Performance Analysis of the Parallel Optical All-pass Filter Equalizer for Chromatic Dispersion Compensation at 10 Gb/s

Transcription

1 Pefomance Analysis of the Paallel Optical All-pass Filte Equalize fo Chomatic Dispesion Compensation at Gb/s Wai Pang Ng, Membe, IEEE, W. Loedhammacaka, Student Membe, IEEE, R.A. Cyan, and Z. Ghassemlooy, Senio Membe, IEEE Nothumbia Communication Reseach Laboatoy (NCRL) School of Computing, Engineeing and Infomation Sciences Nothumbia Univesity, Newcastle upon Tyne, NE 8ST, UK {wai-pang.ng, wisit.loedhammacaka, Abstact Optical fibe is capable of poviding the solution to the need of high bandwidth communication. The main degadation to the optical signal integity in single mode fibes (SMFs) is chomatic dispesion (CD). The effect of CD is pulse speading which in tun leads to inte-symbol intefeence (ISI), thus inceasing the bit eo ate (BER) of the system. This pape pesents a CD compensation technique that utilizes a paallel optical all pass filte (p-oapf), whee the design is based on the invese phase esponse of the SMF. The p-oapf is based on a class of all-pass filte. Simulation esults of the poposed technique show an incease in the epeate-less length of a point-to-point optical communication system by 3 times with Gaussian pulses at Gb/s and BER of -9. A passive infinite impulse esponse filte stuctue is poposed fo the implementation of the p-oapf. Index Tems Paallel optical all pass filte, chomatic dispesion, dispesion compensation, optical communication, phase equalizes. A I. INTRODUCTION TTENUATION, nonlinea effect and dispesion in the optical fibes ae the key challenges that need to be ovecome to achieve highe tansmission speed in optical fibe communication systems []. Attenuation is no longe a main poblem due to the invention of the ebium-doped fibe amplifie (EDFA) []. Nonlinea effects such as fou wave mixing (FWM) can also be educed by intoducing some dispesion [3, 4]. Dispesion emains the key facto affecting the signal quality in long-haul optical fibe communication systems. In the cuent long-haul optical communication system, single mode fibes (SMFs), ITU-T G.65, ae commonly used. The advantage of the SMFs is having zeo dispesion at the opeating wavelengths of.3 µm []. When the wavelength division multiplexing (WDM) system was intoduced to incease fibe bandwidth, the opeating wavelength moved to.55 µm due to the low attenuation egion of the SMF [3] and the opeating wavelength window of EDFA []. Howeve at the wavelength of.55 µm, the SMFs have dispesion of 7 ps/nm-km. This dispesion consists of chomatic dispesion (CD), polaization-mode dispesion (PMD) and thid ode dispesion (TOD) [5]. This pape will concentate on solving the main dispesion degadation effects which is caused by the CD. The CD esults in pulse speading and hence intoduces ISI [6], which in tun inceases the bit eo ate (BER). The length of SMFs in high bit ate long-haul optical communication systems is limited by the bit ate and CD [6]. Doubling the bit ate (B) will educe the optical fibe s length (L) by a facto of 4 fo a fixed dispesion coefficient (D). In a communication system opeating at a wavelength of.55 µm (whee D is 7 ps/nm-km), the level of dispesion detemines the maximum epeate-less span of fibe which is ove times less than the system which opeating at the wavelength of.3 µm (whee D ~ ps/nm-km) [6]. In ode to investigate the effect of dispesion in a SMF, the SMF is modeled as a band pass filte with a flat amplitude esponse and linea goup delay in the data bandwidth with an attenuation facto, α. The tansfe function of the SMF, H f (f), can be modeled using the low pass equivalent model as shown in () [7] L f jd LB c ( B ) H ( f ) = e () whee α is the SMF attenuation (. db/km), is the opeating wavelength, c is the velocity of light and f is the optical fequency. Figue shows the block diagam of the Gb/s optical communication system unde test which includes the tansmitte with non etun to zeo (NRZ) Gaussian pulses, conventional SMF (with dispesion of 7 ps/nm-km), EDFA, optical bandpass filte, the poposed dispesion equalize and eceive. This pape will pesent the design and the chaacteistics of the poposed dispesion equalize. When the length of the SMF (L) eaches 63 km, the CD effect has boadened the pulse to a stage whee BER is high, i.e. the eye patten is totally closed. This scenaio is shown in Fig. whee the nomalized eceived pulse is dispesed and affects the next time slot, i.e. ISI.

