Patent Publication Number: US-8538278-B2

Title: Superimposed training and digital filtering coherent optical receivers

Description:
BACKGROUND 
     1. Technical Field 
     The present invention relates to optical communication systems and methods and, more particularly, systems and methods for coherent optical receivers in polarization multiplexed quadrature phase shift keyed systems. 
     2. Description of the Related Art 
     Continuous expansion of network applications results in a continuous demand on transmission capacities. To keep up with these demands, one can increase the transmission rates of the transceivers, or optimize the utilization of currently available components. In optical networks, increasing the transceivers&#39; transmission rates augments the susceptibility of the transmitted signals to degradation over extended transmission lengths. This is due to the fact that, at higher data rates, the signal quality degrades severely as a result of linear and nonlinear impairments. 
     Chromatic dispersion (CD) and polarization mode dispersion (PMD) are the most dominant optical-channel distortion effects. CD is usually a much larger impairment than PMD, and can be a significant distortion even at relatively low data rates on long fibers. 
     CD is an effect based either in the refractivity of a medium or in the geometric properties of the medium, which cause different frequencies of electromagnetic radiation to travel through the medium at different rates. The result is that a pulse of light spreads out along the fiber as it travels over great distances. The longer the fiber over which a pulse travels, the wider the pulse spreads out. Difficulties arise when the resulting energy from a pulse begins to interfere with that of an adjacent pulse. This interference causes inter-symbol interference in the electrical domain. 
     CD effects are determined by each optical fiber, and can typically be considered stable over time. Because of its stability, CD can be compensated for using a passive device (e.g., medium having dispersion effects which counteract the dispersion of the transmission medium). However, such passive devices have drawbacks, in that they substantially reduce the optical signal-to-noise ratio. 
     PMD, meanwhile, is an effect based on the defects of the transmission medium and cannot be compensated for passively. In an ideal medium, signals traveling in orthogonal polarizations will travel at the same speed. In real media, however, defects cause random differences in the speeds of the respective polarizations, causing the polarizations to drift with respect to one another. PMD, in contrast to CD, is not a significant problem for most fibers until data rates exceed 10 Gb/s. However, in contrast to CD, PMD on long fibers changes randomly over time. The dynamic characteristic of PMD makes it a difficult problem for high-speed optical transmissions. 
     Polarization multiplexing (PolMux) with quadrature phase shift keying (QPSK) has been investigated as one avenue of research for boosting spectral efficiency and transmission rates. However, coherent detection in such systems has been considered too complex, due to phase- and polarization-tracking concerns, to be practical. Previous work has used digital filters with blind equalization to estimate transmission channels. Unfortunately, blind equalization lacks the reliability of a trained system. Conventional trained systems operate by time-multiplexing a training signal with data. This reduces the spectral efficiency. 
     SUMMARY 
     In response to the growing need for high-speed optical communications, embodiments of the present principles provide coherent reception with superimposed training sequences. Embodiments of the present principles include a polarization multiplexing, optical receiver that includes a polarization beam splitter for splitting a received optical signal into two orthogonal polarizations and a training/data recovery module for extracting a superimposed training signal and data signal from the polarized beams. 
     Embodiments of the present principles further include a method for coherent reception of polarization-multiplexed optical communications, including the steps of splitting a received signal into orthogonally polarized signals and recovering superimposed training and data signals from the signals. 
     Embodiments of the present principles further include a polarization-multiplexing, optical transmitter including a plurality of modulators for modulating data sequences and training sequences onto respective signals, a plurality of power combiners for combining training sequences with data sequences into orthogonal polarizations, and a polarization beam combiner for combining two orthogonally polarized signals. 
     These and other features and advantages will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The disclosure will provide details in the following description of preferred embodiments with reference to the following figures wherein: 
         FIG. 1  shows a block diagram of an optical transmitter/receiver system that employs superimposed training signals. 
         FIG. 2  shows a block diagram of an optical receiver that compensates for chromatic dispersion (CD) and polarization dependent impairments (PDI). 
         FIG. 3   a  shows a block diagram of a CD compensation module that produces the real component of an input signal. 
         FIG. 3   b  shows a block diagram of a CD compensation module that produces the imaginary component of an input signal. 
         FIG. 4  shows a block/flow diagram outlining a system/method for transmitting optical, polarization multiplexed communications using a superimposed training signal. 
         FIG. 5  shows a block/flow diagram outlining a system/method for receiving optical, polarization multiplexed communications using a superimposed training signal. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Superimposed training provides a technique for using coherent detection without sacrificing spectral efficiency. The present principles describe a technique for using superimposed training in a polarization multiplexing (PolMux) quadrature phase-shift keyed (QPSK) system. 
