp is the variance of the ASE-ASE beat power for an average error probability of 10-9. 3.1. WDM-DST with 1 nm channel spacing 1 dB for distances ranging from 24.5 to 315 km. If a double or a single-cavity FP demultiplexer is used, In the following, the transmission of three 10 Gbit/s crosstalk penalties are less than 0.8 and 2 dB, WDM channels is studied for 1 nm channel spacing, being respectively, in the region of small linear increase of the emission wavelengths of the lasers of λ1=1533 nm dispersion penalty of the DST method (80-270 km). (channel 1), λ2=1532 nm (channel 2), and λ3=1531 nm (channel 3). -10 for channel 2 [dBm] The average error probability against mean optical DST (ch. 2) -15 TM power at the input of the EDFA preamplifier is shown in Sensitivity Fig. 2, for single-channel DST, and for three-channel DST DC -20 over 204 km SMF. As can be seen, the mean optical SC power required to achieve a BER of 10-9 is -26.17 dBm -25 for single-channel DST, and -26.25, -25.88 and -25.42 dBm for three-channel DST with a three-mirror (TM), a -30 double-cavity (DC), and a single-cavity (SC) demultiplexer, respectively. Therefore, the crosstalk -35 penalty, at BER=10-9, is less than 0.3 and 0.8 dB for 0 50 100 150 200 250 300 350 double-cavity and single-cavity demultiplexers, whereas Fibre length [km] for the three-mirror demultiplexer no crosstalk penalties are estimated. The rejection of interfering channels is Fig. 3. Receiver sensitivity for channel 2 after three- about 16 dB (FWHM=40 GHz) and 20 dB (FWHM=60 channel DST via different fiber lengths, considering a GHz), for single- and double-cavity FP demultiplexers, single-cavity (SC), a double-cavity (DC), or a three- respectively, whereas for the three-mirror demultiplexer, mirror (TM) FPF for selection of channel 2. For crosstalk levels are about 35 dB (FWHM=30 GHz) comparison, the receiver sensitivity for single- bellow the signal level. channel DST is also displayed. -1 3.2. WDM-DST with 0.5 nm channel spacing -3 The low crosstalk penalties obtained with a three- log (BER) -5 mirror demultiplexer allow a reduction of the channel -7 spacing. In this section, we consider a 10 Gbit/s four- 10 channel WDM-DST system with 0.5 nm channel spacing. -9 TM Fig. 4 shows the receiver sensitivity for channel 2 after DC -11 single-channel and four-channel DST via different fiber SC -13 DST(ch.2) lengths. In order to investigate the robustness against pattern dependencies for 0.5 nm channel spacing, the -15 same and the complementary PRBS, with respect to signal -35 -33 -30 -28 -25 -23 -20 channel, was considered for optical transmission in the Mean optical power [dBm] interfering channels. As can be seen in Fig. 4, the differences in crosstalk penalties, using the same and the Fig. 2. Average error probability for channel 2 versus complementary PRBS, are less or equal than 0.37 dB for mean optical power at the input of the optical distances ranging from 50 up to 318 km, and less or equal preamplifier, after DST via 204 km SMF of three 10 than 1.56 dB in the whole range from 0 up to 318 km. For Gbit/s WDM channels, considering a single-cavity both cases, crosstalk penalties are less or equal than 1.1 (SC), a double-cavity (DC), or a three-mirror (TM) dB in the region of small linear increase of dispersion FPF for selection of channel 2. penalty of the DST method (80-270 km). For distances The receiver sensitivity for channel 2, versus fiber ranging from 100 up to 318 km, these crosstalk penalties length, is shown in Fig. 3 for single-channel DST and for are less or equal than 0.44 and 0.67 dB, considering the three-channel DST with a single-cavity, a double-cavity, same and the complementary PRBS, respectively. The or a three-mirror FP demultiplexer. For performance reduction of crosstalk penalties for these link lengths comparison, the receiver sensitivity for single-channel follows the narrowing of the laser spectra for both cases: DST is also shown. As can be seen, if a three-mirror the laser frequency deviation of 15 GHz at 80 km rapidly demultiplexer is used, crosstalk penalties are less than 0.1 decreases with fiber length, being of 4.8 GHz at 270 km. dB in the region of small linear increase of dispersion Fig. 5 shows the receiver sensitivity for channel 2 after penalty of the DST method (80-270 km), and are less than single-channel DST (ch.2) and multichannel DST (ch.1 + ch.2, ch.1 + ch.2 + ch.3, and ch.1 + ch.2 + ch.3 + ch.4) via small linear increase of dispersion penalty of the DST different fiber lengths. The same PRBS was considered to method (80-270 km), if a three-mirror FP demultiplexer is be transmitted in all channels. Comparing the system used. The robustness of the multichannel DST method performance for two-channel and four-channel DST, the against pattern dependencies is verified for long-distance differences in crosstalk penalties are less or equal than WDM-DST. Compared with performance studies for 0.76 dB in the region of small linear increase of WDM-DST systems with 1 nm channel spacing, the use of dispersion penalty of the DST method (80-270 km). For three-mirror demultiplexers allows an increase by a factor three-channel and four-channel DST, the differences in of two in the frequency utilization efficiency with low crosstalk penalties are less or equal than 0.13 dB in the crosstalk penalties. However, the reduction of channel region of small linear increase of dispersion penalty of the spacing to 0.5 nm makes WDM-DST systems more DST method (80-270 km), and less or equal than 0.46 dB susceptible to laser/demultiplexer misalignments. in the whole range from 0 up to 318 km. -10 References DST (ch. 2) for channel 2 [dBm] -15 [1] M. A. Newhouse, L. J. Button, D. Q. Chowdhury, Y. Liu, Same PRBS and V. L. da Silva, “Optical amplifiers and fibers for Sensitivity Complementary PRBS multiwavelength systems”, in Proc. 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