2 B = Gb/s OOK NRZ Gaussian pulse Input Data λ =.55 µm, Pi = mw Optical Souce Theefoe, in ode to ealize high bit ate tansmission ove long distances using SMF, CD compensation techniques must be used to ovecome the signal distotion. Duing the 99s seveal dispesion compensation schemes opeating in the optical domain wee developed. These schemes can be classified into fou categoies: fibes, intefeometes, phase conjugation and dispesion-equalizing filtes [5, 8]. This pape is oganized as follows. In section II, the bief eviews of vaious dispesion compensation techniques ae pesented. Section III intoduces the design of optical all pass filte, (OAPF) and a modified stuctue, the paallel OAPF (p- OAPF) to compensate the dispesion in SMF. The simulation esults ae discussed in section IV, while section V exploes the futue wok and summaize main finding of the pape. II. f jd LB L c B H f ( f) = e D = 7 ps/nm-km, =. db/km, L km Electical signal Optical signal EDFA G = 3 db OBPF BW = 4 GHz Output Data Dispesed Gaussian pulse at 63 km of SMF Fig. : The dispesed Gaussian pulse at wost case scenaio, L = 63 km. DISPERSION COMPENSATION TECHNIQUES p-oapf Equalise Fig. : Block diagam of the optical communication system with the dispesion equalize. Pulses popagating in optical fibe communication systems, which opeate pimaily at wavelengths nea.55 µm, will expeience significant amounts of goup velocity dispesion (GVD), which limits popagation distance. Basically, GVD in SMF is equivalent to CD. This GVD o CD poblem can be ovecome by inseting an element that imposes the opposite GVD effect on the optical signal, theeby compensating fo the natually occuing GVD. Thee ae many methods used fo dispesion compensation in optical domain: the fist categoy uses fibe i.e. dispesion shifted fibe (DSF), dispesion compensating fibe (DCF) and fibe Bagg gating (FBG). The second categoy is intefeomete, i.e. Mach- Zehnde intefeomete (MZI). Thid is the phase conjugation method i.e. optical phase conjugation (OPC). The final categoy uses dispesion-equalizing filtes such as OAPF. The DSF has its zeo dispesion point shifted to the wavelength of.55 µm. Howeve, FWM occus in the DSF and causes the optical equivalent of nea end cosstalk between the optical channels [3]. The DCF is a fibe designed with negative dispesion, to compensate fo positive dispesion ove lage SMF lengths. DCF typically has a much naowe coe than SMF, esulting in highe attenuation [3]. Chiped FBG can compensate the CD in a SMF by vaying the gating to delay the faste wavelengths in elation to the slowe wavelengths of an optical pulse, and when they ecombined, the oiginal pulse is estoed. The chiped FBG is limited by its naow bandwidth and ipple in the opposite GVD [9]. MZI has been poposed fo the compensation of CD by poviding two wavelength dependent paths of diffeent lengths fo diffeent spectal components of the signal. The main limitations of the MZI ae its elatively naow bandwidth and sensitivity to input polaization []. OPC is employed fo CD compensation by inveting the spectum in the middle of the SMF link, thus compensating the oveall GVD. The OPC cannot compensate fo the TOD and it is difficult to be implemented pactically [, ]. This pape poposes the use of the optical all pass filte, which is the final categoy of dispesion compensation technique, as an equalize to povide CD compensation and the next section will discuss the technique in detail. III. OPTICAL ALL PASS FILTER TECHNIQUES The all pass filte (APF) is known as a phase equalize as the phase of a signal can be adjusted by an APF without intoducing amplitude distotion []. The design of an optical all pass filte (OAPF) is based on the APF. The phase esponse of an OAPF can be designed to cancel the phase shift of the SMF, which