     Embodiments described herein may be entirely hardware, entirely software or including both hardware and software elements. In a preferred embodiment, the present invention is implemented in a combination of hardware and software, where software includes but is not limited to firmware, resident software, microcode, etc. 
     Referring now to the drawings in which like numerals represent the same or similar elements and initially to  FIG. 1 , an optical communication system is shown comprising a transmitter  100  and a receiver  101 . The transmitter comprises a laser  102  which forms a carrier signal. The laser is polarized at 45°, such that when the beam is then split in polarization beam splitter  104 , it produces two orthogonal polarizations of equal intensity. The polarized beams then feed into QPSK modulators  108  and  112 . Although the present embodiments are described in terms of a QPSK modulation scheme, other modulation schemes are available and may be employed according to the present principles. 
     QPSK modulators  108  and  112  receive data sequences  114  and  116 , comprising respective in-phase and quadrature signals that represent the substantive data which is to be modulated onto the polarized laser beams. The training sequences  106  and  110  first pass through their own PSK modulators  107  and  111  and are later combined with the modulated data sequences of QPSK modulators  114  and  116 . The PSK modulators  107  and  111  put the training sequences  108  and  110  into a form that may be additively combined with the modulated data sequences  114  and  116 . Although PSK modulation is used in this exemplary embodiment, the present disclosure is not intended to limit the inventive principles to such an embodiment. 
     The QPSK modulators  108  and  112  modulate the data sequences  114  and  116 . The modulated data sequences are additively combined with the modulated training sequences in power combiners  109  and  113  to produce a polarized optical signal with superimposed data and training sequences. The modulated, polarized signals are then combined in polarization beam combiner  118  and are subsequently transmitted over a fiber (not shown). As noted above, QPSK modulators are used for exemplary purposes and are not intended to limit the present principles to QPSK implementations. 
     The transmitted optical signals are received at receiver  101 . The incoming optical signal is split at polarization beam splitter  120  into two orthogonal polarized optical signals. Due to polarization mode dispersion (PMD) and other polarization dependent impairments (PDIs), the two optical signals produced by polarization beam splitter  120  will be rotated with respect to the two polarized transmitted signals. The PDIs change continuously in an unpredictable way. Adaptive filtering may be employed to compensate for the ever-changing PDIs. 
     The polarized beams are passed to coherent receivers  122  and  124 . These receivers may comprise 90° hybrid coherent receivers that produce a complex signal. The complex signal is then passed to a digital signal processing (DSP) module  126  which compensates for both CD as well as PDIs. The DSP produces four outputs, I 1   128 , Q 1   130 , I 2   132 , and Q 2   134  representing the data sequences  114  and  116  input to the transmitter  100 . 
     Referring now to  FIG. 2 , a detailed diagram of the DSP module  126  is shown. Complex inputs  200  and  201  pass through CD compensation modules  202  and  204 . The operation of the CD compensation modules is described in greater detail below with respect to  FIGS. 3   a  and  3   b . Each CD compensation module produces two outputs, representing real and imaginary components of the signal respectively. 
     After CD compensation, polarization dependent effects can be removed from the signal. These effects vary due to polarization dependent loss and polarization mode dispersion. Adaptive filtering can be used to correct for such time-varying effects. The outputs of the CD compensation modules  202  and  204  pass to adaptive filters  206 - 212 . CD compensation module  202 &#39;s output goes to filters  206  and  210 , while module  204 &#39;s output goes to filters  208  and  212 . The output of the filters are then summed, with filters  206  and  208  being summed in adder  214  and filters  210  and  212  being summed in adder  216 . The coefficients of the adaptive filters are updated frequently based on the magnitude of the error between the received signals and a required modulus. Carrier recovery is performed by the compensation of any phase and frequency mismatch between the incoming signal and the local oscillator of the coherent detector during the iterative process. 
     In order to update the adaptive filters, for input signals, s k (n), and output signals x k (n) for k=1,2, for both polarization, the relations are given as follows: 
                 x   1     ⁡     (   n   )       =         ∑     m   =   0       M   -   1       ⁢           ⁢         h   11     ⁡     (   m   )       ⁢       s   1     ⁡     (     n   -   m     )           +         h   12     ⁡     (   m   )       ⁢       s   2     ⁡     (     n   -   m     )                           x   2     ⁡     (   n   )       =         ∑     m   =   0       M   -   1       ⁢           ⁢         h   21     ⁡     (   m   )       ⁢       s   1     ⁡     (     n   -   m     )           +         h   22     ⁡     (   m   )       ⁢       s   2     ⁡     (     n   -   m     )                 
where h pq  for p,q ε{1,2}, are adaptive filters each of length M. For a PolMux-QPSK system, adapting the system equalizer is better performed by a constant modulus algorithm to exploit the fact that each polarization has a constant modulus. In this algorithm, the equalizer minimizes the error in magnitude in the mean square sense. The adaptive filters&#39; coefficients are updated relative to the magnitude of the error between the received signals and the required modulus, dependent on the launching power of the system. The required modulus is a measure of the constant modularity of the transmitted signal. The filter coefficients are initialized with zeros except the central taps of h 11  and h 21 . Updating the coefficients is done as follows:
 
