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, P30 Coimbra, Portugal Abstract This paper presents a simulation methodology for performance assessment of wavelength division multiplexing (WDM) systems using directly modulated quantum-well lasers and optically preamplified direct detection receivers. The methodology is based on a pure semi-analytical method which combines noiseless WDM transmission simulation with noise analysis in those systems. Using this approach, we discuss performance implications of single-cavity, double-cavity and threemirror Fabry-Perot (FP) demultiplexers for dispersion supported transmission (DST) of three WDM channels separated 1 nm. Assuming that a three-mirror filter is used as demultiplexer, the performance of a 40 Gbit/s capacity four-channel WDM-DST system is assessed for 0.5 nm channel spacing. The robustness of the multichannel DST method against pattern dependencies is also investigated for this channel spacing. 1. Introduction Single-channel lightwave systems operated at 10 Gbit/s are being introduced commercially, but long term trends indicate that signaling rates double every two years and it is predicted that there will be a need for 40 Gbit/s by the end of the decade [1]. As a consequence, the next generation of commercial lightwave transmission systems will have transmission capacities over 10 Gbit/s using wavelength division multiplexing (WDM) and optical amplifiers [2]. The method of dispersion supported transmission (DST) has shown to be very powerful for optical transmission at 10 Gbit/s over long spans of standard singlemode fiber (SMF) [3]. However, in a recent DST experiment at 20 Gbit/s, the link length was reduced to 53 km SMF [4], as expected from the principle of dispersion supported transmission [3]. Thus, one solution for high-capacity DST on long spans of SMF is the optical transmission of wavelength division multiplexed (WDM) 10 Gbit/s channels. We have discussed the impact of single- and double-cavity Fabry- Perot (FP) demultiplexers on the performance of dispersion supported transmission of two [5] and three [6] 10 Gbit/s WDM channels separated 1 nm. In a further study, we have assessed the system performance for three 10 Gbit/s WDM channels separated 0.5 nm, assuming that a three-mirror FP filter is used as demultiplexer [7]. In this paper, a modeling and simulation methodology is presented for performance assessment of multichannel optical communication systems. Using this methodology, we compare the performance of three-channel WDM-DST with 1 nm channel spacing for single-cavity, double-cavity and three-mirror FP demultiplexers. The performance of a 40-Gbit/s capacity four-channel WDM-DST system is assessed for 0.5 nm channel spacing, assuming that a three-mirror Fabry-Perot filter is used as demultiplexer. 2. Modeling and simulation methodology The most appropriate performance measure for digital optical communication systems is the average error probability or bit error rate (BER). In the methodology outlined here, the average error probability is estimated using a pure semi-analytical method, which combines noiseless transmission simulation of the signal and interfering channels with noise analysis in wavelengthselective optically preamplified direct-detection receivers. In the following, a description of the model used for simulation of the WDM-DST system is presented. This is followed by the BER estimation and the noise analysis. Fig. 1(a) shows the block diagram of a WDM-DST system with N channels. A brief description of the model used for each system component follows. In this paper, we assume the signal channel was represented by its lowpass
