Abstract:
An arrangement is described for compensating intra-channel nonlinearities in an optical communications system which combines optical dispersion compensation with electronic pre-distortion (EPD). EPD with moderate lookup table size can effectively suppress intra-channel nonlinearities over optical transmission links incorporating optical dispersion compensation. The arrangement can be implemented for a variety of optical communications systems, including 10 Gb/s, 40 Gb/s and higher bit rate systems as well as single-channel and wavelength-division multiplexing (WDM) systems.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to the field of high-speed optical communications, and more specifically to methods and apparatus for effecting intra-channel nonlinearity compensation. 
       BACKGROUND INFORMATION 
       [0002]    The use of electronic pre-distortion (EPD) to compensate chromatic dispersion was proposed as early as two decades ago. (T. L. Koch et al., JLT, vol. 3, 1985, pp. 800-805.) Thanks to progress in high-speed electronic digital signal processing, there has recently been a revived interest in this technique for 10 Gb/s systems. The aim of more recent studies of this technique has been to entirely eliminate inline optical dispersion compensators (ODCs) by compensating chromatic dispersion at the transmitters. (See, e.g., M. M. El Said et al, JLT, vol. 23, 2005, pp. 388-400; D. McGhan et al, OFC&#39;05, paper PDP27; R. I. Killey et al, IEEE PTL, vol 17, 2005, pp. 714-716.) 
         [0003]    Due to large temporal power variations in such systems and the absence of nonlinearity compensation through dispersion mapping, nonlinearities in EPD systems are much larger than systems using ODCs. (See R. J. Essiambre et al, OFC&#39;06, paper OWB1; R. J. Essiambre et al, ECOC&#39;05, paper Tu3.2.2.) 
         [0004]    Although EPD has the ability, in principle, to compensate self-phase modulation (SPM), inter-channel cross-phase modulation (XPM) greatly impacts EPD systems, especially systems operating at  10  Gb/s. Moreover, operation of EPD at 40 Gb/s increases transmitter complexity considerably due to an increase by a factor of 16 in bit overlap. Alternatively, multi-level modulation formats with advanced receivers have been required when implementing EPD at 40 Gb/s. (P. J. Winzer et al, ECOC&#39; 05, paper Tu4.2.2.) 
       SUMMARY OF THE INVENTION 
       [0005]    The present invention is directed to a system and method of compensating intra-channel nonlinearities in an optical communications system which includes optical dispersion compensation and electronic pre-distortion. The present invention can be implemented in a variety of systems, including 10 Gb/s, 40 Gb/s and higher bit rate systems, as well as single-channel and wavelength-division multiplexing (WDM) systems. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0006]      FIG. 1  is a schematic representation of an exemplary embodiment of a system in accordance with the present invention. 
           [0007]      FIGS. 2A and 2B  are block diagrams of exemplary transmitters employing electronic pre-distortion (EPD). 
           [0008]      FIGS. 3A through 3D  are signal eye-diagrams illustrating the performance of various embodiments of a system in accordance with the present invention. 
           [0009]      FIG. 4  is a graph of eye-opening penalty (EOP) plotted against launch power for various embodiments of a single-channel system in accordance with the present invention. 
           [0010]      FIG. 5  is a graph of eye-opening penalty (EOP) plotted against launch power for various embodiments of a wavelength-division multiplexing (WDM) system in accordance with the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0011]      FIG. 1  is a schematic representation of an exemplary embodiment of an optical communications system  100  in accordance with the present invention. The system  100  includes a transmitter  110  which may be coupled via an optional multiplexer  115  to an optical link  120  comprised of several sections of optical fiber and related components, as described more fully below. The optical link  120  is ultimately coupled to a receiver  140 , such as via an optional demultiplexer  135 . 
         [0012]    An electrical input data signal is provided to the transmitter  110 , which processes and converts the electrical signal into an optical signal for transmission over the optical link  120  to the receiver  140 . The optical signal is then processed and converted at the receiver  140  back into an electrical data signal. 
         [0013]    In accordance with the present invention, electronic pre-distortion (EPD) is performed at the transmitter  110  as described more fully below. Additionally, the optical link  120  includes optical dispersion compensators (ODCs). 
         [0014]    The optical link  120  includes multiple ODCs  125 . 1 - 125 .N which are preferably distributed along the length of the optical link. As shown in  FIG. 1 , the ODCs  125 . 1 - 125 .N are arranged between sections of optical fiber  128 . 1 - 128 .N. In the exemplary embodiment shown, optical amplifiers  127 . 1 - 127 .N and  129 . 1 - 129 .N are arranged at either end of each corresponding section of fiber  128 . 1 - 128 .N to compensate the losses in the fiber and the ODCs. 
         [0015]    The ODCs  125 . 1 - 125 .N and the optical amplifiers  127 . 1 - 127 .N can each be implemented conventionally. 
         [0016]    In addition to the electronic pre-distortion that is carried out at the transmitter, there are several electronic processing techniques that may be applied at the receiver, in accordance with an exemplary embodiment of the present invention. Such techniques, may include, for example, maximum likelihood sequence estimation (MLSE), Feed-Forward Equalization (FFE), or Decision-Feedback Equalizer (DFE), among others. 
         [0017]      FIGS. 2A and 2B  are block diagrams of exemplary embodiments of a transmitter incorporating EPD for use in a system in accordance with the present invention. The transmitter embodiments of  FIGS. 2A and 2B  are known and can be implemented conventionally as described below. 