 h   11   →h   11 +μ·(1 −|x   1 | 2 )· x   1   ·s   1   * h   12   →h   12 +μ·(1 −|x   1 | 2 )· x   1   ·s   2 *
 
 h   21   →h   21 +μ·(1 −|x   2 | 2 )· x   2   ·s   1   * h   22   →h   22 +μ·(1 −|x   2 | 2 )· x   2   ·s   2 *
 
where μ is the convergence parameter. μ is a value, usually less than 0.1, that is used to control the speed and the realization of convergence. s k * is the complex conjugate of the input signal at channel k.
 
     Finally, block  222  performs data detection and training sequences processing on the CD- and PMD-corrected signals. The training sequence is used to identify the source channel of a given data sequence which, after detection the data sequences  114  and  116 , may be completely interchanged. Block  222  produces four outputs,  128 - 134 , representing the four data streams encoded in the optical transmission. Demodulation may be performed in the DSP block  222  or may be performed by a separate demodulator, not shown. 
     Referring now to  FIGS. 3   a  and  3   b , detailed diagrams of the real and the imaginary portions of a CD compensation module are shown. A CD compensation module such as those shown as  202  and  204  in  FIG. 2  may comprise a real and an imaginary pathway, using the circuits of both  FIGS. 3   a  and  3   b  respectively. The effect of the transmission channel is given as Y(ω)=X(ω)H CD (ω), where Y(ω) is the received signal, X(ω) is the transmitted signal, and H CD (ω) is a transformation that models the CD effect of the medium. At lower speeds, second order CD effects are too small to be a concern. With the present principles, however, it is possible to reach high enough transmission speeds that second order effects become significant. As such, the present principles advantageously take the second order effects of CD into account in the CD compensation modules. 
     The CD effect of the channel, taken to second order, can be modeled as H CD (ω), the frequency response of the channel: 
                       H   CD     ⁡     (   ω   )       =     exp   ⁡     (     j   ⁢         λ   o   2     ⁢   L   ⁢           ⁢     ω   2         24   ⁢     π   2     ⁢     c   2         ⁢     (       6   ⁢   π   ⁢           ⁢   cD     -     S   ⁢           ⁢     λ   o   2     ⁢   ω     -     2   ⁢           ⁢   D   ⁢           ⁢     λ   o     ⁢   ω       )       )               (   1   )               
where ω is the baseband radial frequency, λ 0  is the transmitter wavelength, D is the fiber dispersion parameter, S is the fiber dispersion slope, L is the propagation distance, and c is the speed of light. As can be readily seen, all of these parameters are static with respect to a particular transmission system, allowing for static compensation. It is also worth noting that the frequency response of the channel for the first order CD,
 
