- Email: [email protected]
Performance of alternate-block-inversion modulation format in optical communication systems with no dispersion compensation
Optical Fiber Technology 14 (2008) 339–342
Contents lists available at ScienceDirect
Optical Fiber Technology www.elsevier.com/locate/yofte
Performance of alternate-block-inversion modulation format in optical communication systems with no dispersion compensation Sergey Lobanov, Srikanth Raghavan ∗ , Kevin Sparks Science & Technology Division, Corning Incorporated, Corning, NY 14831, USA
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 21 August 2007 Revised 17 April 2008 Available online 21 July 2008
Phase-shaped binary transmission (PSBT) is known to be an attractive modulation format in system with no inline dispersion compensation because of its resilience to chromatic dispersion. We show that the phased amplitude-shift signaling alternate-block-inversion (PASS-ABI) modulation format has a more compact spectrum and higher dispersion tolerance than PSBT while requiring similar transmitter complexity. © 2008 Published by Elsevier Inc.
Keywords: Fiber optic communications Chromatic dispersion Dispersion tolerance PSBT Duobinary Alternate block inversion
1. Introduction Optical transmission systems designed for regional, longhaul, and ultralong-haul distances, show the clear trend toward simplicity and lower first-installed cost [1–4]. For example, transmitterbased electronic dispersion compensation (EDC)[1–3] that does not require in-line dispersion compensation [4] has been demonstrated. The underlying idea behind this approach is reduction of system cost by elimination of in-line optical dispersion compensators and reducing system complexity. Another approach to reduce system cost is to use the phase-shaped binary transmission (PSBT) format first introduced by Penninckx et al. [5] over non-zero dispersion shifted (NZDS) fibers (IEEE G.655 category, 1–6 ps/nmkm dispersion in the ITU C-band) without inline compensation [6–8] since PSBT is extremely resilient to accumulated dispersion [6–9] and a PSBT transmitter is similar in complexity and cost to those required for standard non-return-to-zero (NRZ) modulation and needs only standard receiver for detection [10]. For example, the use of PSBT combined with a maximum likelihood sequence estimation (MLSE) receiver enabled transmission over LEAF fiber over 1500 km without in-line dispersion compensation—sufficient distance for long-haul networks [11]. PSBT format is a variant of duobinary coding and owes its high dispersion tolerance to two distinct factors: the narrowness of the signal spectrum, and the nature of the coding scheme, with de-
*
Corresponding author. Fax: +1 607 974 3405. E-mail addresses: [email protected] (S. Lobanov), [email protected] (S. Raghavan), [email protected] (K. Sparks). 1068-5200/$ – see front matter doi:10.1016/j.yofte.2008.06.004
© 2008
Published by Elsevier Inc.
structive interference between adjacent pulses representing ‘0’ and ‘1’ bits [5]. Among the variety of PSBT implementations [5,12–16], perhaps the most popular and simplest is the low-pass filter (LPF) implementation [5]. Stark et al. proposed a new class of modulation formats generalizing duobinary signaling and extending its benefits to new binary and multilevel optical signals [17]. This class of formats is known as phased amplitude-shift signaling (PASS) codes. Forestieri further developed these concepts, introducing improved dispersion-tolerant modulation formats [18]. However, he concluded that the performance of the most promising PASS coding scheme, alternate block-inversion (PASS-ABI), is no better than standard duobinary modulation format. In this paper, we demonstrate that PASS-ABI can outperform even PSBT for practical systems with large amount of uncompensated dispersion. We take care to optimize system parameters and incorporate practical system impairments, and estimate system performance using nonGaussian statistics [19–21]. 2. Numerical comparison of PASS-ABI and PSBT modulation format There are two important differences between PSBT coding and PASS-ABI coding as illustrated in Fig. 1. First, PSBT coding scheme results in a signal where pulses representing ‘1’ bits that are separated by an odd number of ‘0’ bits have different phase (π difference), but ‘1’ bits separated by an even number of ‘0’ bits have the same phase. For transmission over relatively small distances, or for fully compensated transmission, ‘1’ bits do not spread more than one bit period. Thus coding details for bit patterns other than ‘101’
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S. Lobanov et al. / Optical Fiber Technology 14 (2008) 339–342
Fig. 1. Schematics of PSBT and PASS-ABI signals generated for ‘101001’ bit sequence.
