Abstract:
Severe inter-symbol interference (ISI), introduced by narrow-band optical filtering in high spectral efficiency wavelength-division multiplexed (WDM) systems to avoid coherent WDM crosstalk, can be substantially mitigated by the use of maximum-likelihood sequence estimation (MLSE) reception. Compared to conventional threshold detection, the use of an MLSE receiver allows, for example, a 22% reduction in optical receive filter bandwidth. For tight optical filtering, the MLSE receiver benefits from taking into account noise correlation. MLSE receivers with one and with two samples per bit are described and it is shown that while oversampling is beneficial for wide-band optical filters, the benefit goes away for narrow-band optical filtering, thereby facilitating MLSE design for rates beyond 10 Gb/s.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to the field of high-speed optical data communications, and in particular, to the detection of signals in high spectral efficiency optical communication systems. 
       BACKGROUND INFORMATION 
       [0002]    Maximum likelihood sequence estimation (MLSE) receivers have been used in fiber optic communication systems operating at data rates up to 10 Gb/s to counteract signal distortions due to chromatic and polarization-mode dispersion. (See, e.g., H. F. Haunstein et al., “Principles for Electronic Equalization of Polarization-Mode Dispersion,” J. Lightwave Technol., vol. 22, pp. 1169-1182, 2004; F. Buchali et al., “Viterbi equalizer for mitigation of distortions from chromatic dispersion and PMD at 10 Gb/s,” in Proc. Opt. Fiber Commun. Conf. (OFC), MF85, 2004; A. Farbert et al., “Performance of a 10.7-Gb/s receiver with digital equalizer using maximum likelihood sequence estimation,” Proc. European Conf.on Opt. Commun. (ECOC), p. Th4.1.5, 2004; and J. J. Lepley et al., “Excess penalty impairments of polarization shift keying transmission format in presence of polarization mode dispersion,” IEEElectron. Lett., vol. 36, no.8, pp.736-737, 2000.) 
         [0003]    MLSE has also been used to mitigate distortions due to narrow-band electrical filtering such as might be found in optical receivers. (See, e.g., F. Buchali et al., “Correlation sensitive Viterbi equalization of 10 Gb/s signals in bandwidth limited receivers,” Proc. Opt. Fiber Commun. Conf. (OFC), OFO2, 2005; and H. F. Haunstein et al., “Optimized Filtering for Electronic Equalizers in the Presence of Chromatic Dispersion and PMD,” Proc. Opt. Fiber Commun. Conf. (OFC), MF63, 2003.) 
         [0004]    In wavelength-division multiplexed (WDM) optical transmission systems operating at high spectral efficiencies, narrow-band optical filtering by means of WDM multiplexers and demultiplexers has been used to avoid coherent WDM crosstalk. (See P. J. Winzer, et al., “Coherent Crosstalk in Ultradense WDM Systems,” J. Lightwave Technol., vol. 23, pp. 1734-1744, 2005.) 
       SUMMARY OF THE INVENTION 
       [0005]    In an exemplary embodiment, the present invention provides a high spectral efficiency optical communication system comprising narrow-band optical filtering, at the transmitter, the receiver, or within the transmission line, and a maximum likelihood sequence estimation (MLSE) receiver for detecting signals subjected to the narrow-band optical filtering. In accordance with the present invention, MLSE is used to counteract signal distortions due to the narrow-band optical filtering, thereby allowing for narrower optical filters and consequently for systems with higher spectral efficiencies. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0006]      FIG. 1A  is a block diagram of a model of an exemplary embodiment of an optical communication system in accordance with the present invention and  FIG. 1B  is a block diagram of an exemplary embodiment of an optical receiver in the system of  FIG. 1A . 
           [0007]      FIGS. 2A and 2B  are eye diagrams of the detected data signal at the receiver of the exemplary system, illustrating exemplary sampling instants for one and two samples per bit, respectively. 
           [0008]      FIG. 3  is a trellis structure for an exemplary four-state MLSE receiver for use in accordance with the present invention. 
           [0009]      FIGS. 4A through 4C  show the noise correlation between two signal samples spaced apart by two, one, and one-half bit periods, respectively, as a function of the optical receive filter bandwidth. 
           [0010]      FIGS. 5A and 5B  illustrate the performance of exemplary receivers for a first and a third-order Gaussian optical filter, respectively. 
       
    
    
     DETAILED DESCRIPTION 
       [0011]      FIG. 1A  is a block diagram of a model of an exemplary embodiment of an optical communication system  100  in accordance with the present invention. A data bit stream â 1 , â 2 , . . . , â n  is modulated by a modulator  110  into an optical data signal. The modulator  110 , may be, for example, a Mach-Zehnder modulator and the optical signal may be a chirp-free non return-to-zero (NRZ), on-off-keying (OOK) signal with a bit rate R bit  of 43 Gb/s. As will be evident of one of ordinary skill in the art, the present invention is not limited to a particular signal format, modulation or rate. 