                   H   CD     ⁡     (   ω   )       =     exp   ⁡     (     j   ⁢         λ   o   2     ⁢   DL   ⁢           ⁢     ω   2         4   ⁢   π   ⁢           ⁢   c         )         ,         
is not suited to the data rates that become possible with the present principles. Given the channel model, the chromatic dispersion can be reversed using an all-pass infinite impulse response filter.
 
     Because H CD (ω) is a constant amplitude, phase varying function, the inverse of the channel is simply the complex conjugate the of H CD (ω). This produces an expression for the transmitted signal based on the received signal and the complex conjugate of H CD (ω): X(ω)=Y(ω)·H* CD (ω), which, after separating into real and imaginary values, becomes: 
                     (           X   r               X   i           )     =       (           H     CD   ,   r             H     CD   ,   i                 -     H     CD   ,   i               H     CD   ,   r             )     ·     (           Y   r               Y   i           )               (   2   )               
Because the phase response of the channel is even, the channel response is expressed in monotonous phase response functions. This allows the design of a stable all-pass infinite impulse response (IIR) filter.
 
     By defining {tilde over (H)} CD =H CD,r −H hilb ·H CD,i , where H hilb  is the Hilbert transform, H CD,r  is the real component of H CD , and H CD,i  is the imaginary component of H CD , it becomes possible to design CD compensation modules for both the real and the imaginary parts of the transmitted signal. 
     Referring again to  FIGS. 3   a  and  3   b , the CD compensation module can be described in detail. Inputs Y r    302  and Y i    304  represent the real and imaginary components of the received signal, respectively. In  FIG. 3   a , the imaginary component  304  passes through Hilbert transformation  306 , whereas in  FIG. 3   b  the real component  302  is Hilbert transformed. The two components are then combined in adder  308  and subtracter  310 , forming two distinct paths. One path goes through a CD compensation transformation at  312 , while the other path has a CD compensation transformation  316  which is between two y(−t) blocks  314  and  318 . The y(−t) blocks can be considered time reversal blocks. This translates into finding the complex conjugate in the frequency domain. The two paths are then combined in averager  320 , which adds the outputs and divides by two. The averager  320  in  FIG. 3   a  produces as output the real component of the input signal  322 , whereas the averager  320  in  FIG. 3   b  produces as output the imaginary component  324 . 
     A PolMux system has two data channels, corresponding to the two polarizations. Each of these channels is assigned a specific training sequence peak-to-average power ratio of unity so that the channel estimation and data detection is straightforwardly achieved. 
     s k (n) is the kth polarization input signal where k=1 or 2. In superimposed training,
 
 s   k ( n )= b   k ( n )+ c   k ( n ),
 
where b k (n) is the information sequence and c k (n) is a deterministic periodic training sequence. The information sequence is assumed to have a zero mean, and a finite alphabet. The training sequence, on the other hand, is designed to be a nonrandom periodic sequence with the period P.
 