Fig. 3. Comparison of PSBT and PASS-ABI spectra.
Fig. 2. Schematic of PASS-ABI transmitter.
are not important. PASS-ABI coding avoids this problem by introducing different phases for ‘1’ bits separated by any number of ‘0’ bits. Another importance difference between PSBT and PASS-ABI is that whereas the performance of PSBT is enhanced by the presence of non-zero energy with proper phase modulation in the ‘0’ bit slots (see figure), the ‘0’ bit slots in PASS-ABI format do not have any energy [5]. Although PSBT coding is quite efficient and helps to mitigate dispersion-induced impairments, when we consider uncompensated transmission over regional or long-haul distances, pulses can spread over several bit periods and in this case PSBT modulation format confronts a serious limitation. This is due to the fact that the phases of ‘1’ bits separated by even number of ‘0’ bits, e.g., ‘1001,’ ‘100001,’ . . . , are the same. Thus, these patterns will suffer from significant inter-symbol interference when subjected to large amounts of dispersion. On the other hand, since PASS-ABI coding introduces different phases for ‘1’ bits separated by any number of ‘0’ bits, its performance is not seriously affected by large amounts of dispersion. Transmitters for the PASS-ABI modulation format can be implemented by a simple electronic chip, low-pass filter and standard Mach–Zehnder modulator (MZM) as shown in Fig. 2. The electronic chip generates voltage V π for ‘0’ bits and either 0 or 2V π voltage for ‘1’ bits, depending on the count of ‘01’ bit patterns. A 5th-order Bessel filter, with 3 GHz half-width at halfmaximum (HWHM) bandwidth low-pass filter is used to narrow the signal spectrum width. As usual, the MZM should be biased at a transmission null. For PSBT generation, we used a 5th-order Bessel filter, with 2.5 GHz HWHM bandwidth as is standard for optimal PSBT signaling [23]. The values of the various transmitter and receiver filters presented in this paper are specific to 10 Gb/s transmission. Spectra of signals generated by PASS-ABI and PSBT transmitters are shown in Fig. 3. The ABI spectrum is narrower than PSBT spectrum. Given the impact of an improved coding scheme and a narrower spectrum, one would expect that PASS-ABI would offer extended reach over PSBT format. In order to show this we simulated systems for NRZ, PSBT, and PASS-ABI for 8 channels, 10 Gb/s
transmission with 50 GHz channel spacing. The center-channel wavelength was 1550 nm. Fiber that is compliant with G.655 category (e.g., Corning LEAF fiber with D = 4.25 ps/nm-km at 1550 nm) was used for transmission without any dispersion compensation, and EDFAs were placed after each 100 km of fiber. Launch power was optimized for maximum reach for each modulation format. In order to estimate the performance of the system, we incorporated non-Gaussian statistics of the receiver current, applied the analysis presented in [19] to calculate the bit error rate (BER) and reported the results in 20 log( Q ) dB. The analysis in [19] makes no assumption about the statistics of received current but does invoke the accurate approximation that the noise field generated by optical amplifiers is Gaussian in the optical domain. The optical signal field after being propagated along with transmission system using split-step Fourier algorithm [22] is summed with the optical noise field and passed through an optical filter. This filtered combined optical field is passed through a square-law photodetector, and passed through an electrical filter to obtain the electrical current at the receiver. We then apply a Karhunen–Loève eigenfunction expansion to the received current and compute the BER following the analysis presented in [19]. We wish to remark here that our simulation tool has been rigorously validated against experimental results [20]. We used pseudo-random bit stream (PRBS) sequences with increasing number of bits until the results converged. We found that a 29 − 1 PRBS was sufficient to ensure accuracy. In Fig. 4a, we compare performance of three modulation formats for commercially available standard filters. We use a 10GHz full-width at half-maximum (FWHM) optical filter and 7-GHz HWHM electrical filter. For distances above 900 km, PASS-ABI outperforms PSBT and advantage of PASS-ABI grows as distance increases. For standard receiver filters, the reach advantage of PASSABI over PSBT is about 100 km at the forward error correction (FEC) threshold of 8.8 dB (which corresponds to a BER of 3 × 10−3 ). Standard concatenated FEC codes [24] operating at this input Q factor have a net coding gain of about 8.3 dB yielding a corrected BER of about 4 × 10−13 . We also optimized receiver filter parameters for maximum system reach for both PSBT and PASS-ABI and found that the optimum is achieved if a 3-GHz FWHM 3rd-order Bessel optical filter and a 12-GHz HWHM 5th-order Bessel electrical filter are used (Fig. 4b). In this case, the reach advantage of PASS-ABI over PSBT is about 200 km. In Figs. 4a and 4b, we do not exhibit the performance of the various modulation formats at
S. Lobanov et al. / Optical Fiber Technology 14 (2008) 339–342
341
(a)
Fig. 5. PASS-ABI signal for ‘001011011100’ bit sequence.
(b) Fig. 4. (a) Comparison of performance of NRZ, PSBT, and PASS-ABI for standard receiver filters and (b) comparison of PSBT and PASS-ABI for optimized receiver filters.
distances less than 400 km because the Q values are extremely high. We remark here that the standard 7-GHz HWHM electrical filter is typically optimized for NRZ. On the other hand, because both PSBT and PASS-ABI differ from NRZ quite substantially in their pulse and spectral shapes, the optimal value of the electrical filter (12-GHz HWHM) is quite different. As discussed in detail by Bosco et al. in Ref. [25], for duobinary-like modulation formats, the system performance is quite sensitive to filter shape. Our proposed PASS-ABI implementation benefits from tight filtering just because the transmitter generates a 3-level signal which is filtered by a broader filter (compared to PSBT where the 3-level signal is generated by filtering of a 2-level signal) and to compensate for this narrower filters at the receiver are required. However, one must bear in mind that optimum filter widths depend very much on distance and other system parameters. In particular, a different PASS-ABI transmitter implementation could use a different set of optimal filter parameters. 3. Back-to-back performance of PASS-ABI The main limitation in the performance of our proposed implementation of PASS-ABI modulation is the high back-to-back penalty introduced by the low-pass filter needed to suppress spectral side lobes. In Fig. 5, we show a PASS-ABI signal generated for a ‘0101101110’ bit sequence. The peak power of the pulse generated for a ‘010’ bit pattern is significantly smaller than for all other ‘1’ bit patterns, which significantly increases back-to-back penalty. In order to study the ultimate limit of PASS-ABI performance we ex-
cluded the ‘010’ subsequences from the transmitted sequence. The performance of PASS-ABI format after excluding such subsequences is displayed in Fig. 4b where it is clearly seen that PASS-ABI could potentially significantly outperform PSBT for practical systems. We also remark here that although PSBT uses a smaller bandwidth filter at the transmitter compared to PASS-ABI (2.5 GHz for PSBT compared to 3 GHz for PASS-ABI), PASS-ABI suffers from a higher back-to-back penalty compared to PSBT. This can be explained by the fact that the low-pass filter used for PSBT accomplishes two functions—besides helping reducing the spectrum bandwidth, it is part of the PSBT precoder and actually converts a 2-level signal to 3-level