will esult in dispesion cancellation. OAPF is potentially a vey impotant device in optical tansmission systems since they can compensate fo any level dispesion in vey small stuctues with vey low loss []. OAPFs ae linea systems, which have a unity magnitude esponse fo all fequencies. The phase esponse of OAPFs vaies with fequency. []. The tansfe function of an OAPF can be witten as [] [j()] H () e OAPF = () Fom (), the phase of the OAPF ( () ) can be made abitaily close to any desied phase esponse. By changing the coefficients of the function of an OAPF it is possible to ceate a goup delay with the desied chaacteistics. These chaacteistics should be designed such that when the OAPF is placed in cascade with the SMF, the oveall esulting GVD should be zeo thoughout the fequencies of inteest. The desied chaacteistics effectively mean that the OAPF should delay lowe fequency components of a pulse by a lage amount, with the delay deceasing as fequency inceases, thus intoducing the invese effect to that of the

3 fibe. The second ode OAPF tansfe function [] can be witten in the ectangula fom [3] as (3) costcos + cos + jcossin T sin T HOAPF () = costcos + cos + j cossin T sin T (3) whee is the distance of the poles fom the oigin ( < < ) in the z-plane, is the angula position ( < < ) of the pole in the z-plane and T is the time delay. The, and T ae paametes ae used to contol the phase shift of the OAPF. The phase esponse of the second ode OAPF is given by cos sin T sin T cos sin T sin T () = OAPF tan tan cost cos + cos cost cos + cos (4) Having the optimized paametes fo, and T, is the key to the use of an OAPF fo CD compensation. The minimum mean squae eo (MMSE) method, due to its simplicity, is used to optimize these paametes by compaing the phase of OAPF with the phase of an ideal equalize [4] with the invese tansfe function of the SMF. In Fig. 3, the phase of the SMF looks paabolic and at fequency peiods of π the phase gets shote as f moves away fom the cente fequency (93.5 THz), due to the f tem in (). In the egion of inteest (93.5 THz ± GHz) the phase of the Gaussian pulse is always in-phase with the phase of the SMF as shown in Fig. 3. Theefoe the phase of the SMF at 63 km will be used to design the OAPF and hence the p-oapf. The poposed p-oapf technique utilizes two OAPF equalizes to compensate fo the effect of CD in fo the uppe fequency and fo the lowe fequency band. A single OAPF cannot fully compensate fo the phase change in the uppe spectal egion which leads to the tailing edge of the pulse speading into the following bit slot [4]. The optical powe output fom the end of the SMF is equally split into two paths feeding into OAPF equalizes Eq and Eq, espectively. The output signals fom Eq and Eq will be detected and passed to a multiplie as illustated in Fig. 4. The tansfe function of p-oapf can be witten as (5) whee n f is the nomalization facto and τ d is the time delay between the linea time delay of Eq (τ eq ) and Eq (τ eq ), i.e. τ = τ τ. n f is chosen to ensue the magnitude d eq eq esponse of (5) is nomalized to unity hence avoiding amplitude fluctuation and system instability. The value of n f can be deduced as the peak of the compensated pulse in (6), whee t max is the time at the peak of the function, calculated fom (7). Fom (6), n f is elated to the paametes of the OAPF, T, and. T is fixed due to its mino effect and fo ease of implementation, whilst, and change popotional and invesely popotional, espectively, with espect to the Fequency (THz) of oiginal Gaussian pulse of SMF 63 km length of Gaussian pulse at 63 km SMF Fig. 3: The phases of the oiginal Gaussian pulse, the dispesed Gaussian pulse and the SMF at L = 63 km. Splitte length of the SMF. Theefoe n f is also invesely popotional to fibe length, see (5) and (6). jt nf ( tmax ) = Sin( ) H f () HOAPF()e d (6) Eq Eq jt Sin ( ) H f () HOAPF ()e dω = t (7) whee S in () is the input signal of the system. IV. RESULT AND DISCUSSION This section will pesent the pefomance impovement between an uncompensated system and a system utilizing p-oapf. BER is used to show the pefomance of digital optical communication systems which can be calculated by using data fom eye patten of systems and (8) [5, 5, 6]. Q Photo Detecto Photo Detecto Electical signal Optical signal Fig. 4: The paallel OAPF stuctue. e BER =, Imin Imax Q = (8) Q + whee I min is the minimum amplitude of bit one; I max is the maximum amplitude of bit zeo; is the standad deviation of noise when bit one was sent; is the standad deviation of noise when bit zeo was sent. The input to the system is a steam of data patten of 7 bit long, whee the wost case scenaio will be consideed, i.e. the fouth bit with the data patten of and. H poapf cost cos + cos + jcossin T sin T costcos j + cos + jcossin T sin T t () e n j( t d ) -jt = f n f cost cos + cos + j cossin T sin T e e t costcos + cos + j cossin T sin T (5)

4 Dispesed Gaussian pulse at 63 km of SMF Compensated pulse at 63 km by using p-oapf Fig. 5: The oiginal, dispesed and compensated Gaussian pulses at L = 63 km Dispesed Gaussian pulse at 4 km of SMF Compensated pulse at 4 km by using p-oapf Fig. 8: The oiginal, dispesed and compensated Gaussian pulse at L = 4 km Fequency (THz) Compensated phase of Gaussian pulse at 63 km SMF by p-oapf Fig. 6: The compensated phase of the Gaussian pulse at L = 63 km using p-oapf Fig. 7: The eye patten of optical communication system at L = 63 km, employing p-oapf. The simulated esults of an uncompensated and a compensated pulse by using p-oapf equalize whee SMF length is 63 km (when the eye diagam is totally closed) ae shown in Fig. 5 while the compensated phase is shown in Fig. 6. The eye patten of the compensated system at 63 km is shown in Fig. 7 and the esultant BER is eo fee, i.e. BER < -9. In ode to futhe investigate the capability of the p- OAPF in extending the epeate-less distance, it was found that at 4 km, the p-oapf is not longe capable of compensating the dispesed Gaussian pulse to eo fee. The compensated pulse and the eye patten ae shown in Fig. 8 and 9 espectively. Figue shows the uncompensated and compensated phase of the Gaussian pulse. The phase esponse within the fequency of inteest (93.4 ±. THz) becomes Fig. 9: The eye patten of optical communication system at L = 4 km, employing p-oapf Fequency (THz) of Gaussian pulse at 4 km of SMF Compensated phase at 4 km of SMF by using p-oapf Fig. : The uncompensated and compensated phase of the Gaussian pulse at L = 4 km using p-oapf. steepe as the dispesion and length inceases esulting in difficulty of futhe equalization (see Fig. 3 and Fig. ). Without any equalization, the eo fee distance is 34 km and the esult shows an incease of 3 times in the epeateless distance employing the p-oapf equalize. V. FUTURE WORK AND CONCLUSION One technique of inteest fo OAPF implementation is using the infinite impulse esponse (IIR) digital filte stuctue. The IIR OAPF stuctue can be deived fom (3), esulting in z cos( ) + z () OAPF() yz (9) H z = = z cos + z x() z ( )