         [0012]    The system  100  may include a variety of components between the modulator  110  and an optical receiver  120 , including, for example, a WDM multiplexer  112 , one or more optical add/drop multiplexers (OADMs)  113 ,  114 , and a WDM demultiplexer  116 . Each of these components may introduce some optical filtering to the optical data signal before it reaches the optical receiver  120 . The optical receiver  120  may also further optically filter the signal before detecting it. 
         [0013]    As shown in  FIG. 1A , amplified spontaneous emission (ASE) can be added at several points  115 . 1 - 115 . 3  in the communication system. ASE can be modelled as additive white Gaussian noise for both quadratures and can be added independently to each of the polarization modes typically carried by a single-mode optical fiber. 
         [0014]      FIG. 1B  is a block diagram of an exemplary embodiment of the optical receiver  120 . At the optical receiver  120 , the noisy signal is filtered by an optical bandpass filter  125  of variable bandwidth B o . The filter  125  can be implemented in a variety of ways, including, for example, as a first or a third-order Gaussian filter. 
         [0015]    After the filter  125 , the optical signal is provided to an optical-to-electrical converter  130 . The converter  130  can be implemented, for example, with a square-law photodetector. A coherent receiver implementation can also be used. 
         [0016]    The resultant electrical signal is filtered by a low-pass filter  140  of bandwidth B e . The filter  140  can be implemented, for example, as a fifth-order Bessel low-pass filter, with a bandwidth B e  that is approximately 0.5 to 1.0 R bit  (e.g., 0.75R bit ). The filtered electrical signal is then sampled by a sampler  150  at or above the bit rate.  FIGS. 2A and 2B  show the sampling instants for each case, respectively. 
         [0017]    The samples are then processed by a receiver  160 . The detected data sequence is denoted ã 1 , ã 2 , . . . , ã n  which should, ideally, be equal to the transmitted data bit stream â 1 , â 2 , . . . , â n . 
         [0018]    In a first exemplary embodiment of the present invention, the receiver  160  comprises a correlation-insensitive MLSE receiver and the electrical signal is sampled once per bit. As shown in  FIG. 2A , the one sample per bit is preferably taken at or in the vicinity of the maximum eye opening. Note that for severe signal distortions, the eye diagram might be completely closed, and the “eye opening” may disappear. This possibility, however, does not preclude the applicability of the present invention. 
         [0019]    For an optical bandpass filter  125  bandwidth B o &gt;0.8R bit , inter-symbol interference (ISI) will affect the neighboring bits on each side of the interference; i.e. the noisy signal sample r i  is affected by bits a i−1 , a i , and a i+1 . In such an embodiment, the MLSE receiver  160  preferably has a 4-state trellis structure, as shown in  FIG. 3 . The MLSE branch metrics of the underlying 4-state trellis are p(r i |a i−1 , a i , a i+1 ). The MLSE traceback length is 10, i.e. the MLSE receiver makes a decision on a bit after processing 10 steps of the trellis. 
         [0020]    With an optical bandpass filter  125  bandwidth B o &gt;0.5R bit , inter-symbol interference (ISI) will affect the two neighboring bits on each side of the interference; i.e. the noisy signal sample r i  is affected by bits a i−2 , a i−1 , a i , a i+1 , and a i+2 . In such an embodiment, the MLSE receiver  160  preferably has a 16-state trellis structure. The MLSE branch metrics of the underlying 16-state trellis are p(r i |a i−2 , a i−1 , a i , a i+1 , a i+2 ). 
         [0021]    In a further exemplary embodiment of the present invention, the receiver  160  comprises a correlation-sensitive MLSE receiver and the electrical signal is sampled once per bit.  FIGS. 4A-C  depict the noise correlation between two samples r(t) and r(t+Δt) for various Δt as a function of the optical filter  125  bandwidth B o . The correlation can be determined separately for each bit pattern by means of Monte-Carlo simulations, for example. The resultant pattern-dependent spread of the correlation curves reflects the signal-dependent nature of beat noise.  FIG. 4B  shows significant noise correlation across one bit (Δt=1T bit ) for B o &lt;R bit . In comparison, the correlation across two bits (Δt=2T bit ,  FIG. 4A ) is negligibly small. Therefore, in performing the MSLE, it is possible to only take into account the noise correlation across one bit, using the branch metrics p(r i |r i+1 , a i−2 , a i−1 , a i , a i+1 , a i+2 , a i+3 ). The branch metrics can be estimated for each bit pattern individually by a variety of methods, including, for example, using histograms obtained through Monte-Carlo simulations, and subsequent smoothing using a kernel density estimation method. (See, e.g., B. W. Silverman, “Density estimation for statistics and data analysis,” Chapman and Hall, 1986.) 