signal. On the other hand, in the PASS-ABI transmitter that we are proposing the electrical filter is needed only to reduce spectrum width of 3-level signal. In addition, we have found that by decreasing the width of low-pass filter of the PASS-ABI transmitter, we can decrease the slope of the PASS-ABI Q with respect to accumulated dispersion at the cost of increased back-to-back penalty. Thus, the Q value at which PASS-ABI outperforms PSBT decreases. Hence, further study is needed to determine a way to avoid high back-to-back penalty in generating PASS-ABI (and PASS modulation format in general) signals while at the same time preserving its compact spectrum. 4. Conclusions We have shown that the PASS-ABI modulation format has higher dispersion tolerance and a narrower spectrum than PSBT and NRZ. Thus, PASS-ABI offers a 200-km reach advantage over PSBT at FEC threshold for uncompensated 10 Gb/s transmission over G.655 fiber. At the same time, the complexity of PASS-ABI transmitters is similar to that for PSBT modulation. We also identified high back-to-back penalty as the main drawback of our implementation of PASS-ABI modulator. Further study may help identify alternative transmitter implementations to avoid this penalty. References [1] J. McNicol, M. O’Sullivan, K. Roberts, A. Comeau, D. McGhan, L. Strawczynski, Electrical domain precompensation of optical dispersion, in: Proc. OFC 2005, paper WM46-1. [2] R.L. Killey, P.M. Watts, V. Mikhailov, M. Glick, P. Bayvel, Electronic dispersion compensation by signal predistortion using a dual-drive Mach–Zehnder modulator, in: Proc. OFC 2005, paper OThJ2. [3] D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, M. O’Sullivan, 5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation, in: Proc. OFC 2005, paper PDP27.
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[4] M. Vaa, E.A. Golovchenko, L. Rahman, G. Mohs, W. Patterson, A. Pilipetskii, Dense WDM RZ-DPSK transmission over transoceanic distances without use of periodic dispersion management, in: Proc. ECOC 2004, paper Th4.4.4. [5] L.P.D. Penninckx, M. Chbat, J. Thiery, The phase-shaped binary transmission (PSBT): A new technique to transmit far beyond the chromatic dispersion limit, IEEE Photon. Technol. Lett. 9 (1997) 259–261. [6] J.D. Downie, M. Sauer, J.E. Hurley, Technologies and transmission systems for future metro and regional network applications, in: Proc. OECC 2005, paper 5B2-3. [7] J. Downie, M. Sauer, J. Hurley, 40 Gb/s uncompensated 8-channel CWDM system over 30 km of non-zero dispersion shifted fibre, in: Proc. ECOC 2005, paper Th2.3.1. [8] J. Downie, M. Sauer, J. Hurley, Flexible 10.7 Gb/s DWDM transmission over up to 1200 km without optical in-line or post-compensation of dispersion using MLSE-EDC, in: Proc. OFC 2006, paper JThB5. [9] S. Kuwano, K. Yonenaga, K. Iwashita, 10 Gb/s repeaterless transmission experiment of optical duobinary modulation signal, Electron. Lett. 31 (16) (1995) 1359–1360. [10] I. Lyubomirsky, C. Chien, Tailoring of duobinary pulse shape for optimum performance, J. Lightwave Technol. 23 (1) (2005) 3732–3736. [11] J.D. Downie, M. Sauer, J. Hurley, 1500 km transmission over NZ-DSF without inline or post-compensation of dispersion for 38 × 10.7 Gbit/s channels, Electron. Lett. 42 (11) (2006) 650–652. [12] K. Yonenaga, S. Kuwano, S. Norimatsu, N. Shibata, Optical duobinary transmission system with no receiver sensitivity degradation, Electron. Lett. 31 (1) (1995) 302–304. [13] H. Kim, C. Yu, D. Neilson, Demonstration of optical duobinary transmission system using phase modulator and optical filter, IEEE Photon. Technol. Lett. 14 (7) (2002) 1010–1012. [14] X. Wei, X. Liu, S. Chandrasekhar, A. Gnauck, G. Raybon, J. Leuthold, P. Winzer, 40 Gb/s duobinary and modified duobinary transmitter based on an optical delay interferometer, in: Proc. ECOC 2002, paper 9.6.3.