5 The IIR equivalent equation can be fomed fom (9) as shown in (). yn () = cos( ) yn ( ) yn ( ) () + xn () cos( )( xn ) + xn ( ) whee z - is equivalent to a single delay and x(n), y(n) ae the input and output of OAPF equalize, espectively. In ode to ealize a passive IIR stuctue, () can be ewitten as: 3 4 yn () = cos( )( yn ) yn ( ) () + xn () cos( )( xn ) + xn ( ) Fom (), a passive OAPF equalize can be implemented in an IIR stuctue with optical components such as delays, attenuatos, combines and splittes as shown in Fig.. The impulse esponses of the active () and passive () OAPF ae shown in Fig.. The amplitudes of the impulse esponse of the passive OAPF ae smalle due to the passive components used in the stuctue. Howeve, the phase esponses of both stuctues ae compaable as shown in Fig. 3. These esults showed that the passive stuctue could be used in pactical implementation which will be the next stage of the eseach. In this pape, the wost case scenaio was consideed as the benchmak fo the capability of the p-oapf as a CD equalize. At L = 63 km, whee the eye patten is fully closed the p-oapf can compensate the dispesed pulse and obtain eo fee BER. Based on the simulation esults shown in Fig. 8, 9 and, it was found that the p-oapf can compensate up to a maximum distance of 4 km which is 3 times the distance in a system without equalize. The p-oapf is also vesatile in a lage ange of distance as the p-oapf optimized at 4 km can be used in distances down to 34 km with eo fee BER. The p-oapf can be designed to compensate fo CD ove lage bandwidths with low loss and ipple. REFERENCES [] C. K. Madsen and G. Lenz, "Optical All Pass Filte fo Response Design with Application fo Dispesion Compensation," IEEE Photonics Technology Lettes, vol., pp , 998. [] G. P. Agawal, Fibe Optic Communication Systems. New Yok: John Wiley & son Inc, 997. [3] H. J. R. Dutton, Undestanding Optical Communications. New Yok: Pentice Hall Inc, 998. [4] J. Y. Huh, S. B. Jun, J. H. Lee, and Y. C. Chung, "A Novel Fou- Wave Mixing Compensato," IEEE Photonics technology lettes, vol. 9, pp , 7. [5] G. P. Agawal, Lightwave Technology Telecommunication Systems. USA: Wiley-Intescience, 5. [6] A. Ghatak and K. Thyagaajan, Intoduction to Fibe Optics. Cambidge: Univesity Pess, 998. [7] A. F. Elefaie, R. E. Wagne, and D. G. Daut, "Chomatic Dispesion Limitation in Coheent Lightwave Tansmission Systems," Jounal of Lightwave Technology, vol. 6, pp , 988. [8] B. Jopson and A. Gnauck, "Dispesion Compensation fo Optical Fibe Systems," IEEE Communications Magazine, pp. 96-, 995. [9] N. Q. Ngo, S. Y. Li, R. T. Zheng, S. C. Tjin, and P. Shum, "Electically tunable dispesion compensato with fixed cente wavelength using fibe Bagg gating," Jounal of Lightwave Technology, vol., pp , 3. [] S. L. Jansen, v. d. D. Bone, P. M. Kummich, S. G. Spalte, D. Khoe, and d. H. Waadt, "Long-Haul DWDM Tansmission x(n) 8 φ shifte Attenuato cos() Attenuato Attenuato cos() Attenuato 8 φ shifte y(n) Fig. : Block diagam of passive OAPF by using stuctue of IIR. Amplitude n Acive stuctue Passive stuctue Fig. : Impulse esponses of active and passive OAPF. - Omega(pi) () Active Stuctue Passive stuctue Fig. 3: s esponses of active and passive OAPFs. Systems Employing Optical Conjugation," IEEE Jounal of Selected Topics in Quantum Electonics, vol., pp , 6. [] G. Lenz and C. K. Madsen, "Geneal Optical All Pass Filte Stuctues fo Dispesion Contol in WDM Systems," Jounal of Lightwave Technology, vol. 7, pp , 999. [] J. Poakis and D. Manolakis, Digital Signal Pocessing, 3 d ed. New Yok: Pentice Hall Inc, 996. [3] R. G. Lyons, Undestanding Digital Signal Pocessing. USA: Addison-Wesley Publishing Company, 997. [4] W. Loedhammacaka, W. P. Ng, and R. A. Cyan, "Chomatic Dispesion Compensation Employing Optical All Pass Filte by Using IIR Stuctue fo Gb/s Optical Communication System," pesented at The IEE Semina on Optical Fibe Communication and Electonic Signal Pocessing, The IEE Savoy Place London UK, 5. [5] J. D. Downie, "Relationship of Q Penalty to Eye-Closue Penalty fo NRZ and RZ Signals With Signal-Dependent Noise," Jounal of Lightwave Technology, vol. 3, pp. 3-38, 5. [6] R. A. Cyan and M. J. N. Sibley, "Minimising intesymbol intefeence in optical-fibe dicode PPM systems," IEE Poc. Optoelecton, vol. 53, pp. 93 -, 6.