equivalent, and each lowpass equivalent of the other channels (interfering channels) was frequency juxtaposed relatively to the lowpass equivalent of the signal channel, as shown in Fig. 1(b). λ 1... λ 2 λ N WDM MUX EDFA SMF EDFA SMF EDFA SMF FPF EDFA PIN PD AMP LPF Interfering Channels (a) Signal Channel Interfering Channels ch. 1 ch. nsc-1 ch. nsc ch. nsc+1 ch. N......... ω 0 ω... (b) Fig. 1. WDM-DST system with N channels. (a): Block diagram; (b): Lowpass equivalent spectrum. Ω=ω ω nsc The pseudopattern generator () provides a maximal-length pseudorandom binary sequence (PRBS) with 2 7-1 bits at 10 Gbit/s. Each one of the N optical transmitters consists of a laser driver and a MQW-DFB laser. Assuming the laser driver behaves as a non ideal current source, the NRZ drive current applied to the laser is generated with exponential rising and falling edges. For modeling and simulation of the dynamic response of quantum-well lasers, a new rate equation model [8]-[9] has been used, which takes into account carrier transport effects. This model describes the carrier dynamics in the quantum wells and in the separate confinement heterostructure (SCH) layers, and the photon dynamics in the laser cavity, yielding the following set of equations written in terms of volumetric densities: dnb dt I N N N = b b + b, (1) qvw τcap τesc dnw Nb Nw Nw g N w = N 0 0 S,(2) dt τcap τesc 1 + εs ds g N w N S N = Γ 0 S w 0 + Γβsp, (3) dt 1 + εs τp dφ α = Γg ( N N ) ( ) g V 0 w wr + 1 Γ b w ( ) dt V N b N br, 2 s (4) with N N V b = s s, (5) Vw where N b is a fictitious density, N s is the carrier density in the SCH, N w is the carrier density in the quantum wells, S 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, N wr is the carrier density in the quantum wells for the reference bias level, N br is the fictitious density corresponding to the carrier density in the SCH for the reference bias level, and the other symbols are defined in table I, which was obtained from [8]-[9]. Some lasers exhibit a strongly non-linear light versus current characteristic above threshold due to thermal effects. As that was the case of the laser used by Wedding in DST experiments [3], such effects have been taken into account by expressing the bimolecular recombination lifetime, t n, as [9]: K I e = T 0 0, (6) where where t n0 and, K T are given in table I, and I 0 is the laser mean input current. At the WDM optical multiplexer output, the total electric field is the sum of the input electric fields. Erbium doped fiber optical amplifiers (EDFAs) are assumed to be used in the configurations of booster, in-line, and preamplifier, as in reported DST experiments [3]. It is assumed that these optical amplifiers act as wideband linear repeaters with the same optical gain of the booster, in-line and preamplifier EDFAs used in the DST experiments. An equivalent noise bandwidth of 1.25 THz and a spontaneous emission factor of 0.3 db have been considered for the optical preamplifier, as in [7]. The standard singlemode fiber (SMF) was modeled using the lowpass transfer function with first order dispersion of 16.2 ps/(nm.km) at 1532 nm. The transfer functions of single- and double-cavity FPF have been modeled as in [5]. The finesse of the single-cavity FPF was considered to be 150, and for the double-cavity filter with equal cavities, the finesse of each one was also considered to be
150. The three-mirror Fabry-Perot filter (TMF) has been modeled as in [7]. The reflectivities of the outer mirrors of the TMF were considered to be 0.8 and the reflectivity of the center mirror was chosen so that the frequency response of the filter is of the second-order Butterworth type. A PIN photodiode, with a 3-dB cutoff frequency of 9.35 GHz, is assumed to be used. The receiver main amplifier (AMP) and the lowpass filter (LPF) have been jointly modeled as a lowpass RC filter with the 3-dB bandwidth required by the DST method. TABLE I. MQW-DFB laser parameters Description Parameter Value Volume of the quantum wells V w 18 µm 3 Volume of the SCH V s 72 µm 3 Optical confinement factor Γ 0.093 Spontaneous emission factor β sp 10-4 Differential gain in the wells g 0 4 10-12 m 3 /s Parameter of the SCH g b 4.17 10-13 m 3 /s Carrier density at transparency N 0 1 10 24 m -3 Bimolecular recombination τ n0 0.718 ns lifetime