[15] J. Lee, H. Jang, Y. Kim, S. Choi, S.G. Park, J. Jeong, Chromatic dispersion tolerance of new duobinary transmitters based in two intensity modulators without using electrical low-pass filters, J. Lightwave Technol. 22 (10) (2004) 2264– 2270. [16] H. Lee, H. Kim, J. Lee, S.K. Kim, G. Lee, S. Hwang, Y. Oh, J. Jeong, C. Shim, Cost-effective optical chirped duobinary transmitter using an electroabsorption modulator laser, IEEE Photon. Technol. Lett. 17 (2005) 905–907. [17] J. Stark, J. Mazo, R. Laroia, Line coding for dispersion tolerance and spectral efficiency: Duobinary and beyond, in: Proc. OFC 1999, paper OThJ3. [18] E. Forestieri, G. Prati, Novel optical lines codes tolerant to fiber chromatic dispersion, J. Lightwave Technol. 19 (2001) 1675–1684. [19] E. Forestieri, Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and post-detection filtering, J. Lightwave Technol. 18 (2000) 1493–1503. [20] S. Lobanov, S. Raghavan, J. Downie, Y. Mauro, M. Sauer, J. Hurley, Influence of non-Gaussian statistics in duobinary transmission, in: Proc. CLEO 2006, paper CThY6. [21] S. Lobanov, S. Raghavan, J. Downie, Y. Mauro, M. Sauer, J. Hurley, Impact of uncompensated dispersion on non-Gaussian statistics in duobinary transmission, Opt. Eng. Lett. 46 (1) (2007) 010501. [22] G.P. Agrawal, Fiber-Optic Communication Systems, second ed., Wiley, New York, 1997. [23] I. Lyubomirsky, B. Pitchumani, Impact of optical filtering on duobinary transmission, IEEE Photon. Technol. Lett. 16 (8) (2004) 1969–1971. [24] T. Mizuochi, Recent progress in forward error correction and its interplay with transmission impairments, IEEE J. Select. Topics Quantum Electron. 12 (4) (2006) 544–554. [25] G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, Modulation formats suitable for ultrahigh spectral efficient WDM systems, IEEE J. Select. Topics Quantum Electron. 10 (2) (2004) 321–328.
Contents lists available at ScienceDirect
Optical Fiber Technology www.elsevier.com/locate/yofte
Performance of alternate-block-inversion modulation format in optical communication systems with no dispersion compensation Sergey Lobanov, Srikanth Raghavan ∗ , Kevin Sparks Science & Technology Division, Corning Incorporated, Corning, NY 14831, USA
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 21 August 2007 Revised 17 April 2008 Available online 21 July 2008
Phase-shaped binary transmission (PSBT) is known to be an attractive modulation format in system with no inline dispersion compensation because of its resilience to chromatic dispersion. We show that the phased amplitude-shift signaling alternate-block-inversion (PASS-ABI) modulation format has a more compact spectrum and higher dispersion tolerance than PSBT while requiring similar transmitter complexity. © 2008 Published by Elsevier Inc.