         [0022]    In yet a further exemplary embodiment of the present invention, the receiver  160  comprises a correlation-insensitive MLSE receiver and the electrical signal is sampled twice per bit. As shown in  FIG. 2B , the two samples per bit, r i,a  and r i,b  for bit a i , are preferably symmetrically centered around the maximum eye opening, if the distortions are such that an eye opening still exists. The resulting branch metrics are p (r i,a |a i−2 , a i   i−1 , a i , a i+1 , a i+2 )·p(r i,b |a i−2 , a i−1 , a i , a i+1 , a i+2 ) for the 16-state trellis. Because of significant noise correlation at Δt=T bit  for B o &lt;R bit , the probability density function of sample r i,a  depends on two other samples, r i,b  and r i+1,a . 
         [0023]    In yet a further exemplary embodiment of the present invention, the receiver  160  comprises a correlation-sensitive MLSE and the electrical signal is sampled twice per bit. 
         [0024]    Performance results of the various embodiments described above will now be discussed with reference to  FIGS. 5A and 5B . The optical-signal-to-noise ratio (OSNR) at the input to the optical receiver  120  that is required for operation at a predetermined bit error ratio (BER) (e.g., 10 −3 ) can be used for purposes of measuring performance. The OSNR is defined as P s /(2N ASE B ref ), where P s  is the optical signal power entering the receiver, N ASE  is the ASE power spectral density per polarization, B ref  is the reference bandwidth (e.g., 12.5 GHz), and the factor of 2 takes into account both ASE polarizations. 
         [0025]      FIGS. 5A and 5B  show the required OSNR (into the receiver  120 ) as a function of receive filter bandwidth B o  for MLSE and conventional threshold receivers, for 1st-order and 3rd-order Gaussian optical filter characteristics, respectively. Eye diagrams of the electrical signal at the sampling circuit for different optical filter bandwidths are shown in insets  601 - 604 . Note that for the sake of simplicity, the optical filtering introduced by the various components ( 112 ,  113 ,  114 ,  116 ,  120 ) in the system  100 , discussed above in connection with  FIG. 1A , are modeled by the optical BPF  125  for purposes of generating the results of  FIGS. 5A and 5B . 
         [0026]    In  FIGS. 5A and 5B , the dash-dotted curves  610  represent the OSNR performance using a conventional threshold receiver with optimized decision threshold where the data received is a de Brujin bit sequence (DBBS). The dotted curves  620  represent the ISI-free performance of the conventional threshold receiver as a baseline, assuming the transmission of isolated ‘1’s and ‘0’s (i.e., isolated to the extent that the bits are far enough apart so that the filter-induced spreading of the ‘1’-bit will not affect the ‘0’ bit.) 
         [0027]    For small B o , the performance of the threshold receiver using the DBBS data ( 610 ) degrades due to ISI and due to attenuation by spectral signal truncation. The ISI-free curve  620  is affected by only the latter of the two effects. The difference between the two curves  610  and  620  for the conventional threshold receiver quantifies the ISI penalty. 
         [0028]    The solid black curves  630  in  FIGS. 5A and 5B  represent the performance of the correlation-insensitive MLSE receiver with one sample per bit, described above. The curves  630  show that this receiver partially compensates for ISI, as it outperforms the conventional threshold receiver for at least the entire range of B o  shown (0.5-2.5R bit ). Using an MLSE receiver therefore allows for narrower optical filtering, which in turn reduces coherent wavelength division multiplex (WDM) crosstalk, thereby facilitating high spectral efficiency WDM systems. For example, as indicated in  FIG. 5B  by the arrow  640  for a 3rd-order Gaussian optical filter, the use of an MLSE receiver allows for a filter bandwidth reduction from approximately 0.98R bit  to as low as 0.76R bit  with only a 1 dB OSNR penalty. 
         [0029]    In  FIGS. 5A and 5B , the dashed curves  650  represent the correlation-sensitive MLSE receiver with one sample per bit, as described above. For B o &lt;R bit , for which  FIG. 4B  predicts significant noise correlation, the correlation-sensitive MLSE receiver shows improved performance over the correlation-insensitive MLSE receiver. For larger optical filter bandwidths, the correlation-sensitive MLSE accurately reproduces the results of the correlation-insensitive MLSE (represented by the curves  630 ). 
         [0030]    In  FIGS. 5A and 5B , the gray curves  660  represent the performance of the correlation-insensitive MLSE receiver with two samples per bit, as described above. This receiver shows a better performance than the MLSE receiver with one sample/bit for large optical filter bandwidths (as represented by the curves  630  and  650 ). As can be seen in  FIGS. 5A and 5B , however, the improvement that results from having a second sample per bit goes away for narrow-band optical filtering. This can be understood from the fact that small optical filter bandwidths make adjacent signal samples less independent, thus reducing the additional information that can be obtained from over-sampling. Avoiding over-sampling significantly facilitates the implementation of MLSE receivers that operate at rates beyond 10 Gb/s. 
         [0031]    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 present 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.