Transport time across the SCH τ cap 56.8 ps Thermionic emission time out τ esc 225 ps of the quantum wells Photon lifetime τ p 3.95 ps Differential quantum η 0.0442 W/A efficiency per facet Gain compression factor ε 2.33 10-23 m 3 Linewidth enhancement factor α 3.22 Thermal Constant K T 15.9 Emission wavelength λ nsc 1532 nm (signal channel) For performance evaluation, a pure semi-analytical method has been used, which combines noiseless transmission simulation of the signal and interfering channels with receiver noise analysis. Using the Gaussian approximation, the average error probability may be estimated by [10]: L 1 P Q v e = L i = 1 ( τk) τ ( ) V th, (7) k where L is the length of the used PRBS, Q is the well known Q-function, v(τ k ) is the value of the signal voltage at the sampling instants t k, V th is the decision threshold level, and k is the standard deviation of the noise voltage for the k-th bit of the PRBS, which is given by: 2 2 2 2 2 k = s sp + sp sp + sh + th, (8) where 2 s-sp is the variance of the signal-ase beat noise voltage, 2 sp-sp is the variance of the ASE-ASE beat noise voltage, 2 sh is the variance of the shot noise voltage, and 2 th is the variance of the thermal noise voltage. The optical amplifier noise model we use here is based on the model originally derived for single-channel systems using semiconductor optical amplifiers [11], and further extended to fiber amplifiers [12]. The model is used for multichannel systems, and signal dependent noise terms are evaluated for each bit of the PRBS. The signal photocurrent, I k, is obtained by simulation, which, for multichannel systems, is contaminated by crosstalk due to the imperfect response of the optical filter used as demultiplexer. Thus, for multichannel systems, the variance of the signal-ase beat noise voltage includes the contribution of the signal-ase (signal channel) plus the crosstalk-ase beat noises. Being I sp the spontaneous emission noise photocurrent given by [12]: ηq I sp = 2 ( ) h n sp G 1 h ν B o L a, (9) ν the variance of the noise voltage terms are given by: 2 2 B e s sp = 2 ZR IkIsp, (10) Bo 2 Be Be sp sp = Z 2 R I 2 sp 1, (11) Bo 2Bo [ ] 2 2 sh = 2BqZ e R Ik + Isp, (12) 2 2 2 th = Z R I th Be, (13) where B e is the electrical bandwidth, B o is the optical bandwidth, η is the quantum efficiency of the PIN photodiode, q is the electronic charge, h is Planck's constant, ν is the optical frequency, G is the optical preamplifier gain, L a is the loss between the optical preamplifier output and the photodetector input, n sp is the spontaneous emission factor of the EDFA, Z R is the receiver transimpedance, and I th is the spectral current density of the thermal noise, which is assumed to be 25 pa/ Hz. 3. Simulation results and discussion In this section, we assess the performance of WDM systems with dispersion supported transmission at 10 Gbit/s. The performance assessment was focused on channel 2 (signal channel). Synchronous data patterns are assumed to be transmitted in all channels, as in [5]-[7], since this is the worst case for crosstalk. For each fiber length, the system parameters, namely the bias current, the modulation current, the bandwidth of the FPF, and the receiver cutoff frequency, have been adjusted in order to minimize the EDFA preamplifier input mean optical power for an average error probability of 10-9.
3.1. WDM-DST with 1 nm channel spacing In the following, the transmission of three 10 Gbit/s WDM channels is studied for 1 nm channel spacing, being the emission wavelengths of the lasers of λ 1 =1533 nm (channel 1), λ 2 =1532 nm (channel 2), and λ 3 =1531 nm (channel 3). The average error probability against mean optical power at the input of the EDFA preamplifier is shown in Fig. 2, for single-channel DST, and for three-channel DST over 204 km SMF. As can be seen, the mean optical power required to achieve a BER of 10-9 is -26.17 dbm for single-channel DST, and -26.25,.88 and.42 dbm for three-channel DST with a three-mirror (TM), a double-cavity (DC), and a single-cavity (SC) demultiplexer, respectively. Therefore, the crosstalk penalty, at BER=10-9, is less than 0.3 and 0.8 db for double-cavity and single-cavity demultiplexers, whereas for the three-mirror demultiplexer no crosstalk penalties are estimated. The rejection of interfering channels is about 16 db (FWHM=40 GHz) and 20 db (FWHM=60 GHz), for single- and double-cavity FP demultiplexers, respectively, whereas for the three-mirror demultiplexer, crosstalk levels are about 35 db (FWHM=30 GHz) bellow the signal level. log (BER) 10-1 -3-5 -7-9 TM DC -11 SC -13 DST(ch.2) -33-28 -23 Mean optical power [dbm] Fig. 2. Average error probability for channel 2 versus mean optical power at the input of the optical preamplifier, after DST via 204 km SMF of three 10 Gbit/s WDM channels, considering a single-cavity (SC), a double-cavity (DC), or a three-mirror (TM) FPF for selection of channel 2. The receiver sensitivity for channel 2, versus fiber length, is shown in Fig. 3 for single-channel DST and for three-channel DST with a single-cavity, a double-cavity, or a three-mirror FP demultiplexer. For performance comparison, the receiver sensitivity for single-channel DST is also shown. As can be seen, if a three-mirror demultiplexer is used, crosstalk penalties are less than 0.1 db in the region of small linear increase of dispersion penalty of the DST method (80-270 km), and are less than 1 db for distances ranging from 24.5 to 315 km. If a double or a single-cavity FP demultiplexer is used, crosstalk penalties are less than 0.8 and 2 db, respectively, in the region of small linear increase of dispersion penalty of the DST method (80-270 km). DST (ch. 2) TM DC SC Fig. 3. Receiver sensitivity for channel 2 after threechannel DST via different fiber lengths, considering a single-cavity (SC), a double-cavity (DC), or a threemirror (TM) FPF for selection of channel 2. For comparison, the receiver sensitivity for singlechannel DST is also displayed. 3.2. WDM-DST with 0.5 nm channel spacing The low crosstalk penalties obtained with a threemirror demultiplexer allow a reduction of the channel spacing. In this section, we consider a 10 Gbit/s fourchannel WDM-DST system with 0.5 nm channel spacing. Fig. 4 shows the receiver sensitivity for channel 2 after single-channel and four-channel DST via different fiber lengths. In order to investigate the robustness against pattern dependencies for 0.5 nm channel spacing, the same and the complementary PRBS, with respect to signal channel, was considered for optical transmission in the interfering channels. As can be seen in Fig. 4, the differences in crosstalk penalties, using the same and the complementary PRBS, are less or equal than 0.37 db for distances ranging from 50 up to 318 km, and less or equal than 1.56 db in the whole range from 0 up to 318 km. For both cases, crosstalk penalties are less or equal than 1.1 db in the region of small linear increase of dispersion penalty of the DST method (80-270 km). For distances ranging from 100 up to 318 km, these crosstalk penalties are less or equal than 0.44 and 0.67 db, considering the same and the complementary PRBS, respectively. The reduction of crosstalk penalties for these link lengths follows the narrowing of the laser spectra for both cases: the laser frequency deviation of 15 GHz at 80 km rapidly decreases with fiber length, being of 4.8 GHz at 270 km. Fig. 5 shows the receiver sensitivity for channel 2 after 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 different fiber lengths. The same PRBS was considered to be transmitted in all channels. Comparing the system performance for two-channel and four-channel DST, the differences in crosstalk penalties are less or equal than 0.76 db in the region of small linear increase of dispersion penalty of the DST method (80-270 km). For three-channel and four-channel DST, the differences in crosstalk penalties are less or equal than 0.13 db in the region of small linear