     The training sequences are designed to be polarization specific, with the ratio of peak-to-average power to be unity. Each of the training sequences is assigned a unique cycle frequency of the periodic hidden training sequence. This is done by choosing a period base sequence of a period {tilde over (P)}, and using it to build up the k th  training sequence. The base training sequence is denoted by  c   0 (n). The kth training sequence which is of twice the length of the base sequence is determined by: 
                   c   k     ⁡     (   n   )       =       ∑       m   ′     =   0       P   -   1       ⁢           ⁢       c       m   ′     ⁢   k       ⁢     ⅇ       j   ⁡     (       2   ⁢   π   ⁢           ⁢     m   ′         P   ~       )       ⁢   n             ,     ∀   n           
where,
 
               c       m   ′     ⁢   k       =     {               σ   ck     ⁢       c   _       m   ⁢           ⁢   0         ,               if   ⁢           ⁢     m   ′       =     k   -   1   +     2   ⁢           ⁢   m         ,           m   =     ⌊         m   ′     -   k   +   1     2     ⌋                 0   ,         elsewhere                             
and
 
                   c   _       m   ⁢           ⁢   0       =       1     P   ~       ⁢       ∑     n   =   0         P   ~     -   1       ⁢           ⁢           c   _     0     ⁡     (   n   )       ⁢     ⅇ       -     j   ⁡     (       2   ⁢   π   ⁢           ⁢   m       P   ~       )         ⁢   n               ,         
where P is the length of the kth training sequence, and
 
 s   ck =√{square root over ( P   −1 Σ n=0   P−1   |c   k ( n )| 2 )}.
 
     The detection process takes place in two distinct parts. The first part is based on the first order statistics, as it observes the data sequences from the other polarization as interference. The fact that the training sequences are periodic and that the information sequence is zero mean leads to the conclusion that the mean of the received signal y(n)=x 1 (n)+x 2 (n)+v(n) is periodic in n with the period P with distinct cycle frequencies, where x k (n) is the kth output signal, and v(n) is the noise. Using this fact in addition to the known training sequences, and the zero mean data sequences, the mean of the received signal becomes a function of the training sequences, the channel response, and the mean of the noise, 
                   y   ~     ⁡     (   n   )       =       y   ⁡     (   n   )       -       ∑     k   =   1     2     ⁢           ⁢       ∑     l   =   0     L     ⁢           ⁢           h   ^     k     (   1   )       ⁡     (   l   )       ⁢       c   k     ⁡     (     n   -   1     )             -       m   ^       (   1   )           ,         
where {tilde over (v)}(n) is the mean of the received signal, L is the channel length, ĥ k   (1)  is the initial estimate of the channel, and {circumflex over (m)} (1)  is the estimate of the noise mean. Omitting the terms related to the noise, an initial estimate of the channel response is produced.
 
     The second part of the detection process is based on iterative linear minimum mean-square error (LMMSE) equalization. First take the channel estimate derived above and use it to estimate the data sequences using the LMMSE equalizer with hard decision by the known alphabets. At this point, it is assumed that the estimated data sequences are correct. The estimated data sequences can then be used to estimate the multi-polarization channel. Given that 
                 α   mk     =         2   ⁢   π     P     ⁢     (       2   ⁢           ⁢   m     +   k   -   1     )         ,         
the c k (n) mentioned above can be formed as
 
                   c   k     ⁡     (   n   )       =       ∑     m   =   0         P   ~     -   1       ⁢       c   mk   ′     ⁢     ⅇ       jα   mk     ⁢   n             ,     ∀   n           
as well (where all variables are as defined earlier). Using these c′ mk , one can define
 