Keywords: Fiber optic communications Chromatic dispersion Dispersion tolerance PSBT Duobinary Alternate block inversion
1. Introduction Optical transmission systems designed for regional, longhaul, and ultralong-haul distances, show the clear trend toward simplicity and lower first-installed cost [1–4]. For example, transmitterbased electronic dispersion compensation (EDC)[1–3] that does not require in-line dispersion compensation [4] has been demonstrated. The underlying idea behind this approach is reduction of system cost by elimination of in-line optical dispersion compensators and reducing system complexity. Another approach to reduce system cost is to use the phase-shaped binary transmission (PSBT) format first introduced by Penninckx et al. [5] over non-zero dispersion shifted (NZDS) fibers (IEEE G.655 category, 1–6 ps/nmkm dispersion in the ITU C-band) without inline compensation [6–8] since PSBT is extremely resilient to accumulated dispersion [6–9] and a PSBT transmitter is similar in complexity and cost to those required for standard non-return-to-zero (NRZ) modulation and needs only standard receiver for detection [10]. For example, the use of PSBT combined with a maximum likelihood sequence estimation (MLSE) receiver enabled transmission over LEAF fiber over 1500 km without in-line dispersion compensation—sufficient distance for long-haul networks [11]. PSBT format is a variant of duobinary coding and owes its high dispersion tolerance to two distinct factors: the narrowness of the signal spectrum, and the nature of the coding scheme, with de-
*
Corresponding author. Fax: +1 607 974 3405. E-mail addresses: [email protected] (S. Lobanov), [email protected] (S. Raghavan), [email protected] (K. Sparks). 1068-5200/$ – see front matter doi:10.1016/j.yofte.2008.06.004
© 2008
Published by Elsevier Inc.
structive interference between adjacent pulses representing ‘0’ and ‘1’ bits [5]. Among the variety of PSBT implementations [5,12–16], perhaps the most popular and simplest is the low-pass filter (LPF) implementation [5]. Stark et al. proposed a new class of modulation formats generalizing duobinary signaling and extending its benefits to new binary and multilevel optical signals [17]. This class of formats is known as phased amplitude-shift signaling (PASS) codes. Forestieri further developed these concepts, introducing improved dispersion-tolerant modulation formats [18]. However, he concluded that the performance of the most promising PASS coding scheme, alternate block-inversion (PASS-ABI), is no better than standard duobinary modulation format. In this paper, we demonstrate that PASS-ABI can outperform even PSBT for practical systems with large amount of uncompensated dispersion. We take care to optimize system parameters and incorporate practical system impairments, and estimate system performance using nonGaussian statistics [19–21]. 2. Numerical comparison of PASS-ABI and PSBT modulation format There are two important differences between PSBT coding and PASS-ABI coding as illustrated in Fig. 1. First, PSBT coding scheme results in a signal where pulses representing ‘1’ bits that are separated by an odd number of ‘0’ bits have different phase (π difference), but ‘1’ bits separated by an even number of ‘0’ bits have the same phase. For transmission over relatively small distances, or for fully compensated transmission, ‘1’ bits do not spread more than one bit period. Thus coding details for bit patterns other than ‘101’
340
S. Lobanov et al. / Optical Fiber Technology 14 (2008) 339–342
Fig. 1. Schematics of PSBT and PASS-ABI signals generated for ‘101001’ bit sequence.
Fig. 3. Comparison of PSBT and PASS-ABI spectra.
Fig. 2. Schematic of PASS-ABI transmitter.