increase of dispersion penalty of the DST method (80-270 km), and less or equal than 0.46 db in the whole range from 0 up to 318 km. DST (ch. 2) Same PRBS Complementary PRBS Fig. 4. Receiver sensitivity for channel 2 versus fiber length after single-channel, and four-channel DST with 0.5 nm channel spacing. ch.2 (DST) ch.1 + ch.2 ch.1 + ch.2 + ch.3 ch.1 + ch.2 + ch.3 + ch.4 Fig. 5. Receiver sensitivity for channel 2 versus fiber length, after DST via SMF of one, two, three and four 10 Gbit/s WDM channels separated 0.5 nm. 4. Conclusions Using a simulation methodology for performance assessment of WDM-DST systems, we have discussed performance implications of single-cavity, double-cavity and three-mirror FP demultiplexers for dispersion supported transmission of three 10 Gbit/s WDM channels separated 1 nm. It was shown that crosstalk penalties for 10 Gbit/s four-channel WDM-DST, with 0.5 nm channel spacing, are less or equal than 1.1 db in the region of small linear increase of dispersion penalty of the DST method (80-270 km), if a three-mirror FP demultiplexer is used. The robustness of the multichannel DST method against pattern dependencies is verified for long-distance WDM-DST. Compared with performance studies for WDM-DST systems with 1 nm channel spacing, the use of three-mirror demultiplexers allows an increase by a factor of two in the frequency utilization efficiency with low crosstalk penalties. However, the reduction of channel spacing to 0.5 nm makes WDM-DST systems more susceptible to laser/demultiplexer misalignments. References [1] M. A. Newhouse, L. J. Button, D. Q. Chowdhury, Y. Liu, and V. L. da Silva, Optical amplifiers and fibers for multiwavelength systems, in Proc. LEOS'95, San Francisco, Vol. 2, pp. OC 5.1, 1995. [2] D. A. Fishman, and J. A. Nagel, Next generation WDM lightwave Systems, in Proc. LEOS'95, San Francisco, Vol. 2, pp. WDM 1.1, 1995. [3] B. Wedding, B. Franz, and B. Junginger, "10-Gb/s optical transmission up to 253 km via standard single-mode fiber using the method of dispersion-supported transmission", IEEE J. Lightwave Tech., Vol. 12, No. 10, pp. 1720-1727, 1994. [4] B. Wedding, K. Köffers, B. Franz, D. Mathoorasing, C. Kazmierski, P. Monteiro, J. Nuno Matos, "Dispersion-supported transmission at 20 Gbit/s over 53 km standard singlemode fibre", Electron. Lett., Vol. 31, No. 7, pp. 566-568, 1995. [5] M. M. Freire and H. J. A. da Silva, "Performance assessment of two-channel dispersion-supported transmission systems using single- and double-cavity Fabry-Perot filters as demultiplexers", IEEE Photon. Technol. Lett., Vol. 7, No. 11, pp. 1360-1362, 1995. [6] M. M. Freire and H. J. A. da Silva, "Performance assessment of WDM dispersion supported transmission systems using single and double-cavity Fabry-Perot demultiplexers", in Proc. LEOS'95, San Francisco, Vol. 2, pp. OC 6.4, 1995. [7] M. M. Freire, A. M. F. de Carvalho, and H. J. A. da Silva, performance implications of three-mirror Fabry-Perot demultiplexers for 10-Gb/s WDM dispersion-supported transmission with 0.5 nm channel spacing, IEEE Photon. Technol. Lett, Vol. 9, No. 9, pp. 1261-1263, 1996. [8] R. F. S. Ribeiro, J. R. F. da Rocha, A. V. T. Cartaxo, H. J. A. da Silva, B. Franz, and B. Wedding, "FM response of quantumwell lasers taking into account carrier transport effects", IEEE Photon. Technology Lett., Vol. 7, No. 8, pp. 857-859, 1995. [9] R. F. S. Ribeiro, "Simulation of DST dispersion range", contribution to deliverable 25 of TRAVEL-RACE 2011, University of Aveiro, Portugal, 1994. [10] M. C. Jeruchim, Techniques for estimating the bit error rate in the simulation of digital communication systems, J. Select. Areas Commun. Vol. SAC-2, No. 1, pp.153-170, 1984. [11] N. A. Olsson, Lightwave systems with optical amplifiers, IEEE J. Lightwave Technol., Vol. 7, No. 7, pp. 107182, 1989. [12] Y. K. Park, and S. W. Granlund, Optical preamplifier receivers: application to long-haul digital transmission, Optical Fiber Technol., Vol. 1, pp. 59-71, 1994.