         [0018]    In the embodiment of  FIG. 2A , data to be transmitted is provided to a memory  210 . The output of the memory  210  is provided to a look-up table  220 . The output of the lookup table  220  is provided to digital-to-analog (D/A) converters  222  and  224 . The outputs of the D/A converters  222  and  224  are provided to a modulator  230  which modulates the output of a laser  240  in accordance with the D/A converter outputs to generate a pre-distorted output optical signal for transmission over the optical link. The modulator  230  may be, for example, an in-phase and quadrature (I/Q) modulator or a magnitude/phase modulator. 
         [0019]    In the embodiment of  FIG. 2B , the data to be transmitted is provided to finite- impulse-response (FIR) filters  252  and  254 . The outputs of the filters  252  and  254  are provided to the modulator  230  which modulates the output of a laser  240  in accordance with the filter outputs to generate a pre-distorted output optical signal for transmission over the optical link. 
         [0020]    Simulations were performed to investigate the performance of an exemplary system in accordance with the present invention. In the simulations, the optical transmission link consisted of 20 spans of 100 km TRUEWAVE fiber with chromatic dispersion of 6.0 ps/(km.nm), nonlinear coefficient of 1.7 km −1 W −1  and loss coefficient of 0.21 dB/km. After each span, the chromatic dispersion in the transmission fiber was compensated by dispersion compensation fiber (DCF), resulting in residual dispersion per span (RDPS) of 20 ps/nm. All-Raman amplification was used with 22/78 forward/backward pumping gain (in dB) in the transmission fiber and all backward pumping in the DCF. The nonlinearity in DCF was neglected in the simulations. Both transmission fiber and DCF were pumped at transparency. Pre-compensation of −400 ps/nm was employed, the numerically determined optimum value for the exemplary system simulated. The optical dispersion compensation was first optimized at each launch power for the ODC-only system, and was set to have 70 ps/nm net residual dispersion for the system with EPD, the optimum value at large launch powers for the ODC-only system. 
         [0021]    The transmitter generated a 42.7-Gb/s, 2 9  De Bruijn bit sequence (DBBS) non-return-to-zero (NRZ) pre-distorted signal. The transmitter was assumed to be of the embodiment shown in  FIG. 2A  in which the lookup table outputs an m-bit word to each D/A converter according to each n-bit input sequence, and the outputs of the two D/A converters drive the I/Q modulator to generate an ideal pre-distorted optical field. The simulations did not include the degradations caused by finite over-sampling and D/A converter resolution. 
         [0022]    A lookup table was generated using backward propagation for different launch powers, then the pre-distorted optical signal at the transmitter was obtained from the lookup table according to the n-bit input sequence. A 50-GHz Gaussian filter was used to smooth the signal in the lookup table. The receiver used in the simulations had an 85-GHz bandwidth 4 th -order super-Gaussian optical filter and a 5th-order Bessel electrical filter with a 3 dB bandwidth of approximately 32 GHz. Noise was neglected in the simulations. The eye-opening penalty of the systems was studied. 
         [0023]    A single-channel transmission system was simulated first.  FIGS. 3A-3D  show the eye-opening diagrams of the transmission system at 2000 km without ( FIG. 3A ) and with EPD with various lookup table sizes with n=9, 11 and 13 ( FIGS. 3B-3D , respectively). The launch power was set at −1 dBm. 
         [0024]    As shown in  FIG. 3A , for the ODC-only system, the eye-diagram is completely closed at the simulated distance and launch power, whereas with the use of EPD, the eye-diagrams are open, with the eye-diagrams improving with larger lookup tables. With a lookup table having n=13 bit addressing, there is little distortion in the eye-diagram ( FIG. 3D ). It should be noted that the maximum chromatic dispersion that the signal experiences after 2000 km in the exemplary system simulated is approximately 600 ps/nm, which causes a pulse to spread to about 15 bits. 
         [0025]      FIG. 4  plots the eye-opening penalty (EOP) versus the launch power for the single channel 40-Gb/s system without EPD and with EPD of different size lookup tables. EOP is defined as the ratio (in dB) of the back-to-back eye-opening to the eye-opening after transmission. The eye-opening is defined as the height of the highest rectangle with a 20% bit period width that can fit into the eye-diagram. 
         [0026]    The results indicate that due to the suppression of intra-channel nonlinearities, the system with EPD can have a larger launch power. Furthermore, increasing the lookup table size increases the launch power for a given EOP. At an EOP of 1 dB, the launch power is limited to approximately −4.0 dBm for the ODC-only system. When EPD with n=7 to n=13 lookup tables is applied, the launch power can be increased approximately by 1 to 5 dB. 
         [0027]      FIG. 5  plots the EOP of the center channel for a 9-channel 40-Gb/s WDM system with 100 GHz channel spacing. In the WDM system, the multiplexer and demultiplexer filter bandwidths are 85 GHz. Comparison between  FIGS. 4 and 5  shows that the inter-channel XPM effect becomes dominant when the intra-channel nonlinearities are suppressed. As the inter-channel XPM effect increases with launch power, it becomes the ultimate limit for system performance. For EOP up to 2 dB, there is almost no difference between the WDM EPD system with n=11 and n=13 lookup tables, as the degradation is mainly induced by inter-channel XPM, which cannot be suppressed by EPD. At 1 dB EOP, the launch power of the WDM system can be increased by 3 dB. 
         [0028]    Although EPD with lookup table addressing size (n) of 7 to 13 have been simulated, the present invention can be implemented with a wide range of lookup tables sizes (e.g., 5 to 30) and is not limited to any particular size or range of sizes. 
         [0029]    It is understood that the above-described embodiments are illustrative of only a few of the possible specific embodiments which can represent applications of the invention. Numerous and varied other arrangements can be made by those skilled in the art without departing from the spirit and scope of the invention.