are not important. PASS-ABI coding avoids this problem by introducing different phases for ‘1’ bits separated by any number of ‘0’ bits. Another importance difference between PSBT and PASS-ABI is that whereas the performance of PSBT is enhanced by the presence of non-zero energy with proper phase modulation in the ‘0’ bit slots (see figure), the ‘0’ bit slots in PASS-ABI format do not have any energy [5]. Although PSBT coding is quite efficient and helps to mitigate dispersion-induced impairments, when we consider uncompensated transmission over regional or long-haul distances, pulses can spread over several bit periods and in this case PSBT modulation format confronts a serious limitation. This is due to the fact that the phases of ‘1’ bits separated by even number of ‘0’ bits, e.g., ‘1001,’ ‘100001,’ . . . , are the same. Thus, these patterns will suffer from significant inter-symbol interference when subjected to large amounts of dispersion. On the other hand, since PASS-ABI coding introduces different phases for ‘1’ bits separated by any number of ‘0’ bits, its performance is not seriously affected by large amounts of dispersion. Transmitters for the PASS-ABI modulation format can be implemented by a simple electronic chip, low-pass filter and standard Mach–Zehnder modulator (MZM) as shown in Fig. 2. The electronic chip generates voltage V π for ‘0’ bits and either 0 or 2V π voltage for ‘1’ bits, depending on the count of ‘01’ bit patterns. A 5th-order Bessel filter, with 3 GHz half-width at halfmaximum (HWHM) bandwidth low-pass filter is used to narrow the signal spectrum width. As usual, the MZM should be biased at a transmission null. For PSBT generation, we used a 5th-order Bessel filter, with 2.5 GHz HWHM bandwidth as is standard for optimal PSBT signaling [23]. The values of the various transmitter and receiver filters presented in this paper are specific to 10 Gb/s transmission. Spectra of signals generated by PASS-ABI and PSBT transmitters are shown in Fig. 3. The ABI spectrum is narrower than PSBT spectrum. Given the impact of an improved coding scheme and a narrower spectrum, one would expect that PASS-ABI would offer extended reach over PSBT format. In order to show this we simulated systems for NRZ, PSBT, and PASS-ABI for 8 channels, 10 Gb/s
transmission with 50 GHz channel spacing. The center-channel wavelength was 1550 nm. Fiber that is compliant with G.655 category (e.g., Corning LEAF fiber with D = 4.25 ps/nm-km at 1550 nm) was used for transmission without any dispersion compensation, and EDFAs were placed after each 100 km of fiber. Launch power was optimized for maximum reach for each modulation format. In order to estimate the performance of the system, we incorporated non-Gaussian statistics of the receiver current, applied the analysis presented in [19] to calculate the bit error rate (BER) and reported the results in 20 log( Q ) dB. The analysis in [19] makes no assumption about the statistics of received current but does invoke the accurate approximation that the noise field generated by optical amplifiers is Gaussian in the optical domain. The optical signal field after being propagated along with transmission system using split-step Fourier algorithm [22] is summed with the optical noise field and passed through an optical filter. This filtered combined optical field is passed through a square-law photodetector, and passed through an electrical filter to obtain the electrical current at the receiver. We then apply a Karhunen–Loève eigenfunction expansion to the received current and compute the BER following the analysis presented in [19]. We wish to remark here that our simulation tool has been rigorously validated against experimental results [20]. We used pseudo-random bit stream (PRBS) sequences with increasing number of bits until the results converged. We found that a 29 − 1 PRBS was sufficient to ensure accuracy. In Fig. 4a, we compare performance of three modulation formats for commercially available standard filters. We use a 10GHz full-width at half-maximum (FWHM) optical filter and 7-GHz HWHM electrical filter. For distances above 900 km, PASS-ABI outperforms PSBT and advantage of PASS-ABI grows as distance increases. For standard receiver filters, the reach advantage of PASSABI over PSBT is about 100 km at the forward error correction (FEC) threshold of 8.8 dB (which corresponds to a BER of 3 × 10−3 ). Standard concatenated FEC codes [24] operating at this input Q factor have a net coding gain of about 8.3 dB yielding a corrected BER of about 4 × 10−13 . We also optimized receiver filter parameters for maximum system reach for both PSBT and PASS-ABI and found that the optimum is achieved if a 3-GHz FWHM 3rd-order Bessel optical filter and a 12-GHz HWHM 5th-order Bessel electrical filter are used (Fig. 4b). In this case, the reach advantage of PASS-ABI over PSBT is about 200 km. In Figs. 4a and 4b, we do not exhibit the performance of the various modulation formats at
S. Lobanov et al. / Optical Fiber Technology 14 (2008) 339–342
341
(a)
Fig. 5. PASS-ABI signal for ‘001011011100’ bit sequence.