               C   k     =         [           c     1   ⁢           ⁢   k     ′         0       ⋯       0           0         c     2   ⁢           ⁢   k     ′         ⋱       ⋮           ⋮       ⋱       ⋱       0           0       ⋯       0         c       (       P   ~     -   1     )     ⁢           ⁢   k     ′           ]     [           ⁢         1         ⅇ     -     jα     1   ⁢           ⁢   k               ⋯         ⅇ       -     jα     1   ⁢           ⁢   k         ⁢   L               1         ⅇ     -     jα     2   ⁢           ⁢   k               ⋯         ⅇ       -     jα     2   ⁢           ⁢   k         ⁢   L               ⋮       ⋮       ⋮       ⋮           1         ⅇ     -     jα       (       P   ~     -   1     )     ⁢           ⁢   k               ⋯         ⅇ       -     jα       (       P   ~     -   1     )     ⁢           ⁢   k         ⁢   L             ]     ⊗             [           ⁢         1       0       ⋯       0           0       1       ⋱       ⋮           ⋮       ⋱       ⋱       0           0       ⋯       0       1         ]     .               
The channel estimation is done as follows:
 
 Ĥ   k =( C   k   H   C   k ) −1   C   k   H   {circumflex over (D)}   k  
 
where Ĥ k  is the vector of the channel estimates, {circumflex over (D)} k  is the vector of the {circumflex over (d)} mk &#39;s. {circumflex over (d)} mk  is a function of the received signal and is defined as:
 
                 d   ^     mk     =       1   T     ⁢       ∑     n   =   0       T   -   1       ⁢           ⁢       y   ⁡     (   n   )       ⁢       ⅇ       -     jα   mk       ⁢   n       .                 
The H shown as a superscript of C k  indicates that C k   H  is the Hermitian transpose of C k .
 
     This process of iteratively updating the multi-polarization channel keeps repeating until reaching the point where the incremental difference between two successive estimates of the channel reaches a predefined threshold. This threshold value may depend on several factors, including the amount of time allowed to reach the estimate of the channel, the speed of convergence, and the allowed margin of error for the channel estimate. Usually, the smaller the threshold, the more time is required to realize the convergence, but the results produced are closer to the final convergence value. 
     Referring now to  FIG. 4 , a block/flow diagram is shown which outlines a method for transmitting polarization-multiplexed, optical communications with a superimposed training signal according to the present principles. First, a laser beam is split into two orthogonal polarizations in block  402 . Next, data and training sequences are modulated onto respective orthogonal polarizations in block  404 , such that a first data sequence and a first training sequence are modulated according to one polarization and a second data and a second training sequence are modulated according to another polarization, orthogonal to the first. In block  406 , the first data sequence and the first training sequence are additively combined. In block  408 , the second data sequence and the second training sequence are additively combined. The two orthogonal polarizations are then combined at block  410  and transmitted along an optical fiber. 
     Referring to  FIG. 5 , a block/flow diagram is shown which outlines a method for receiving polarization-multiplexed, optical communications with a superimposed training signal according to the present principles. An optical signal having two data sequences encoded at orthogonal polarizations is received at block  502 . The optical signal is then split into two orthogonal polarizations at block  504 . Because of the time-dependent nature of PDI, the two polarized beams that are produced at block  504  will be varying in time with respect to the original polarizations. Additionally, the transmission medium will have produced CD effects. 
     Block  506  compensates for first- and second-order CD effects. This compensation may be performed using IIR filters as described above. The beams are then adaptively filtered at block  508  to remove the time-varying PDI. 
     Having compensated for the dispersion effects of the transmission medium, the data and training sequences can be extracted and processed at block  511 . The detection of the data sequences includes estimating channel response based on the mean of the received signal at block  509  and iterative LMMSE equalization at block  510 . The extracted training sequences can then be used to update the adaptive filter coefficients in block  512 , thereby allowing the PDI compensation to track changes. 
     Having described preferred embodiments of a system and method (which are intended to be illustrative and not limiting), it is noted that modifications and variations can be made by persons skilled in the art in light of the above teachings. It is therefore to be understood that changes may be made in the particular embodiments disclosed which are within the scope of the invention as outlined by the appended claims. Having thus described aspects of the invention, with the details and particularity required by the patent laws, what is claimed and desired protected by Letters Patent is set forth in the appended claims.