(b) Fig. 4. (a) Comparison of performance of NRZ, PSBT, and PASS-ABI for standard receiver filters and (b) comparison of PSBT and PASS-ABI for optimized receiver filters.
distances less than 400 km because the Q values are extremely high. We remark here that the standard 7-GHz HWHM electrical filter is typically optimized for NRZ. On the other hand, because both PSBT and PASS-ABI differ from NRZ quite substantially in their pulse and spectral shapes, the optimal value of the electrical filter (12-GHz HWHM) is quite different. As discussed in detail by Bosco et al. in Ref. [25], for duobinary-like modulation formats, the system performance is quite sensitive to filter shape. Our proposed PASS-ABI implementation benefits from tight filtering just because the transmitter generates a 3-level signal which is filtered by a broader filter (compared to PSBT where the 3-level signal is generated by filtering of a 2-level signal) and to compensate for this narrower filters at the receiver are required. However, one must bear in mind that optimum filter widths depend very much on distance and other system parameters. In particular, a different PASS-ABI transmitter implementation could use a different set of optimal filter parameters. 3. Back-to-back performance of PASS-ABI The main limitation in the performance of our proposed implementation of PASS-ABI modulation is the high back-to-back penalty introduced by the low-pass filter needed to suppress spectral side lobes. In Fig. 5, we show a PASS-ABI signal generated for a ‘0101101110’ bit sequence. The peak power of the pulse generated for a ‘010’ bit pattern is significantly smaller than for all other ‘1’ bit patterns, which significantly increases back-to-back penalty. In order to study the ultimate limit of PASS-ABI performance we ex-
cluded the ‘010’ subsequences from the transmitted sequence. The performance of PASS-ABI format after excluding such subsequences is displayed in Fig. 4b where it is clearly seen that PASS-ABI could potentially significantly outperform PSBT for practical systems. We also remark here that although PSBT uses a smaller bandwidth filter at the transmitter compared to PASS-ABI (2.5 GHz for PSBT compared to 3 GHz for PASS-ABI), PASS-ABI suffers from a higher back-to-back penalty compared to PSBT. This can be explained by the fact that the low-pass filter used for PSBT accomplishes two functions—besides helping reducing the spectrum bandwidth, it is part of the PSBT precoder and actually converts a 2-level signal to 3-level signal. On the other hand, in the PASS-ABI transmitter that we are proposing the electrical filter is needed only to reduce spectrum width of 3-level signal. In addition, we have found that by decreasing the width of low-pass filter of the PASS-ABI transmitter, we can decrease the slope of the PASS-ABI Q with respect to accumulated dispersion at the cost of increased back-to-back penalty. Thus, the Q value at which PASS-ABI outperforms PSBT decreases. Hence, further study is needed to determine a way to avoid high back-to-back penalty in generating PASS-ABI (and PASS modulation format in general) signals while at the same time preserving its compact spectrum. 4. Conclusions We have shown that the PASS-ABI modulation format has higher dispersion tolerance and a narrower spectrum than PSBT and NRZ. Thus, PASS-ABI offers a 200-km reach advantage over PSBT at FEC threshold for uncompensated 10 Gb/s transmission over G.655 fiber. At the same time, the complexity of PASS-ABI transmitters is similar to that for PSBT modulation. We also identified high back-to-back penalty as the main drawback of our implementation of PASS-ABI modulator. Further study may help identify alternative transmitter implementations to avoid this penalty. References [1] J. McNicol, M. O’Sullivan, K. Roberts, A. Comeau, D. McGhan, L. Strawczynski, Electrical domain precompensation of optical dispersion, in: Proc. OFC 2005, paper WM46-1. [2] R.L. Killey, P.M. Watts, V. Mikhailov, M. Glick, P. Bayvel, Electronic dispersion compensation by signal predistortion using a dual-drive Mach–Zehnder modulator, in: Proc. OFC 2005, paper OThJ2. [3] D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, M. O’Sullivan, 5120 km RZ-DPSK transmission over G652 fiber at 10 Gb/s with no optical dispersion compensation, in: Proc. OFC 2005, paper PDP27.
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